Happy Halloween. Determine the sampling distribution of the mean when you choose any 2 pumpkins out of 4 with the following weight, 35% of children prefer pumpkin D, 30% prefer pumpkin B,I and 20% prefer pumpkin A. Consider sampling without replacement. Pumpkin A B C DWeight(lbs) 10 12 8 14 Question 2 The amount of a particular impurity in a batch of a certain chemical product is a random variable with mean value 4.0 g and standard deviation 1.5 g. If 50 batches are independently prepared, what is the (approximate) probability that the sample average amount of impurity X is between 3.5 and 3.8 g?
Answers
1) The standard deviation is 0.275
2) The approximate probability is 0.165
Sampling distribution: The sampling distribution is a probability distribution of a statistic determined from a larger number of samples. A statistic, such as a mean or a standard deviation, is a numerical quantity calculated from data and used to make inferences about the population's parameters.
For the first question, we can use the hypergeometric distribution to find the sampling distribution of the mean when we choose any 2 pumpkins out of 4.
Let X be the number of pumpkins preferred by the 2 children we sample. Then X follows a hypergeometric distribution with N = 4 (total number of pumpkins), n = 2 (number of pumpkins we choose), and K = {0, 1, 2} (possible number of pumpkins preferred).
The probability mass function of X is given by:
P(X = k) = (K choose k) * (N - K choose n - k) / (N choose n)
where (a choose b) is the binomial coefficient "a choose b".
Using this formula and the given weights, we can calculate the probabilities for k = 0, 1, and 2:
P(X = 0) = (2 choose 0) * (2 choose 2) / (4 choose 2) = 1/6
P(X = 1) = (2 choose 1) * (2 choose 1) / (4 choose 2) = 2/3
P(X = 2) = (2 choose 2) * (2 choose 0) / (4 choose 2) = 1/6
Now we can find the mean and standard deviation of the sampling distribution of the mean, which is approximately normal by the central limit theorem since the sample size is relatively small:
Mean = E(X) = n * (K/N) = 2 * [(00.2)+(10.3)+(2*0.35)] / 4 = 0.95
Standard deviation = sqrt(n * K/N * (1 - K/N) * (N - n)/(N - 1))
= sqrt(2 * 0.95 * (1 - 0.95) * 2/3)
= 0.275
For the second question, we can use the central limit theorem to approximate the sampling distribution of the sample mean. Since we have a large sample size (n = 50), the sample mean X follows an approximately normal distribution with mean μ = 4.0 g and standard deviation
σ/sqrt(n) = 1.5/sqrt(50) ≈ 0.212 g.
Then, we can calculate the z-scores for the lower and upper bounds of the interval:
z_1 = (3.5 - 4.0) / 0.212 ≈ -2.36
z_2 = (3.8 - 4.0) / 0.212 ≈ -0.94
Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:
P(Z < -2.36) ≈ 0.009
P(Z < -0.94) ≈ 0.174
Then, we can find the probability that X falls within the interval [3.5, 3.8] by taking the difference between these probabilities:
P(3.5 ≤ X ≤ 3.8) ≈ P(-2.36 ≤ Z ≤ -0.94) ≈ 0.174 - 0.009 ≈ 0.165
Therefore, the approximate probability that the sample average amount of impurity X is between 3.5 and 3.8 g is 0.165.
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Related Questions
A rabbit is running with a constant speed of 3m/s. Find out the distance covered by rabbit in 10 seconds
Answers
The rabbit covers a distance of 30 meters in 10 seconds at a constant speed of 3m/s.
As we know that distance is equal to speed multiplied by time, we can use this formula to calculate the distance covered by the rabbit in 10 seconds. Given that the speed of the rabbit is constant at 3m/s, we can use this value to calculate the distance it covers in 1 second.
So, distance covered by rabbit in 1 second = Speed of rabbit = 3m/s
Now we can use this value to find the distance covered by the rabbit in 10 seconds, which is equal to 10 times the distance covered by the rabbit in 1 second.
Distance covered by rabbit in 10 seconds = 3m/s x 10 seconds
= 30 meters
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Stanley is making trail mix out of 10 bags of nuts and 20 bags of dried fruits. He want each new portion of trail mix to be identical, containing the same combination of dried fruits with no bags left over. What is the greatest number of portions of trail mix Stanley can make?
Answers
To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.
The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.
We start with 10 and 20 as our starting numbers.
10 = 2 * 5
20 = 2 * 2 * 5
We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.
Therefore, the greatest number of portions of trail mix Stanley can make is 10.
a relationship that is noted between two or more variables is termed
Answers
The relationship that is noted between two or more variables is termed a correlation. Correlation refers to the statistical association or relationship between two or more variables.
It indicates the degree to which the variables are related or how they are related to each other. Correlation can be positive, negative, or zero, depending on the direction and strength of the relationship between the variables.
A positive correlation indicates that as one variable increases, the other variable also increases. A negative correlation indicates that as one variable increases, the other variable decreases. Zero correlation indicates that there is no relationship between the variables.
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Are the given functions y1 and y2 linearly independent or linearly dependent on the interval (0, 1) and why? Choose the correct statement below. Yi = cscº(t) - cot? (t), y2 = 9a. Since yi = - 42 on (0, 1), the functions are linearly independent on (0,1). b. Since yı = 5y2 on (0,1), the functions are linearly independent on (0,1). c. Since yı = 3y2 on (0,1), the functions are linearly dependent on (0,1). d. Since yi = - Žy2 on (0, 1), the functions are linearly dependent on (0,1).
Answers
The given functions [tex]y_1[/tex] and [tex]y_2[/tex] are linearly dependent on the interval (0, 1)
(a) Since [tex]y_1 = -42[/tex] on (0,1), the functions are linearly independent on (0,1).
This option does not make sense because [tex]y_1[/tex] is not always -42 on the interval (0,1).
(b) Since [tex]y_1 = 5y_2[/tex] on (0,1), the functions are linearly independent on (0,1).
This option is not correct because if we substitute y1 with 5y2 in the equation [tex]c_1 y_1 + c_2 y_2 = 0[/tex], we get [tex]5c_2 y_2 + c_2 y_2 = 0,[/tex] which means we can write [tex]y_1[/tex]as a constant times [tex]y_2[/tex], so they are dependent.
(c) Since [tex]y_1 = 3y_2[/tex] on (0,1), the functions are linearly dependent on (0,1)."
To see why, we can substitute [tex]y_1[/tex] with [tex]3y_2[/tex] in the equation [tex]c_1 y_1 + c_2 y_2 = 0[/tex]:
[tex]c_1 (3y_2) + c_2 y_2 = 0[/tex]
Simplifying this, we get:
[tex](3c_1 + c_2) y_2 = 0[/tex]
Since [tex]y_2[/tex] is not equal to 0 for any value of t in the interval (0,1), this means that [tex]3c_1 + c_2[/tex] must equal 0. This is a non-trivial solution for [tex]c_1[/tex] and [tex]c_2[/tex], which means that [tex]y_1[/tex] and[tex]y_2[/tex] are linearly dependent on the interval (0,1).
(d) Since[tex]y_1 = -1/2 y_2[/tex]on (0,1), the functions are linearly dependent on (0,1).
This option is also correct because if we substitute [tex]y_1[/tex] with -1/2 y2 in the equation [tex]c_1 y_1 + c_2 y_2 = 0,[/tex] we get [tex]-1/2 c_2 y_2 + c_2 y_2 = 0[/tex], which means we can write[tex]y_1[/tex]as a constant times [tex]y_2[/tex], so they are dependent.
Therefore, the correct answer is either option d, and the functions [tex]y_1[/tex] and [tex]y_2[/tex] are dependent on the interval (0,1).
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Shari is drawing triangles that had the same area the base of each triangle varies inversely with the height what are the possible base and height of the second triangle if the first triangles base is 12 and its height is eight find the height of the triangle whose base is 16
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If the first triangles base is 12 and its height is eight, the height of the second triangle whose base is 16 is 6.
If the area of all the triangles Shari is drawing is the same, and the base of each triangle varies inversely with the height, then we can use the formula for the area of a triangle:
A = (1/2) * b * h
where A is the area, b is the base, and h is the height.
Since the area is the same for all the triangles, we can set the equation for each triangle equal to a constant, say k:
A = k = (1/2) * b * h
If the base varies inversely with the height, then we can write:
b = k/h
We can substitute this into the equation for the area:
k = (1/2) * (k/h) * h
Simplifying, we get:
k = (1/2) * k
This implies that k = 0, which is not possible since the area of a triangle cannot be zero. Therefore, we conclude that the base of each triangle cannot vary inversely with the height.
For the second part of the question, we are given that the base of the first triangle is 12 and its height is 8. Using the formula for the area of a triangle, we can solve for the area:
A = (1/2) * 12 * 8 = 48
We can then use the same formula to solve for the height of the second triangle whose base is 16:
48 = (1/2) * 16 * h
Simplifying, we get:
h = 6
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In culinary class, you made fudge brownies and peanut butter brownies. Each batch of fudge brownies makes 1 pan. Each batch of peanut butter brownies makes 9 pans. The class made 5 batches and ended up with 29 pans. How many batches of each type of brownie were made?
Answers
Answer: 4 batches of fudge brownies and 1 batch of peanut butter brownies were made.
Step-by-step explanation:
Let x be the number of batches of fudge brownies made, and y be the number of batches of peanut butter brownies made.
From the problem, we can write two equations based on the information given:
Each batch of fudge brownies makes 1 pan: x = number of pans of fudge brownies.
Each batch of peanut butter brownies makes 9 pans: 9y = number of pans of peanut butter brownies.
We also know that the class made 5 batches in total, and ended up with 29 pans:
x + 9y = 29 (total number of pans)
We can now solve for x and y by using a system of two equations:
x + 9y = 29 (equation 1)
x + y = 5 (equation 2)
Solving for x in equation 2 and substituting into equation 1, we get:
(5 - y) + 9y = 29
Simplifying and solving for y:
8y = 24
y = 3
Substituting y = 3 into equation 2, we get:
x + 3 = 5
x = 2
Therefore, the class made 2 batches of fudge brownies (2 pans) and 1 batch of peanut butter brownies (9 pans), for a total of 29 pans. Alternatively, we can say that the class made 4 batches of fudge brownies (4 pans) and 1 batch of peanut butter brownies (9 pans) for a total of 29 pans.
A regular hexagon has side lengths of 2x and has a perimeter that is equal to an isosceles triangle with legs of x + 4 and a base that is 3 less than one of the legs. Write and solve equation to find the length of one side of the hexagon.
Answers
According to the formula, the length of one side of the hexagon is 21/4 or 5.25 units.
What is the perimeter of the regular hexagon?
Let's call the length of one side of the regular hexagon "s". Since a hexagon has six sides, the perimeter of the hexagon is 6s.
According to the problem, this is equal to the perimeter of an isosceles triangle with legs of x+4 and a base that is 3 less than one of the legs.
The perimeter of the isosceles triangle is given by:
perimeter = 2(x+4) + (x+1)
where (x+1) is the length of the base (which is 3 less than one of the legs).
Setting the perimeters equal, we get:
6s = 2(x+4) + (x+1)
6s = 3x + 9
s = (3/2)x + (3/4)
We also know that the side lengths of the hexagon are 2x. Substituting this into the equation for "s", we get:
2x = (3/2)x + (3/4)
x = 3
Therefore, the length of one side of the hexagon is:
s = (3/2)x + (3/4) = (3/2)(3) + (3/4) = 9/2 + 3/4 = 21/4
So the length of one side of the hexagon is 21/4 or 5.25 units.
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five program systems are prepared so that they work independently of each other. each system has a 0.3 chance of detecting an error. find the probability that at least one program system will detect an error. use 4 decimal places.
Answers
The probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
How to find the probabilityGiven information:
five program systems are prepared so that they work independently of each other. Each system has a 0.3 chance of detecting an error.
Find the probability that at least one program system will detect an error. Use 4 decimal places.The probability of a system detecting an error is 0.3.
The probability of a system not detecting an error is 1 - 0.3 = 0.7.
Probability that none of the five systems detects an error is, P(error not detected in any of the five systems) = P(not detected in 1st) x P(not detected in 2nd) x ... x P(not detected in 5th) = 0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807.
The probability that at least one system detects an error is, P(at least one system detects an error) = 1 - P(error not detected in any of the five systems) = 1 - 0.16807 = 0.8319 (approx).
Therefore, the probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
Hence, the correct option is 0.832.
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I need some help please
Answers
Given:-
[tex] \texttt{c = 1}[/tex][tex] \: [/tex]
[tex] \texttt{d = 3}[/tex][tex] \: [/tex]
Solution:-
[tex] \texttt{3(2c + d ) -4 ( c - d ) + d² }[/tex][tex] \: [/tex]
put the given values in tha equation
[tex] \texttt{= 3( 2 ( 1 ) + 3 ) -4 ( 1 - 3 ) + ( 3 )² }[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 2 + 3 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 5 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 15 + 8 + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 23 + 9}[/tex][tex] \: [/tex]
[tex] \boxed{ \texttt{ \purple{= 32}}}[/tex][tex] \: [/tex]
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refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
Answers
Confidence interval = (y ± t∗s/√n)g1 = y - t*s/√ng2 = y + t*s/√n Substituting the values, g1 = 26.22 - 1.860*(0.11)/√9 = 25.84g2 = 26.22 + 1.860*(0.11)/√9 = 26.59Therefore, the statistics g1 and g2 that will satisfy the required inequality are 25.84 and 26.59 respectively.
The formula for finding the confidence interval is as follows: n − 1, where t is the value of the t-distribution corresponding to the specified confidence level and the sample size minus one.
As per the given exercise 7.11, suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample.
If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p(g1 ≤ (y - u) ≤ g2) = 90
To find the statistics g1 and g2 that will satisfy the required inequality
the following formula can be used: Confidence interval = [tex](y ± t∗s/√n)[/tex]
From the formula, we can see that the confidence interval depends on the values of y, s, t and n.
The value of y is the sample mean
the value of s is the sample standard deviation
And the value of n is the sample size.
The value of t depends on the confidence level desired and the degrees of freedom for the t-distribution. In this case, the confidence level is 90%, which means that we want to find the value of t that will give us a total area of 0.90 under the t-distribution curve with 8 degrees of freedom .Using the t-table, the value of t can be found to be 1.860, where the value for 90% and 8 degrees of freedom is 1.860.t = 1.860Now, we need to calculate the value of s, which is the sample standard deviation.
Since we do not have any information about the population standard deviation, we will use the sample standard deviation as an estimate of the population standard deviations = σ/√nσ = s*√nσ = 0.11*√9σ = 0.33Substituting the values in the confidence interval formula
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The graph below shows petrol prices at two petrol stations, Station X and Station
Y.
Ellie went to one of the petrol stations and bought 20 litres of petrol for £24.
a) Did Ellie go to Station X or Station Y?
b) How much would 15 litres of petrol cost at the same station?
Give your answer in pounds (£).
Cost (£)
Cost against amount of petrol
40
30
20
10-
5
10 15 20 25
Amount of petrol (litres)
Key
Station X
Station Y
Answers
At Station Y, 15 litres of gasoline would cost £18.
What is cost in?Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.
Ellie must have visited Station Y because she paid $24 for 20 litres of gasoline, proving that she did.
b) We can observe from the graph that 20 litres of gasoline at Station Y costs £24. With the help of this data, we can calculate how much a litre of gasoline costs:
Cost of 1 litre of petrol = Cost of 20 litres of petrol / 20
Cost of 1 litre of petrol = £24 / 20
Cost of 1 litre of petrol = £1.20
Therefore, 15 litres of petrol at Station Y would cost:
Cost of 15 litres of petrol = Cost of 1 litre of petrol x 15
Cost of 15 litres of petrol = £1.20 x 15
Cost of 15 litres of petrol = £18
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Find the distance between the points ( – 9, – 7) and ( – 3,1).
Answers
Answer:
10 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 9, - 7 ) and (x₂, y₂ ) = (- 3, 1 )
d = [tex]\sqrt{(-3-(-9))^2+(1-(-7)^2}[/tex]
= [tex]\sqrt{(-3+9)^2+(1+7)^2}[/tex]
= [tex]\sqrt{6^2+8^2}[/tex]
= [tex]\sqrt{36+64}[/tex]
= [tex]\sqrt{100}[/tex]
= 10 units
[tex] \: [/tex]
[tex] \textrm{( -3 , 1 )}[/tex][tex] \: [/tex]
To find:-[tex] \textrm{Distance between two points = ?}[/tex][tex] \: [/tex]
By using formula:-[tex] \underline{ \star \small \boxed{{ \rm{ \purple{Distance = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²} }}}}}[/tex][tex] \: [/tex]
Solution:-[tex] \rm \: D =\sqrt{ ( x_2 - x_1 )² + ( y_2 - y_1 )²} [/tex][tex] \: [/tex]
where ,
[tex] \: \: \star \rm \red{x_1 = -9 , x_2 = -3 } \\\star \green {\rm y_1 = -7 , y_2 = 1}[/tex]
[tex] \: [/tex]
[tex] \rm \: D = \sqrt{ ( -3 - ( - 9 ))² + ( 1 - (-7 ))²} [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{( -3 + 9)² + ( 1 + 7 )²} [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{( 6 )² + ( 8 )²} [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{36 + 64 } [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{100} [/tex][tex] \: [/tex]
[tex] \boxed{ \textrm{ \color{green}{D = 10 \: }}}[/tex][tex] \: [/tex]
Therefore , the distance between two points is 10 units !
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Someone please help with this? Thank you!
Answers
Table values are -3, -1, 3, 5, 13
Define the term function?A function is a mathematical object that maps each element from one set to a unique element in another set. Functions are represented using symbols and can be described using graphs, tables, or equations.
Given function is,
[tex]f(x)=2x +3[/tex]
Solve for x = -3, f(-3) = 2×(-3) + 3 = -6 + 3 = -3
f(-3) = -3
Solve for x = -2, f(-2) = 2×(-2) + 3 = -4 + 3 = -1
f(-2) = -1
Solve for x = 0, f(0) = 2×(0) + 3 = 0 + 3 = +3
f(0) = 3
Solve for x = 1, f(1) = 2×(1) + 3 = 2 + 3 = 5
f(1) = 5
Solve for x = 5, f(5) = 2×(5) + 3 = 10 + 3 = 13
f(5) = 13
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Miko bought five 2-litre bottles of water. She poured all the water equally into 15 bowls. What was the volume of water in each bowl?
Answers
The volume of water in each bowl is approximately 666.67 ml.
Miko bought five 2-liter bottles of water, which means that she had a total of 10 liters of water. She then poured all the water equally into 15 bowls. To find out the volume of water in each bowl, we need to divide the total volume of water by the number of bowls.
We can start by converting the 10 liters of water into milliliters (ml), which will make it easier to work with. To do this, we multiply 10 by 1000, since there are 1000 ml in one liter. This gives us a total of 10,000 ml of water.
Next, we divide the total volume of water (10,000 ml) by the number of bowls (15) to find the volume of water in each bowl. This can be written as:
Volume of water in each bowl = Total volume of water / Number of bowls
Volume of water in each bowl = 10,000 ml / 15
Volume of water in each bowl = 666.67 ml (rounded to two decimal places)
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Anyone know the answer?
Answers
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
what is volume ?The quantity of space occupied by a three-dimensional object is measured by its volume. Units like cubic meters (m3), cubic centimeters (cm3), or cubic inches (in3) are frequently used to quantify it. Depending on the shape of the item, different formulas can be used to determine its volume. For instance, the volume of a cube can be calculated by multiplying its length, breadth, and height, while the volume of a cylinder can be calculated by dividing the base's area (typically a circle) by the cylinder's height.
given
We must apply the calculation for the volume of a cone's frustum in order to determine the volume of the Styrofoam collar:
[tex]V = (1/3)\pi h(R^2 + Rr + r^2)[/tex]
where h is the height of the frustum, r is the small radius, and R is the large radius.
Given the numbers, we can determine:
R = 5 in.
3 centimeters is r.
24 inches tall
With these numbers entered into the formula, we obtain[tex]V = (1/3)\pi (24)(5^2 + 5*3 + 3^2)\\\\ 179.594 cubic inches[/tex]
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
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Say my population is USA voters. If I interviewed people in front of a major grocery supermarket. Making sure that I selected supermarkets in high median salary areas. What type of sampling best fits my experiment?
Answers
The sampling method that best fits your experiment is convenience sampling.
Describe Sampling?Sampling is the process of selecting a subset of individuals or items from a larger population in order to gather information and draw conclusions about the entire population. Sampling is often used in scientific research, market research, and other fields where it is impractical or impossible to measure the entire population.
There are many different types of sampling methods, including random sampling, stratified sampling, cluster sampling, and convenience sampling. Each method has its own advantages and disadvantages, and the choice of sampling method depends on the specific research question and the resources available.
The sampling method that best fits your experiment is convenience sampling. Convenience sampling is a non-probability sampling method that involves selecting individuals who are readily available and accessible to the researcher. In your case, you are selecting individuals who are present in front of a major grocery supermarket, which is a convenient location. Convenience sampling is often used in situations where it is difficult or impractical to obtain a random sample, and is commonly used in market research and pilot studies.
However, it is important to note that convenience sampling has some limitations. Since the sample is not randomly selected, it may not be representative of the population as a whole. In your case, selecting supermarkets in high median salary areas may introduce bias into the sample, as it may not accurately represent the entire population of USA voters. Additionally, the sample size and characteristics may be affected by factors such as time of day, day of the week, and other factors that may affect who is present in front of the supermarket at a given time. Therefore, the results obtained from this sampling method may not be generalizable to the entire population of USA voters.
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Warren is constructing an open box from a piece of paper that is 8 in wide and 11. 5 in long
Answers
The sides of the squares be to obtain a box with the largest volume is 114.20 inch³.
Quadratic functions are used in various fields of engineering and science to obtain the values of various parameters. Graphically, they are represented by parabolas. Determines the direction of the curve based on the highest order coefficient. The word "quadratic" is derived from the word "Quad", which means square. In other words, a quadratic function is a "polynomial function of degree 2.
According to the Question:
Let a be the size of the square to be cut at 4 corners.
The cardboard is folded along the dotted line such that following are the box dimensions
Given that
Length, L= 11.5–2a ; Width. B = 8–2a ; Height, H = a
Volume of box, V = (18–2a )(8–2a) a
V = (11.5-2a)(8-2a)a
⇒ V = 92a -3a²-16+ 4a³
⇒ V = 4a³-3a² +92a -16
Now,
The condition for volume to be maximum is that,
dV/da = 0
⇒ [tex]\frac{dv}{da} (4a^3)- \frac{dv}{da} (3a^2) +\frac{dv}{da}(92a) - \frac{dv}{da} (16)[/tex]
⇒ 12a² -6a + 92
Taking common 2 from the above equation, we get:
⇒ 6a² - 3a + 46
Therefore,
The roots of this quadratic equation are,
a = 6.93 and 1.729
Case 1: If a = 6.93,
then B= -5.87 < 0 which is not a valid dimension.
Case 2: If a =1.729 then,
L = 14.54 ; B= 4.54 ; H=1.729
Therefore,
Volume of the box = 14.54 x 4.54 x 1.729 = 114.20
Therefore, the sides of the squares be to obtain a box with the largest volume is 114.20 inch³
Complete Question:
An open box is to be made from 8 inches by 11.5 inches piece of cardboard by cutting squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to obtain a box with the largest volume?
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What method could have been used to collect the data
Answers
The method used to collect data will depend on the specific research question being asked and the resources available to the researcher.
One common method for collecting data is through experimentation. This involves designing a controlled experiment that allows researchers to manipulate one or more variables while keeping all other factors constant.
Observational data can be particularly useful when it is not possible or ethical to manipulate variables in an experiment.
Surveys and questionnaires are another way to collect data. These methods involve asking people to provide information about their attitudes, beliefs, and behaviors.
Other methods for collecting data include case studies, in which researchers closely examine a single individual or group, and archival research, in which data is collected from existing records, such as census data or medical records.
By carefully selecting the right method for their research, scientists can gather accurate and reliable data that can help to advance our understanding of the world around us.
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HELP PLS combine the like terms 3x+5-x+3+4x
Answers
Answer:
3x, 4x | 5, 3
Step-by-step explanation:
60°
d. Opposite C:
e. Adjacent C:
B
90°
1. Consider the triangle ABC. Which side is being described by the following labels?
a. Hypotenuse:
b. Opposite A:
c. Adjacent A:
30°
Answers
Side BC is the hypotenuse of the right triangle ABC. Against A: The side that is opposed to angle A is side BC. Adjacent A: Side AB is the side that faces angle A. The side that is in opposition to angle C is side AB.
What does a math hypotenuse mean?
An "opposite" side in a right triangle is the one that is across from a specific angle, while a "adjacent" side is the one that is next to a specific angle. The hypotenuse is the longest side in a right triangle. The sides of right triangles are described with particular terminology. It goes without saying that the side opposite the right angle is the hypotenuse of a right triangle.
Side BC is the hypotenuse of the right triangle ABC. Against A: The side that is opposed to angle A is side BC. Adjacent A: Side AB is the side that faces angle A. The side that is in opposition to angle C is side AB.
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If the mean of 8 9 x and 12 is 10 find the range and its coefficient
Answers
As per the given mean value, the coefficient of range is 40%.
We know that the mean of these numbers is 10, which means that if we add them all up and divide by 4 (since there are 4 numbers in the set), the result will be 10. Using algebra, we can set up the following equation:
(8 + 9 + x + 12) / 4 = 10
If we simplify this equation, we get:
(29 + x) / 4 = 10
Multiplying both sides by 4, we get:
29 + x = 40
Subtracting 29 from both sides, we get:
x = 11
So we now know that the four numbers are 8, 9, 11, and 12. To find the range, we simply subtract the lowest value (8) from the highest value (12):
12 - 8 = 4
Therefore, the range of the numbers is 4.
To find the coefficient of range, we use the formula:
Coefficient of range = (Range / Mean) x 100%
Plugging in the values we just found, we get:
Coefficient of range = (4 / 10) x 100%
Coefficient of range = 40%
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A man deposited sh. 600,000 to a savings account in a bank that offers an interest rate of 15% p.a. What amount will be on his account after 8months
Answers
We can start by calculating the interest earned by the man over 8 months.
First, we need to convert the annual interest rate of 15% to a monthly rate by dividing it by 12:
15% / 12 = 1.25%
Next, we can use the formula for simple interest to calculate the interest earned:
Interest = Principal x Rate x Time
where:
Principal = sh. 600,000 (the amount deposited)
Rate = 1.25% (the monthly interest rate)
Time = 8/12 (8 months is 2/3 of a year)
Plugging in the values, we get:
Interest = 600,000 x 1.25% x 8/12
Interest = 5,000
Therefore, the man will earn sh. 5,000 in interest over 8 months.
To find the total amount in his account after 8 months, we simply add the interest earned to the initial deposit:
Total amount = Principal + Interest
Total amount = 600,000 + 5,000
Total amount = sh. 605,000
Therefore, the amount on the man's account after 8 months will be sh. 605,000.
Determine whether the set StartSet left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 0 3rd Row 1st Column negative 3 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 3 2nd Row 1st Column 1 3rd Row 1st Column 6 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 1 3rd Row 1st Column 0 EndMatrix right bracket EndSet 1 0 −3 , −3 1 6 , 1 −1 0 is a basis for set of real numbers R cubedℝ3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans set of real numbers R cubedℝ3. Which of the following describe the set?
Answers
The set [1 0 −3 , −3 1 6 , 1 −1 0] is not a basis for set of real numbers R cubed(ℝ3).
The reason why it is not a basis is because it is not linearly independent. However, the set does span set of real numbers R cubed(ℝ3).To determine if the given set is a basis for set of real numbers R cubed(ℝ3), we need to test for linear independence and for span.Linear independence
The given set is said to be linearly independent if and only if the only solution to the equation a[1 0 −3] + b[−3 1 6] + c[1 −1 0] = [0 0 0] is the trivial solution where a, b and c are constants.If the given set is linearly independent then it is a basis for R3; if it is not linearly independent, it is not a basis for R3.
SpanThe given set is said to span R3 if every vector in R3 can be written as a linear combination of vectors in the given set.
If the given set spans R3, then it can be considered a basis for R3.For us to test if the given set is linearly independent, we can form a matrix by placing the three given vectors into the columns of a 3 x 3 matrix as follows:[1 0 1] [−3 1 −1] [−3 6 0]
By expanding the determinant of the matrix above, we get: det(A) = 0 - 0 - (-3) = 3
Since the determinant is non-zero, we can say that the given set is linearly independent. Since the given set is linearly independent, we can then use it to span R3. Hence the given set does not form a basis for R3 but it is linearly independent and spans R3.
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Required information M7-20 to 22(Supplement 7A) Calculating Cost of Goods Sold and Ending Inventory under Perpetual FIFO,LIFO,and Weighted Average Cost [LO 7-S1] In its first month of operations,Literacy for the Iliterate opened a new bookstore and bought merchandise in the following order400 units at $5 on January 1,2600 units at $7 on January 8,and 3830 units at $8 on January 29.Assuming 1.030 units are on hand at the end of the month M7-22(Supplement 7A) Calculating Cost of Goods Sold and Ending Inventory under Perpetual Weighted Average Cost [LO 7-S1] Calculate the cost of goods available for sale,cost of goods sold,and ending inventory under the weighted average cost flow assumptions.Assume perpetual inventory system and sold 800 units between January 9 and January 28.(Round your intermediate calculations to 2decimal places.) Weighted Average Cost Goods Avallable for Sale Cost of Goods Sold Ending Inventory Aetivate Window
Answers
Calculating Cost of Goods Sold and Ending Inventory under Perpetual FIFO, LIFO, and Weighted Average Cost [LO 7-S1] In its first month of operations, Literacy for the Illiterate opened a new bookstore and bought merchandise in the following order 400 units at $5 on January 1, 2600 units at $7 on January 8, and 3830 units at $8 on January 29.
Assuming 1.030 units are on hand at the end of the month M7-22(Supplement 7A) Calculating Cost of Goods Sold and Ending Inventory under Perpetual Weighted Average Cost [LO 7-S1]
In order to calculate the cost of goods available for sale, cost of goods sold and ending inventory under the weighted average cost flow assumptions, you need to first calculate the weighted average cost of the goods.
Weighted Average Cost = (400 units x $5) + (2600 units x $7) + (3830 units x $8) / (400 + 2600 + 3830)
= $6.62
Cost of Goods Available for Sale = Weighted Average Cost x (400 + 2600 + 3830)
= $6.62 x 7,830
= $51,916.60
Cost of Goods Sold = Weighted Average Cost x 800 units
= $6.62 x 800
= $5,296.00
Ending Inventory = Cost of Goods Available for Sale - Cost of Goods Sold
= $51,916.60 - $5,296.00
= $46,620.60
The cost of Goods Available for Sale is $51,916.60
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If P = 2y² + 4xy + 4
Q = − 3y² + 7 - 3xy
R=- 3xy + 8
Find P+Q=R.
Answers
Answer:
P = [tex]2y^{2}[/tex] + 4xy +4
Q = [tex]-3y^{2}[/tex] + 7 -3xy
R = -3xy +8
Step-by-step explanation:
solve( 3x^ 2)+2y +4=0
Answers
Answer:
Step-by-step explanation:
You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.
an equation of a circle is given by (x+3)^2+(y_9)^2=5^2 apply the distributive property to the square binomials and rearrange the equation so that one side is 0.
Answers
The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].
Given:
Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]
Expand the equation
[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]
[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]
[tex]5^2 = 25[/tex]
Then, substitute the expanded expressions into the equation
[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]
Simplify and combine like terms
[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]
Rearrange the equation so that one side is 0
[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.
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which of the following are presentation methods? (select all that apply)multiple select question. reciprocal training traditional classroom instruction audiovisual training distance learning
Answers
There are four presentation methods to choose from. These include reciprocal training, traditional classroom instruction, audiovisual training, and distance learning. The multiple selection question format asks which presentation methods are included.
What is a presentation method?
A presentation method refers to a way to deliver information to a group of individuals. Presentation methods are often used to teach concepts, inform, or persuade the audience. Various presentation methods are available for different types of information, such as traditional classroom instruction, audiovisual training, and distance learning. These methods vary in how information is presented and how participants engage with the material.Presentation methods that are available Reciprocal Training, Reciprocal Training, often known as reciprocal teaching, is a technique that involves individuals exchanging roles as teachers and learners. This method has been shown to be effective in developing students' comprehension of academic material.Traditional Classroom Instruction, Traditional classroom instruction, also known as classroom instruction, is a technique that has been used for centuries. A teacher is in front of a group of students, who are expected to engage with the material and participate in activities.Audiovisual Training Audiovisual training refers to the use of video, audio, and other visual aids in the delivery of instruction. This approach is thought to be more engaging and memorable than other teaching methods.Distance Learning Distance learning, or online learning, is a form of education that is delivered via the internet. This allows individuals to learn from any location, as long as they have access to the internet. This type of education is often more cost-effective than traditional classroom instruction.Therefore, all of the above presentation methods are effective.
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Which of the options below are inequalities? Choose all of the correct answers. 3h-7-19 h≥14 h=60 3h +12 < 18 20=h+h 8> h
Answers
All the equation shown as inequalities:
3h-7-19 ; h≥14 ; h=60 ; 3h +12 < 18 ; 20=h+h ; 8> h
Explain about the inequalities of the numbers?When resolving an inequality, you can do one of the following:
Add the same amount to each side; •Subtract the same amount from each side;Multiply but rather divide both side with a single positive amount. You must flip the inequality sign if you multiply as well as divide each side from a negative number. On a number line, inequalities are represented by making a straight path and designating the end points through an open or closed circle. An empty circle indicates that the value is not included. A closed circle indicates that the value is included.Thus, all the equation shown as inequalities:
3h-7-19 ; h≥14 ; h=60 ; 3h +12 < 18 ; 20=h+h ; 8> h
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The complete question is-
Which of the options below are inequalities? Choose all of the correct answers.
3h-7-19 ; h≥14 ; h=60 ; 3h +12 < 18 ; 20=h+h ; 8> h
Jennifer bought 14.75 gallons of gasoline for her car at a cost of $2.95 a gallon. which is closest to the amount she paid for the gasoline?
Answers
The total amount paid by Jennifer for 14.75 gallons of gasoline at the cost of $2.95 per gallons is equal to $43.51.
Total gallons of gasoline bought by Jennifer for her car = 14.75 gallons
Cost of gasoline per gallons= $2.95
The total amount Jennifer paid for the gasoline is equal to, amount paid by Jennifer= number of gallons of gasoline* cost per gallon
substitute the value in the formula we get, = amount paid by Jennifer= 14.75 gallons* $2.95/gallon= $43.51
Therefore, the closest amount Jennifer paid for the gallons of gasoline is equal to $43.51.
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