Answers
Related Questions
The volume of this prism is 4950cm3.
The area of the cross-section is 110cm2.
Work out x
Answers
Answer:
45cm
Step-by-step explanation:
length × cross section = volume
in this case we call the unknown [tex]x[/tex]
so
[tex]x[/tex] x 110 = 4950
to get [tex]x[/tex] you divide the volume by the cross section
[tex]\frac{4950}{110}[/tex]= [tex]x[/tex]
so [tex]x[/tex] = 45cm
find the volume of a pyramid with a square base, where the area of the base is 4.6 cm 2 4.6 cm 2 and the height of the pyramid is 2.3 cm 2.3 cm. round your answer to the nearest tenth of a cubic centimeter.
Answers
The volume of pyramid is 3.5 cm³.
To find the volume of a pyramid with a square base, where the area of the base is 4.6 cm² and the height of the pyramid is 2.3 cm, we can use the following formula:
V = (1/3)B*h
Where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid. Substitute the given values into the formula and solve:
V = (1/3)(4.6)(2.3)V = 3.53 cm³
Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is 3.5 cm³. Therefore, the volume of pyramid is 3.5 cm³.
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how does the graph of the function g(x) = 2x – 3 differ from the graph of f(x) = 2x?
Answers
Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)
Mrs. Murphy by balloons garlands paper lanterns and banners to decorate a school party she got three times as many bags of balloons as paper lanterns seven more garlands than paper lanterns and for banners she paid $5. 25 for each banner $6. 50 for each paper lantern five dollars for each bag of balloons and $3. 50 for each garland how many of each kind of decoration did she purchase if she paid $145. 50
Answers
She purchased 4 Paper Lanterns, 12 Bags of Balloons, 11 Garlands, and 4 Banners if she paid $145. 50.
The cost of lanterns is $6.50
Mrs Murphy bought 4 lanterns
Multiply the cost of one lantern ($6.50) by the number of lanterns bought (4) 6.50 multiplied by 4 equals 26
The cost of banners is $5.25
Mrs Murphy bought 4 banners
Multiply the cost of one banner ($5.25) by the number of banners bought (4) 5.25 multiplied by 4 equals 21
Mrs Murphy bought 3 times as many balloons as she did lanterns
So, you multiply the number of lanterns bought (4) by 3
This gives 12
We then multiply the cost of each balloon ($5.00) by the number of balloons bought (12)
5.00 multiplied by 12 equals 60
Mrs Murphy bought 7 more garlands as she did lanterns
So, we add 7 to the number of lanterns bought (4)
7 plus 4 equals 11
To find the cost of the total garlands bought
We multiply the cost of each garland ($3.50) by the number of garlands bought (11)
3.50 multiplied by 11 equals 38.5
Now we can add up the costs of all the items
26+21+60+38.5=145.50
145.50 was the total amount she spent so we know it is the correct answer.
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Consider the following statement. If a and b are any odd integers, then a2 + b2 is even. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Suppose a and b are any odd integers. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s. By definition of odd integer, a = 2r + 1 and b = 2s + 1 for some integers r and s. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2. Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer. Suppose a and b are any integers. Let k = 2(r2 + 52) + 2(r + 5) + 1. Then k is an integer because sums and products of integers are integers. Hence a2 + b2 is even by definition of even. By substitution and algebra, a2 + b2 (2r)2 + (25)2 = 2(2r2 + 2s2). Proof: 1. ---Select--- 2. ---Select-- 3. ---Select--- 4. ---Select--- 5. ---Select--- 6. ---Select-
Answers
If a and b are any odd integers, then a2 + b2 is even.
And the proof for that we can explain as,
So we have a and b are any odd integers. By definition of odd integer,
a = 2r + 1 and b = 2r + 1 for any integers r and s.
By definition of odd integer,
a = 2r + 1 and b = 2s + 1 for some integers r and s.
By substitution and algebra,
a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2.
Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer.
Proof: 1. Suppose a and b are any odd integers.
Proof:2. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s.
Proof:3. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 + s2) + 2(r + s) + 1].
Proof:4. Let k = 2(r2 + s2) + 2(r + s) + 1. Then k is an integer because sums and products of integers are integers.
Proof:5. Hence a2 + b2 is even by definition of even.
Proof:6. Thus, a2 + b2 = 2k, where k is an integer.
Hence we proved that "If a and b are any odd integers, then a2 + b2 is even".
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A manufacturer of paper used for packaging requires a minimum strength of 1400 g/cm2. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. The standard deviation of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 140 g/cm2, and the strength measurements are normally
distributed.
a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?
b) If the mean of the population of strength measurements is 1450 g/cm2, what is the
approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400?
Answers
The sample mean is 1450g/cm², the standard deviation is 44.3 g/cm² and the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2 is 0.8708
What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?a) The sampling distribution of the sample mean of n = 10 test pieces of paper is approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:
mean of sample mean = mean of population = 1450 g/cm²
standard deviation of sample mean = standard deviation of population / square root of sample size
= 140 g/cm2 / √(10)
= 44.3 g/cm²
Therefore, the sampling distribution of the sample mean is approximately normal with mean 1450 g/cm2 and standard deviation 44.3 g/cm2.
b) To find the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2, we need to standardize the sample mean using the sampling distribution calculated in part (a):
z = (x - mean of sample mean) / standard deviation of sample mean
= (1400 - 1450) / 44.3
= -1.13
Using a standard normal distribution table or calculator, we can find the probability that z is less than -1.13 and subtract that probability from 1 to find the probability that z is greater than -1.13:
P(z > -1.13) = 1 - P(z < -1.13)
= 1 - 0.1292
= 0.8708
Therefore, the approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm² is 0.8708.
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Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Answers
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
solve simultaneously 4x-y=3x+1y 4x+3y=x+6y
Answers
(x, y) = (0,0) is the solution of the system of equations.
simultaneous equationSimultaneous equations are a set of two or more equations that contain multiple variables, which must be solved at the same time. The solution to the system of equations is the set of values of the variables that satisfy all of the equations in the system simultaneously.
The given system of equations is:4x - y = 3x + y
4x + 3y = x + 6y
Simplifying the first equation by moving all the y-terms to the left-hand side and all the x-terms to the right-hand side, we get:
4x - 3x = y + y
x = 2y
Substituting this value of x into the second equation, we get:
4(2y) + 3y = (2y) + 6y
8y + 3y = 8y
11y = 0
y = 0
Substituting y = 0 into the equation x = 2y, we get:
x = 2(0)
x = 0
Therefore, the solution to the system of equations is:
x = 0 and y = 0
Hence, (x, y) = (0,0) is the solution of the system of equations.
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Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answers
Answer:
D
Step-by-step explanation:
First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.
Hope this helps.
Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum.
Answers
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000
Step-by-step explanation:
Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint.
0.82 0.88 0.88 1.06 1.09 1.14 1.30 1.33
1.48 1.50 1.57 1.64 1.64 1.70 1.76 1.83
Determine the z percentile associated with each sample observation. (Round your answers to two decimal places.)
I have the answers below but I don't know how they were computed. z = (X - ?) / ? does not provide the correct value. Can someone provide how the answers below were computer?
z percentile .82 = -1.86
z percentile .88 = -1.32
z percentile .88 = -1.32
z percentile 1.06 = -0.78
z percentile 1.09 = -0.58
z percentile 1.14 = -0.40
z percentile 1.30 = -0.24
z percentile 1.33 = -0.08
z percentile 1.48 = 0.08
z percentile 1.50 = 0.24
z percentile 1.57 = 0.40
z percentile 1.64 = 0.58
z percentile 1.64 = 0.58
z percentile 1.70 = 1.01
z percentile 1.76 = 1.32
z percentile 1.83 = 1.86
Answers
The normal probability plot for the following sample deduce by z = (X - mean) / standard deviation as following steps.
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
The steps to calculate the z-percentiles for the given sample:
Find the mean of the sample:
mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16 = 1.235
Find the standard deviation of the sample:
First, find the sum of the squared differences between each observation and the mean:
(0.82 - 1.235)^2 + (0.88 - 1.235)^2 + (0.88 - 1.235)^2 + (1.06 - 1.235)^2 + (1.09 - 1.235)^2 + (1.14 - 1.235)^2 + (1.30 - 1.235)^2 + (1.33 - 1.235)^2 + (1.48 - 1.235)^2 + (1.50 - 1.235)^2 + (1.57 - 1.235)^2 + (1.64 - 1.235)^2 + (1.64 - 1.235)^2 + (1.70 - 1.235)^2 + (1.76 - 1.235)^2 + (1.83 - 1.235)^2 = 2.9878
Next, divide the sum by the sample size minus 1 and take the square root: standard deviation = sqrt(2.9878 / 15) = 0.4323
Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.
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To calculate the z-percentile for each observation in the sample.: Find the mean of the sample, Find the standard deviation of the sample and then use the formula z = (X - mean) / standard deviation.
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
The steps to calculate the z-percentiles for the given sample:
Find the mean of the sample:
mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16
mean = 1.235
Find the standard deviation of the sample:
First, find the sum of the squared differences between each observation and the mean:
(0.82 - 1.235)² + (0.88 - 1.235)² + (0.88 - 1.235)² + (1.06 - 1.235)² + (1.09 - 1.235)² + (1.14 - 1.235)² + (1.30 - 1.235)² + (1.33 - 1.235)² + (1.48 - 1.235)² + (1.50 - 1.235)² + (1.57 - 1.235)² + (1.64 - 1.235)² + (1.64 - 1.235)² + (1.70 - 1.235)² + (1.76 - 1.235)² + (1.83 - 1.235)² = 2.9878
Next, divide the sum by the sample size minus 1 and take the square root:
standard deviation = √(2.9878/15)
standard deviation = 0.4323
Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.
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Let A be a set With 12 elements. (a) Find the number of subsets of A. (b) Find the number of subsets of A having one or more elements. (c) Find the number of subsets of A having exactly one element. (d) Find the number of subsets of A having two or more elements. [Hint: Use the answers to parts (b) and (c).]
Answers
(a) Total Number of Subsets of A:
In set theory, any set is a subset of itself. Additionally, the empty set is a subset of every set. As a result, there are 2^12 subsets of A.
Number of Subsets of A = 2^12 = 4096
(b) Number of Subsets of A having One or More Elements:
To find the number of subsets of A having one or more elements, we must subtract the empty set from the total number of subsets of A.
∴ Number of Subsets of A having One or More Elements = (2^12) − 1 = 4095
(c) Number of Subsets of A having Exactly One Element:
We can use the formula given below to compute the number of subsets of A having exactly one element. Here, n represents the number of elements in the set.
Formula: nC1 = n
∴ Number of Subsets of A having Exactly One Element = 12C1 = 12
(d) Number of Subsets of A having Two or More Elements:
Using parts (b) and (c), we can obtain the number of subsets of A having two or more elements by subtracting the number of subsets of A having exactly one element from the number of subsets of A having one or more elements.
∴ Number of Subsets of A having Two or More Elements = (2^12) − 1 − 12 = 4083.
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Calculate the area and perimeter of this rectangle.
Answers
Answer:
Area: 391.92 ft²
Perimeter: 84.4 ft
Step-by-step explanation:
Area of rectangle = L × W
We Take
13.8 × 28.4 = 391.92 ft²
Find the Perimeter of the Rectangle
We Take
28.4 + 13.8 + 28.4 + 13.8 = 84.4 ft
So, Area: 391.92 ft²
Perimeter: 84.4 ft
Answer:
Area = 391.92 square feet
Perimeter = 84.4 feet
Step-by-step explanation:
The area of a rectangle is the product of its width and length.
The perimeter of a rectangle is twice the sum of its width and length.
Given the width of the rectangle is 28.4 feet and its length is 13.8 feet:
[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf width \times length\\&=28.4 \times 13.8\\&=391.92 \sf \;\;square\;feet\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=\sf 2(width +length)\\&=2(28.4 +13.8)\\&=2(42.2)\\&=84.4 \sf \;\;feet\end{aligned}[/tex]
A researcher randomly chooses 1000 Kentucky families to estimate the proportion of all American families who routinely eat dinner together. What is the population? a) The 1000 Kentucky families b) All Kentucky families c) All American families d) All families around the world
Answers
The population in the given scenario of a researcher randomly choosing 1000 Kentucky families to estimate the proportion of all American families who routinely eat dinner together is all American families (option c).
In the given scenario, the population is all American families. The researcher has randomly chosen 1000 families from Kentucky to estimate the proportion of all American families who routinely eat dinner together. The researcher is using the sample of 1000 Kentucky families to make inferences about the population of all American families. By assuming that the sample is representative of the population, the researcher can use statistical methods to estimate the proportion of all American families who routinely eat dinner together. So, option C is the correct answer.
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an urn contains p black balls, q white balls, and r red balls; and n balls are chosen without replacement. a. find the joint distribution of the numbers of black, white, and red balls in the sample. b. find the joint distribution of the numbers of black and white balls in the sample. c. find the marginal distribution of the number of white balls in the sample.
Answers
a. The joint distribution of the numbers of black, white, and red balls in the sample is given by P(x, y, z) = nCx * nCy * nCz / (p + q + r)Cn, where x is the number of black balls, y is the number of white balls, z is the number of red balls, and n is the total number of balls chosen.
b. The joint distribution of the numbers of black and white balls in the sample is given by P(x, y) = nCx * nCy / (p + q)Cn, where x is the number of black balls, y is the number of white balls, and n is the total number of balls chosen.
c. The marginal distribution of the number of white balls in the sample is given by P(y) = nCy / qCn, where y is the number of white balls, and n is the total number of balls chosen.
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Y=3x+3 what is the slope and y intercept
Answers
Answer:
y-intercept is (0,3) and the slope is 3
Step-by-step explanation:
Answer: the slope is 3x while 3 is the y-intercept.
Step-by-step explanation:
Evaluate the expression
z + 3x4
A. 27
B. 32
C. 56
D. 1,304
Answers
The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.
The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.
z + 3x4 = 15 + 3x4
= 15 + 12
= 27
Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).
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____The given question is incomplete , the complete question is given below:
Evaluate the expression, where z = 15
z + 3x4
A. 27
B. 32
C. 56
D. 1,304
5my × 5ym = ?
Can you multiply two terms with the same 2 coefficients in different positions like the example above?
Answers
Answer:
In the example given, 5my × 5ym, you can simplify it using the commutative property of multiplication as follows:
5my × 5ym = 5 × 5 × m × m × y × y
= 25m²y²
So, the answer is 25m²y².
a random sample of 15 recent college graduates found that starting salaries for attorneys in new york city had a mean of $102,342 and a standard deviation of $21,756. there are no outliers in the sample data set. construct a 95% confidence interval for the average starting salary of all attorneys in the city.
Answers
The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a p-value of 1-∝.
So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]
Now, find M as such
[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ
In which is the standard deviation of the population and n is the size of the sample.
[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.
The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.
So the correct answer is:
(91331.94, 113352.06)
Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.
Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.
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Complete Question:
A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices
A). (89869.82, 114814.18)
B). (90292.73, 114391.27)
C). (91331.94, 113352.06)
D). (90371.37, 114312.63)
pls help Are the following lines parallel, perpendicular, or neither?
y = 2/3x − 4
y = −3/2x − 7
Responses
Parallel
Perpendicular
Neither
Answers
Answer:
Perpendicular.
Step-by-step explanation:
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form
y = 2/3x - 4 ==> slope = 2/3
y = -3/2x - 7 ==> slope = -3/2
Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.
Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1
(2/3) * (-3/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular.
Therefore, the answer is: perpendicular.
How much greater is 0.05723 then 0.005?
Answers
0.05723 is 0.05223 greater than 0.005.
What is greater than?"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol ">".
What is lesser than?"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "<".
In the given question,
To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223
Therefore, 0.05723 is 0.05223 greater than 0.005.
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design a context-free grammar (cfg) for the following language (20 points). if your grammar has multiple variables, please briefly describe the strings derived by each variable of your grammar (5 points, please see the lecture notes on cfg design for examples). l
L={aibi| 3i=0, j >=0}
Answers
Answer: 67
Step-by-step explanation:67 x1
Classify each as Polynomial or Not a Polynomial.
1.) 9x-^3 - 2y
2.) 2x^2 - 4√x
3.) 2x 2/3 - 4y
4.) 20x^2
5.) w/2 + 7
6.) 4y/2x
7.) -20x^2 + y
Answers
Not a Polynomial
Not a Polynomial
Polynomial
Not a Polynomial
Not a Polynomial
Polynomial
I need help. A explanation and how you got the answer would be amazing. Thx
Answers
Answer: What is this equation
Step-by-step explanation:
Suppose we select one 2015 Spotify user at random
and record his or her age and whether his or her favorite music genre is pop.
(a) Draw a tree diagram to model this chance process.
(b) Find the probability that the person identifies his or her favorite music genre as pop.
(c) Suppose the chosen person identifies his or her favorite music genre as pop. What’s the probability
that he or she is aged 13–24?
Answers
Answer:11
Step-by-step explanation:
Write and solve an equation to answer the following question. The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $80 plus $0.50 per mile. How many miles were driven if the total cost was $1350?
Answers
Answer: 2540
Step-by-step explanation: 1350-80=1270. 1270/0.5=2540
A sports club had 130 members last summer. This summer, due to some renovations, it has 182 members. What is the percent of increase in the number of members?HELP PLSSSSS
Answers
Answer:
Step-by-step explanation:
312
Answer:
36.92%
Step-by-step explanation:
180-132=48. Now we have to find 48 of 130 to find the percentage increase. 48 out of 130 = which equals 36.92.
the national football league (nfl) records a variety of performance data for individuals and teams. to investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 nfl teams for one full season.
Answers
The National Football League (NFL) is an American football league that is based in the United States. The NFL records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 NFL teams for one full season.The data collected by the NFL shows that passing has a significant impact on the percentage of games won by a team. Teams that have a higher average number of passing yards per attempt tend to win more games than those with a lower average. Additionally, teams that have a lower number of interceptions thrown per attempt also tend to win more games than those with a higher number of interceptions thrown per attempt.The data also shows that the conference a team plays in does not have a significant impact on the percentage of games won by a team. This means that a team's conference is not a good indicator of its performance.The NFL should continue to record data on passing to help teams improve their performance. Coaches can use this data to identify areas for improvement and develop strategies to help their teams win more games.
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The general form of the equation of a circle is x2 y2 8x 22y 37 = 0. the equation of this circle in standard form is (x )2 (y )2 = . the center of the circle is at the point ( , ).
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The centre οf the circle is (-4, -11).
What is a circle's general equatiοn?We knοw that the general equatiοn fοr a circle is (x - h)² + (y - k)² = r² with (h, k) representing the centre and r representing the radius. Sο multiply bοth sides by 21 tο get the cοnstant term οn the right side οf the equatiοn. Then, fοr the y terms, cοmplete the square.
Tο write a circle equatiοn in standard fοrm, we must cοmplete the square fοr bοth x and y.
Tο begin, cοnsider the fοllοwing equatiοn: x²+ y² + 8x + 22y + 37 = 0.
Let's separate the terms with x frοm the terms with y:
[tex](x^2 + 8x) + (y^2 + 22y) + 37 = 0[/tex]
We add (8/2)² = 16 tο bοth sides tο cοmplete the square fοr x: (x²+ 8x + 16) + (y² + 22y) + 37 = 16
Simplifying the left side οf the equatiοn and cοmbining cοnstants οn the right:
[tex](x + 4)^2 + (y^2 + 22y + 121) = 16 - 37 - 121\s(x + 4)^2 + (y + 11)^2 = 50[/tex]
The equatiοn can nοw be written in standard fοrm:
[tex](x + 4)^2/50 + (y + 11)^2/50 = 1[/tex]
The circle's centre is (-4, -11).
As a result, the standard fοrm οf the circle's equatiοn is (x + 4)²/50 + (y + 11)²/50 = 1, and the circle's centre is (-4, -11).
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In Exercise 5.12 , we were given the following joint probability density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide: f(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhere
Are Y1 and Y2 independent?
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The conclude that the Y1 and Y2 are not independent.
The joint probability density function for the random variables Y1 and Y2 for a mixture of insecticide isf(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhereTo verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Therefore, we need to find the marginal density functions of Y1 and Y2.Probability Density Function:We know that for a given joint probability density function, the probability density function of Y1 is given by integrating over all possible values of Y2, and vice versa.Mathematically,P(Y1)=∫0∫1f(y1,y2)dy2... (1)P(Y2)=∫0∫1f(y1,y2)dy1... (2)Using equation (1) to calculate P(Y1), we get, P(Y1)=∫0∫1f(y1,y2)dy2=∫0∫1(2)dy2=2... (3)Similarly, we can use equation (2) to calculate P(Y2) as follows:P(Y2)=∫0∫1f(y1,y2)dy1=∫0∫1(2)dy1=2... (4)Product of marginal density functions:Now we can find the product of marginal density functions as follows:P(Y1)P(Y2)=2×2=4... (5)Thus, to verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Since 2 ≠ 4, Y1 and Y2 are not independent. Hence, we can conclude that the Y1 and Y2 are not independent.
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