If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.
To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):
Average speed = distance ÷ time
Average speed = 12 miles ÷ (1/5) hour
To divide by a fraction, we can multiply by its reciprocal, so:
Average speed = 12 miles × 5/1 hour
Average speed = 60 miles per hour
Therefore, Idil drove at an average speed of 60 miles per hour.
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Liz flips a coin 70 times. The coin lands heads up 42 times and tails up 28 times. Complete each statement
All the experimental probabilities of the coin lands heads up 42 times and tails up 28 times as discuss below 5 points.
Define the term experimental probabilities?Experimental probability is the ratio of the number of times an event occurs to the total number of trials or experiments conducted. It is calculated by performing an experiment or observation and recording the outcomes, and then finding the ratio of the number of times the desired outcome occurred to the total number of trials.
The experimental probability of the coin landing heads up is 42/70, or 0.6.The experimental probability of the coin landing tails up is 28/70, or 0.4The theoretical probability of the coin landing heads up is 1/2, or 0.5.The theoretical probability of the coin landing tails up is 1/2, or 0.5.Liz is more likely to flip heads than tails, based on the experimental probability.To know more about probability, visit:
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As discussed in the next five paragraphs, the coin lands heads up 42 times and tails up 28 times in all experimental probability.
Define the term experimental probabilities?The ratio of the frequency of an occurrence to the total number of trials or experiments is known as the experimental probability. It is determined by carrying out an experiment or making an observation, noting the results, and then calculating the ratio of the number of times the desired result appeared to the total number of trials.
42/70, or 0.6, is the experimental likelihood that the coin will land facing up.
The experimental likelihood that the coin will fall tails up is 28/70, or 0.4.
Theoretically, there is a 0.5 percent chance that the coin will land with its head up.
Theoretically, there is a 0.5 percent chance that the coin will fall tails up.
According to the experimental probability, Liz is more likely to flip heads than tails.
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8. Students were asked to simplify the following expressions on a test. (154 Four different student answers are shown below: Student A 21 - 3h 15-4h+6+h Student B 18h Student C 3h + 21 600p Student D 21 +- 3h Which student or students simplified the expression correctly? Explain
Student A and Student D have correctly simplified the expression. The expression 154 can be written as 3h + 21 + 15-4h+6+h, which is the same as 21 - 3h + 3h + 21. Student A and Student D both simplified the expression to 21 - 3h. Student B simplified the expression to 18h and Student C simplified the expression to 600p, which are both incorrect.
Write each equation in slope-intercept form. Identify the slope and y-intercept.
x - 3y = 12
*Work must be shown.*
Answer:
slope is 1/3
y-intercept is -4
Step-by-step explanation:
x - 3y = 12
3y = x - 12
y = 1/3x - 4
according to y = mx + b, m is slope and b is y-intercept
slope is 1/3
y-intercept is -4
the expression when y=-6 y^2+8y-9
Answer:
-21
Step-by-step explanation:
y^2 + 8y - 9 y = -6
(-6)² + 8(-6) - 9
36 - 48 - 9
-21
So, the answer is -21
Answer:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
Step-by-step explanation:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}
alex makes a fruit puree by mixing blackcurrants and raspberries in the ratio 2:5 he then makes a milkshake by mixing milk and the fruit puree in the ratio 3:1. what fraction of his drink is made from blackcurrants?
For the given ratio of ingredients 3/14 of Alex's drink is made from blackcurrants.
What are ratios?Comparing two numbers or values using ratios, which are often stated as fractions or colons. In mathematics, ratios are used to represent connections between various objects or numbers, such as the ratio of a rectangle's length to breadth or the proportion of boys to girls in a class. Ratios can be sped up or stated in a variety of ways, such decimals or percentages.
The given ratio for blackcurrants to raspberries is 2:5.
The total ratio is:
2 + 5 = 7
Hence, the fraction of the puree made from blackcurrants is = 2/7.
Now, ratio of fruit puree to milk is 3:1 = 3 + 1 = 4.
Hence, the fraction of the milkshake made from fruit puree is = 3/4.
For blackcurrants we have:
(2/7) * (3/4) = 6/28 = 3/14
Hence, for the given ratio of ingredients 3/14 of Alex's drink is made from blackcurrants.
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You want to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units. You will sample the GPAs of 40 SJSU students. Select the correct model from the list. - One sample, Chi-square test of variance - Unequal variance t-test - Matched pairst-test - One sample. Z test of proportion - F-test comparing variances - One sample, t test for mean - Pooled variance t-test
The Chi-square test of variance is appropriate to use.
The correct model from the list to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units by sampling the GPAs of 40 SJSU students is the "One sample, Chi-square test of variance. "The Chi-square test of variance is used to determine whether the variance of a population is equal to a specific value. In the Chi-square test of variance, the null hypothesis is that the variance of the population is equal to the specific value or the variance is not greater than the specific value. The Chi-square test of variance is used when the sample is random, the sample is normally distributed, and the variable is measured on a continuous scale. In the given problem, the researcher wants to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units.
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What is the value of x in this triangle?
Enter your answer in the box.
X =
xº
44°
5
53°
6 7
(O
Answer:
83°
Step-by-step explanation:
the total angle of a triangle is 180° degree so 180°-(44°+53°)=83°
A function is graphed on the coordinate grid. Possible inputs for the quadratic when the output is 3 are ___ or ___.
Step-by-step explanation:
This graph shows a quadratic curve with roots 0 and -4
The polynomial is therefore
x² -x(α+β) + αβ
x² -x(0-4) + 0(-4)
x² +4x +0
x² + 4x
But it's an n-shaped curve, meaning a is negative
Multiply through by -1
-x² - 4x
y = -x² - 4x
So when the input value y = 3, we have
3 = -x² - 4x
Rearrange
x² + 4x + 3 = 0
Factorize
x² + 3x + x + 3 = 0
x(x + 3) +1(x + 3) = 0
(x + 1) (x + 3) = 0
x + 1 = 0 and x + 3 = 0
x = 0-1 and x = 0-3
Therefore,
x = -1 and -3
Check the graph to confirm
Simplify 4m^2n-7mn^2
Answer:
mn(4m - 7n)
Step-by-step explanation:
➠ 4m^2n-7mn^2
➠ 2^2 x m^2n - 7mn^2
➠ mn([tex](\frac{2^2*m^2n}{mn} -\frac{7mn^2}{mn} )[/tex]
➠ mn([tex]2^2*m^{2-1}-(7n^{2-1}))[/tex]
➠ mn(4m - 7n)
Find Compund Interest of P = ₹4000, N = 3 years, R = 5 p. C. P. A
The compound interest on ₹4000 at a rate of 5% p.a. for 3 years is ₹631.03.
The formula to calculate compound interest is:
[tex]A= P(1+\frac{R}{N} )^{nt}[/tex]
Where:
A = Final amount (including interest)
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, P = ₹4000, N = 3 years, R = 5% per annum (p.a.), which means r = 0.05 and n = 1 (compounded annually).
So, plugging in the values in the formula:
[tex]A= 4000(1+\frac{0.05}{1} )^{1*3}[/tex]
[tex]A= 4000(1.05)^{3}[/tex]
[tex]A = 4631.03[/tex] (rounded to 2 decimal places)
Compound interest is a type of interest that is calculated not only on the initial amount of money borrowed or invested but also on the accumulated interest from previous periods. In other words, the interest earned in each period is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.
This compounding effect can result in significant growth in the value of an investment or debt over time, especially if the interest rate is high and the period of investment or debt repayment is long. For example, if you invest $1,000 at an annual interest rate of 5% compounded annually, you will earn $50 in interest at the end of the first year, and your new total will be $1,050.
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*NEED HELP PLEASE*
Solve each radical equation for x
and check your solution. (Isolate,
solve, check)
Step-by-step explanation:
1. sqrt(x + 6)/5 = 2
sqrt(x + 6) = 10
x + 6 = 100
x = 94
sqrt(94 + 6)/5 = 2
sqrt(100)/5 = 2
10/5 = 2
2 = 2
confirmed.
2.
sqrt(9x + 2) = sqrt(11x - 12)
9x + 2 = 11x - 12
14 = 2x
x = 7
sqrt(9×7 + 2) = sqrt(11×7 - 12)
sqrt(63 + 2) = sqrt(77 - 12)
sqrt(65) = sqrt(65)
confirmed.
3.
cubic root(6x + 3) + 10 = 13
cubic root(6x + 3) = 3
6x + 3 = 27
6x = 24
x = 4
cubic root(6×4 + 3) + 10 = 13
cubic root(24 + 3) + 10 = 13
cubic root(27) + 10 = 13
3 + 10 = 13
13 = 13
confirmed.
4.
2×sqrt(5x - 4) - 24 = -6
sqrt(5x - 4) - 12 = -3
sqrt(5x - 4) = 9
5x - 4 = 81
5x = 85
x = 17
2×sqrt(5×17 - 4) - 24 = -6
2×sqrt(85 - 4) - 24 = -6
2×sqrt(81) - 24 = -6
2×9 - 24 = -6
18 - 24 = -6
-6 = -6
confirmed.
Q.4. A shopkeeper bought 18 sets of kurthas at the rate of Rs.1000 each. If 3 sets of kurthas were damaged and the remaining sets of kurthas were sold at the rate of Rs. 1250. Find the profit or loss of the shopkeeper.
Answer:
Rs 750
Step-by-step explanation:
Given, No. of kurtas: 18, Each with CP = Rs 1000.
So, SP of 18 kurtas: 18*1000 = Rs. 18000
Also, 3 sets of kurtas were damaged.
Therefore, Remaining kurtas: 18-3 = 15. SP of each: Rs 1250.
SP of 15 kurtas: 15*1250 = Rs. 18750
So, Clearly SP>CP, Profit.
We know Profit= SP-CP
= 18750-18000 = Rs 750
Square root of
3a^2/10b^6
Answer:
Step-by-step explanation:
Rewrite
3
a
2
10
b
6
as
(
a
b
3
)
2
3
10
.
√
(
a
b
3
)
2
3
10
Pull terms out from under the radical.
a
b
3
√
3
10
Rewrite
√
3
10
as
√
3
√
10
.
a
b
3
⋅
√
3
√
10
Combine.
a
√
3
b
3
√
10
Multiply
a
√
3
b
3
√
10
by
√
10
√
10
.
a
√
3
b
3
√
10
⋅
√
10
√
10
Combine and simplify the denominator.
√
3
√
10
b
3
⋅
10
Simplify the numerator.
Tap for more steps...
a
√
30
b
3
⋅
10
Move
10
to the left of
b
3
.
a
√
30
10
b
3
Step-by-step explanation:
[tex]{ \tt{ \sqrt{ \frac{3 {a}^{2} }{10 {b}^{6} } } }} = { \tt{ \frac{ {(3a {}^{2}) }^{ \frac{1}{2} } }{ {(10b {}^{6} )}^{ \frac{1}{2} } } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }}[/tex]
Which is the conclusion in the following argument. "Since the good, according to Plato, is that which furthers a person's real interests, it follows that
Group of answer choices
- the good, according to Plato, is that which furthers a person's real interests
- Neither of the above.
- in any given case, when the good is known, men will seek it
The conclusion in the argument is "the good, according to Plato, is that which furthers a person's real interests." which it is the correct answer.
In a well-structured argument, the conclusion is what the argument aims to prove.
The conclusion can be located at the beginning or end of the argument, and it should always be precise, clear, and understandable.
The conclusion in the argument above is that "the good, according to Plato, is that which furthers a person's real interests."
The argument tries to explain that the good in Plato's philosophical teachings is a thing that advances a person's genuine interests.
The statement "it follows that" is the premise that links the argument with the conclusion.
The premise and the conclusion have a relationship of cause and effect, and this implies that the argument's conclusion is "the good, according to Plato, is that which furthers a person's real interests."
Therefore, the right option is: the good, according to Plato, is that which furthers a person's real interests.
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PLEASE HELP... In each right triangle, find the missing side length to the nearest tenth.
The side length x of the right angle triangle is 25 units.
How to find the sides of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The sides of a right triangle can be found using Pythagoras's theorem. Let's use Pythagoras's theorem to find the side x.
Hence,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
a = 24 units
b = 7 units
Hence,
24² + 7² = x²
576 + 49 = x²
625 = x²
square root both sides of the equation
x = √625
x = 25 units
Therefore,
x = 25 units
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Expand and simplify (3x - 1)(9x² + 3x + 1)
1. What are a forensic scientist's taxes on a salary of
$86,200.85?
Answer: $27,306
Step-by-step explanation: Forensic Scientist's take home pay is around $58,894
You do 86,200-58,894=27,306
Ashley and Stephanie went shopping for Father's Day at the same store. Stephanie spent $105 for 2 t-shirts and 3 pairs of shorts. Ashley bought 3 t-shirts and 2 pairs of shorts for $95. What was the cost of a pair of shorts? (Hint The equation for Ashley's purchases is 3T+2S = 95 First determine the equation for Stephanie's purchases and then solve the system of equations using matrices) a. $10 for shorts b. $17 for shorts c. $25 for shorts d. $15 for shorts
The cost of a pair is D) $15 for shorts.
To solve this problem, we need to set up a system of equations based on the information given for both Stephanie and Ashley's purchases. Let T be the cost of a t-shirt and S be the cost of a pair of shorts.
For Stephanie's purchases, we have:
[tex]2T + 3S = 105[/tex]
For Ashley's purchases, we have:
[tex]3T + 2S = 95[/tex]
Using matrices, we can solve this system of equations by setting up the augmented matrix and using row operations:
[2 3 | 105]
[3 2 | 95]
After row operations, we get:
[1 0 | 15]
[0 1 | 25]
Therefore, the cost of a pair of shorts is $15.
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help!!
(1.58 x 10 ^15) - (9.82 x 10^13)
ANSWER:
10^11 * 14818
Expand: factor out 10^11: 10^11 (15800-982) = 10^11 * 14818
Question 2
On a bicycle, Ivanna rides for 5 hours and is 12 miles from her house. After riding for 9 hours, she is 20 miles
away.
What is Ivanna's rate?
By answering the presented question, we may conclude that As a result, expressions Ivanna's average speed is approximately 2.311 miles per hour.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
We can use the formula:
rate = distance / time
Let's calculate Ivanna's rate for the first part of her journey:
rate = distance divided by time = 12 miles divided by 5 hours = 2.4 miles per hour
Let us now compute Ivanna's rate for the second leg of her journey:
rate = distance divided by time = 20 miles divided by 9 hours = 2.222... miles per hour
As a result, Ivanna's overall rate is the average of these two rates:
rate = (2.4 miles per hour + 2.222... miles per hour) / 2 = 2.311... miles per hour
As a result, Ivanna's average speed is approximately 2.311 miles per hour.
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Use the following circle to solve for x
We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;
[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]
[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]
How much was one movie ticket in 2008
Answer: 7 dollars 18 cents.
Step-by-step explanation:
sam made fruit punch for a party. he mixed 3 gallons of orange juice, 2 quarts of pineapple juice, 4 pints of cranberry juice, and 6 cups of apple juice. how many quarts did he make in all? (2 points) a 14 b fifteen and one half c seventeen and one half d 20
The answer is c): 17 and one-half quarts
To answer the question, we need to find the total amount of juice Sam made by adding the given quantities. However, the given quantities are in different units, which makes the addition difficult. Therefore, we need to convert all quantities to the same unit before adding them.
1 gallon = 4 quarts (since 1 gallon is equal to 128 ounces, and 1 quart is equal to 32 ounces,
thus 1 gallon = 128/32 = 4 quarts)
1 quart = 2 pints
1 pint = 2 cups
Therefore, 3 gallons = 3 x 4 = 12 quarts
2 quarts = 2 x 1 = 2 quarts
4 pints = 4 / 2 = 2 quarts
6 cups = 6 / 4 = 1.5 quarts
Now, we can add all the quantities in quarts to get the total amount of juice that Sam made:
12 + 2 + 2 + 1.5 = 17.5 quarts
Therefore, Sam made 17 and one-half quarts in all. Thus, the correct option is (c) seventeen and one half.
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23 people attend a party. each person shakes hands with at most 22 other people. what is the maximum possible number of handshakes, assuming that any two people can shake hands at most once?
The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.
What is the maximum possible number of handshakes?Twenty-three people attend a party. each person shakes hands with at most 22 other people.
To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.
nCr (combination) to find the number of unique pairs of people.
Therefore,[tex]^nC_r = \frac{n!}{(n-r)! r!}[/tex]
where n is the total number of people and r is the number of people in a handshake at a time.
Therefore, the number of unique pairs of people that can shake hands at most once is:
[tex]^{23}C_2 = \frac{23!}{(23-2)! (2!)}[/tex] [tex]=\frac{23 X22}{2} = 253[/tex]
Hence, the maximum possible number of handshakes that can happen at the party is 253.
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in a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. complete the following statement with what you can conclude about the system.
In a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. This statement is indicative of a system of linear equations which will have no solution.
A system of linear equations is a collection of two or more linear equations with the same variables. A system of linear equations is a collection of two or more linear equations with the same variables. A solution of a system of linear equations is a set of values that make all of the equations true.
Let's look at the general form of two linear equations that are given:
y = mx + by = nx + c
where m and n are the slopes of each line. If m and n have different signs, one is positive and one is negative, then they will never meet and therefore will have no solution. We can thus conclude that the system of two equations has no solution.
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a particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. twenty fish are placed in a tank containing this concentration of chemical in water. a find the probability that exactly 14 survive. b find the probability that at least 10 survive.
A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore
a. The probability that exactly 14 fish survive is 0.263b. The probability that at least 10 fish survive is 0.983How do we calculate the probability?a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263
b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.
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Draw a shape with fractional side lengths. Describe how you will find its area.
Therefore, the area of the rectangle is 6 7/8 square inches.
What is area?Area is a measurement of the amount of space inside a 2-dimensional shape, such as a rectangle, triangle, circle, or any other polygon. It is usually measured in square units, such as square inches, square feet, square meters, etc. The formula for finding the area of a shape depends on the type of shape. For example, the area of a rectangle is calculated by multiplying its length by its width, while the area of a circle is calculated by multiplying the square of its radius by pi (3.14).
Here,
Here's how to draw a shape with fractional side lengths and find its area:
Draw a rectangle with side lengths of 2 1/2 inches and 3 3/4 inches.
Divide the rectangle into smaller squares or rectangles to make it easier to calculate the area.
For example, you can divide the rectangle into two smaller rectangles with side lengths of 2 1/2 inches and 1 3/4 inches, and 2 1/2 inches and 2 inches respectively.
Calculate the area of each smaller rectangle by multiplying the length by the width.
The total area of the rectangle is the sum of the areas of the smaller rectangles.
So the area of the rectangle would be:
Area = (2 1/2 inches x 1 3/4 inches) + (2 1/2 inches x 2 inches)
Area = (5/2 inches x 7/4 inches) + (5/2 inches x 2 inches)
Area = (35/8 square inches) + (10/4 square inches)
Area = (35/8 square inches) + (20/8 square inches)
Area = (55/8 square inches)
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Lisa's school is 3 miles west of her house and 3 miles south of her friend Roxanne's house.
Every day, Lisa bicycles from her house to her school. After school, she bicycles from her
school to Roxanne's house. Before dinner, she bicycles home on a bike path that goes straight
from Roxanne's house to her own house. How far does Lisa bicycle each day? If necessary, round to the nearest tenth.
The total distance travelled by Lisa in a day is found to be 10.24 miles.
Explain about the Pythagorean theorem?Pythagoras (born 570 BC) developed a theorem known as the Pythagorean Theorem, which is exclusively applicable to right triangles.
According to the Pythagorean Theorem, a right triangle's hypotenuse square is equal to the sum of its other two sides. The side opposite the right angle is known as the hypotenuse.
Pythagoras theorem:
a² + b² = c²
Given case:
Roxanne's house is 3 miles south of Lisa's school say 'a', which is 3 miles west of Lisa's home say 'b'. Lisa commutes to school by bicycle each day from her home. She rides her bicycle to Roxanne's house after school. She rides her bicycle home before dinner along a bike route that connects Roxanne's home to her own.Here,
a = b = 3 units
Put the values;
3² + 3² = c²
2*9 = c²
c = 3√2
c = 4.24
Total distance = 4.24+ 3 + 3
Total distance = 10.24 miles
Thus, the total distance travelled by Lisa in a day is found to be 10.24 miles.
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Using the inverse transform method for discrete distribution, define a process for generating random variates from a binomial distribution with N 6 and p 0.4. (sixth decimal place.)
The another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
The process of generating random variates from a binomial distribution using the inverse transform method for discrete distribution is done as follows:Step 1: Determine the probability mass function (pmf) of the binomial distribution with parameters n and p. For example, for a binomial distribution with n = 6 and p = 0.4, the pmf is given by:P(X=k) = (6 choose k)(0.4)^k(1-0.4)^(6-k), where k=0,1,2,3,4,5,6Step 2: Calculate the cumulative distribution function (CDF) of the binomial distribution by summing the pmf up to each value of k. The CDF is given by:F(k) = P(X ≤ k) = ΣP(X=i) for i=0 to k, where k=0,1,2,3,4,5,6Step 3: Generate a uniform random variate, U, between 0 and 1. For example, U=0.23456.Step 4: Find the smallest value of k such that F(k) ≥ U. This value of k is the random variate X. For example, if U=0.23456, then F(0)=0.10737, F(1)=0.38223, and F(2)=0.74304. Since F(1) is the smallest value of F(k) that is greater than or equal to U, X=1. Therefore, a random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=1.To find another random variate from the same distribution, repeat steps 3 and 4. For example, U=0.987654, F(0)=0.10737, F(1)=0.38223, F(2)=0.74304, F(3)=0.91892, F(4)=0.98544, and F(5)=0.99856. Since F(3) is the smallest value of F(k) that is greater than or equal to U, X=3. Therefore, another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.
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a. in the sample: i. what is the average value of birthweight for all mothers? ii. for mothers who smoke? iii. for mothers who do not smoke? b. i. use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers. ii. what is the standard error for the estimated difference in (i)? iii. construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers.
a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.
ii. For mothers who smoke is 6.82 pounds.
iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:
Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.
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