Question 1 نت You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 369 randomly selected caterpillars observed, 45 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 369 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion. Hint: Hints Video [+]​

Answers

Answer 1

a) The 99% confidence interval for the proportion of all caterpillars that lived to become a butterfly is between 0.078 and 0.166.

b) About 99% of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

What is a confidence interval of proportions?

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The sample size and the estimate for this problem are given as follows:

[tex]n = 369, \pi = \frac{45}{369} = 0.122[/tex]

The lower bound of the interval is given as follows:

0.122 - 2.575 x sqrt(0.122 x 0.878/369) = 0.078.

The upper bound of the interval is given as follows:

0.122 + 2.575 x sqrt(0.122 x 0.878/369) = 0.166.

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Related Questions

PLEASE HELP WHAT IS 7 x 4

Answers

Answer:

THE ANSWER OF 7×4=28 !!!!!!!

It is 7/4 is 28 simple

The radius of the circle with a central angle of 6 radians that intercepts an arc with
length 53 cm is
____cm.
The radius of the circle with a central angle of 56° that intercepts an arc with length
19 miles is____miles

Answers

For the first question, we can use the formula for the length of an arc of a circle: L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

We are given that the length of the arc is 53 cm and the central angle is 6 radians. Solving for r, we get:

r = L/θ = 53/6 = 8.833 cm

Therefore, the radius of the circle is 8.833 cm.

For the second question, we need to convert the central angle from degrees to radians. We know that 360° is equal to 2π radians, so 1° is equal to (2π/360) radians, or approximately 0.01745 radians.

The central angle of 56° is equal to 56 x 0.01745 = 0.9772 radians.

We are given that the length of the arc is 19 miles. Using the same formula as before, we get:

r = L/θ = 19/0.9772 = 19.44 miles

Therefore, the radius of the circle is 19.44 miles.

Can u mark my answer as the Brainlyest if it work Ty

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
F(x) = (x^4/5)((x − 5)^2)

Answers

The critical values of the function are x = 0 and x = 4.

The critical values of a function f(x) are the values of x for which f'(x) = 0.

In this problem, the function is:

f(x) = [tex]\frac{x^4}{5(x-2)^2}[/tex]

The derivative is found as follows, applying the quotient rule:

f'(x) = [tex]\frac{2x^3(x-4)}{5(x-2)^3}[/tex]

The zeros of the function are the zeros of the numerator, thus:

2x³(x-4) = 0

∴ x = 0, 4

Hence, the critical values of the function are x = 0 and x = 4.

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12. An inequality is given, where r is a positive rational number.
r.9 <09/1
Jala:
bo
true?

Answers

Since r is a positive rational number, an inequality must also be true include the following: A.) q < 0.

What is a rational number?

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.

Next, we would solve the given inequality in order to determine all of the solutions that satisfies the variable q. This ultimately implies that, we would simplify the inequality by cancelling out the variable r as follows;

r × q/r < 0 (r is a positive rational number).

q < 0

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Complete Question:

An inequality is given, where r is a positive rational number.

r • q/r < 0

Which inequality must also be true?

A.) q < 0

B.) q > 0

C.) q < - r

D.) q/r < - r

Find the probability that a day in Dayton will include rain or snow.

Answers

The probability that a day in Dayton will include rain or snow is 38%.

Let's assume that there are 365 days in a year (not considering leap years), and we are aware that Dayton typically experiences 25 days of snow per year, in addition to 110 days of rain. We can add the total number of rainy and snowy days in Dayton and then divide that total by the number of days in a year to determine the likelihood that a given day will be either one of those things:

probability of rain or snow = [tex]\frac{110+25}{365}[/tex]

                                             =0.38

The probability that a day in Dayton will have rain or snow is 0.38 or 38%.

The question is incomplete, complete question is " Dayton is a small town in Ohio, which receives  110 days of rain and 25 days of snow per year. Ignoring leap years, Find the probability that a day in Dayton will include rain or snow."

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How do I find the quadratic formula?

Answers

Answer:

x = -31 maybe

Step-by-step explanation:

Evaluate the algebraic expression t + s - r when r=13, s=10, t = 7 and u=15,

A) 2
B) 4
C) 16
D) 30​

Answers

7+10-13= 4.

Therefore the answer would be B. 4

which expression is equivalent to -16x squared +36 in factored form?

Answers

Expression for -16x squared +36 in factored form is [tex]-4(2x - 3)(2x + 3).[/tex]

The given equation is [tex]-16x^{2} +36[/tex]

simplifying the equation,

[tex]-16x^2 + 36 = 4(-4x^2 + 9)[/tex]

[tex]=-4x^2 + 9\\ = -(2x)^2 + 3^2 \\= -(2x - 3)(2x + 3)[/tex]

when compared together,

[tex]-16x^2 + 36 = 4(-4x^2 + 9) = 4(-(2x - 3)(2x + 3)) = -4(2x - 3)(2x + 3)[/tex]

The expression for the equation in factored form is -4(2x - 3)(2x + 3).

The question is incomplete. complete question will be "which of these expression is equivalent to [tex]-16x^{2} +36[/tex] in factored form?

options- 4(x+2)(3-2x) , -4(2x - 3)(2x + 3) or (4x+2x)(9x-2x)"

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Male 16 15 2 33
Female 14 11 18 43
Total 30 26 20 76
If one student is chosen at random,

Find the probability that the student was female:

Find the probability that the student was female AND got a "C":

Find the probability that the student was female OR got a "C":

If one student is chosen at random, find the probability that the student was female GIVEN they got a 'C':

Answers

a) The probability that the student was female is 43/76

b) The probability that the student was female AND got a "C" is 9/38

c) The probability that the student was female OR got a "C" is 45/76

We have,

             A   B   C  

Male     16  15  2  33

Female 14  11  18  43

Total     30 26 20 76

a) The probability that the student was female

= 43/76

b) The probability that the student was female AND got a "C"

= 18/76

= 9/38

c) The probability that the student was female OR got a "C"

= 43 /76 + 20/76 - 18/76

= 45/76

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John is w years old. His sister is 16 years old and his brother is twice
John's age. All three siblings have a total age of 31.
a) Write an equation to represent this.
b) Solve your equation to find out John's age.

Answers

Answer: 16* 2

Step-by-step explanation:

I heard you might have to increase your prices by 12% if i normally pay $45 per order, how much would my order be if the price increse happens?

Answers

The order will be $50.4 with the price increase

How much would the order be with the price increase?

From the question, we have the following parameters that can be used in our computation:

Order = $45

Percentage increase = 12%

Using the above as a guide, we have the following:

New order = Order * (1 + Percentage increase)

Substitute the known values in the above equation, so, we have the following representation

New order = 45* (1 + 12%)

Evaluate

New order = 50.4

Hence, the new order is $50.4

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NEED HELP I HAVE 20 MIN WILL RATE AND GIVE BRAINLIEST!

Answers

Answer:

A) [tex]x = \dfrac{\log_6(46) + 6}{4}[/tex]

B) [tex]x = \dfrac{\ln(11)}{2}[/tex]

C) [tex]x = \dfrac{11}{5}[/tex]

Step-by-step explanation:

A) We can solve for x by taking log base 6 of both sides.

[tex]\log_6(6^{4x-6}) = \log_6(46)[/tex]

[tex]4x - 6 = \log_6(46)[/tex]

[tex]4x = \log_6(46) + 6[/tex]

[tex]\boxed{x = \dfrac{\log_6(46) + 6}{4}}[/tex]

B) First, we have to divide both sides by 2.

[tex]2e^{2x} / 2= 22 / 2[/tex]

[tex]e^{2x} = 11[/tex]

Then, we can solve for x by taking the natural log (log base e) of both sides.

[tex]\ln(e^{2x})= \ln(11)[/tex]

[tex]2x= \ln(11)[/tex]

[tex]\boxed{x = \dfrac{\ln(11)}{2}}[/tex]

C) We can solve for x by raising 2 to the power of each side.

[tex]2^{\log_2(5x + 5)} = 2^4[/tex]

This cancels the log base 2 on the left.

[tex]5x + 5 = 16[/tex]

[tex]5x = 11[/tex]

[tex]\boxed{x = \dfrac{11}{5}}[/tex]

I am unsure about how to do this problem, pictured below.

Answers

The time taken to reach a population of 500 is gotten from  500=50e^0.55t

What is the exponential growth?

Exponential growth is a process that increases quantity over time as in the bacterial culture here.

We know that from the question, we have;

P(t)=Poe^rt

P(t) = population at time t

Po= Initial population

r = growth rate

t = time taken

Then we have that;

150 = 50e^2r

3=e^2r

ln3 = 2r

r = ln3/2

r = 0.55

If the rate of growth is 0.55, then to reach a population  of 500;

500=50e^0.55t

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The functions s and t are defined as follows. s (x) ニーx+5 t(x) =2x+2 Find the value of t (s (2)).

Answers

The value of the composite function t(s (2)) is 8

Finding the value of the composite function t(s (2))

From the question, we have the following parameters that can be used in our computation:

s(x) = -x + 5

t(x) = 2x + 2

The composite function t(s(x)) is calculated as

t(s(x)) = 2s(x) + 2

Substitute the known values in the above equation, so, we have the following representation

t(s(x)) = 2(-x + 5) + 2

Again, substitute the known values in the above equation, so, we have the following representation

t(s(2)) = 2(-2 + 5) + 2

Evaluate

t(s(2)) = 8

Hence, the value of t(s(2)) is 8

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Use the graph to answer the question.

Graph of polygon VWXYZ with vertices at 3 comma 2, 3 comma 0, 6 comma negative 7, 9 comma 0, 9 comma 2. A second polygon V prime W prime X prime Y prime Z prime with vertices at 3 comma negative 10, 3 comma negative 8, 6 comma negative 1, 9 comma negative 8, 9 comma negative 10.

Determine the line of reflection.

Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 6
Reflection across y = −4

Answers

The requried line of reflection is the x-axis.

To determine the line of reflection, we need to find the line that maps each vertex of the first polygon to the corresponding vertex of the second polygon.

We can start by reflecting the first polygon across the x-axis. This will map V to V', W to W', X to X', Y to Y', and Z to Z', as shown below:

First Polygon (VWXYZ) Second Polygon (V'W'X'Y'Z')

(3, 2) V (3, -10) V'

(3, 0) W (3, -8) W'

(6, -7) X (6, -1) X'

(9, 0) Y (9, -8) Y'

(9, 2) Z (9, -10) Z'

Next, we can compare the coordinates of each vertex in the first and second polygons to determine the line of reflection. We notice that reflecting the first polygon across the x-axis negates the y-coordinates of all vertices. Therefore, the line of reflection must be the x-axis.

Therefore, the line of reflection is the x-axis.

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if det [a 10 e b d 0] = [2 10 3 6 -1 0],find a,d and e

Answers

Answer:

The given equation is:

det [a 10 e b d 0] = [2 10 3 6 -1 0]

The determinant of a 3x3 matrix is calculated as follows:

|a b c|

|d e f| = a(ei - fh) - b(di - fg) + c(dh - eg)

Applying this formula to the given matrix, we get:

det [a 10 e b d 0] = a(d0 - b-1) - 10(ed - b0) + e(10*-1 - d*3)

= ab + 10b - 10ed - 3e

Substituting the given values, we get:

ab + 10b - 10ed - 3e = 2(6-0) - 10(3-(-1)) + 3(10-(-1))

ab + 10b - 10ed - 3e = 12 + 40 + 33

ab + 10b - 10ed - 3e = 85

We can simplify this equation by factoring out b and e:

b(a + 10) - e(10d + 3) = 85 - 10b

We can solve for a, d, and e by setting up a system of equations using the given values of the determinant:

ab + 10b - 10ed - 3e = 85

From this equation, we can solve for b:

b(a + 10) - e(10d + 3) = 85 - 10b

Substituting the value of b from the determinant equation, we get:

(a+10)(-1) - e(10d+3) = -8.5

Simplifying, we get:

-a - 10e - 3.3d = -8.5 ...(1)

Also, from the determinant equation, we have:

6a + 10d + 3e = 29

Solving for e in terms of a and d, we get:

e = (29 - 6a - 10d)/3 ...(2)

Substituting equation (2) into equation (1), we get:

-a - 10[(29 - 6a - 10d)/3] - 3.3d = -8.5

Simplifying and multiplying both sides by -3, we get:

3a + 20d - 29e = 25.5

Substituting equation (2) into this equation, we get:

3a + 20d - 29[(29 - 6a - 10d)/3] = 25.5

Simplifying, we get:

a + 6d - 29 = 1.5

a + 6d = 30.5

We have two equations in two variables:

-a - 10e - 3.3d = -8.5

a + 6d = 30.5

Solving for a and d using any method (substitution, elimination, etc.), we get:

a = 7

d = 4

Substituting these values into equation (2), we get:

e = (29 - 6a - 10d)/3 = (29 - 6(7) - 10(4))/3 = -3

Therefore, a = 7, d = 4, and e = -3.

Step-by-step explanation:

Sean A y B dos sucesos tales que:
P(A)= 0. 4;
P(Bc)= 0. 7 y P(AUB)= 0. 6, donde Bc
es el suceso contrario de B. Determinar si son independientes A y B

Answers

Para determinar si A y B son independientes, se debe cumplir que P(A∩B) = P(A)P(B).

Primero, se debe encontrar P(B) utilizando la probabilidad complementaria:
P(B) = 1 - P(Bc) = 1 - 0.7 = 0.3.

Luego, se puede encontrar P(A∩B) utilizando la fórmula de la unión:
P(A∩B) = P(A) + P(B) - P(AUB) = 0.4 + 0.3 - 0.6 = 0.1.

Finalmente, se puede verificar si A y B son independientes:
P(A)P(B) = 0.4 x 0.3 = 0.12.

Como P(A∩B) ≠ P(A)P(B), se concluye que A y B no son independientes

Carla does 25 jumping jacks 3 times per day. How many jumping jacks will Carla do in 7 days?

Answers

Answer: 525 jumping jacks

Step-by-step explanation:

she does 25 x 3 = 75 jumping jacks per day.

so in a week, (7 days) she will do 7 x 75 = 525 jumping jacks

Help me please I don’t know

Answers

Answer:21y -78

Step-by-step explanation: Distribute the 7 to 3y and -10 to get 21y and -70.

Then combine like terms so the equation would be 21y -78

Answer: 21y-78

Step-by-step explanation:

-8+7(3y-10)

-8+21y-70

21y-70+8

21y-78

Last step because there is no more like terms to combine

Hope this helps

help me please fr i just need these questions

Answers

The base area of the cylinder is 78.54 ft².

The height of the cylinder is 2 ft.

How to find the height and base area of the cylinder?

The cylinder has a volume of 157.08 ft cube and the radius of the cylinder is 5 ft.

Therefore, the area of the base of the cylinder can be found as follows:

base area of the cylinder = πr²

base area of the cylinder = 3.1416 × 5²

base area of the cylinder = 3.1416 × 25

base area of the cylinder = 78.54 ft²

Therefore, let's find the height of the cylinder.

volume of the cylinder = πr²h

where

h = height of the cylinder

157.08 = 78.54 h

divide both sides by 78.54

h = 157.08 / 78.54

h = 2 ft

Therefore,

height of the cylinder = 2 ft

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The number of runs scored by the Lions for six games is shown below.
5, 8, 1, 5, 2, 7
If the Lions scored 14 runs in their seventh game, which of the following statements is true?
OA. The median increases and the mean remains the same.
OB. The mean increases and the median remains the same.
OC. The mean and the median both increase.
OD. The median and the mean both remain the same.

Answers

If the Lions in their "seventh-game" scored 14 runs, then the true statement is (b) The mean increases and the median remains the same.

To determine how the additional 14 runs affect the mean and median, we need to calculate the original mean and median.

The mean is the sum of all the runs divided by the number of games:

So, Mean = (5 + 8 + 1 + 5 + 2 + 7)/6 = 28/6 = 4.67,

The median is defined as "middle-value" when data is arranged in order. In this case, the data in order is : 1, 2, 5, 5, 7, 8

So, the median is 5.

If the Lions scored 14 runs in their seventh game, the total number of runs for seven games is:

⇒ 5 + 8 + 1 + 5 + 2 + 7 + 14 = 42,

The new mean is the sum of all the runs for seven games divided by the number of games:

⇒ Mean = 42/7 = 6,

The new data in order is : 1, 2, 5, 5, 7, 8, 14,

So, the new median is also 5.

Comparing the original mean and median to the new mean and median, we can see that:

⇒ The median remains the same.

⇒ The mean increases from 4.67 to 6.

Therefore, the correct option is (b).

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Which of the following is not a characteristic of both experiments and
surveys?
O A. Data are collected about a population.
B. Subjects should be randomly selected.
OC. The data collected might be studied for patterns.
OD. The researcher exercises direct control over at least one variable.
SUBMIT

Answers

"Data are collected about a population," is not a characteristic of both experiments and surveys. Option A

What is the difference between survey and experiment?

A survey is a technique for gathering data about a study variable from the respondents of the population. An experiment is a technique used in science to isolate the problem being examined and test a theory.

Options B, C, and D are characteristics obtained in the case of the  experiments and surveys. In both types of research, subjects may be randomly selected (option B), the data collected may be studied for patterns (option C).

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Three squares are placed to form a right triangle as shown.

Which statement must be true?

A The sum of the areas of the smaller
squares is always equal to the area of the largest square.

B The sum of the areas of the smaller squares is always greater than the area of the largest square.

C The difference of the areas of the smaller squares is always equal to the area of the largest square.

D The difference of the areas of the smaller squares is always greater than the area of the largest square.

Answers

If three squares are placed to form a right triangle as shown. The statement that must be true is: C .The difference of the areas of the smaller squares is always equal to the area of the largest square.

Which statement is true?

Let's use the letters a, b, and c to denote the side lengths of the squares, with c standing for the hypotenuse of the right triangle. Assuming that an is the shortest side length to preserve generality a2 is the area of the smallest square. The largest square has a surface area of c2 whereas the medium square has a surface area of b2.

The Pythagorean theorem demonstrates that a + b equals c. If we rewrite this equation, we obtain:

c^2 - b^2 = a^2

c^2 - a^2 = b^2

This means that the size of the largest square is equal to the difference between the areas of the two smaller squares, which is either a2 or b2.

Therefore the correct option is C.

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Which statement is true? (1 point)

a
An equilateral triangle is always an isosceles triangle.

b
A right triangle is never an isosceles triangle.
c
An obtuse triangle is sometimes an acute triangle.

d
An isosceles triangle is always a scalene triangle.




Please help!!

Answers

The True statement is An equilateral triangle is always an isosceles triangle.

An equilateral triangle is always an isosceles triangle is True because isosceles triangle have two sides equal and equilateral have three sides equal.

A right triangle is never an isosceles triangle is False statement.

An obtuse triangle is sometimes an acute triangle is False statement.

An isosceles triangle is always a scalene triangle is False statement.

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Population of a city grows by 14% every year. Initial population of the city is 5,741. Find how many people will be in the city after 3 years

Answers

The estimated population of the city after 3 years would be 8,537 people.

To find the population of the city after 3 years, we can use the formula for compound interest;

A = P ×[tex](1+r)^{t}[/tex]

where;

A = the final amount (population after 3 years)

P = the initial amount (initial population of the city) = 5,741

r = the annual growth rate (as a decimal) = 14% = 0.14

t = the number of years = 3

Plugging in the values, we get

A = 5,741 × (1 + 0.14)³

Simplifying the expression inside the parentheses first;

A = 5,741 × (1.14)³

Then, raising 1.14 to the power of 3;

A = 5,741 × 1.485136

A ≈ 8,536.98

So, the estimated population of the city after 3 years would be approximately 8,536.98 people. Since population cannot be in decimal numbers, we can round it to the nearest whole number;

A ≈ 8,537

Therefore, the estimated population of the city after 3 years would be 8,537 people.

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What is the solid formed when rotated around the side length of 4?
O cylinder with a height of 3 units and a radius of 4 units
O cone with a height of 4 units and a radius of 3 units
cylinder with a height of 3 units and a radius of 5 units
O cone with a height of 5 units and a radius of 4 units
Find the volumes and surface areas of the solids. Give your answers in terms of .
Surface Area: square units
Volume: cubic units

Answers

Answer: B: cone with a height of 4 units and a radius of 3 units

Step-by-step explanation:

Surface Area: 9pi + 15pi = 24pi square units

Volume: 9pi x 4 x 1/3 = 12pi cubic units

What is the y-intercept of the line of fit?
b=?
m=5​

Answers

The y-intercept of the line of best fit is: y = 20

What is the y-intercept?

The formula for equation of a line of best fit is:

y = mx + c

where:

m is slope

c is y-intercept

Now, the y-intercept is simply defined as the point where the line crosses the y-axis.

In this case, the line crosses the y-axis at y = 20.

Thus, we can conclude that it is the y-intercept

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A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of dress is designed to be 29 inches. The company regularly tests the lengths of the garments to ensure quality control, and if the mean length is found to be significantly longer or shorter than 29 inches, the machines must be adjusted. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches. Assume that the population distribution is approximately normal. Perform a hypothesis test on the accuracy of the machines at the 0.005 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. Answer Tables Keypad Keyboard Shortcuts We reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the O particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted. O We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.005 level of significance that the mean length of the particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted. O We reject the null hypothesis and conclude that there is sufficient evidence at a 0.005 level of significance that the mean length of the particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length O of the particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

Answers

We will conduct a one-sample t-test to determine if the mean length of the particular size of dress is significantly different from 29 inches.

Null Hypothesis: The mean length of the particular size of dress is equal to 29 inches. Alternative Hypothesis: The mean length of the particular size of dress is significantly longer or shorter than 29 inches. We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom. Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis. Therefore, we conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of dress is significantly longer or shorter than 29 inches and the machines do not need to be adjusted.

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We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

What is the null hypothesis?

The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.

Here, we have

Given: A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of the dress is designed to be 29 inches. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches.

We will conduct a one-sample t-test to determine if the mean length of the particular size of the dress is significantly different from 29 inches.

In the null hypothesis, the mean length of the particular size of the dress is equal to 29 inches.

In the alternative hypothesis, the mean length of the particular size of the dress is significantly longer or shorter than 29 inches.

We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom.

Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774

Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis.

Hence, We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

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3.
You have two credit cards. If you budget $375 to pay off your credit card debt and you payoff the highest interest card first while maintaining the interest accrued on the other card, how many months does it take you to pay it off?

Card Name (APR %) Existing Balance Credit Limit
Murk (5.6%) $675.49 $1,500.00
Mini (9.85%) $902.43 $1,000.00



5 months


2 months


4 months


3 months

Answers

It takes A. 5 months to pay off (Mini) the highest interest card.

How many months to pay off the highest interest card debt?

To determine the number of months it takes to pay off the credit card debt, we shall calculate the monthly payment to pay off the highest interest card first.

First, calculate interest accrued on each card per month:

Murk: (5.6/100)/12 * $675.49 = $2.98 per month

Mini: (9.85/100)/12 * $902.43 = $7.42 per month

Next, we determine the order in which to pay off the cards, which is highest interest card first, we can allocate the entire $375 to Mini and leave a minimum for interest accrued on Murk.

This should be a percentage of the balance.

Assuming it's 2% of the balance, which is $13.51.

So, in month 1, we will pay:

Mini: $375

Murk: $13.51

Leaving these balances:

Murk: $675.49 + $2.98 - $13.51 = $664.96

Mini: $902.43 - $375 + $7.42 = $534.85

In month 2:

Mini: $534.85 + $7.42 = $542.27

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $664.96 + $2.98 - $16.49 = $651.45

Mini: $542.27 - $375 + $7.42 = $174.69

month 3:

Mini: $174.69 + $7.42 = $182.11

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $651.45 + $2.98 - $16.49 = $638.94

Mini: $182.11 - $174.69 + $5.52 = $12.94

month4:

Mini: $12.94 + $7.42 = $20.36

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $638.94 + $2.98 - $16.49 = $625.43

Mini: $20.36 - $12.94 + $0.54 = $8.96

month 5:

Mini: $8.96 + $7.42 = $16.38

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $625.43 + $2.98 - $16.49 = $612.92

Mini: $16.38 - $8.96 = $7.42

So, Mini's balance is paid off here.

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Note:

And we can allocate the entire $375 budget to Murk.

This means we will pay off Murk in month 6:

Murk: $612.92 + $2.98 + $375 - $13.51 = $977.39

Identify the fractions labeled with the letters A and B on the scale below.

Answers

Answer:Assuming that the number on the end of the number line is a 1 (I cant read it too clearly), this number line goes to 7/7ths so that means A would be 1/7th and B would be 4/7th

Step-by-step explanation: thats how Number lines work

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