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Answer:

Step-by-step explanation:

Using confidence interval concepts, it is found that:

a)

The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).

The interpretation is:

iii. We are 99% confident that this interval contains the true population mean.

b)

A sample size of 664 would be required.

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.

\(\pi \pm M\)

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).

The interpretation of a x% confidence interval between a and b is that we are x% confidence that the true population mean lies in this interval, thus, option iii is correct.

In this problem:

Then:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 2.575\sqrt{\frac{0.27(0.73)}{2005}}\)

\(M = 0.026\)

The interval is:

\(M - \pi = 0.27 - 0.026 = 0.244\)

\(M + \pi = 0.27 + 0.026 = 0.296\)

The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).

Item b:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.05 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.05\sqrt{n} = 2.575(0.5)\)

Dividing both sides by 0.05.

\(\sqrt{n} = 2.575(10)\)

\((\sqrt{n})^2 = [2.575(10)]^2\)

\(n = 663.1\)

Rounding up:

A sample size of 664 would be required.

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C. Not likely, recurring debt is higher than what is allowed.

edge 2021

Mandy's approval based on her debt - to - income ratio is;

C: Not likely, recurring debt is higher than what is allowed.

Debt to income ratio is simply the percentage of your gross monthly income that goes to paying your monthly debt payments.

Now, her annual salary is $37,580. This means that her monthly income is; 37580/12 = $3131.67

Her monthly debt servicing = $265 + $120 =$385

Using the 28/36 ratio, the maximum allowable recurring debt for someone with a monthly income of $3,200 is $256.

Since her recurring monthly debt is $385 it is more than the maximum recurrent limit and so her home loan will not be approved.

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Answer:

0.074088

Step-by-step explanation:

Let

A:Value of order over $1000

B:Customer pay with credit card

We are given that

Probability of value of order over $1000,P(A)=0.42

If an order is valued at over $1000, then the probability that the customer will pay with a credit card, P(B/A)=0.63

We have to find  the probability that the next three independent orders will each be valued at over $1000

We know that

When two two events A and B are independent then

\(P(A\cap B)=P(A)\cdot P(B)\)

Using the formula

The probability that the next three independent orders will each be valued at over $1000=\(0.42\times 0.42\times 0.42\)

The probability that the next three independent orders will each be valued at over $1000=0.074088

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:13

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

5/15=3/v

5v=15×3

5v=75

5v/5=75/5

v=15

The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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Answer:

0

Step-by-step explanation:

Answer:

B is the correct answer as it qualifies for all the answers correctly.

Answer:

4/15 of an inch

Step-by-step explanation:

A worm wriggled forward 4/5 of an inch in 3 minutes.

=> At that rate, the distance the worm would go in 1 minute is:

D = (4/5)/3 = 4/(5x3) = 4/15 of an inch

Hope this helps!

The worm would go 0.267 inches in 1 minute.

How far would the worm go in 1 minute?

By Unitary method,we can solve this problem.

But now question is what is the use of Unitary method ?

By some examples we can understand this concept.

Let cost of 5 book is 500 rupees.

By Unitary method, cost of 1 book is

\(\frac{500}{5} \\ = 100 \: rupees\)

Cost of 100 books is \((100 \times 100) = 10000 \: rupees\)

Again for another example let length of 1 rope is 5 m

Then by Unitary method length of 5 rope is \((5 \times 5) = 25 \: m\)

Given,a worm wriggled forward 4/5 of an inch in 3 minutes.

So,in 3 minutes the worm can cover 4/5 of an inch

\( = \frac{4}{5} \times 1 \: inch \\ = \frac{4}{5} \: inch\)

Now we want to find how far would the worm go in 1 minute ?

In 3 minutes the worm covers 4/5 inche

By Unitary method, in 1 minute the worm covers

\( \frac{4}{5} ÷ 3 = \frac{4}{15} = 0.267 \: inches\)

Therefore,the worm would go 2.4 inches in 1 minute

This is a Unitary method related problem.

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Answer:

Factors

Step-by-step explanation:

Factor*factor=product

Answer:

The numbers to be multiplied are generally called the "factors". The number to be multiplied is the "multiplicand", and the number by which it is multiplied is the "multiplier". ... The result of a multiplication is called a product.

Step-by-step explanation:

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Answer:

0.3125 of a yard

Step-by-step explanation:

Answer:

a = 0

b = 8

c = 53

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

8r + 62 - 7 = 2

Step 2: Rewrite

Step 3: Identify Variables

a = 0

b = 8

c = 53

For number 5 - .3 ( 3.60 ÷ 12 = .3)

For number 6 - .32 ( 2.56 ÷ 8 = .32)

For number 7 - 2 ( 2.36 ÷ 2 = 1.18)

The answer is , (a) Empirical probability of sunfish rental = 0.5417 or 54.17% , (b) Empirical probability of kayak rental = 0.125 or 12.5% , (c) Empirical probability of rowboat rental = 0.3333 or 33.33% .

Empirical probability is an estimate of the probability of an event based on the frequency of its occurrence in a sample of data. It is calculated by dividing the number of times the event occurred by the total number of observations in the sample. Empirical probability is often used when there is no theoretical probability available, or when the theoretical probability is difficult to calculate or unknown. It is a useful tool in fields such as statistics, finance, and machine learning.

a) The empirical probability that the next boat rental is a sunfish is the number of sunfish rentals divided by the total number of rentals:

Empirical probability of sunfish rental = number of sunfish rentals / total number of rentals

Empirical probability of sunfish rental = 26 / 48

Empirical probability of sunfish rental = 0.5417 or 54.17%

b) The empirical probability that the next boat rental is a kayak is the number of kayak rentals divided by the total number of rentals:

Empirical probability of kayak rental = number of kayak rentals / total number of rentals

Empirical probability of kayak rental = 6 / 48

Empirical probability of kayak rental = 0.125 or 12.5%

c) The empirical probability that the next boat rental is a rowboat is the number of rowboat rentals divided by the total number of rentals:

Empirical probability of rowboat rental = number of rowboat rentals / total number of rentals

Empirical probability of rowboat rental = 16 / 48

Empirical probability of rowboat rental = 0.3333 or 33.33%

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The interviewer should provide clear and concise feedback on the candidate's performance in the interview, and ensure that the feedback is related to the job requirements.

In addition, the interviewer should ask relevant questions to get an idea about the interviewee's knowledge, skills, and abilities.Overall, the interviewer should strive to be fair and objective throughout the interview process, to minimize the risk of Unbiased Errors.

An interviewer officer selects a person not suitable for the job, this error is known as Unbaised Error.What is an Unbiased Error?An Unbiased error happens when you make an incorrect judgment regarding the interviewee, which may occur when the interviewer is unable to assess the interviewee objectively.

There are many factors that could contribute to an Unbiased Error, such as the interviewer's opinions and preconceptions, their biases or prejudices, the interviewer's inadequate understanding of the job requirements, or the applicant's inadequate preparation for the interview.In an unbiased interview, the interviewer does not have any preconceived ideas or predetermined judgments about the interviewee's knowledge, skills, or abilities.

The interviewer should be able to provide equal chances for all applicants, regardless of their gender, ethnicity, or any other factors that are not related to the job requirements.The interviewer should also assess the interviewee objectively, with no favoritism or bias.

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The number of tickets that will be sold is 5560.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Ticket sales for Six Flags White Water totaled $94,520 this summer.

Tickets for the water park cost $17 each.

The number of tickets sold will be = 94520/17 = 5560.

Hence, the number of tickets that will be sold is 5560.

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Answer:

Step-by-step explanation:

-7-1=-8

no jjjjjjjjjjjjjjjjj

The size of angle ACB to the nearest degree is 88 degree.

Construction Steps:

Create a line segment BC with the property AC = 4 cm.

Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.

Join AB and AC now. Consequently, the necessary triangle is ABC.

With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.

Cut an arc of 3 cm from point B.

Embrace BC and AC

Triangle with  angle ABC is necessary.

< ACB = 88 degree

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Kim needs 2711/12 square inches of construction paper for her project of rectangles.

Geometry is defined as "the branch of mathematics concerned with the measurements, properties, and relationships of points, lines, angles, areas, and solids." More simply, geometry is a branch of mathematics that deals with points, lines, shapes(like rectangle), and surfaces. 

According to information given in the question:

For the first rectangle, the area is:

9 inches × 13 1/3 inches = 9 inches × (40/3) inches = 360/3 inches² = 120 inches²

For the second rectangle, the area is:

10 1/4 inches × 10 1/3 inches = (41/4) inches × (31/3) inches = (41 × 31) / (4 × 3) square inches = 1271/12 inches²

Therefore, total area :

120 inches² + 1271/12 inches² = (1440 + 1271)/12 inches² = 2711/12 inches²

Therefore, Kim needs 2711/12 inches² of construction paper for her project. This can also be expressed as 225 7/12 inches².

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Answer:

1.632 ft^3

Step-by-step explanation:

3.4 times .8 times .6 = 1.632 ft.

therefore the volume of the rectangle is 1.632 ft^3

Step-by-step explanation:

at 2=-2

at -3= -6

\(y = ax + b \\ - 2 = 2a + b \\ - 6 = - 3a + b\)

\( - 2 - ( - 6) = 2a - ( - 3a) \\ 4 = 5a \\ a = 0.8\)

\( - 2 = 2(0.8) + b \\ b = - 2 - 1.6 \\ b = - 3.6\)

\(y = 0.8x - 3.6\)

Answer:

Step-by-step explanation:

If the roots are 7 and 3, then x = 7 and x = 3 are solutions. In factor form, x = 7 is (x - 7); in factor form, x = 3 is (x - 3). We FOIL these together to get

\(x^2-3x-7x+21\) which simplifies to

\(x^2-10x+21\) and we distribute in the 4:

\(4(x^2-10x+21)\) to get

\(4x^2-40x+84\) which is another way to write the last choice you're given.

From the following obeservation done by Kate, the hypothesis that the population proportions is equal for all four locations is not true. Also, the population of male fish are not equal in all four locations and the p-value is greater than 0.10

A chi square ( χ2) test is performed in order to find a co relation between two unrelated variables. The main objective of the test is to prove whether the relationship holds true or is just a product of mere chance. For example, if we are conducting a survey of two different paramters, first being the population of people who are married and the other about their educational qualififcation, we will get two distinct table of values without any significant corelation. But now if we wnt to establish a relationship, lets say that married people have less educational qualifications, we need to prove our statement by performing a chi square test. The final value can either be a null hypothesis which states that their is no convinving relationship betwwen the two paramters or can be a alternate hypothesis with significant corelation.

For this problem lets focus on the male fish population alone and perform the test:

                                                       Population (Observed)

                              A                      B                    C                 D           TOT

Male fish                49                   44                   49               39           181

Female fish            41                    46                   36               44           167

                              90                   90                   85               83           348

                                                        Population(Expected)

Male fish                 46.81              46.81               44.20           43.16

Female fish              43.18             43.18               40.79           39.83

χ2 = ∑\(\frac{(Obsereved-Expected)^2}{Expected}\);

=\(\frac{4.79}{46.81} +\frac{7.89}{46.81} +\frac{23.04}{44.20} +\frac{17.30}{43.16}\)

= 0.10+0.16+0.52+0.40 = 1.18

Now to calculate degree of freedom= (coulmn-1)(row-1)= 3×1= 3.

Looking at the reference table at 0.05 significance level, the value shows 7.815

Thus as our value of 1.18 is less than the given value, null hypothesis cannot be rejected.

Hence the population proportions are not equal at all four locations. Whether this conclusive difference in gender proportions is due to varied contaminants cant be answered with this single observation and further tests are needed to be performed to construct a well found connection.

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Answer: Point P

Step-by-step explanation: over 2 up 1 (2,1)

Answer: M

Step-by-step explanation:

(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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