You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value? [Hint: proportion est. = 0.5] Round your answer to whole number

Answer:

[See Below]

Step-by-step explanation:

Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]

'm' is the slope

(x1, y1) is a coordinate point.

Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points (-1,5) and (3,-3).

[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]

The slope of the line is -2.

I will use (-1,5) as the point:

[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]

Slope intercept is: [tex]y=mx+b[/tex]

'm' - Slope

'b' - y-intercept

We can use the point slope equation to convert it into slope intercept form:

[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]

Standard form is [tex]Ax+By=C[/tex]

Using out slope intercept form equation:

[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]

Answer:

Minimum population of fish in lake = 2400 - 155 = 2245

Maximum population of fish in lake = 2400 + 155 = 2555

Step-by-step explanation:

population of fish in lake = 2400

Variation of fish = 155

it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.

For example

for increase

population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc

but it cannot be beyond 2400 + 155.

It cannot be 2400 + 156

similarly for decrease

population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc

but it cannot be less that 2400 - 155.

It cannot be 2400 - 156

Hence population can fish in lake can be between 2400 - 155 and 2400 + 155

minimum population of fish in lake = 2400 - 155 = 2245

maximum population of fish in lake = 2400 + 155 = 2555

Answer:

2x/3 + 2= 16

=21

Step-by-step explanation:

Standard form:

2

3

x − 14 = 0  

Factorization:

2

3 (x − 21) = 0  

Solutions:

x = 42

2

= 21

Answer:

Step-by-step explanation:

When the time is 3:40pm

(a)The angle between the two hands in standard position is drawn and attached below.

(b)Now, each hour = 30 degrees

Therefore, the angle between 3 and 8 in an anticlockwise movement

= 7 X 30 =210 degrees

Stating the angle as a negative angle, we have:

[tex]210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ[/tex]

Answer:

0.75 ML of insulin contains 75 units of insulin

Step-by-step explanation:

U - 100 insulin hold 100 units of insulin per ml

This means that:

1 ML = 100 units

∴ 0.75 ML = 100 × 0.75 = 75  units

Therefore 0.75 ML of insulin contains 75 units of insulin

Answer:

Step-by-step explanation:

Ray

Answer:

ray

Step-by-step explanation:

ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray

hope this helps

Answer:

no solutions

Step-by-step explanation:

6-3x=4-x-3-2x

Combine like terms

6-3x =1 -3x

Add 3x to each side

6 -3x+3x = 1-3x+3x

6 =1

This is not true so there are no solutions

Answer:

No solutions.

Step-by-step explanation:

6 - 3x = 4 - x - 3 - 2x

Add or subtract like terms if possible.

6 - 3x = -3x + 1

Add -1 and 3x on both sides.

6 - 1 = -3x + 3x

5 = 0

There are no solutions.

Answer:

No

Step-by-step explanation:

It is not divisible by 6, for if you divide by 6, you will get a non natural number,

It is obviously divisible by 2.

So, No.

Answer:

no

Step-by-step explanation:

only by 2

614/2 = 307

614/6 = 102.33

Answer:

C (the third graph)

Step-by-step explanation:

This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.

Answer:

see below

Step-by-step explanation:

This graph has an asymptote at y = 0 and x=0

This excludes these values

The domain excludes x =0

The range excludes y=0

Answer:

225º or 3.926991 radians

Step-by-step explanation:

The area of the complete circle would be π×radius²: 3.14×8²=200.96

The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.

[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).

There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.

We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.

Answer:

225º

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

We can write the equation as

y = a(x - 28)(x + 28)   as -28 and 28  ( +/- 1/2 * 56) are the zeros of the equation

y has coordinates (0, 32) at the top of the parabola so

32 = a(0 - 28)(0 + 28)

32 = a * (-28*28)

32 = -784 a

a = 32 / -784

a = -0.04082

So the equation is y = -0.04082(x - 28)(x + 28)

y = -0.04082x^2 + 32

The second part  is found by first finding the value of x corresponding to  y = 22

22 = -0.04082x^2 + 32

-0.04082x^2 = -10

x^2 = 245

x = 15.7 inches.

This is the distance from the centre of the door:

The distance from the edge = 28 - 15.7

= 12,3 inches.

Step-by-step explanation:

2) 63

3) 7000

4) 10

These are some answers

Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

Answer:

P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

Using formula:

[tex]P(\text{diabetes diagnosis})\\[/tex]:

[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]

[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]

[tex]\text{P(have been diagnosed with diabetes)}[/tex]:

[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]

[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]

Learn more about the probability:

brainly.com/question/18849788

Answer:

[tex]-15.11[/tex]

Step-by-step explanation:

[tex]-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11[/tex]

Answer:

-15.11

Step-by-step explanation:

-12.48+2.99-5.62=

-9.49 - 5.62= - (9.49+5.62)=-15.11

Answer:

101-120=4

Step-by-step explanation:

All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups

Therefore, the answer to the blank is 4. If possible, please mark brainliest.

Answer:

There are 4 numbers between 101 and 120.

Step-by-step explanation:

101-120: 105, 111, 111, 113 (4 numbers)

Complete Question:

A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.

Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.

(a) Find the interest that will be owed after 4 months

(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months

Answer:

a) Interest that will be owed after 4 months , I = $131.48

b) Amount owed by the restaurant after 4 months = $16231.48

Step-by-step explanation:

Note that the question instructs not to round any intermediate computations except the final answer.

Annual rate = 2.45%

Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]

R = 0.20416666666%

Time, T = 4 months

Interest, [tex]I = \frac{PRT}{100}[/tex]

[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]

b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)

Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)

Amount owed by the restaurant after 4 months = 16100 + 131.48

Amount owed by the restaurant after 4 months = $16231.48

Answer:

plane

Step-by-step explanation:

Answer:

D. Plane

Step-by-step explanation:

A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.

Answer:

To solve for x we can write:

x² - y² = 55

x² = y² + 55

x = ±√(y² + 55)

To solve for y:

x² - y² = 55

y² = x² - 55

y = ±√(x² - 55)

Answer:

21/55

Step-by-step explanation:

Simply multiply the top 2 together:

3 x 7 = 21

And the bottom 2 together:

5 x 11 = 55

21/55 is your answer!

Answer:

0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The components operate independently. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Eight components:

This means that [tex]n = 8[/tex]

Probability of 0.45 of failing in less than 1,000 hours.

So 1 - 0.45 = 0.55 probability of working for longer than 1000 hours, which means that [tex]p = 0.55[/tex]

Find the probability that the subsystem operates longer than 1000 hours.

We need at least four of the components operating. So

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{8,4}.(0.55)^{4}.(0.45)^{4} = 0.2627[/tex]

[tex]P(X = 5) = C_{8,5}.(0.55)^{5}.(0.45)^{3} = 0.2568[/tex]

[tex]P(X = 6) = C_{8,6}.(0.55)^{6}.(0.45)^{2} = 0.1569[/tex]

[tex]P(X = 7) = C_{8,7}.(0.55)^{7}.(0.45)^{1} = 0.0548[/tex]

[tex]P(X = 8) = C_{8,8}.(0.55)^{8}.(0.45)^{0} = 0.0084[/tex]

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2627 + 0.2568 + 0.1569 + 0.0548 + 0.0084 = 0.7396[/tex]

0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.

Answer:

The relative change from 6546 and 4392 is 49.04

Step-by-step explanation:

Answer:

B, C and D

Step-by-step explanation:

Given:

Statement: "Every integer has an additive inverse"

To find: statement that is equivalent to the given statement

Solution:

For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.

Here, 0 is the additive identity.

Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and  ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".

Answer:

The 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two means is:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

It is provided that:

[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]

The critical value of z for 90% confidence level is,

z = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:

[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]

    [tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]

Thus, the 90% confidence interval for the difference in mean number of days meeting the goal  is (4.49, 18.11).

Answer:

r = -10*cos(t)

Step-by-step explanation:

To write the rectangular equation in polar form we need to replace x and y by:

[tex]x=r*cos(t)\\y=r*sin(t)[/tex]

Replacing on the original equation, we get:

[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]

Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:

[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]

Answer:

Step-by-step explanation:

Answer:

its b on edge

Step-by-step explanation:

Answer:

a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.

b. Test statistic z=-1.001

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]

The significance level is 0.01.

The sample has a size n=199.

The sample proportion is p=0.462.

[tex]p=X/n=92/199=0.462[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]

As the P-value (0.16) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

a) Real range of employees hired by each organization surveyed = 56

b) The cumulative percent of "new" employees with the lowest tenure =        30%

Step-by-step explanation:

a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.

Real range of employees hired by each organization surveyed = (89 - 34) + 1

Real range of employees hired by each organization surveyed = 56

b) It is clearly stated in the question that  the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.

Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%

Answer:

(x-1)/13

Step-by-step explanation:

y = 13x+1

To find the inverse, exchange x and y

x = 13y+1

Solve for y

Subtract 1 from each side

x-1 =13y+1-1

x-1 = 13y

Divide each side by 13

(x-1)/13 = y

The inverse is (x-1)/13

Answer:

f(x) = 13x + 1

To find the inverse let f(x) = y

y = 13x + 1

x = 13y + 1

13y = x - 1

y = (x-1)/13

The inverse is x-1/13.