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erma4kov [3.2K]

3 years ago

5

Caleb bought a boogie board and used a coupon for $8.50 off of the cost. Fill in the box with the expression that represents the

total cost. Let t represent the total cost and b represent the original cost of the boogie board.

1 answer:

jenyasd209 [6]3 years ago

4 0

I think this is the answer sorry if I'm wrong
(B)-8.50=T

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Sally makes $3,000 each month. What is the most she can spend on housing?

valentina_108 [34]

Following the 30% rule of thumb, Sally should only spend a maximum of $900 on her rent

<h3>Numbers and percentage</h3>

Given Data

Monthly Salary = $3000
Percentage spent on rent = 30%

Let us find 30% of $3000

= 30/100* $3000

= 0.3*$3000

= $900

Learn more about percentages here:

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SPJ1

4 0

2 years ago

According to the National Institute of Allergy and Infectious Diseases, 6% of American adults have a food allergy. A large compa

Vinil7 [7]

Answer:

a) The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

b) The expected value is 30 and the standard deviation is 5.31.

c) Close to 0% probability that none of the 500 employees has a food allergy

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have food allergy, or they do not. The probability of an adult having allergy is independent of other adults. 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.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

6% of American adults have a food allergy

This means that $p = 0.06$

500 employees.

This means that $n = 500$

(a) What are the assumptions/requirements of a Binomial distribution? Does this situation meet all these requirements?

The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

(b) What are the expected value and standard deviation of X (i.e., of the population)?

$E(X) = np = 500*0.06 = 30$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.06*0.94} = 5.31$

The expected value is 30 and the standard deviation is 5.31.

(c) What is the probability that none of the 500 employees has a food allergy?

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{500,0}.(0.06)^{0}.(0.94)^{500} \cong 0$

Close to 0% probability that none of the 500 employees has a food allergy

4 0

3 years ago

-8 (y - 1.25)=4<br> what is y?

wlad13 [49]

-8y+10=4
-8y=-10+4
-8y=-6
Y=0.75

7 0

3 years ago

A square has a side that measures 55 units. What is the area of a circle with a circumference that equals the perimeter of the s

Taya2010 [7]

<h3><u>Given</u>:-</h3>

$\rightarrow$ Side of square = 5.5 units.

$\rightarrow$ Circumference of circle = perimeter of square.

<h3><u>To Find</u>:-</h3>

$\rightarrow$ Area of circle.

<h3><u>Solution</u>:-</h3>

$\rightarrow$ To find the area of circle firstly we have to find the perimeter of the square, then we will find the radius of circle and after that area of circle. So, let's begin:

$\rightarrow$ Perimeter of square = $\sf{4×side}$ (putting the value of side from the above given)

$\rightarrow$ $\sf{=\: 4 × 5.5}$

$\rightarrow$ $\sf{=\: 22units.}$

Therefore, perimeter of square = 22units.

Now, according to the question, perimeter of square = circumference of the circle. So, circumference of circle = 22units.

Now, using the formula of circumference of circle we can find the radius.

$\rightarrow$ Circumference of circle = $\sf{2πr}$ (putting the value of perimeter)

$\rightarrow$ $\sf{22\:=\: 2×3.14×r}$

$\rightarrow$ $\sf{22\:=\: 6.28×r}$

$\rightarrow$ $\sf{\frac{22}{6.28}\:=\: r}$

$\rightarrow$ $\sf{3.50units\:=\: r}$

Therefore, radius of circle = 3.50units.

Now, let's find area of the circle:

$\rightarrow$ Area of circle = $\sf{πr^2}$

$\rightarrow$ $\sf{πr^2}$ (putting the value of pie(π) and radius(r))

$\rightarrow$ $\sf{3.14×3.50^2}$

$\rightarrow$ $\sf{3.14×12.25}$

$\rightarrow$ $\sf{38.46unit^2}$

Therefore, area of circle = $\sf{38.46unit^2}$

4 0

2 years ago

Read 2 more answers

A sample of 200 observations from the first population indicated that X1 is 170. A sam- ple of 150 observations from the second

nikitadnepr [17]

Answer:

a. If the P-value is smaller than the significance level, the null hypothesis is rejected.

b. Pooled proportion = 0.8

c. z = 2.7

d. As the P-value (0.0072) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

We will use the P-value approach, so the decision rule is that if the P-value is lower than the significance level, the null hypothesis is rejected.

The claim is that the proportions differ significantly.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.85.

$p_1=X_1/n_1=170/200=0.85$

The sample 2, of size n2=150 has a proportion of p2=0.7333.

$p_2=X_2/n_2=110/150=0.7333$

The difference between proportions is (p1-p2)=0.1167.

$p_d=p_1-p_2=0.85-0.7333=0.1167$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{170+110}{200+150}=\dfrac{280}{350}=0.8$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.8*0.2}{200}+\dfrac{0.8*0.2}{150}}\\\\\\s_{p1-p2}=\sqrt{0.0008+0.00107}=\sqrt{0.00187}=0.0432$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.1167-0}{0.0432}=\dfrac{0.1167}{0.0432}=2.7$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z>2.7)=0.0072$

As the P-value (0.0072) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

6 0

3 years ago