Why can't you use the product of powers rule to simplify
this expression? Explain.
3^4 * 2^8

Answer:

21 inches

Step-by-step explanation:

1 inch = 6 miles

126/6 = 21

Answer:

im pretty sure its B

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

Answer:

Square pizza is the better deal.

Step-by-step explanation:

The better deal will be the one that has larger area of pizza. So, find the area of pizza in the case of square pizza and in the case of round pizza.

Below is the calculation of area of pizzas.

[tex]\text{Area of square pizza} = (Side)^{2} \\\text{Area of square pizza} = (12)^2 \\\text{Area of square pizza} = 144 \ in^2 \\[/tex]

[tex]\text{Now area of round pizza.} \\\text{ The area of round pizza} = \pi r^{2} \\\rm Diameter = 12 \\So, \ radius = \frac{12}{2} = 6 \\\text{ The area of round pizza} = \pi r^{2} \\= \frac{22}{7}\times (6)^2 \\= 113.1 \ in^2[/tex]

Since the area of square pizza is greater than round pizza. Thus, square pizza is better deal.

Answer:

As the P-value (0.086) 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 return rate is less than 15%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the return rate is less than 15%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.15\\\\H_a:\pi<0.15[/tex]

The significance level is 0.01.

The sample has a size n=5000.

The sample proportion is p=0.143.

[tex]p=X/n=717/5000=0.143[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.15*0.85}{5000}}\\\\\\ \sigma_p=\sqrt{0.000026}=0.005[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.143-0.15+0.5/5000}{0.005}=\dfrac{-0.007}{0.005}=-1.366[/tex]

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

[tex]P-value=P(z<-1.366)=0.086[/tex]

Answer:

[tex]z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307[/tex]  

Now we can calculate the p value with the following probability:

[tex]p_v =P(z<-1.307)=0.0956[/tex]  

For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.

Step-by-step explanation:

Information provided

n=5000 represent the random sample taken

X=717 represent the surveys returned

[tex]\hat p=\frac{717}{5000}=0.1434[/tex] estimated proportion of urvyes returned

[tex]p_o=0.15[/tex] is the value to verify

[tex]\alpha=0.01[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the return rate is less than 15% the system of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.15[/tex]  

Alternative hypothesis:[tex]p < 0.15[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307[/tex]  

Now we can calculate the p value with the following probability:

[tex]p_v =P(z<-1.307)=0.0956[/tex]  

For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.

Step-by-step explanation:

y4 - 2y3 = 0

y3(y - 2) = 0

y3 = 0

y = 0

Y - 2 = 0

Y = 2

Answer:

The radius is 5 cm

Step-by-step explanation:

The formula for the area of a circle is :  [tex]\p*radius^2[/tex]

To work out the length of the radius you would first need to divide the area of  78.5 cm by pi (pi=3.14), this gives you [tex]25cm^2\\[/tex]. This is because by dividing the area by pi we are isolating the value of the radius squared.

The final step is to work out the radius. You can do this by finding the square root of the radius squared which is 25, this gives you 5 cm. This means that the radius is 5 cm. This is because the square root is a number that when squared equals that number.

1) Divide 78.5 by pi.

[tex]78.5/\pi=25cm^2[/tex]

2) Find the square root of 25 cm squared.

[tex]\sqrt{25} =5 cm[/tex]

In this question pi is 3.14

Answer:

Step-by-step explanation: yes because when rewritten in standard form the x term will still be raised to the 2nd power.

Answer: 90/8=11.25

Step-by-step explanation:

Answer:D)36

Step-by-step explanation:

Took the test

Answer:

Multiplication

Step-by-step explanation:

Answer:

The sample mean hours per week spent studying for statistics is 7.55 hours.

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]

The 95% confidence interval for the population mean hours per week that students spend studying for statistics was (6.83, 8.27).

Compute the sample mean hours per week spent studying for statistics as follows:

[tex]\frac{\text{UL + LL}}{2}=\frac{(\bar x+ z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}})+(\bar x- z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}})}{2}\\\\\frac{8.27+6.83}{2}=\frac{2\cdot \bar x}{2}\\\\7.55=\bar x[/tex]

Thus, the sample mean hours per week spent studying for statistics is 7.55 hours.

Answer:

Answer is the first one :)

Step-by-step explanation:

√(-7-5)² + (-7-9)²

answer is 20

hope this helps

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: motor skills of a sober subject.

n= 20

X[bar]= 37.1

S= 3.7

The claim is that the average score for all sober subjects is equal to 35.0, symbolically: μ= 35.0

The hypotheses are:

H₀: μ = 35.0

H₁: μ ≠ 35.0

α: 0.01

The statistic to use, assuming all conditions are met, is a one sample t- test

[tex]t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}[/tex]

[tex]t_{H_0}= \frac{37.1-35.0}{\frac{3.7}{\sqrt{20} } } = 2.34[/tex]

This test is two-tailed, meaning, the rejection region is divided in two and you'll reject the null hypothesis to low values of t or to high values of t:

[tex]t_{n-1;\alpha /2}= t_{19; 0.005}=-2.861[/tex]

[tex]t_{n-1;1-\alpha /2}= t_{19; 0.995}= 2.861[/tex]

The decision rule using this approach is:

If [tex]t_{H_0}[/tex] ≤ -2.861 or if [tex]t_{H_0}[/tex] ≥ 2.861, you reject the null hypothesis.

If -2.861 < [tex]t_{H_0}[/tex] < 2.861, you do not reject the null hypothesis.

The value is within the non rejection region, the decision is to not reject the null hypothesis.

I hope this helps!

Answer:

1.56% probability that the student gets all three questions right

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the answer correctly, or he does not. The probability of the student guessing the answer of a question correctly is independent of other questions. 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.

Each question has 4 possible answers, one of which is correct.

So [tex]p = \frac{1}[4} = 0.25[/tex]

Three questions.

This means that [tex]n = 3[/tex]

What is the probability that the student gets all three questions right?

This is [tex]P(X = 3)[/tex]

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

[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]

1.56% probability that the student gets all three questions right

Step-by-step explanation:

here,

6x+6x = -35-12

12x= -47

x= -47

[tex] \frac{ - 47}{12} [/tex]

Answer:

13 packages of Granola

Step-by-step explanation:

74.25 - 6 = 68.25

68.25 divided by 5.25= 13

Answer: 25,67%

Step-by-step explanation:

We have 11 girls and 14 boys, this is a total of 11 + 14 = 25 students.

If all the students have the same probability of being infected, the probability that a girl will get infected first is equal to the number of girls dividedthe total number of students:

p1 = 11/25

Now we get a boy infected, the number of boys is 14, and the total number of students is now 24 (because we already have a girl infected)

this probability is p2 = 14/24

The probability for both events is equal to the product of the probabilities:

P = p1*p2 = (11/25)*(14/24) = 0.2567

or 25,67%

Answer:

40 cm

Step-by-step explanation:

To find the area of a trapezoid, you have to do...

(4+6)times 8 divided by 2

so its 10 times 8 which is 80 divided by 2 is 40 cm!!

hope this helps!!

48 + 32 divided by 2 is 40

Step-by-step explanation:

The area is 40

Answer:

Inches

Step-by-step explanation:

the praying mantis is too small for the other units.

The length of a praying mantis would measure in inches.

It is defined as the numerical quantity that gives an idea about an object's weight length, width, and many more. It can be used to compare two objects.

We know feet, inches, yards, and miles are the unit of measuring the length.

We have an object that is a praying mantis. Usually, the mantis's length is about 3 to 4.5 inches.

We also know 1 foot = 12 inches

1 yard = 36 inches

1 mile = 63360 inches

As we can see the feet, yard, and mile are the units to measure the long length.

Thus, the length of a praying mantis would measure in inches.

Learn more about the measurements here:

brainly.com/question/4725561

Answer:

[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]    

Now we can find the degrees of freedom:

[tex]df=n-1=80-1=79[/tex]  

Now we can calculate the p value with the alternative hypothesis using the following probability:

[tex]p_v =P(t_{(79)}>2.236)=0.0141[/tex]  

Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed

Step-by-step explanation:

Information given

[tex]\bar X=130[/tex] represent the sample mean

[tex]s=40[/tex] represent the sample standard deviation

[tex]n=80[/tex] sample size  

[tex]\mu_o =120[/tex] represent the value to verify

t would represent the statistic  

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if  shoppers participating in the loyalty program spent more on average than typical shoppers (120) , the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 120[/tex]  

Alternative hypothesis:[tex]\mu > 120[/tex]  

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]    

Now we can find the degrees of freedom:

[tex]df=n-1=80-1=79[/tex]  

Now we can calculate the p value with the alternative hypothesis using the following probability:

[tex]p_v =P(t_{(79)}>2.236)=0.0141[/tex]  

Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed

Answer:

None of the options are correct.

The cumulative incidence of stroke in patients classified as hypertensive at baseline = 0.625

Step-by-step explanation:

The table properly drawn is that

Baseline - Not hypertensive

Free of stroke at 5 years | Stroke | Total

1000 | 50 | 1050

Baseline - Hypertensive

Free of stroke at 5 years | Stroke | Total

300 | 501 | 801

Compute the cumulative incidence of stroke in patients classified as hypertensive at baseline.

Number of patients classified as hypertensive at baseline = 801

number of stroke incidents amongst patients classified as hypertensive at baseline = 501

The cumulative incidence of stroke in patients classified as hypertensive at baseline = (501/801) = 0.625

Hope this Helps!!!

Answer:

a= 14

b= 111

Step-by-step explanation:

just took it

Answer:

84 square inches

Step-by-step explanation:

First, separate this shape into two shapes you can easily find the area of. You can do this by turning it into a rectangle and a rhombus.

Say the rectangle has measurements of 5 by 6 inches. The area of that rectangle will be 30 square inches. Save this value to add on later.

The rhombus now has a height of 4 (because the side length 10 minus the side length 6 equals 4), and two bases by the values of 12 and 15. The area of a rhombus can be found with the equation:

a = 1/2(b1 + b2) x h

Simply plug in those values to find the area of the rhombus, 54. Now add the area of the rhombus and the area of the rectangle to get 84 square inches as your final area.

Answer:

We don't have the statements but I can tell you the following info:

Step-by-step explanation:

83.4/60= $1.39 for each horn

18*1.39= $25.02 for the 18 additional horns.

$83.40+25.02= $108.42 for the total 78 horns

There are 7 rows of 9 people then there will be 63 people in all.

Multiplication refers to the product of two numbers or more than two numbers. It states the result when a number is taken times.

There are 7 rows of 9 people.

This means in each row, there are 9 people.

Then the number of people in 7 rows will be 7 multiplied by 9 i.e.,

[tex]7\times9=63[/tex]

So, the number of people will be 63.

Learn more about multiplication here- https://brainly.com/question/10590363

#SPJ2

Answer:

5/6

Step-by-step explanation:

plug into calculator

Answer:

Can confirm it is 5/6.

Step-by-step explanation:

Simply put into a calculator.

Answer:

Step-by-step explanation:

Since you did not post answer choices, there's not too much I can tell you. One thing for sure is that the equation must have 1/2x. This represents the slope at which the equation is increasing. To find which equation passes through (5,1), all you have to do is plug in 5 into the x in your equation. After you solve, if the y you get is equal to the y value of 1, you know that is the line that alsses through (5,1). I hope this helps.

Answer b

Step-by-step explanation:

It’s fast

Answer:

  area: 144.5 cm^2

Step-by-step explanation:

Maybe you want the area of this figure.

The area of a trapezoid is given by the formula ...

  A = (1/2)(b1 +b2)h

Using the given dimensions, the area is ...

  A = (1/2)(9.7 cm +24.3 cm)(8.5 cm)

  A = (1/2)(34 cm)(8.5 cm) = 144.5 cm^2