Students at a certain school were​ surveyed, and it was estimated that 20​% of college students abstain from drinking alcohol. To estimate this proportion in your​ school, how large a random sample would you need to estimate it to within 0.08 with probability 0.95​, if before conducting the study​ (a) you are unwilling to predict the proportion value at your school and​ (b) you use the results from the surveyed school as a guideline.

Answer:

290 m

Step-by-step explanation:

3*6*5=90

5*5*8= 200

200+90=290

Answer:

10.93% probability of observing 51 or fewer vapers in a random sample of 300

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 300, p = 0.2[/tex]

So

[tex]\mu = E(X) = np = 300*0.2 = 60[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.2*0.8} = 6.9282[/tex]

What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?

Using continuity corrections, this is [tex]P(X \leq 51 + 0.5) = P(X \leq 51.5)[/tex], which is the pvalue of Z when X = 51.5 So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{51.5 - 60}{6.9282}[/tex]

[tex]Z = -1.23[/tex]

[tex]Z = -1.23[/tex] has a pvalue of 0.1093.

10.93% probability of observing 51 or fewer vapers in a random sample of 300

Answer:

10.908

Step-by-step explanation:

Answer:

H0: μ = 8.3 hours

Ha: μ > 8.3 hours

We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:

D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.

Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified

Step-by-step explanation:

For this case we want to determine if mean running time has increased as a result of the new change so then the system of hypothesis are given by:

Note: we assume that the value to check in order to be consistent with the options is 8.3

H0: μ = 8.3 hours

Ha: μ > 8.3 hours

We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:

D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.

Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified

Answer:

5/12

Step-by-step explanation:

The probability of rolling an odd number is 3/6, which is 1/2

The probability of rolling a factor of 12 is 5/6 (1,2,3,4,6)

1/2 x 5/6 = 5/12

Answer:

[tex]V = \frac{4}{3} \pi r^{2}[/tex] - is the formula for the volume of a circle.

Step-by-step explanation:

Step 1:

   - Insert your values:

       -  [tex]V = \frac{4}{3} \pi 4^{2}[/tex]

Step 2:

   - Simplify using order of operations:

       - Exponents First:

            - [tex]V = \frac{4}{3} \pi 64[/tex]

       - Division Second:

           - [tex]V = 1.333 \pi 64[/tex]

       - Multiplication Last:

           - [tex]V = 268.01555[/tex]

       - And Simplified:

           - V = 268 (approx.)

Hope this helps! Good luck!

Answer:

2.82% probability that all of the sprinklers will operate correctly in a fire

Step-by-step explanation:

For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The probability of a sprinkler operating correctly is independent of other sprinklers. 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.

The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.

This means that [tex]p = 0.7[/tex]

10 sprinklers.

This means that [tex]n = 10[/tex]

What is the probability that all of the sprinklers will operate correctly in a fire?

This is P(X = 10).

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

[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]

2.82% probability that all of the sprinklers will operate correctly in a fire

The probability that all sprinklers will operate correctly in a fire is 0.028

The given parameters are:

p = 0.7 ---- the probability that a sprinkler to activate correctly

n = 10 --- the number of sprinklers

The probability that all sprinklers activate correctly is calculated as:

[tex]P(10) = p^n[/tex]

So, we have:

[tex]P(10) = 0.7^{10[/tex]

Evaluate

[tex]P(10) = 0.028[/tex]

Hence, the probability that all sprinklers will operate correctly in a fire is 0.028

Read more about probability at:

https://brainly.com/question/25870256

Answer:

  denominator zeros are excluded

Step-by-step explanation:

The domain is the set of values of the independent variable where the function is defined. A rational function is "undefined" where the denominator is zero.

The exclusions of interest are generally those values of the variable that make any denominator be zero.

__

Example:

  f(x) = (2/(x-3)) / (4/(x -6))

has denominators of x-3 and x-6. These are zero for x=3 and x=6, so those two values are excluded from the domain of this function. We observe that the function can be simplified to ...

  f(x) = (x -6)/(2(x -3))

but x=6 remains excluded from the domain because of its effect in the original function definition.

_____

Additional comment

If the rational function includes functions that have domain restrictions (such as square root, for example), then those restrictions apply as well.

Usually, but not always, the rational functions where you're asked about domain are the ratios of polynomials. So, you need to factor or otherwise find the zeros of any denominator polynomials in such functions.

We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.

First of all, we will use z-score formula to find z-score corresponding to 146 and 163.

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{146-150}{5}[/tex]

[tex]z=\frac{-4}{5}[/tex]

[tex]z=-0.8[/tex]

[tex]z=\frac{163-150}{5}[/tex]

[tex]z=\frac{13}{5}[/tex]

[tex]z=2.6[/tex]

Our next step is to find percentage of data scores falls between both z-scores.

[tex]P(-0.8<z<2.6)=P(z<2.6)-P(z<-0.8)[/tex]

Using normal distribution table, we will get:

[tex]P(-0.8<z<2.6)=0.99534-0.21186[/tex]

[tex]P(-0.8<z<2.6)=0.78348[/tex]

Let us convert our answer into percentage.

[tex]0.78348\times 100\%=78.348\%[/tex]

Upon rounding our answer to nearest thousandths, we will get:

[tex]78.348\%\approx 78.35\%[/tex]

Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately [tex]78.35\%[/tex].

Answer:

0.624

Step-by-step explanation:

DeltaMath

The general form for the equation of a line is:

[tex]y = mx + c[/tex]

Where:

m is the gradient of the line

c is the y intercept of the line  (y - intercept is where the graph crosses the y-axis)

So if you had the following equation:

[tex]y = 3x + 2[/tex]

Then:

m = 3

c = 2

So gradient = 3, and y intercept = 2

---------------------------------------------------

Rearranging

So first rearrange both of the equations in the form y = mx + c :

[tex]3x + 2y = -1[/tex]   becomes  [tex]y = -\frac{3}{2} x-\frac{1}{2}[/tex]      [tex](where: \ m = -\frac{3}{2} \ and, \ c = -\frac{1}{2} )[/tex]

and:

[tex]2x+7y=2[/tex]  becomes  [tex]y=-\frac{2}{7}x +\frac{2}{7}[/tex]     [tex](where: \ m = -\frac{2}{7} \ and, \ c = \frac{2}{7})[/tex]

---------------------------------------------

The question tells us that the equation of the line we are looking for has the same y-intercept as:

[tex]2x+7y=2[/tex]

So the line we are trying to work out will also have a y intercept of   [tex]\frac{2}{7}[/tex]

(refer to rearranging)

----------------------------

The question also tells us that the line is perpendicular to  [tex]3x + 2y = -1[/tex]

Perpendicular gradient = negative reciprocal of the gradient of the line it is perpendicular to.

So the gradient of the new line will be the  negative reciprocal of the gradient of  [tex]3x + 2y = -1[/tex]

Gradient of  [tex]3x + 2y = -1[/tex]  is: [tex]-\frac{3}{2}[/tex]

(refer to rearranging)

Gradient of new line: = negative reciprocal of  [tex]-\frac{3}{2}[/tex] , which is  [tex]\frac{2}{3}[/tex]

(just flip fraction and change the sign)

------------------------------------

So for the new line: [tex]m = \frac{2}{3} \ and, \ c = \frac{2}{7}[/tex]

So just substitute in the values for m and c into: y = mx + c

[tex]y = mx + c\\y = \frac{2}{3} x + \frac{2}{7}[/tex]

-----------------------------

Answer:

So equation of the new line is:

[tex]y = \frac{2}{3}x + \frac{2}{7}[/tex]

------------

Any questions, just ask.

Answer:

  20 times

Step-by-step explanation:

The faster swimmer can swim twice the length of the pool in ...

  (2·90 ft)/(3 ft/s) = 60 s

The slower swimmer can do it in ...

  (2·90 ft)/(2 ft/s) = 90 s

The least common multiple of these times is 180 s = 3 minutes, after which time each swimmer will be back where they started.

A graph of position vs. time shows the swimmers pass 5 times in that 3-minute period. 4 of those are passes when they are going in opposite directions. A 5th pass occurs at one end of the pool, when the faster swimmer passes the slower one going in the same direction.

Since there are 5 passes in each 3-minute period, there are 20 passes in 12 minutes.

The swimmers pass each other 20 times in 12 minutes.

Answer:

[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]

So then after 8 years we will have in the account 3283.153

And in order to find the interest we can do the following operation:

[tex] I = 3283.153 -1986 = 1297.153[/tex]

Step-by-step explanation:

For this case we can use the formula for the future value using compound interest given by:

[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]

Where P= 1986 the initial amount invested. r = 0.063 represent the interest rate. n=12 represent the number of times that the rate is compounded in a year. And t =8 years . Replacing the info we got:

[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]

So then after 8 years we will have in the account 3283.153

And in order to find the interest we can do the following operation:

[tex] I = 3283.153 -1986 = 1297.153[/tex]

Answer: Hot Dog $1.50 Drinks $2.00

Step-by-step explanation:

Answer:

40 cm.

Step-by-step explanation:

So what I tried to do in this case is compare 96  to 64. I subtracted those two numbers which is 32. So since thats the difference between those two shapes, I did the same thing with 72 and I subtracted it but 32, which led me to 40.

Hope this helped :)

Answer:

u=48

Step-by-step explanation:

In similar triangles, corresponding sides have the same ratio.

64/96=u/72

Step 1: Cross-multiply

(64)*(72)=u*(96)

4608=96u

Step 2: Flip the equation.

96u=4608

Step 3: Divide both sides by 96.

96u /96=4608 /96

u=48

Answer:

a) 252 square feet

Surface area of triangular prism = 252 square feet

Step-by-step explanation:

Explanation:-

Given diagram  Base = 3 feet

Height of the triangular = 4 feet

The slant height of triangular prism 'l' =20 feet

The hypotenuse of the triangle 'c' = 5 feet

 prism base area 'p' = h+b+c =  = 4 +3+5 =12

Surface area of triangular prism

                          = [tex]2 (\frac{1}{2} )bh +lA[/tex]

                           = b h + p l

                           = 3 ×4 + 12×20

                          = 252 square feet

Final answer:-

Surface area of triangular prism = 252 square feet

Answer:

252

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

Product means the answer of a multiplication problem. So 75 x 0.45 = 32.4.

[tex]75 \times 0.45 = 32.4[/tex]

Hope this helped :)

So the right answer is p^12.

Look at the attached picture

Hope it will help you

Good luck on your assignment..

Answer:

[tex] {p}^{12} [/tex]

Step-by-step explanation:

[tex]( {p}^{6} ) ^{2} [/tex]

[tex]p ^{6 \times 2} [/tex]

[tex] {p}^{12} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

17, 23

Step-by-step explanation:

First, to find the radius, we need to find the distance between the center of the circle, (-7, -1), and the point that the circle passes through, (8, 7). Plugging these coordinates into the distance formula we do [tex]\sqrt{(-7-8)^2+(-1-7)^2}[/tex] which gives us 17. Therefore, the radius of the circle is 17 units.

Next to find the y-coordinate of the point (-15, ), we need to write out the equation of the circle and then plug in the point. The equation of the circle would be [tex](x+7)^{2} +(y-8)^{2}=289[/tex]. Now we can plug in -15 for x and solve for y. So now we have [tex](-15+7)^{2} +(y-8)^{2}=289[/tex].

Simplifying the equation we have [tex](8)^{2} +(y-8)^{2}=289[/tex]. Subract [tex]8^{2}[/tex] from 289 and now the equation is [tex](y-8)^{2}=225[/tex]. Square root both sides to get [tex]y-8=15[/tex]. We solve for y to get 23. Therefore, the point is (-15, 23).

Answer:

Well, the answer would be 17,23 Also i had the same question as you so i already know the answer

Answer:

A prism is a three-dimensional shape with the same cross-section all the way through.

Step-by-step explanation: Im not sure if i got the second right

A prism is a three-dimensional shape with the same cross-section all the way through.

A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.

A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve.

To learn more about prism, refer

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Answer:

(3, -10)

Step-by-step explanation:

let A(x,y) and B(x1,y1)=(1,4)

by midpoint formula i.e. (x+x1)/2 ; (y+y1)/2

as midpoint is centre so,

(2, -3) = (x+1)/2 ; (y+4)/2

2=(x+1)/2  and -3=(y+4)/2

4-1=x    and   -6-4=y

x=3       and    y=-10

therefore A(x,y)=A(3,-10)

Answer:

$71

Step-by-step explanation:

Since x denotes the number of miles and we know that the car rode 100 miles, this means that x=100, and when we plug this in, we get C(x) = 0.5* 100 + 21 = 50 + 21 = $71. Hope this helps!

Answer:

C(100) = 71

Step-by-step explanation:

C(x) = .5x+21

Let x= 100

C(100) = .5(100)+21

         = 50+21

        = 71

Answer:

1/4(8/3+9)-3

Step-by-step explanation:

1/4(8/3+9)-3

Part A is correct; good job.

The universe is even numbers between 1 and 25, that's 2 thru 24. Count; there are twelve of them.

There's only one of them in the intersection of A and B, namely 8.

So the probability is one in twelve.

Answer: 1/12

Answer:

16

Step-by-step explanation:

3x² + 4y² where x = 2, y = 1, and z = -3

Here we just need to plug in the given values to their respective variables

Answer:

0 if the original expression is : 3x^2 + 4yz

Step-by-step explanation:

3x^2 + 4yz ; I guess this is the original expression.

When x=2, y = 1 z =-3

3x^2 + 4yz = 3(2)^2 + 4 × (1)×(-3)

= 3×4 + 4 × (-3) = 12 - 12 = 0

Answer:

Step-by-step explanation:

Think about a right triangle with legs AB and AC. Then you have ...

  AB² +AC² = BC² = 10² = 100

If AB and AC are shorter than that, the sum of their squares will be less than 100. When the legs of a right triangle are shortened, the angle between them must increase in order for them to continue to form a triangle.

The triangle with AB² +AC² < 100 is an obtuse triangle.

__

Conversely, if AB and AC are lengthened so the sum of their squares is greater than 100, the angle between them will have to decrease for them to form a triangle.

The triangle with AB² +AC² > 100 is an acute triangle.

Answer:

Student A says this estimate is reasonable because… Get ... Student A says this estimate is reasonable because the product is negative and about half of 1.5. Student B says you could find the product using a calculator as follows: "Divide −18 by 35, multiply the quotient by 1.43, then round the product

Step-by-step explanation:

calculations with a calculator or computer we need a way of checking that the answers it ... introduce students to this way of thinking and give them practice at estimating simple ... Do they always get the right answer no matter what? Invent a story illustrating a calculator error that you may have made or use the following.

Answer:

A. 40 degree+ 90 degree = x

The sum of the angles = 130 degree

Step-by-step explanation:

[tex]Given:\:\:\angle RSV = 40\degree,\:\:\angle VST = 90\degree\\\because \angle RSV + \angle VST = \angle RST\\\therefore 40\degree + 90\degree = x[/tex]

x = 130 degree

Answer:

16%

percentage is calculated by 100

A. 2500 × 1/100 = 25%

B. 4100 x 1/100 = 41%

41% - 25%

16%

therefore bridge A is 16% shorter than bridge B