The base of a cylinder has a radius of 9 centimeters. The cylinder is 12 centimeters tall. What is the approximate lateral area of the cylinder? Use 3.14 for π and round to the nearest whole number.

Answer:

The mean of the the random variable X is 1200.

The standard deviation of the random variable X is 21.91.

Step-by-step explanation:

The random variable X is defined as the number of city residents in the sample who support the proposal.

The random variable X follows a Binomial distribution with parameters n = 2000 and p = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

Check the conditions as follows:

[tex]np=2000\times 0.60=1200>10\\\\n(1-p)=2000\times (1-0.60)=800>10[/tex]  

Thus, a Normal approximation to binomial can be applied.

So,  the random variable X can be approximate by the Normal distribution .

Compute the mean of X as follows:

[tex]\mu=np[/tex]

  [tex]=2000\times 0.60\\=1200[/tex]

The mean of the the random variable X is 1200.

Compute the standard deviation of X as follows:

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

  [tex]=\sqrt{2000\times 0.60\times (1-0.60)}\\=\sqrt{480}\\=21.9089\\\approx 21.91[/tex]

The standard deviation of the random variable X is 21.91.

Answer: $200

Step-by-step explanation:

Answer:

The answer is C.

Answer:

a) removing a vowel, not replacing it, and then removing another vowel

Step-by-step explanation:

This question is from the topic Probability. In Probability, a dependent event is one in which the outcome of one event alters or changes the outcome of another event. A classic example of this is seen when sampling without replacement is done. When sampling without replacement is done, the outcome of another event within the same set changes. When sampling with replacement is done, the outcome of the events are independent because every item in the population still has an equal chance of being chosen. However, in the case of sampling without replacement, once an item has been selected from a population, the outcome of every other event after it is altered based on the item that was initially chosen.

Let's assume that the bag has 26 tiles (one for each alphabet from a - z)

Population = 26, consonant = 21, vowel = 5

If a vowel or consonant is removed & is replaced, we have:

Pr (choosing "a") = number of item ÷ population

Pr = 1 ÷ 26 = 1/26

Pr (choosing "y") = 1 ÷ 26 = 1/26

Doing this for over & over again, produces the same probability

However, if an item was selected without replacement, we have:

Pr (choosing "a") = 1 ÷ 26 = 1/26

Without replacement implies that if I choose tile letter "a", tile letter "a" will not be included in subsequent events, hence:

Population = 25

Pr (choosing "u") = 1 ÷ 25 = 1/25

Without replacement, population = 24

Pr (choosing "y") = 1 ÷ 24 = 1/24

So, we see the dependent nature of the events in how that the outcome of the next event is being altered. As such, option a describes a dependent event & is the correct answer

Answer:

A. removing a vowel, not replacing it, and then removing another vowel

simple answer ^^

Step-by-step explanation:

EDGE 2021    : )

Answer:

Wat is the question?

Step-by-step explanation:

Answer:

Ermm here I graphed it :)

Sorry for dark mode..

Answer:

because I said one is the best number

Step-by-step explanation:

[tex](2x^2-6x^3+4)+(2x^3+3x^2+4)[/tex]

Since this is addition, you can just easily combine the terms.

[tex](2x^2+3x^2)+(-6x^3+2x^3)+(4+4)[/tex]

[tex]5x^2 -4x^3+8[/tex]

Now, all we have to do is put it in standard form meaning the exponents have to go in descending order. Largest exponent to smallest exponent.

[tex]-4x^3+5x^2+8[/tex]

So, this is your answer in standard form.

Answer:

The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{2.8}{\sqrt{772}} = 0.26[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 69.7 - 0.26 = 69.44 inches

The upper end of the interval is the sample mean added to M. So it is 69.7 + 0.26 = 69.96 inches

The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.

Answer:

3238.37571429

Step-by-step explanation:

or 3238.4

Answer:

b) The margin of error is approximately 3.24

e) The critical value is 1.7921.

Step-by-step explanation:

Step(i):-

Given sample size 'n' =20

Given sample standard deviation 's' = 10

Margin of error

The margin of error is determined by

[tex]M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }[/tex]

The level of significance ∝ =0.95

The degrees of freedom = n-1 = 20-1=19

t₀.₉₅ = 1.729

[tex]M.E = \frac{1.729 X10 }{\sqrt{20} }[/tex]

Margin of error = 3.866

Step(ii):-

Margin of error

The margin of error is determined by

[tex]M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }[/tex]

Given another sample size n =30

The level of significance ∝ =0.95

The degrees of freedom = n-1 = 30-1=29

t₀.₉₅ = 1.70

[tex]M.E = \frac{1.7021 X10 }{\sqrt{30} } =3.24[/tex]

Margin of error = 3.24

Answer:

2,100 people.

Step-by-step explanation:

If 2 out of 5 people were in favor of a new high school being built, we know that 3 out of 5 people are against the decision. We can simply use this as a fraction to find the amount of people against:

[tex]3500 * \frac{3}{5}= 2100[/tex]

Therefore, 2,100 people are against the decision.

Answer:

x = ± 6sqrt(5)

Step-by-step explanation:

x^2 = 180

Take the square root of each side

sqrt(x^2) = ±sqrt(180)

x =±sqrt(36)sqrt(5)

x = ± 6sqrt(5)

Answer:

Edge 2020

A

-13.42, 13.42

Step-by-step explanation:

Answer:

honestly this is very confusing could you send a graph?

Step-by-step explanation:

Answer:75/8

Step-by-step explanation:

weight gain=81/4-87/8

weight gain=(2x81-1x87)/8

Weight gain=(162-87)/8

weight gain =75/8

Answer:

405

Step-by-step explanation:

To find sample size, use the following equation, where n = sample size, za/2 = the critical value, p = probability of success, q = probability of failure, and E = margin of error.

[tex]n=\frac{(z_{\frac{\alpha }{2} })^{2} *p*q }{E^2}[/tex]

The values that are given are p = 0.84 and E = 0.03.

You can solve for the critical value which is equal to the z-score of  (1 - confidence level)/2.  Use the calculator function of invNorm to find the z-score.  The value will given with a negative sign, but you can ignore that.

(1 - 0.9) = 0.1/2 = 0.05

invNorm(0.05, 0, 1) = 1.645

You can also solve for q which is 1 - p.  For this problem q = 1 - 0.84 = 0.16

Plug the values into the equation and solve for n.

[tex]n =\frac{(1.645)^2*0.84*0.16}{(0.03)^2}\\n= 404.0997333[/tex]

Round up to the next number, giving you 405.

The answer is 5.381!

The number 5.3809 rounded to the nearest thousandth is 5.381 because the thousandth is 3 decimals.

Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.

We have a number:

= 5.3809

The thousandth(3 decimals) place is:

Rounded to the nearest 0.001 or the Thousandths Place.

The number becomes:

= 5.381

Thus, the number 5.3809 rounded to the nearest thousandth is 5.381 because the thousandth is 3 decimals.

Learn more about the rounding off number here:

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Answer:

We conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

Step-by-step explanation:

We are given that 513 employed persons and 604 unemployed persons are independently and randomly selected, and that 287 of the employed persons and 280 of the unemployed persons have registered to vote.

Let [tex]p_1[/tex] = percentage of employed workers who have registered to vote.

[tex]p_2[/tex] = percentage of unemployed workers who have registered to vote.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex]      {means that the percentage of employed workers who have registered to vote does not exceeds the percentage of unemployed workers who have registered to vote}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex]     {means that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote}

The test statistics that would be used here Two-sample z test for proportions;

                          T.S. =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of employed workers who have registered to vote = [tex]\frac{287}{513}[/tex] = 0.56

[tex]\hat p_2[/tex] = sample proportion of unemployed workers who have registered to vote = [tex]\frac{280}{604}[/tex] = 0.46

[tex]n_1[/tex] = sample of employed persons = 513

[tex]n_2[/tex] = sample of unemployed persons = 604

So, the test statistics  =  [tex]\frac{(0.56-0.46)-(0)}{\sqrt{\frac{0.56(1-0.56)}{513}+\frac{0.46(1-0.46)}{604} } }[/tex]

                                       =  3.349

The value of z test statistics is 3.349.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of z as 3.349 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

Answer:

Respuesta D

Step-by-step explanation:

Paola afirma: Todo número compuesto par, se puede escribir como la multiplicación de factores primos.

Esta afirmación es cierta, pues es un caso  de la afirmación de que todo número natural mayor que uno se puede escribir como multiplicación de números primos. A este proceso se le llama descomposición en factores primos.

Edwin afirma: Todo número compuesto impar se puede escribir como la suma de dos números primos.

Esta afirmación es falsa. Note que al sumar dos números impares de la forma 2k+1 y 2m+1 para k distinto de m, se obtiene

[tex] 2k+1+2m+1 = 2(km+1)[/tex]

Es decir, la suma de dos números impares es siempre par.

Note que a excepción de 2, todo número primo es impar. Para que esta afirmación fuera cierta, necesariamente tendría que pasar que cualquier número impar k se escriba de la forma p+2 donde p es un número primo. Esto es equivalente que para cualquier número impar k, el número k-2 sea primo.

Basta con dar un ejemplo para ver que esto no pasa. Tomemos k=11. En este caso, k-2 = 9, el cuál no es un número primo. Entonces 11 no se puede  descomponer como la suma de dos números primos.

Answer:

The first one is false and the second is vertex

Step-by-step explanation:

Answer:

The null hypothesis is represemted as

Null: p ≥ 0.80

The alternative hypothesis is given as

Alternative: p < 0.80

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.

For this question, the survey that involved comparison was the proportion of US students at the university that owned a smartphone and the proportion of college students in the US that own a smartphone (80%).

Specifically, we want to check if the proportionof smartphone owners at the university is lower than the overall proportion of smartphone owners amongst US college students (80%).

Hence,

The null hypothesis would be that there isn't significant evidence to conclude that the proportion of smartphone owners is lower at this university than the general proportion of smartphone owners amongst college students.

That is, the proportion of smartphone users at this university isn't lower than the proportion of college students in the U.S. that own a smartphone or the proportion of smartphone owners at this university is higher than or equal to the proportion of college students in the U.S. that own a smartphone.

The alternative hypothesis is then that there is significant evidence to conclude that the proportion of smartphone users at this university is lower than the proportion of college students in the U.S. that own a smartphone.

Mathematically,

The null hypothesis is represemted as

Null: p ≥ 0.80

The alternative hypothesis is given as

Alternative: p < 0.80

Hope this Helps!!!

The null hypothesis states that the proportion of smartphone owners at the university is not lower than 80%, while the alternative hypothesis states that the proportion is lower. A hypothesis test can be conducted using the data from the survey to determine if the proportion is significantly lower.

The research question is whether the proportion of smartphone owners at this university is lower than the national average of 80%. We can state the hypotheses as:

Null Hypothesis (H0): The proportion of smartphone owners at this university is not lower than 80%.

Alternative Hypothesis (Ha): The proportion of smartphone owners at this university is lower than 80%.

To test these hypotheses, we need to analyze the data from the survey and perform a hypothesis test. We can use statistical software to calculate the proportion of smartphone owners at the university and conduct the test.

Answer:

54

Step-by-step explanation:

because it is

Answer: The volume of the composite solid is about 589.5 cubic feet.

Step-by-step explanation:

Step-by-step explanation:

-13 > x - 43

-13 + 43 > x

30 > x

Answer:

b

Step-by-step explanation:

Answer:

The 95% confidence interval about the mean age is between 17.6 years and 57.6 years.

This means that we are 95% sure that the mean age of an inmate in the death row is in this interval. 39.2 is part of this interval, which implies that the mean age of a​ death-row inmate has not changed since then.

Step-by-step explanation:

We have the sample standard deviation, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 32 - 1 = 31

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 31 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0395

The margin of error is:

M = T*s = 2.0395*9.8 = 20

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 37.6 - 20 = 17.6 years

The upper end of the interval is the sample mean added to M. So it is 37.6 + 20 = 57.6 years.

The 95% confidence interval about the mean age is between 17.6 years and 57.6 years.

This means that we are 95% sure that the mean age of an inmate in the death row is in this interval. 39.2 is part of this interval, which implies that the mean age of a​ death-row inmate has not changed since then.

Final answer:

To construct a 95% confidence interval about the mean age of death-row inmates, we can use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size). In this case, the 95% confidence interval is approximately 35.8 to 39.4 years old.

Explanation:

To construct a 95% confidence interval about the mean age, we can use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size).

In this case, the sample mean is 37.6, the standard deviation is 9.8, and the sample size is 32. To find the critical value, we look up the z-score for a 95% confidence level, which is approximately 1.96.

Substituting these values into the formula, we have:

37.6 ± 1.96 * (9.8 / √32)

Simplifying the equation gives us the 95% confidence interval of approximately 35.8 to 39.4. This means that we are 95% confident that the true mean age of death-row inmates falls within this interval.

Answer:

that is the solution to the question

Answer:

9:45 pm

Step-by-step explanation:

1 1/2 hours is 1 hour 30 min

11:15 - 1 hr 30 = 9:45

Answer:

9:45 im pretty sure :)

Step-by-step explanation:

So they canoed for 1 hour and 30 minutes. so you subtract 1:30 from 11:15

Answer:

(a)Yes, it is an exponential function.

(b)[tex]P(t)=200\cdot 2^{t/20}[/tex]

Step-by-step explanation:

(a)A population grows exponentially if it increases by a common ratio(called the growth ratio). We can see from the given information that the population of E.coli doubles every 20 minutes, therefore it is an exponential growth with a growth ratio of 2.

(b)The population, P(t) at any time t of an initial population, [tex]P_o[/tex]  with a growth ratio of r over a period k can be modeled using the function:

[tex]P(t)=P_o\cdot r^{t/k}[/tex]

In this Case:

[tex]P_o[/tex]=200

Growth rate,r=2

Growth Period,k=20 minutes

Therefore, the equation that models the function is:

[tex]P(t)=200\cdot 2^{t/20}[/tex] , t is in minutes

Jenny is correct that E. coli growth can be modeled with an exponential function, characterized by doubling in population size at regular time intervals. An equation representing this growth is N(t) = N0 x 2^(t/20), where N0 is the initial amount of E. coli and t is time in minutes.

I agree with Jenny, the E. coli growth can indeed be modeled with an exponential function. This is supported by the fact that the E. coli population doubles after each consistent time period (20 minutes). In an exponential growth model, the rate of increase of a population is proportional to the current population size, which means as the population gets larger, it grows at an even faster rate.

Part B: Equation of Exponential Growth:

The exponential growth model for a population starting with N0 individuals and a growth rate r can be described by the equation N(t) = N0ert, where N(t) is the population at time t, N0 is the initial population size, e is the base of the natural logarithm, and r is the growth rate per unit time. For E. coli, with a doubling time of 20 minutes, the growth rate can be calculated using the doubling formula: Td = ln(2)/r, solving for r gives r = ln(2) / 20 minutes. The continuous exponential growth equation can be simplified to a discrete model for this case: N(t) = N0 * 2(t/20), where t is given in minutes.

Answer:

Inside a checkbook is the register. This is where you record events in your checking account such as checks you've written, cash withdrawals, and deposits. It's very important to write down every transaction so you know exactly how much money you have in the bank.

Step-by-step explanation:

Answer:

You can store your money in an organized fashion, separating them by type (penny, dime, $1, $5, etc.).

Answer:

45°-(315°) = 360°

-315°-45°=-360°

Second part: WOULD

Step-by-step explanation:

Trust me I gotchu

Subtracting angles involves accounting for the directions implied by their positive or negative signs. The subtraction of 45°-(-315°) equates to an addition, giving a resultant angle of 360°. Conversely, -315° – 45° provides a resultant angle of -360°.

The question involves the mathematical concept of angles, specifically, subtracting them. Here, we are dealing with angles of 45° and -315°. When subtracting angles, consider the directions indicated by the positive and negative signs. A positive angle is measured counterclockwise from the initial side to the terminal side, while a negative angle is measured clockwise.

So, for 45°-(-315°), you're essentially adding 45 and 315 because subtracting a negative number becomes the addition of the positive equivalent. This gives you a resultant angle of 360°.

And in the case of -315° – 45°, you're subtracting 45 from -315 which gives you a resultant angle of -360°.

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Answer:

Step-by-step explanation:

Let the cost of a bag of popcorn=p

Let the cost of a drink=d

Mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks.

Christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks.

The required system of equations is:

Multiply the first equation by 2 to eliminate p

6p+12d=91.5

6p+4d=71.50

Subtract

8d=20

d=20/8=$2.5

Substitute d=2.5 into any of the equations to obtain p.

6p+12d=91.5

6p+12(2.5)=91.5

6p=91.5-12(2.5)

6p=91.5-30

6p=61.5

Divide both sides by 6

p=$10.25

Therefore: