A movie theater has a seating capacity of 317. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2296, How many children, students, and adults attended?

Rewrite the percent as a decimal by moving the decimal point 2 places to the left:

97% = 0.97

Now multiply:

698.04 x 0.97 = 677.0988

Round to 2 decimal places= 677.10

To find 97% of £698.04, you simply multiply £698.04 by 0.97. This gives you an answer of £677.30, rounded to 2 decimal places.

The question is asking for 97% of £698.04. To find this, you would need to multiply £698.04 by 0.97 (which is the decimal equivalent of 97%). Let's do this calculation:

£698.04 * 0.97 = £677.30

Here, the result (rounded to 2 decimal places) is £677.30. So, 97% of £698.04 is £677.30.

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Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The standard deviation of sample mean is inversely proportional to the sample size, n.

So, if n increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for n = 64 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7[/tex]

The standard deviation of the sample mean for n = 196 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4[/tex]

The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for n = 784 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2[/tex]

The standard deviation of the sample mean for n = 49 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8[/tex]

The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.

Hence, the variance also increases.

Variance has decreased in first case and Variance has increased in second case.

What information do we have?

Mean tensile stength = 78.3 kilograms

Standard variance = 5.6 kilogram

Variance = sigma² / n

A.

Variance of sample mean with sample size 64 = 5.6² / 64

Variance of sample mean with sample size 64 = 0.49

Variance of sample mean with sample size 196 = 5.6² / 196

Variance of sample mean with sample size 196 = 0.16

Variance has decreased.

B.

Variance of sample mean with sample size 784 = 5.6² / 784

Variance of sample mean with sample size 784 = 0.04

Variance of sample mean with sample size 49 = 5.6² / 49

Variance of sample mean with sample size 49 = 0.64

Variance has increased.

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Answer:

Check the explanation

Step-by-step explanation:

(a) Best decision based on maximax criterion= large facility

maximum in the two facilities is $300 and $800 of which $800 is the maximum, So larger facility satisfies maximax.

(b) Best decision based on maximin criterion= small facility

minimum in the two facilities is $100 and -$200 of which $100 is the maximum, So smaller facility satisfies maximin.

(c) Best decision based on minimax regret= large facility

maximum in the two facilities is $300 and $800 of which $300 is the minimum, So larger facility satisfies minimax regret.

Final answer:

Explanation of maximax, maximin, and minimax regret criteria for decision-making in uncertain scenarios.

Explanation:

Maximax criterion: This criterion involves selecting the decision with the maximum possible payoff under each possible outcome. In this case, the manager would choose the large facility due to the potential high payoff of $800 in case of high demand.

Maximin criterion: This criterion involves selecting the decision with the maximum possible payoff under the worst-case scenario. Here, the manager would choose the small facility to minimize the loss to -$200 in case of low demand.

Minimax regret: This criterion involves minimizing the maximum regret that could be incurred based on the wrong decision. The manager would need to calculate regrets for each decision and choose the one with the least possible regret

Answer:

Each friend would get 100000000

Step-by-step explanation:

1000000000 ÷ 10 = 100000000

Answer:

$100,000,000

Step-by-step explanation:

divide 1,000,000,000 by 10, be sure to count your zeros.

Answer:

0.1111... = 0.1 = 1/9

Step-by-step explanation:

0.1111.. Is a repeating decimal which can be written as 0.1 and 1/9

It is important to know that the decimals which have only 1 digit repeating all come from the fractions which are ninths.

The fraction form of a number 0.11... is,

⇒ 1/9

We have to given that,

A number 0.1 repeating.

Now, We can find the fraction of number 0.111.. as,

Let us take,

x = 0.1111.....   .. (i)

Multiply by 10,

10x = 1.1111....  .. (ii)

Subtract (ii) from (i);

10x - x = 1.111.. - 0.1111....

9x = 1

x = 1/9

Hence, The fraction form of a number 0.11... is,

⇒ 1/9

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Answer:

The net, when folded into a cube, has a total surface area of 2,400 sq.units

Step-by-step explanation:

The length of all sides of a cube are the same.

Now, the surface area of a cube is the sum of the area of all of its faces.

Since the length of all sides are the same and we are told that the length of a side is 20 units, thus, the area of one face is;

A = 20 x 20 = 400 sq.units

So, one the area of a face is 400 sq.units.

Now, since all the faces are the same measurement, thus each face will have an area of 400 sq.units. Cubes have 6 faces, thus the total surface Area is;

Total = 400 x 6 = 2400 sq.units

The net, when folded into a cube, has a total surface area of 2,400 sq.units

Answer:

it would have to be a 99

The solution is, the measure of angle A is 79°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

we know that

the law of cosines establish

c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]

in this problem

a=11 units

b=11 units

c=14 units

C=angle A

so, we get,

cos C=[11²+11²-14²]/[2*11*11]

-----> cos C=0.19008

C=arc cos (0.19008)

------> C=79.04°

the answer is

the measure of angle A is 79°.

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Answer:

  2³n²

Step-by-step explanation:

An exponent signifies the number of times the base is a factor in the product. Here, 2 is a factor 3 times; n is a factor 2 times. Their exponents will be 3 and 2, respectively:

  2•2•2•n•n = 2³n²

Answer:

30

Step-by-step explanation:

6*5= 30

3*10= 30

5*6= 30

The Lowest Common Multiple of 3, 5, and 6. is 30

The lowest common multiple of a group of numbers is the smallest number that is a multiple of all the numbers.

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Answer:

3³ = 27

This is because:

3x3x3 = 27

Answer:

4.17

Step-by-step explanation:

Answer:

4.17 is greater than 4.085

Step-by-step explanation:

Answer:

[tex]2t^3+15t^2+19t+6[/tex]

Step-by-step explanation:

Height of the Rectangle[tex]=t^2+7t+6[/tex]

Width of the Rectangle[tex]=2t+1[/tex]

Area of the Rectangle = Height X Width

[tex]=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\[/tex]

The area of the rectangle is [tex]2t^3+15t^2+19t+6[/tex]

The height of the rectangle is[tex]t^4 + 26t^3 + 169t^2 + 7t + 6,[/tex] and the width is 26t + 1.

It seems there might be some confusion in the way the dimensions of the rectangle are presented. To clarify, let's break down the height and width of the rectangle:

Height:

The height of the rectangle is given as [tex](t^2 + 7t + 6t)^2[/tex] + 7t + 6.

To simplify the expression inside the parentheses:

[tex](t^2 + 7t + 6t)^2[/tex] = [tex](t^2 + 13t)^2[/tex]= [tex]t^4 + 26t^3 + 169t^2[/tex]

So, the height of the rectangle is[tex]t^4 + 26t^3 + 169t^2 + 7t + 6.[/tex]

Width:

The width of the rectangle is given as 2t + 12t + 12t + 1.

Combine like terms in the width expression:

2t + 12t + 12t + 1 = 26t + 1

So, the width of the rectangle is 26t + 1.

Now you have the height and width of the rectangle expressed as functions of "t":

Height = [tex]t^4 + 26t^3 + 169t^2 + 7t + 6.[/tex]

Width = 26t + 1

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Answer:

  A.  Three points

Step-by-step explanation:

Tangent circles will intersect at the one point of tangency.

Circles that cross each other will intersect in two points.

Circles that are coincident will intersect in infinitely many points.

It is not possible for two circles to intersect in exactly 3 points.

answer

graph a

speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead

graph b

speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (3,∞) instead

step-by-step explanation

looking at the velocity graphs, when the absolute value of velocity is increasing (moving away from the x axis), the particle must be speeding up. we say absolute value because while velocity has direction, speed only has magnitude, so we need to take the absolute value of velocity to get speed.

for graph a, we can see the velocity moving away from the x axis during the interval (0,1), moving towards the x axis during the interval (1,2) and then moving away again during the interval (2,3)

so it speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead since this is at an endpoint

repeat for graph b where it moves toward the x axis from (0,1), moves away from (1,2), moves towards from (2,3), and moves away again from (3,4)

so it speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (2,∞) instead since this is at an endpoint

Answer:

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1012, \pi = 0.38[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 - 1.645\sqrt{\frac{0.38*0.62}{1012}} = 0.3549[/tex]

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

Answer:

-3

Step-by-step explanation:

i know because i took the test

Answer:

-3 a)

Step-by-step explanation:

bc

Step-by-step explanation:

[tex](7g + 3)( - g - 3) \\ = 7g( - g - 3) + 3( - g - 3) \\ = - 7 {g}^{2} - 21g - 3g - 9 \\ \red{ \bold{ = - 7 {g}^{2} - 24g - 9 }} \\ is \: in \: the \: standard \: form.[/tex]

-7g² - 24g - 9 is the polynomial in standard form.

In equations like the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

Given an equation (7g+3)(−g−3) to convert it into the polynomial form we need to simplify it. Hence,

(7g+3)(−g−3) => -7g² - 21g- 3g -9

=>  -7g² - 24g - 9

Therefore, for the given problem -7g² - 24g - 9 is the polynomial in standard form.

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Answer:

The probability is 0.9583

Step-by-step explanation:

First, we have 2 possibilities, Bob's outcome is heads or Bob's outcome is tails.

If Bob's outcome is heads, the probability that Chuck doesn't get a king is equal 1, because there aren't kings in the poker deck. it means that if Bob's outcome is heads, the probability that David raises a green flag is 1.

On the other hand, if Bob's outcome is tails, the probability that Chuck doesn't get a king is equal to:

[tex]\frac{44}{48}=0.9166[/tex]

Because there are 48 cards in the poker deck (without the 4 aces) and 44 of them aren't kings. So, if Bob's outcome is Tails, the probability that David raises a green flag is 0.9166.

Now, the probability that David raises a green flag is calculated as:

[tex]P=0.5(1)+0.5(0.9166)=0.9583[/tex]

Because there is a probability of 0.5 that Bob's outcome is heads and there is a probability of 0.5 that Bob's outcome is Tails.

Answer:the answers is B

Step-by-step explanation:

Answer:

A Non-Bank Financial Institution (NBFI)

Step-by-step explanation:

A Non-Bank Financial Institution (NBFI) can be described as any institution without full banking license but offers loans and other financial services.

They are able to provide low cost loans due to the fact that they are privately owned and operated by individuals, as a result of this, they're mostly used by small and medium-sized enterprise.

A Non-Bank Financial Institution (NBFI) includes;

- Insurance companies.

- Pension funds.

- Pawn shops.

- Thrift or mutual credit societies.

- Credit unions.

The carnivores mammals are (1/2) of the total animals in the natural park.

Step-by-step explanation:

Let the total no. of animals be 'a'

The amount of mammals = (3/5)a

The amount of carnivores= (5/6) (3/5) a

= (1/2) a

So, the carnivores mammals are (1/2) of the total animals in the natural park.

Answer:

[tex]t=\frac{180-175}{\frac{4}{\sqrt{15}}}=4.84[/tex]    

[tex]df=n-1=15-1=14[/tex]  

[tex]p_v =P(t_{(14)}>4.84)=0.000131[/tex]  

We got a very low value for the p value so then we have enough evidence to reject the null hypothesis at any significance level commonly used. And the best conclusion based on the possible options are:

None of the above are true

Step-by-step explanation:

Data given

[tex]\bar X=180[/tex] represent the sample mean

[tex]s=4[/tex] represent the sample standard deviation

[tex]n=15[/tex] sample size  

[tex]\mu_o =175[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is above the limit of 175 degrees, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 175[/tex]  

Alternative hypothesis:[tex]\mu > 175[/tex]  

The statistic is given by:

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

And replacing we got:

We can replace in formula (1) the info given like this:  

[tex]t=\frac{180-175}{\frac{4}{\sqrt{15}}}=4.84[/tex]    

P-value

The degrees of freedom are given by:

[tex]df=n-1=15-1=14[/tex]  

Since is a one sided test the p value would be:  

[tex]p_v =P(t_{(14)}>4.84)=0.000131[/tex]  

We got a very low value for the p value so then we have enough evidence to reject the null hypothesis at any significance level commonly used. And the best conclusion based on the possible options are:

None of the above are true

Answer:

The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.

Step-by-step explanation:

We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.

A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.

Let p = probability of voters preferring the incumbent = 66%

n = number of voters polled = 500

So, the mean of the number preferring the incumbent is given by;

         Mean = [tex]n \times p[/tex] = [tex]500 \times 0.66[/tex]

                                = 330 voters

And, standard deviation of the number preferring the incumbent is given by;

          Variance =  [tex]n \times p\times (1-p)[/tex]  

                          =  [tex]500 \times 0.66 \times (1-0.66)[/tex]

                          =  112.2

So, Standard deviation =  [tex]\sqrt{Variance}[/tex]

                                       = [tex]\sqrt{112.2}[/tex]  = 10.59

Based on the binomial distribution and the probability of 66%, the mean number of likely voters favoring the incumbent is 330, and the standard deviation is approximately 18.17.

In this scenario, we are working with a binomial distribution where we have a fixed number of trials, each trial has two possible outcomes (in this case, favoring the incumbent or not), the probability of success is constant, and the trials are independent. Here, a success is a likely voter favoring the incumbent.

To find the mean of the number preferring the incumbent, we use the formula μ = np, where n is the number of trials (or voters), and p is the probability of a success. Thus, the mean is 500 voters times 66%, which gives us:

μ = 500 * 0.66 = 330.

The formula for the standard deviation (σ) of a binomial distribution is σ = √npq, where q is the probability of failure (1 - p). Therefore, standard deviation is:

σ = √(500 * 0.66 * (1 - 0.66)) = 18.17.

The correct answer is: mean = 330, standard deviation = 18.17

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Answer:

27 stripes

Step-by-step explanation:

162/6=27

Since each zebra has the sam amount of stripes, you will divide the amount of stripes my the amount of zebras.

Final answer:

The probability of one of the minority candidates being hired is 40%.

Explanation:

To find the probability that one of the minority candidates is hired, we need to determine the number of favorable outcomes (one of the minority candidates being selected) and divide it by the total number of possible outcomes (selecting any candidate from the final list of five).

Since there are two minority candidates and five candidates total, the probability of selecting one of the minority candidates is

P(one of the minority candidates being hired) = 2/5 = 0.4 = 40%

To create a scale drawing of an Olympic standard swimming pool with a scale of 1 inch to 10 meters, the scaled dimensions would be approximately 2.5 inches for the width and 5 inches for the length.

To create a scale drawing of an Olympic standard swimming pool using a scale of 1 inch to 10 meters, we need to find the scaled dimensions. The actual dimensions of the pool are given as 50 meters in length and 25 meters in width.

Width:

Actual width: 25 meters

Scale factor: 10 meters per 1 inch

Scaled width = Actual width / Scale factor

Scaled width = 25 meters / 10 meters per 1 inch

Scaled width = 2.5 inches

Length:

Actual length: 50 meters

Scale factor: 10 meters per 1 inch

Scaled length = Actual length / Scale factor

Scaled length = 50 meters / 10 meters per 1 inch

Scaled length = 5 inches

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Answer:

3.704 Hours

Step-by-step explanation:

This problem can be solved by using concept of relative speed. relative speed is speed of one body in comparison of other.

If two bodies are moving in same direction their relative speed is calculated by taking difference of each other speed.

If two bodies are moving in opposite direction their relative speed is calculated by taking sum of each other speed.

In the problem stated two bodies are moving in north and south direction, hence they are moving in opposite direction, thus their speed can be taken sum of individual speed.

which is

(60+65) Km/Hr =  135 km/hour

Now given in question distance between two bodies is 500 KM

and relative speed = 135 km/hour

using formula of speed distance and time

Time = distance / speed  = 500/135 = 3.704 Hours

Therefore it will take 3.704 Hours for both of the trains to be 500 km apart.

Answer:

PLEASE MARK AS BRAINLIEST PLZ

NOPE

Step-by-step explanation:

14:18 if you want to find the divisible number it is 2 now divide them both by 2it will be 7:9 and that's the most simple way

Answer:

No

Step-by-step explanation:

A way you can do it is to simplify the ratio, to make it smaller, but still equal to 14:18.

14:18 can be divided by 2, and turn to 7:9

This cannot be simplified so it is not equivalent.

Final answer

No