Students pay $2 per ticket and adults pay $5 per ticket. Although the stadium is filled to its capacity of
2000, 254 of those seats are given free of charge to band members, pep squad members, and faculty members. the ticket-booth manager reports to the athletic director that the total income from the sale of tickets for the current game is $5766. How many student and adult tickets were sold?

When the expected value and variance are 3.5 and 15.25, the statistic probability distribution will be 5/10, 3/10, and 2/10.

Given that,

A box contains ten sealed envelopes labelled 1, 2, 3, and 10. Six of them are empty, two have $5 apiece, and the remaining two each contain a $10 bill. You obtain the most money in any chosen envelope when replacement is used; a sample of size 3 is selected (forming a random sample). The statistic of interest is m if the quantities in the selected envelopes are represented by x1, x2, and x3.

We know that,

The probability distribution will be

P(X=0) = 5/10

P(X=5) = 3/10

P(X=10) = 2/10

In probability theory, the expected value is a development of the weighted average. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the expected value.

The expected value is

E =0(5/10)+5(3/10)+10(2/10) = 3.5

The variance is

V = 0² x (5/10) + 5² ( 3/10 ) + 10² x (2/10) - 3.5² = 15.25

Therefore, the statistic probability distribution will be 5/10, 3/10, and 2/10 when the expected value and variance are 3.5 and 15.25.

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The derivative of given function is D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814  

We have to find the directional derivative of the given function  

f(x,y,z) = yz+e^x at (x0,y0,z0)=(1,1,1) in the direction of the vector

d⃗ =(3,−5,5)  

Find the gradient of the function and evaluate it at the given point:  

To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.  

∇f= (∂f/∂x,∂f/∂y,∂f/∂z)  

∂f/∂x = ∂( yz+e^x )/∂x  

The derivative of a sum/difference is the sum/difference of derivatives:  

∂f/∂x = ∂( yz)/∂x +∂(e^x )/∂x since the derivative of y and z with respect of x is zero.  

∂f/∂x = e^x The derivative of exponential is d(e^x)/dx=e^x.  

Similarly  

d(yz+e^x)/dy = z and d(yz+e^x)/dz = y  

∇(yz+e^x)(x0,y0,z0)=(e^x,z,y)  

Finally plug in the point we get the result  

∇(yz+e^x)|(x0,y0,z0)=(1,1,1)=(e,1,1)  

∇(yz+ex)|(x0,y0,z0)=(1,1,1)=(e,1,1)  

Now we Find the length of the vector: |d⃗ |=((3)^2+(−5)^2+(5)^2)^1/2 =(59)^1/2  

To normalize the vector, divide each component by length:  

d = ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)  

Finally, the directional derivative is the dot product of the gradient and the normalized vector:  

D(yz+e^x)d(1,1,1) = (e,1,1). ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)  

D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814  

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The missing features of the Venn diagram include the following:

I=472, II=449 ,IV=459 ,V=218 , VI=456,

A Venn diagram is a circular illustration of how variables are interrelated to each other.

To solve for I;

Total number of students taking dance = 1031

Total number of students taking science and dance= 449

Total number of students taking all three courses= 218

Total number of students taking science and English = 459

Therefore, the number of students taking only science;

I =( II-V)+ (IV-V)

I= (449-218)+(459-218)

I = 231+241

I= 472

The number of students that took Science, Dance, or English =V= 218

The number of students took Dance and English, but not Science = VI = 456

The number of students took Science or didn't take Dance = IV = 459

The number of students took none of the courses = VIII = U

The number of students took Science or English, but not Dance = 459 students.

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The resulting conditional mean squared error of the LMS estimator, given N=3 is 0.0383746

In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). If X and Y are independent, discrete random variables, then the following are true: pX|Y(x|y)=pX(x)pY|X(y|x)=pY(y)

The full conditional for a given node (parameter) is simply the product of the probability model (likelihood or prior) for that node and its parent node (at least up to a constant of proportionality).

1) fY|N(y∣N=3)=84 y^6 (1-y)^3

2)0.0636363

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Answer: Im sorry I cant help im just doing this for points

Step-by-step explanation:

The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].

In mathematical notation, the null hypothesis can be written as:

H_0: p = 0.24

where p is the proportion of uninsured motorists in Florida.

The alternative hypothesis can be written as:

H_1: p < 0.24

This means that we are testing the hypothesis that the proportion of uninsured motorists has decreased to a level that is less than 24%.

The null hypothesis is the default assumption, and we will only reject it if we have enough evidence to support the alternative hypothesis. In this case, we would need to collect data that suggests that the proportion of uninsured motorists has decreased to a level that is significantly less than 24%.

The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].

The other options are incorrect because they either do not specify the direction of the hypothesis test (i.e., whether we are testing whether the proportion of uninsured motorists has increased or decreased) or they are not supported by the given information.

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Answer:

There are 5 possible outcomes when the first spinner is spun, and 2 possible outcomes when the second spinner is spun. Therefore, the sample space of possible outcomes when both spinners are spun is 5 x 2 = <<5*2=10>>10.

The possible outcomes are:

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

Of these, 3A, 2A, 1A, and 4B have a number less than 3 or an A. Therefore, there are 4 possible outcomes that have a number less than 3 or an A.

Step-by-step explanation:

The value of Safeco stock given the required return growth rate and the dividend of the stock is $89.60.

The value of the stock can be determined using the constant growth dividend model. According to the model, the value of the stock is a function of the growth rate, dividend and the required return of the stock.

Value of the stock = [dividend x (1 + g)] / (r - g)

where

r = required return

g = growth rate

Value of the stock = [1.60 x (1.12) / (0.14 - 0.12)

Value of the stock = 1.792 / 0.02

Value of the stock = $89.60

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Answer:

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

Given expression:

Distribute and simplify:

The correct statements are:

a) The independent variable is the number of people.

b) The initial value (initial fee) for the picnic is $40.

d) As the number of people increases, the total cost of the picnic increases.

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:

m = (y - y')/x - x'

Now let's analyze the table:

The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:

(6, 52) and (9, 58).

Then the slope is:

a = (58 - 52)/9 -6 = 2

Then the line is something like:

y = 2*x + b

To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.

We will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b = 40

Then the linear equation is:

y = 2*x + 40

Now let's see which statements are correct.

a) The independent variable is the number of people.

True, the "x" represents the number of people.

b) The initial value (initial fee) for the picnic is $40.

True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.

c)The rate of change is $8.67 per person.

False, the rate of change is equal to the slope, in this case is $2 per person.

d) As the number of people increases, the total cost of the picnic increases.

True.

e)  If 4 people attended the picnic, the total cost would be $46.

To see if this is true or not, we just need to evaluate the function that we got in x = 4.

y = 2*4 + 40 = 48

So we can see that this is false.

Therefore, the correct statements are A, B, D

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The volume of the cone is approximately 134 ft cube.

The cone would fit in 4 times in the red beach ball.

The diameter of the red beach ball is 8 inches, then the cone has the same radius and a height of 8 inches .

Therefore, to know the number of times the beach ball will fit into the cone, we have to find the volume of each solid shape.

Therefore,

volume of the beach ball(sphere) = 4πr³

where

r = 8  /2 = 4 inches

volume of the beach ball(sphere) = 4 × π × 4³

volume of the beach ball(sphere) = 256π ft³

Therefore,

volume of the cone = 1 / 3 πr²h

where

volume of the cone = 1 / 3 × π × 4²  × 8

volume of the cone = 128π / 3

volume of the cone = 42.7π

volume of the cone = 134.078

volume of the cone ≈ 134 ft³

Therefore,

volume of beach ball / volume of cone = 256π / 42.7π = 5.99531615925

Therefore, the cone will fit 4 times into the red beach ball.

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Answer:

Mark's salary after 25 years is $52,499.39

Step-by-step explanation:

This situation can be modelled exponentially. We are given the starting amount, 32000, and the annual growth rate, 2%. This means that, for every year that passes, we'd have [tex][(32000)(1.02)][/tex] $ as the salary. As such, the model would be [tex]S(t) = 32000(1.02)^t[/tex]. We want to find Mark's salary 25 years from the starting point, t=25. Having developed a model for this situation, we can simply plug in 25 for t:

[tex]S(25) = 32000(1.02)^{(25)}[/tex]

[tex]S(25) = 52499.39[/tex]

Answer:

1095

Step-by-step explanation:

The result for all expressions are

a) r(t) = 6.5t radians

b) C(t) = 20cos(6.5*t) feet

c) H(t) = 36 - C(t)

The situation is depicted in the picture attached considering the center of the wheel as the center of the coordinates system.

Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply:

6.5 radians __________ 1 minute

r(t) radians ____________  t minutes

and obviously, r(t) = 6.5t radians

The height C(t) above the center after t minutes is given by

C(t) = 20cos(r(t)) ===>  C(t) = 20cos(6.5*t) feet

When C(t) < 0 means that derek wheel is below the center of the wheel.

Since the center of the Ferris wheel is 36 feet above the ground, the height H(t) above the ground after t minutes is given by

H(t) = 36 - C(t)

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well, he has left only 6 oz.

now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]

Answer:

C {(7, 2), (7, 0), (3,-2), (1,4)}

Step-by-step explanation:
In a function, x = 7 can't be at both 2 and 0 because it would not pass the vertical line test.

Answer:

9,510,223.49 galones!

Step-by-step explanation:

Primero, tienes que saber la cauntidad de los litros en un galon.

Hay 3.7854 litres en un galon

ahora, hacemos un ratio

1 galon = 3.7854 litres

? galones = 600,000 litres

Para encontrar la respuesta, divide 600,000 por 3.7854 para obtener la cauntidad de los galones

600,000 ÷ 3.7854 = 158,503.725 galones

158,503. 725 litres fluyen por segundo.

Hay 60 segundos en un minuto asi que, tenemos que multiplica nuestra respuesta por 60 para calcular nuestra respuesta final.

158,503. 725 × 60 = 9,510,223.49 galones!

A is negative semidefinite if and only if all the kth order principal minors of A are ≤ 0 if k is odd and ≥ 0 if k is even. The given statement is true.

What is a negative semidefinite matrix?

A Hermitian matrix with all of its eigenvalues being nonpositive is known as a negative semidefinite matrix. Using the Wolfram Language's NegativeSemidefiniteMatrixQ[m], a matrix may be checked to see if it is negative semidefinite.

The direction of space is inverted when the determinant is negative. If you give your fingers dimensions before transformation and they remain true after, it indicates that the orientation of space has not changed and the determinant is positive.

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The option that represents the arithmetic series is;

Option C: sum from k equals 0 to 4 of negative 12 plus 7 times k

An arithmetic series is defined as an arithmetic sequence, whereby each term of the series is gotten from the previous term by the addition or subtraction of a common term.

The series is given as;

-12 + (-5) + 2 + 9 + 16

By careful observation, we see that each term in the series is gotten from the previous term by the addition of 7.

The series here is therefore an example of arithmetic sequence.

The equation of the series when the first term is -12 can therefore be written as; -12 + 7·k

Where;

-12 is the first term

7 is the common difference

n is the number of terms

k = n - 1

When k = 0, we have;

-12 + 7·k

= -12 + 7 × 0

= -12

When k = 1, we have;

-12 + 7·k

= -12 + 7 × 1

= -5

When k = 2, we have;

-12 + 7·k

= -12 + 7 × 2

= 2

When k = 3, we have;

-12 + 7·k

= -12 + 7 × 3

= 9

When k = 4, we have;

-12 + 7·k

= -12 + 7 × 4

= 16

Therefore, we conclude that  using values of k that range from k = 0 to k = 4, the expression that represents the series is therefore the option C

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The exponential form of the given sequence is - [tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex] where x is a set of whole numbers and n is a set of natural numbers.

The given sequence is -  4, 5, 7, 11, 19, 35, 67, ...

the first term - [tex]t_1[/tex] is 4

Hence, we can write the sequence as follows-

4 + [tex]2^0[/tex] = 5

5+[tex](2)^1[/tex]=7

7+[tex](2)^2[/tex]=11

11+[tex](2)^3[/tex]=19

and so on.

Here, we are adding the previous term with the exponential form of 2.

thus, we can conclude that -

[tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex]

where,  x is a set of whole numbers, and n is a set of natural numbers.

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The polynomial that is the product of (4x−3)(x²+2x−6) is 4x³ + 5x² - 30x + 18

A polynomial simply refers to the expression that is composed of constant, variables, and exponents that are combined by mathematical operations.

The product of the polynomial will be:

= (4x −3)(x² + 2x − 6)

= 4x³ + 8x² - 24x - 3x² - 6x + 18

= 4x³ + 5x² - 30x + 18

The product is 4x³ + 5x² - 30x + 18.

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The probability the card drawn is a face card is 3/13. The probability the card drawn is not a face card is 10/13. The odds in favor of drawing a face card is 3/10. The odds against drawing a face card are 10/3.

There are 52 cards in a standard deck, and 12 of them are face cards (jack, queen, and king). Therefore, the probability of drawing a face card is 12/52, or 3/13.

The probability of not drawing a face card is 1 minus the probability of drawing a face card. Since the probability of drawing a face card is 3/13, the probability of not drawing a face card is 1 - 3/13, which is 10/13.

The odds in favor of drawing a face card are 3:10, or 3/10. The odds against drawing a face card are 10:3, or 10/3.

In summary:

The probability the  card drawn is a face card: 3/13

The probability the card drawn is not a face card: 10/13

Odds in favor of drawing a face card: 3/10

Odds against drawing a face card: 10/3

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Answer:

a. (0,1)

b. slope is -2

y-1=-2x

Step-by-step explanation:

Answer:

[tex]6^{\frac{1}{12}}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} } =\frac{6^{\frac{1}{3} } }{6^\frac{1}{4} }[/tex]

[tex]= 6^{\frac{1}{3}[/tex] ÷ [tex]6^{\frac{1}{4}}[/tex]

= [tex]6^{\frac{1}{3}-\frac{1}{4}}[/tex]

=[tex]6^{\frac{4}{12}-\frac{3}{12}}[/tex]

[tex]= 6^\frac{1}{12}[/tex]

Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 44 and 54 minutes is 0.8150= 81.5%.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

The relative frequency of classical CDs with playing time X between 44 and 54 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 44, hence:

X = 54:

Z = 3

Z = 3 has a p-value of 0.9987.

X = 54:

Z = -1

Z = -1 has a p-value of 0.1584.

0.9987 - 0.1584 = 0.8150

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Answer:

2n + 5 ≤ 7  The first choice

Step-by-step explanation:

2n + 5 ≤ 7  Subtract 5 from both sides.

2n + 5 - 5 ≤ 7 - 5

2n ≤ 2  Divide both sides by 2

[tex]\frac{2n}{2}[/tex] ≤ [tex]\frac{2}{2}[/tex]

n [tex]\leq[/tex] 1

Answer:

2x +5 ≤ 7

I hope my answer helps you.

To find out how much Mark still owes on his debt, we need to calculate the amount of interest that has accrued on the loan over the time that he has been paying it off. The interest on the loan is compounded semi-annually, so the amount of interest that accrues on the loan will be added to the principal every six months. Since Mark has been paying off his debt for 8 years and the interest is compounded semi-annually, he will have made 16 payments of $500.

To calculate the total amount of interest that has accrued on the loan, we need to know the original principal amount of the loan. Since we don't have that information, we won't be able to calculate the exact amount that Mark still owes on his debt. However, we can use the information that we have to make an educated guess.

If Mark has been making payments of $500 every six months for eight years, then he has paid a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest payments. If the interest on the loan is 2% compounded semi-annually, then the total amount of interest that has accrued on the loan over the past eight years is $8000 x 2% = $<<80002*.01=160>>160. This means that the original principal amount of the loan was $8000 - $160 = $<<8000-160=7840>>7840.

Since Mark still has 8 years left to pay off the debt, and he is making payments of $500 every six months, he will need to make a total of 8 years x 2 payments per year = <<82=16>>16 more payments of $500 to pay off the debt. This means that he will have to pay a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest over the next eight years.

Since the total amount of interest that has accrued on the loan over the past eight years was $160, the total amount of interest that will accrue on the loan over the next eight years is also $160. This means that the total amount of interest that Mark will have to pay over the next eight years is $160 x 2 = $<<160*2=320>>320.

Adding the amount of interest that Mark will have to pay over the next eight years to the amount of principal that he will have to pay, we find that the total amount that Mark will owe on the loan over the next eight years is $8000 + $320 = $<<8000+320=8320>>8320.

Therefore, if Mark has been paying off his debt for eight years and still has eight years left to pay, he still owes a total of $8320 on the loan.

Answer: The answer is -2.34

Step-by-step explanation: Get Good