A carnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. The probability of scoring 50 points is 60%, 75 points is 30%, and 150 points is 10%. The game operator designed a simulation using a random number generator to predict how many points would be earned for a turn.

Integer Value Points Frequency
0 - 5 50 55
6 - 8 75 32
9 150 13


10. What is game’s expected value of points earned for a turn?
(SHOW WORK)

The distance traveled by a car and the amount of gas used are directly proportional. The more distance covered, the more gas is consumed. This relationship can be quantified to make estimates for a specific car's fuel needs over given distances.

The relationship between the distance traveled by a car and the amount of gas in the car is directly proportional, that is, the more distance the car travels, the more gas it consumes. This correlation can be quantified for a specific car and then used to estimate gas consumption for given distances based on the car's average speed.

For example, let's say that a 2014 Lamborghini Aventador Roadster travels from Philadelphia to Atlanta, covering a distance of about 1250 km, and uses 213 L of gasoline. This gives us a standard ratio of gas consumption against the distance. We could say that for every 1250 km traveled, the car would need about 213 L of gas. This is a simplified model as there are other variables at play such as traffic conditions, velocity, etc.

Gasoline powers the engine which provides the force needed to move and maintain the car's speed. As the path traced (distance) increases, more fuel is consumed. This relationship of distance traveled and fuel consumed can be defined as a directly proportional relationship.

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A point is written as ( h, k) when a point is rotated 90 degrees about the origin the new point becomes (-k,h)

s is located at (5,4) where h = 5 and k = 4

The rotated point would be located at (-4,5 )

Answer:

54 cm^2

Step-by-step explanation:

The area of a right triangle is the easiest triangle for which you can find the area.

The area of any triangle is Base * height / 2

The base and height of a right triangle are always the two sides that are not the hypotenuse. In this case

base = 9

height = 12

Area = 9 * 12/2

Area = 54 square cm.

Answer: A

Answer:

The book value for the van at the end of first year will be $30400

Step-by-step explanation:

Cost of van = $38,000

Amount of depreciation after one year = 20%

Finding 20% of 38,000

=38,000 *(20/100)

= 7600

so, amount of van after 1 year = 38,000 - 7600

= 30400

So, the book value for the van at the end of first year will be $30400

The book value of the Shining Star Preschool's van at the end of the first year is $30,400, after depreciating 20% of its original cost of $38,000 using the MACRS method.

Using the Modified Accelerated Cost Recovery System (MACRS), the van is depreciated over 6 years with fixed percentages assigned to each year. The first year's depreciation is 20% of the purchase price.

To calculate the depreciation expense for the first year, we multiply the purchase price by the first year's depreciation rate:

Depreciation Expense (Year 1) = Purchase Price  imes Depreciation Rate

Depreciation Expense (Year 1) = $38,000  imes 20%

Depreciation Expense (Year 1) = $7,600

Now, we subtract this depreciation expense from the purchase price to find the book value at the end of the first year:

Book Value (End of Year 1) = Purchase Price - Depreciation Expense (Year 1)

Book Value (End of Year 1) = $38,000 - $7,600

Book Value (End of Year 1) = $30,400

Therefore, the book value of the van at the end of the first year is $30,400.

Answer:

One Solution

(2, 1)

Step-by-step explanation:

We have the following system of equations

[tex]x+4y = 6\\y=2x-3[/tex]

To solve the system, substitute the second equation in the first equation and solve for the variable x

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

[tex]x+8x-12 = 6[/tex]

[tex]9x = 6+12[/tex]

[tex]9x = 18[/tex]

[tex]x = \frac{18}{9}[/tex]

[tex]x = 2[/tex]

Now substitute the value of x into any of the two equations and solve for the variable y.

[tex]y=2(2)-3[/tex]

[tex]y=4-3[/tex]

[tex]y=1[/tex]

Finally the system of equations has one solution

(2, 1)

Answer:

x = 5/2

Step-by-step explanation:

log4(x^2+5x)-log8(x^3)=1/log3(4)

log(x^2 + 5 x) / log(4) - log(x^3) / log(8) = log(3) / log(4)

log(x (x+5))/log(4) - log(x^3) / log(8) = log(3) / log(4)

(3 log(x (x+5)) - 2 log(x^3)) / log(64) = log(3) / log(4)

3 log(x (x+5)) - 2 log(x^3) = 3 log(3)

log((3 x)/(x+5))=0

x=5/2

Answer:

5/2

Step-by-step explanation:

So first of all 1/log_3(4) can be written as log_4(3)...

So everything is base 4 except the log_8(x^3)...

We can play with this to get it so that the base is 4.

Let y=log_8(x^3) then 8^y=x^3

Rewrite 8 as 4^(3/2) so we have

4^(3/2 *y)=x^3

Now rewriting in log form gives: log_4(x^3)=3/2*y

Then solving that for y gives 2/3*log_4(x^3) or log_4(x^2)... let's put it back into the equation:

log_4(x^2+5x)-log_4(x^2)=log_4(3)

log_4((x^2+5x)/x^2)=log_4(3)

Set insides equal:

(x^2+5x)/x^2=3

Cross multiply:

x^2+5x=3x^2

Subtract 3x^2 on both sides:

-2x^2+5x=0

Factor

-x(2x-5)=0

So solutions are 0 and 5/2.  

We have to verify these...

0 isn't going to work because we can't do log of 0

it makes x^2+5x 0 and x^3 0

The only solution is 5/2.

Answer:

D

Step-by-step explanation:

Using the rules of exponents

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

• [tex]a^{\frac{1}{2} }[/tex] ⇔ [tex]\sqrt{a}[/tex]

Hence

[tex]36^{-\frac{1}{2} }[/tex] = [tex]\frac{1}{36^{\frac{1}{2} } }[/tex] = [tex]\frac{1}{\sqrt{36} }[/tex] = [tex]\frac{1}{6}[/tex]

For this case we must find an expression equivalent to:

[tex]36 ^ {- \frac {1} {2}}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, rewriting the expression we have:

[tex]\frac {1} {36 ^ {\frac {1} {2}}}=[/tex]

By definition of power properties we have to:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]\frac {1} {\sqrt {36}} =\\\frac {1} {\sqrt {6 ^ 2}} =\\\frac {1} {6}[/tex]

Answer:

Option D

Answer:

See below.

Step-by-step explanation:

The zeroes of the equation will  not be real so the graph will not pass through the x-axis.

Answer:

17

Step-by-step explanation:

QS and RS equal the same

5x - 8 = 3x + 2

-3x  +8    -3x +8

2x = 10

x = 5 you would then plug x into QS

5(5) - 8

25 - 8

17

Answer:

17

YA

Step-by-step explanation:

Answer:

tan(x) = 0

Step-by-step explanation:

We know that tan = sin /cos

tan (x) = sin(x)/ cos (x)

Substituting what we know, sin (x) =0 and cos(x) =1

          = 0/1

         =0

Answer:

Its tan(x) = 0 on Edge 2020.

Step-by-step explanation:

On jah.

Answer:

12/5

Step-by-step explanation:

tan(F)    =opposite side to angle F  over (Fraction Bar) adjacent side to angle F

[tex] \tan(F)=\frac{\text{ opposite side to angle F } }{ \text{ adjacent side to angle F} } [/tex]

The side that is opposite is the side that doesn't include F.

The side the is adjacent will include F (this is not the hypotenuse which is opposite the 90 degree angle).

So

[tex]\tan(F)=\frac{12}{5}[/tex]

The standard equation of a circle is in the form:

(x-a)^2 + (y-b)^2 = r^2

where; a is the x coordinate of the center, b is the y coordinate of the center, and r is the radius of the center.

In this case, a is -5, b is 2, and r is 7.

Therefore, the equation of this circle would be

(x+5)^2 + (y-2)^2 = 49

Answer:

Second option: [tex](x +5)^2 + (y -2)^2 =49[/tex]

Step-by-step explanation:

The center-radius form of the circle equation is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where "r" is the radius and the center is at the point [tex](h,k)[/tex]

Since the center of this circle is at the point [tex](-5, 2)[/tex], we can identify that:

[tex]h=-5\\k=2[/tex]

We know that the radius is 7, then:

[tex]r=7[/tex]

Now we must substitute these values into the equation  [tex](x - h)^2 + (y - k)^2 = r^2[/tex] to find the equation of this circle.

This is:

 [tex](x - (-5))^2 + (y - 2)^2 = (7)^2[/tex]

 [tex](x +5)^2 + (y -2)^2 =49[/tex]

Answer:

Option 2) When the x-value is 0, the y-value is 1.

Step-by-step explanation:

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Remember that in a direct variation

For x=0, the value of y is equal to zero too

therefore

The graph is not a direct variation , because

When the x-value is 0, the y-value is 1.

Answer:

c = $5.00

Step-by-step explanation:

Let c = the cost of each candy bar

3 + 8c = 43

8c = 40

Answer:

Option C.

Step-by-step explanation:

Domain of any function is always represented by x - values when graphed.

Option A.

it has only one x value that is x = 2

Not correct.

Option B.

In this graph straight line doesn't intersect x - axis at x = -2 and -4.

So Not correct.

Option C.

If we see the x- values of the given set of coordinates, we find domain of the given function is { -4, -2, 2, 4}

Therefore, it's correct option.

Option D.

Given set with the coordinates shows domain set as {1, 0, 2, 6}

So it's not the answer.

Therefore, option C is correct.

Answer: 5/6

Step-by-step explanation:

2/3=4/6

1/6 + 4/6 = 5/6

Answer:

5/6

Step-by-step explanation:

you can rewrite 2/3 plus 1/6 as:

2/3+1/6

To add fractions you need to have a common denominator (the bottom half of the fraction). In this case 6 is a common denominator. To convert 2/3 we need to multiply it by the appropriate form of 1. We can multiply by 1 because 1 times anything does not change the value:

(2/2⋅2/3)+1/6⇒2/2⋅2/3+1/6⇒4/6+1/6⇒5/6

Answer:

6e^2f (3f^2-2e)

Step-by-step explanation:

18 e^2 f^3 - 12 e^3 f

18 e^2 f^3 = 2*3*3 ee fff

12 e^3 f = 2*2*3 eee f

The common terms are 2 *3*eef

Factor that out

2*3*eef (3ff - 2e)

Combine like terms

6e^2f (3f^2-2e)

Answer:

T'={1}

Step-by-step explanation:

Definition:

Given a set T, the complement of T is the set of all elements in the universal set U, but not in T.

We can write T^c  

You can also say complement of T in U

Complement of T( T')= U-T

where U={1,2} and T={2}

Now put the sets of U and T in the formula:

T'=U-T

T'={1,2}-{2}

T'{1}

Thus the Complement of T(T')={1}....

The complement of a set T in a universal set U is all the elements in U that are not in T. If U={1,2} and T={2}, the all the elements in U that are not in T corresponds to {1}. So, the complement of T is {1}.

In the field of Mathematics, specifically in set theory, the complement of a set T in a universal set U is the set of all elements in U that are not in T. When we say complement of T, we are referring to the set of all outcomes in the universal set U that are NOT in T.

In this case, the universal set U={1,2}, and the event T={2}. Therefore, the complement of the set T in relation to U would be the set of all elements in U that are not in T. Hence, since 2 is in T, the only number left in U that is not in T is 1. So, the complement of T is {1}.

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Answer:

6

Step-by-step explanation:

I added 2 cracker jacks to get how much money he had left the kept subtracting. 99 from the money he had left

Answer:

step 4 it not overdrawn any more it postive 46 not negtive

Step-by-step explanation:

Answer:

Step 4 : the account is overdrawn by $46

Step-by-step explanation:

Please see that when an account is in negative figure , we call it overdrawn. but when it is in positive figure we called is in credit.

Here we see from the calculation that the final balance available in the account of teller is $46, hence the account is having positive balance . hence it is not overdrawn.

So the mistake is in last step.

Answer:

a. 2016-112x

Step-by-step explanation:

because each month he need to pay $112 so it have to be multiplied to the number of month and then answer should be subtracted from 2016

Answer:

Step-by-step explanation:

Answer:

= 5.099 i

Step-by-step explanation:

The problem tells us to find the square root of -36 +10

√(-36 + 10)

= √(-26)

Which is an imaginary number

Lets remember that, √(-1) = i

= i*√(26)

= 5.099 i

Please see attached images for more information

[tex]\bf \cfrac{15\sqrt{6}}{3\sqrt{5}}\implies \cfrac{15\sqrt{6}}{3\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{15\sqrt{6}\cdot \sqrt{5}}{3(\sqrt{5})^2}\implies \cfrac{15\sqrt{6\cdot 5}}{3(5)} \\\\\\ \cfrac{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\sqrt{30}}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \sqrt{30}[/tex]

Answer:

11-3i-4-5i

=11-4-3i-5i

=7-8i

Follow below steps:

The difference of the complex numbers (11-3i) and (4+5i) is computed by subtracting the real and imaginary parts separately. The real parts are 11 and 4, and their difference is 11 - 4 = 7. The imaginary parts are -3i and +5i, and their difference is -3i - 5i = -8i. Therefore, the difference of the two complex numbers is 7 - 8i.

Answer:

The diameter of circle d is 9.03

Step-by-step explanation:

Circumference of Circle = 28.36

We need to find the diameter of circle.

The formula used to find the circumference of circle is:

C = 2πr

we know that radius is half of diameter

so r = d/2

Putting value of r in above equation

C = 2π(d/2)

C = πd

The value of π is 3.14. finding value of d

28.36 = 3.14 * d

=> d = 28.36 / 3.14

d = 9.03

So, the diameter of circle d is 9.03

Answer:

The diameter is approximately 9 units

Step-by-step explanation:

Circumference is given by

C = pi *d

28.36 = pi *d

Let use 3.14 for pi

28.36 = 3.14 *d

Divide each side by 3.14

28.36 /3.14 = 3.14 d/3.14

9.031847134 = d

The diameter is approximately 9 units

Answer:

[tex]\boxed{\text{A. 7 in}}[/tex]

Step-by-step explanation:

The formula for the arc (s) of a circle is

[tex]s = r\theta \times \dfrac{\pi}{180^{^{\circ}}}[/tex]

where θ is measured in degrees.

Data:

r = 5 in

θ = 75°

Calculation:

[tex]s = \text{5 in} \times 75^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{7 in}\\\\\text{The length of the arc is }\boxed{\textbf{7 in}}[/tex]

Answer:

3V2

Step-by-step explanation:

V18

V9 times 2 equals 18

V3 to the second power because 3 times 3=9 so we get 3V2

Answer:

0.625N

Step-by-step explanation:

                                        0.50N

0.80M = 0.50N, so M = ------------

                                          0.80

and so:

                0.50N

N*M = N*------------ = (5/8)N, or 0.625N

                   0.80

For this case we must find the value of the variable "x" of the following expression:

[tex]2 (3x-1) \geq4x-6[/tex]

We apply distributive property to the terms within parentheses: [tex]6x-2 \geq4x-6[/tex]

We subtract 4x on both sides:

[tex]6x-4x-2 \geq-6\\2x-2 \geq-6[/tex]

We add 2 to both sides:

[tex]2x \geq-6 + 2\\2x \geq-4[/tex]

We divide between 2 on both sides:

[tex]x \geq \frac {-4} {2}\\x \geq-2[/tex]

Answer:

[tex]x \geq-2[/tex]

Answer: [tex]x\geq -2[/tex]

Step-by-step explanation:

Given the inequality [tex]2(3x - 1) \geq 4x -6[/tex] you need to solve for "x".

Apply Distributive property on the left side of the equation:

 [tex]6x - 2 \geq 4x -6[/tex]

Now add 2 to both sides:

 [tex]6x - 2+(2) \geq 4x -6+(2)[/tex]

 [tex]6x \geq 4x -4[/tex]

The next step is to subtrac [tex]4x[/tex] from both sides:

 [tex]6x-(4x) \geq 4x -4-(4x)[/tex]

 [tex]2x \geq -4[/tex]

And finally, divide both sides by 2:

[tex]\frac{2x}{2}\geq  \frac{-4}{2}\\\\x\geq -2[/tex]