One month Trey rented three movies and five video games for a total of $35. The next month he rented six movies and two video games for a total of $20. Find the rental cost for each movie and each video game.

(f . g)(x) is multiplication of f(x) and g(x). So,

(f. g)(x) = [tex]49x^{4}-70x^{3}+319x^{2} -420x+150[/tex] . Option (c) is correct answer.

A new function that is the product of the original two functions is created when two independent functions are multiplied together.

To multiply two functions together, perform these steps:

In given question we have two functions

f(x) = 7x³-5x²+42x-30

g(x) = 7x - 5

we need to find (f.g)(x) that is nothing but multiplication of f(x) and g(x).

So multiplying both the functions, we get

(f.g)(x) = f(x). g(x)

=( 7x³-5x²+42x-30)*(7x - 5)

=(49[tex]x^{4}[/tex]-35x³-35x³+25x²+294x²-210x-210x+150)

= [tex]49x^{4}-70x^{3}+319x^{2} -420x+150[/tex]

So, option (c) is correct answer.

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The statement that is true about the proportional relationship:

C = 13.99*p

Is "For $13.99, you can buy 1 pound of shrimp"

Here we have the proportional relationship:

C = 13.99*p

Where c is the total cost and p is the number of pounds of shrimp bought at a grocery store.

This means that if you buy one pound  (p = 1) the total cost will be:

C = 13.99*1

C = 13.99

So each pound costs $13.99

Then the true statement about the proportional relationship is:

" For $13.99, you can buy 1 pound of shrimp."

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Answer:

"For $13.99, you can buy 1 pound of shrimp"

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

we 2 minus 1 and plus 3 (i forgot)

By conducting mathematical operations, we know that John's gross pay will be $1,012 if he works 44 hours a week.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.

The order of operations refers to the rules that specify how to solve an expression including many operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, we know that:

John earns $22 per hour for the first 40 hours of a week.

After every additional hour, he earns 1.5 times $22 each hour.

22 * 1.5 = $33

So, John's gross pay if he worked 44 hours will be:

22*40 + 33*4

880 + 132

$1,012

Therefore, by conducting mathematical operations, we know that John's gross pay will be $1,012 if he works 44 hours a week.

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Hello,

I hope you and your family are doing well!

The answer is y = 5 (See below for the explanation).

To find a linear equation representing a line passing through two points, you can use the slope-intercept form of the equation, which is written as y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To find the slope of the line, you can use the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the two given points, we get:

m = (5 - 5) / (-8 - 3) = 0 / -11 = 0

Since the slope of the line is 0, the line is horizontal and passes through both points at the same y-value (5). The x-intercept (the point at which the line crosses the x-axis) is not relevant in this case.

Therefore, the linear equation representing this line is y = 5.

Happy Holiday & New Year!

Please give this answer 5 stars and brainliest if you find it helpful.

Best,

Answer:

y=5

Step-by-step explanation:

y=mx+b

if you put your two point on a graft, they are on same line for the y-intersept. So if that is true then your answer has to y=5

3. x < 3

Explanation:

The inequality represents the greater than ">" or lesser than "<".

∵ The temperature is less than 3 the answer is x < 3.

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The following inequality represents temperatures below 3°F

c. x < 3

A relationship between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. So inequality results from an imbalance. For instance, let's say you want to spend $250 on a new bicycle but only have $225. The fact that you are comparing two non-equal numbers makes it an inequality as well.

When two quantities are equal, the symbol "=" is used, and when they are not equal, the symbol "" is used to denote that. When two values are not equal, the first value may be greater than (>), less than (<), greater than equal to (≥), less than equal to (≤). In light of the example given above, 250 > 225.

Solution:

The less than symbol represented as < is only available in x < 3, it is also available in  x < -3 but we have given that temperature ins 3°F and not -3°F.

Thus the correct answer is c. x < 3

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The graph of the function f(x) = { x + 1 } at different domain are plotted and attached

{ if x < 0 }

{ if 0 < x < 1 }

{ if x > 1 }

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

The graph of f(x) = x + 1 for different domain is plotted and attached

{ if x < 0 } the domain includes { -∞....-3 -2 -1}

{ if 0 < x < 1 } the domain includes { 0...0.7 0.8 0.9}

{ if x > 1 } the domain includes { 0 1 2 3 4 5...∞ }

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The ratio of the volume of the second cylinder to the volume of the first cylinder is 25.

To find the ratio of the volume of the second cylinder to the volume of the first cylinder, we need to calculate the volumes of both cylinders and then compare them.

The formula to calculate the volume of a right circular cylinder is given by V = πr^2h, where V represents the volume, r is the radius, and h is the height.

For the first cylinder:

Radius (r₁) = 3 centimeters

Height (h₁) = 5 centimeters

Volume of the first cylinder (V₁) = π * (3 cm)^2 * 5 cm

                             = 45π cm³

For the second cylinder:

Radius (r₂) = 15 centimeters

Height (h₂) = 5 centimeters

Volume of the second cylinder (V₂) = π * (15 cm)^2 * 5 cm

                              = 1125π cm³

To find the ratio of the volumes, we divide the volume of the second cylinder by the volume of the first cylinder:

Ratio = V₂ / V₁

     = (1125π cm³) / (45π cm³)

     = 25

Therefore, the ratio of the volume of the second cylinder to the volume of the first cylinder is 25.

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The required fraction that makes the equation true is 3/15.

What is a fraction?

Fractions represent parts of a whole or group of objects. A fraction is made up of two parts. The number at the top of the line is referred to as the numerator. It specifies the number of equal parts of the whole or collection that are taken. The denominator is the number below the line. It displays the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.

Let x be the required fraction.

Blank divided by 3/7 = 7/15

Then, [tex]\frac{x}{3/7} = \frac{7}{15}[/tex]

or, [tex]\frac{7x}{3} = \frac{7}{15}[/tex]

or, 7x = 21/15

or, x = 3/15

Hence the required fraction that makes the equation true is 3/15.

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The system of linear equations that represents the given situation is

x = y + 10

x + y = 64

From the question, we are to write a system of linear equations that represents the given situation

From the given information,

"There are a total of 64 students in a drama club and a yearbook club"

Then, we can write that

x + y = 64

Also,

"The drama club has 10 more students than the yearbook club"

Then, we can write that

x = y + 10

Hence, the system of equations is

x = y + 10

x + y = 64

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Answer:

30%

Step-by-step explanation:

See Venn diagram below

The population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

What is an exponential function?

The definition of an exponential function is given by the equation

y = aeᵇˣ, where a and b are constants.

The given function is f(x) = 87000(0.9)ˣ.

Given that x = 0 represents the year 2010.

Therefore, x= 5 represents the year 2015.

Substitute x = 5 into the given function:

f(5) = 87000(0.9)⁵

    ≈ 51373

Hence, the population of Orange country is about 51373 in 2015.

Now, the population of Greene country was 78000 in 2010 and has decreased exponentially at a rate of 8% each year.

The population of Greene city after 5 years is given by:

78000(1-8%)⁵

= 78000(1 - 0.08)⁵

= 78000(0.92)⁵

= 51408

Therefore, the population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

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A rectangular prism with 10 inches in height and 2 inches in base length and height. The sides are labeled A and the base is labeled B. the total area of all the copies of Rectangle A is 80 square inches.

b) 8 square inches.

c) 88 square inches.

Generally, To find the area of the Face A rectangles, you need to multiply the length and the height of one rectangle.

In this case, the length is 10 inches and the height is 2 inches, so the area of one rectangle is 10*2=20 square inches.

There are four copies of Rectangle A in the prism, so the total area of all the copies of Rectangle A is

20*4=80 square inches.

b) To find the area of the Face B squares, you need to multiply the length and the height of one square. In this case, both the length and the height are 2 inches, so the area of one square is

2*2=4 square inches.

There are two copies of Square B in the prism, so the total area of all the copies of Square B is

4*2=8 square inches.

To find the total surface area of the prism, you need to add the areas of all the faces. In this case, the total surface area is

80+8=88 square inches.

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THE COMPLETE QUESTION WAS NOT FOUND

(a) The probability of each possible number of sets that are acceptable without any adjustment can be found using the binomial distribution formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where:

P(x) is the probability of x successes in n trials

n is the number of trials (in this case, the number of sets produced in a week)

x is the number of successes (in this case, the number of sets that are acceptable without any adjustment)

p is the probability of success (in this case, the probability that a set is acceptable without any adjustment, which is 0.70)

Plugging in the values, we get:

P(0) = (3 choose 0) * 0.70^0 * (1-0.70)^(3-0) = 0.028

P(1) = (3 choose 1) * 0.70^1 * (1-0.70)^(3-1) = 0.081

P(2) = (3 choose 2) * 0.70^2 * (1-0.70)^(3-2) = 0.162

P(3) = (3 choose 3) * 0.70^3 * (1-0.70)^(3-3) = 0.126

(b) To find the expected number of sets that are tested and found to be acceptable without adjustment, we can use the formula:

E(x) = n * p

Plugging in the values, we get:

E(x) = 3 * 0.70 = 2.1

The expected number of sets that are tested and found to be acceptable without adjustment is 2.1.

(c) The cumulative probability distribution for the number of sets that are tested and found to be acceptable without adjustment is the sum of the probabilities of each possible number of successes. For example, the probability of 0 or 1 successes is the sum of the probabilities of 0 and 1 successes: P(0 or 1) = P(0) + P(1) = 0.028 + 0.081 = 0.109. The probability of 0, 1, or 2 successes is the sum of the probabilities of 0, 1, and 2 successes: P(0 or 1 or 2) = P(0) + P(1) + P(2) = 0.028 + 0.081 + 0.162 = 0.271.

The cumulative probability distribution for the number of sets that are tested and found to be acceptable without adjustment is:

P(0) = 0.028

P(0 or 1) = P(0) + P(1) = 0.028 + 0.081 = 0.109

P(0 or 1 or 2) = P(0) + P(1) + P(2) = 0.028 + 0.081 + 0.162 = 0.271

P(0 or 1 or 2 or 3) = P(0) + P(1) + P(2) + P(3) = 0.028 + 0.081 + 0.162 + 0.126 = 0.397

The corresponding graph would be a step function with a step at each possible value of x (in this case, 0, 1, 2, and 3) and the corresponding probability at each step.

Answer:

a²b²

Step-by-step explanation:

Variables cancel out when they are divided by itself because they represent the same thing.

a³ / a = a²

b^4/b² = b²

Thus, the final answer is a²b².

Answer:  Choice B

[tex]2k^5\sqrt[3]{25}[/tex]

================================================

Work Shown:

[tex]\sqrt[3]{200k^{15}}\\\\\sqrt[3]{8*25k^{5*3}}\\\\\sqrt[3]{8*25(k^5)^3}\\\\\sqrt[3]{8(k^5)^3*25}\\\\\sqrt[3]{8(k^5)^3}*\sqrt[3]{25}\\\\2k^5\sqrt[3]{25}[/tex]

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

Explanation:

The goal is to factor the radicand in such a way that we pull out perfect cube factors.

Notice that 200 = 8*25 and 8 is a perfect cube (since 2^3 = 8). It is the largest perfect cube factor of 200.

We can rewrite the k^15 as k^(5*3) which is equivalent to (k^5)^3

Once these perfect cube factors are pulled out, they cancel with the cube root to get what you see above.

The inequality which represents the number of people who can go to the amusement park will be 14.75 + 11.25x ≤ 80.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given,

Total budget = $80

Tickets cost of x number of tickets = 11.25x

Parking cost + tickets cost ≤ total budget

14.75 + 11.25x ≤ 80

Hence"The inequality which represents the number of people who can go to the amusement park will be 14.75 + 11.25x ≤ 80".

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Answer:32

Step-by-step explanation:

Assuming this is a triangle, there are three sides.

All sides of a triangle must add up to 180 degrees

180-108-40 = 32

The corresponding z-score for each student are as follows;

College student, z = 0.73.

University student; z = 0.67.

Mathematically, the z-score of a given sample size or data set can be calculated by using this formula:

Z-score, z = (x - μ)/σ

Where:

For the College student, we have the following:

Sample score = $9935.

Standard deviation = $1867.

Mean score = $8581

Z-score, z = (9935 - 8581)/1867

Z-score, z = 1354/1867

Z-score, z = 0.73.

For the University student, we have the following:

Sample score = $11,757.

Standard deviation = $2133.

Mean score = $10,339

Z-score, z = (11,757 - 10,339)/2133

Z-score, z = 1,418/2133

Z-score, z = 0.67.

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You can afford the amount of $24588.44 expensive a car.

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

The monthly payment = Total payback / No. of payment

$325 = Total payback / 108

Total payback = $325 x 108 = $351,00

Let the affordable amount of the car would be P

The total payback = P× r/100 × T + P

Here P, r = 4.75, and T = 9 years

$351,00 = P × (4.75/100 × 9 + 1)

$351,00 = P × ( 0.4275 + 1)

$351,00 = P × 1.4275

P = 351,00 / 1.4275

Apply the division operation, and we get

P = $24588.44

Therefore, you can afford the amount of $24588.44 expensive a car.

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The number of possible combinations is 330.

What is combination?

The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.

The toppings for a pizza is pepperoni, pineapple, sausage, onions, frogs. peppers, ham, fish, olives, mushrooms, tomatoes.

The number of toppings is 11.

you choose exactly 4 toppings for a pizza.

Here r = 4

n = 11

The formula of combination rCn.

The number of possible combinations of a pizza is

₁₁C₄ = 11!/[4! (11-4)!]

₁₁C₄ = 11!/[4! 7!]

₁₁C₄ = 330

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Step-by-step explanation:

Exponential Function, example y=e×;

Cubic Function, example y=x³;

Quadratic Function, example y=x²;

Linear Function, example y=x-1;

Absolute Function, example y=|x|;

Cube Root Function, example y=∛x;

Constant Function, example y=2.

Using inequality graphing, we get

1 = option A and E

2= none

3= option B and G

4= option C and I

How can graph inequalities?

1. Rewrite the equation with "y" on the left and the rest of the terms on the right.

2. Draw the "y=" line (with a solid line for y or y and a dotted line for y or Y>).

3. Use a shaded line to indicate larger than or less than (y> or y) or vice versa.

The graph corresponding to the options is as follows

graph 1 corresponds to equations A and E

Graph 3 corresponds to equations B and G

Graph 4 corresponds to equations C and I

The 4-letter word is CAGE

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Answer: Assign the numbers 1-9 to represent a made goal and the number 10 to represent a missed goal.

Step-by-step explanation: The coach wants to ESTIMATE the number of goals the player will make out of 10 attempts. Since someone can’t make 8.8 goals, we can round up to 9 goals.

Answer:

9g

Step-by-step explanation:

Answer:

from the options given it seems that it can only be divided by 3 or –3 which will give you 147 or – 147

Step-by-step explanation:

i hope this helps

Answer:3/c

i am doing this for extra characters

Answer:

[tex]y=-1/4x+3[/tex]

Step-by-step explanation:

Slope-intercept form is of the form y=mx+b where m is the slope and b is they y-intercept. To solve for the slope, we take the difference of two y-coordinates divided by the x-coordinates difference. Doing this, we get

[tex](3-1)/(0-4)[/tex]

[tex]=-1/4[/tex]

This is our slope. The y-intercept is 3, because the line hits the y-axis when y=3.

Thus, our equation is y=-1/4x + 3.

Feel free to contact me with any questions. I hope this helps!

Answer:

(0,3)

Step-by-step explanation:

(0,3) is not on the graph

After 25 years, about 52g of the sample will be left and the sample never reaches half of its original amount

From the question, we have the following parameters that can be used in our computation:

A(t)= 200е⁻⁰⁰⁵⁴⁺

Also from the question, we have

The variable t represents the number of years

This means that

t = 25, in this case

So, we have

A(25)= 200е⁻⁰⁰⁵⁴ ˣ ²⁵

Evaluate the above equation

A(25)= 51.848052128

Approximate

A(25) = 52

This means that the remaining sample is 52 grams

Here, we have

A(t) = 0.5 * 200

A(t) = 100

Substitute the known values in the above equation, so, we have the following representation

200е⁻⁰⁰⁵⁴⁺ = 100

Divide both sides by 100

е⁻⁰⁰⁵⁴⁺ = 0.5

Take the natural logarithm of both sides

0.054t = -0.69314718056

So, we have

t = -0.69314718056/0.054

Evaluate

t = -13

Time cannot be negative

This means that it never reaches half of its original amount

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Answer:

To earn $65 in interest in 16 months at a simple interest rate of 3%, you would need to invest $2,166.67. The formula for calculating simple interest is I = P * R * T, where I is the interest earned, P is the principal amount invested, R is the interest rate, and T is the time in years. In this case, we are given that the interest rate is 3%, the time is 16 months, and the interest earned is $65, so we can plug these values into the formula to solve for the principal amount invested:I = P * R * T

$65 = P * 0.03 * (16/12)

$65 = P * 0.03 * (4/3)

$65 = P * 0.01

P = $2,166.67Therefore, to earn $65 in interest in 16 months at a simple interest rate of 3%, you would need to invest $2,166.67.