what's the domain and range of the function f(x) = 5(4)^x + 2​

The required slope of the linear function is $30, and the y-intercept is $75.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

To find the slope of the linear function, we need to calculate the change in cost divided by the change in time.

Change in cost = $285 - $105 = $180

Change in time = 7 - 1 = 6

Slope = Change in cost / Change in time = $180 / 6 = $30

To find the y-intercept, we can use the point-slope form of a linear equation, y = mx + b, where y is the cost, x is the time, m is the slope, and b is the y-intercept.

Using the point (1, $105), we can substitute x = 1 and y = $105 into the equation and solve for b:

$105 = $30(1) + b

b = $105 - $30 = $75

Therefore, the slope of the linear function is $30, and the y-intercept is $75.

The linear function can be written as: y = $30x + $75, where x is the number of months of membership and y is the cost of the membership.

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The value of the hypotenuse , x is 19.2

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

Rise = 17

Length = 9

The value of the hypotenuse , x is calculated as

x^2 = Rise^2 + Length^2

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

x^2 = 17^2 + 9^2

So, we have

x^2 = 370

Take the square root of bpth sides and evaluate

x = 19.2

Hence, the value of x is 19.2

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The exponential function that models this situation is y = 11,000 (0.85)ˣ. The correct answer would be an option (B).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The table below shows the value in dollars of a car at the end of x years.

Number of Years,       xValue, v(x) (dollars)

0                                              11,000

1                                                9,350

2                                               7,948

3                                               6,755

Let the formula for an exponential function would be as

⇒ v(x) = abˣ

Substitute the value of x = 0 and v(x) = 11,000 in the above equation,

⇒ 11,000 = ab⁰

⇒ a = 11,000

Now, substitute the value of x = 1 and v(x) = 9,350, and we get

⇒ 9,350 = ab¹

⇒ 9,350 = (11,000)b

⇒ b = 9,350/11,000

⇒ b = 0.85

Substitute the value of a = 11,000 and b = 0.85 in v(x) = abˣ,

⇒ y = 11,000 (0.85)ˣ

Thus, the exponential function is y = 11,000 (0.85)ˣ.

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No, the table is not a square.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

Given that, Seth made a small rectangular table having sides 36" and 18", and the diagonal measures 43",

Squares has congruent sides,

But here the sides are 36" and 18"

Hence, the table is not a square.

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The value for x is x= [tex]sin^{-1[/tex] (0.5425).

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

H= 25

B = 21

Using Pythagoras theorem

P = √H² - B²

P = √25² - 21²

P = √184

P =  2√46

Using Trigonometry

sin x = P / H

sin x = 2√46 / 25

x= [tex]sin^{-1[/tex] (0.5425)

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Based on the provided information, a. Ramon reads faster and b.it will take Ramon approximately 16.77 hours to read the entire novel if he continues to read at his current rate.

To answer this question, we need to calculate the reading rate of both Skyler and Ramon, and then compare them to see who reads faster. We also need to use Ramon's reading rate to calculate how long it will take him to read the entire novel.

a. To calculate Skyler's reading rate, we can divide the number of pages she has read by the number of hours she has spent reading:

Skyler's reading rate = 145 pages / 5 hours = 29 pages/hour

Similarly, we can calculate Ramon's reading rate:

Ramon's reading rate = 124 pages / 4 hours = 31 pages/hour

Since Ramon's reading rate is higher than Skyler's, Ramon reads faster.

b. To calculate how long it will take Ramon to read the entire novel, we can use his reading rate and the total number of pages in the novel:

Time = Total number of pages / Reading rate

Time = 520 pages / 31 pages/hour = 16.77 hours

So, it will take Ramon approximately 16.77 hours to read the entire novel if he continues to read at his current rate.

In conclusion, Ramon reads faster than Skyler, and it will take him approximately 16.77 hours to read the entire Vigo the Vampire Hunter novel at his current reading rate.

Note: The question is incomplete. The complete question probably is: The new Vigo the Vampire Hunter novel is 520 pages. Skyler has read 145 pages in 5 hours. Ramon has read 124 pages in 4 hours. a. Who reads faster, Skyler or Ramon? b. How long will it take Ramon to read the entire novel if he continues to read at his current rate? Explain.

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The conversion from ml to teaspoon is 1 ml = 0.202884 tsp. This means that 30 ml is equal to 6.08652 teaspoons.

This conversion can be calculated by multiplying the volume in ml with 0.202884. The formula for this conversion is Volume (tsp) = Volume (ml) x 0.202884. For example, if the volume is 30 ml, the calculation would be 30 ml x 0.202884 = 6.08652 tsp. This means that 30 ml is equal to 6.08652 teaspoons.To convert between other units of volume, such as liters and gallons, the conversion factor must be changed. For example, to convert from liters to teaspoons, the conversion factor would be 0.0147867. To convert from gallons to teaspoons, the conversion factor would be 76.7526. It is important to remember that the conversion factor must be changed depending on the units being converted.In conclusion, 30 ml is equal to 6.08652 teaspoons. The conversion from ml to teaspoon is done by multiplying the volume in ml with 0.202884. To convert between other units of volume, the conversion factor must be changed.

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The value of x in the triangle is 8.2 units

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

Angle = 12 degrees

Hypotenuse = x

Length = 8

The length of hypotenuse, x is calculated as

cos(12) = 8/x

Make x the subject of the formula

x = 8/cos(12)

Evaluate the expression

x = 8.2

Hence, the value of x is 8.2 units

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We know that 60 second is equal to 01 Minutes.

and 90 second is equal to 01 and half minutes.

Therefore, 04 minutes and 10 seconds consists 250 second.

Second:

The second is the critical unit of time. The default unit of time in the SI system of units. It can be defined as the time required for an electromagnetic field to propagate through a vacuum of 3 x 10 5 km.

1 solar day consists of 86,400 seconds. One minute is 60 seconds.

The second is not small enough and is limited to use by scientists and engineers, so we got a smaller unit like this:

Minutes:

Minutes are a significant unit of time. Equal to 60 seconds. One hour includes 60 minutes. Minutes can be expressed as min. Included in the SI measurement system.

According to the Question:

250 seconds = 4 minutes and 10 seconds.

To obtain this result proceed as follows:

Divide 250/60, take the integer part of INT(250/60) and write it as minutes: 4.

Calculate the remainder, MOD(250,60), and write it down as seconds: 10.

Proof: (4 × 60) + 10 = 250.

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The exponential equation representing the given table is -

y = 2.84(1.072)ˣ.

Given is a function table as shown in below -

{X}   0     5        10       15       20

{Y}   0  4.02   5.69   6.97    8.05

Let the expression be -

y = A(B)ˣ

At {x} = 5, y = 4.02.

We can write -

4.02 = A(B)⁵                                               ... Eq { 1 }

At {x} = 10, {y} = 5.69

We can write -

5.69 = A(B)¹⁰                                            ... Eq { 2 }

Refer to the graph. The point of intersection represents -

A = 2.84
B = 1.072

The equation would be -

y = 2.84(1.072)ˣ                                      ... Eq { 3 }

Therefore, the exponential equation representing the given table is -

y = 2.84(1.072)ˣ.

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Explanation:

90/360 = 1/4

We have 1/4 of a pizza here. This slice is equal to an area of 9pi square units. The full pizza is 4*9pi = 36pi square units.

Use the circle area formula to determine r.

A = pi*r^2

36pi = pi*r^2

36 = r^2

r = sqrt(36)

r = 6

The circle has radius 6 units.

This statement is False as the probability of intersection of two events is always less than the probability of union.

This assertion is untrue. Contrary to popular belief, the likelihood of two occurrences coming together is always higher than or on pair with the likelihood of them colliding.

The chance of two events A and B occurring together can be calculated using the following formula to see why:

According to this equation, the probability of A and B joining together is equal to the total of their individual probabilities less the likelihood of their colliding.

When we rewrite this calculation and focus only on the likelihood of the intersection, we obtain:

Now it is clear that the probability of the intersection is determined by subtracting the probability of their union from the sum of the probabilities of A and B.

P(A) and P(B) are both less than or equal to P(A B), since probabilities can never be negative. P(A + B) is therefore less than or equal to twice P(A + B) when they are added together. Thus, it follows:

This indicates that, contrary to what the original statement implied, the probability of the intersection is not greater than or equal to the probability of the union.

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The cost of 1 kilogram of pears is $5.70.

The cost of 1 kilogram of pears can be found by using the given information and setting up an equation. First, let's repeat the question: "1 kilogram of pears cost as much as 1.5 kilograms of apples. Alex paid $34.20 for 4 kilograms of pears and 3 kilograms for apples. How much did 1 kilogram of pears cost?"

Let's assign variables to the unknowns:

- P = cost of 1 kilogram of pears

- A = cost of 1 kilogram of apples

From the question, we know that:

- 1P = 1.5A - 4P + 3A = 34.20

Now, we can use substitution to solve for P.

1. Substitute 1.5A for P in the second equation: 4(1.5A) + 3A = 34.20

2. Simplify: 6A + 3A = 34.20

3. Combine like terms: 9A = 34.20

4. Solve for A: A = 34.20/9 A = 3.8

5. Substitute 3.8 for A in the first equation: 1P = 1.5(3.8)

6. Solve for P: P = 5.7

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The segments in the figure are:

segment QT

segment QR

segment QS

segment RS

segment ST

segment RT

A line is a straight path of points that has no beginning or end.

A ray is a portion of a line which has one endpoint and extends forever in one direction.

Note: the arrow is an indication no endpoint.

Let's put the definitions:

Line QT (lines are bound by two arrows pointing left and right)

ray ST (rays are bound by a dot and an arrow)

ray RT

ray QT

ray TQ

ray SQ

ray RQ

segment QT (segments are bound by two dots)

segment QR

segment QS

segment RS

segment ST

segment RT

Check the attached image for the correct selection

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Answer:

The answer is C, as you'd need to multiply the chance of getting a convertible by the chance of getting a red car, or vice versa.

Step-by-step explanation:

Notice in A it says OR, meaning that it can't be both red and a convertible. B would be impossible, and D would be adding and not multiplying, so C would be the answer. 0.40*0.25=0.10

Answer:

x=3

y=-34

this should be correct

An independent variable is a variable that can be changed or manipulated in a scientific experiment.

Independent variables are variables in an experiment or research study that are independent of other variables, meaning they are unaffected by the other variables in the experiment. Independent variables are often manipulated by the researcher and are used to observe the effect on a dependent variable. Examples of independent variables include the type of treatment, the level of education, the amount of money offered, and the type of incentive.

It is used to determine the effect that the change has on the dependent variable, which is the variable being tested and measured in the experiment. By changing the independent variable, researchers can observe how the change affects the dependent variable. Examples of independent variables include the amount of light, temperature, time, type of material, and other factors that could influence the outcome of the experiment.

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The total mass of the 135 boxes that the woman bought is 2358.7 kg

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Each bottle of water has a mass of 728g. A box of mineral water contains 24 bottles from a given factory, hence:

Mass of each box = 24 bottles * 728 g per bottle = 17472 g

The woman bought 135 boxes, therefore:

Total mass of boxes =  135 boxes * 17472 g per box = 2358720 g

But 1 kg = 1000 g

2358720 g = 2358720 g * 1 kg per 1000 g = 2358.7 kg

The total mass is 2358.7 kg

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Answer:

36 degrees

Step-by-step explanation:

since your trying to find x you know that a wright angle is 90 degrees you minus 54 from 90

The woods, Sarah’s dog picked up 3 sticks, 2 rocks, and an amount of leaves. An algebraic expression for this is, 3 + 2 + x

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

The total number of items that Sarah's dog picked up in the woods can be represented by the algebraic expression:

3 + 2 + x

where x represents the number of leaves the dog picked up.

The expression 3 + 2 + x represents the sum of the 3 sticks, 2 rocks, and the unknown number of leaves that the dog picked up.

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Answer:

40

Step-by-step explanation:

you can multiply 88 by 5/11 to get 40

Answer: C. 0.75

Step-by-step explanation:

formulate 15 ÷ 20
= 15/20
= 3/4 (convert 3/4 to a decimal)
= 0.75

The amount will be after 4 years at interest rate of 6%, $624.76

To calculate the total amount you will pay after borrowing $500 for 4 years at an annual interest rate of 6%, you can use the formula for compound interest:

A = P x (1 + r/n)^(nt)

where:

A is the total amount,

P is the principal amount (the initial amount borrowed),

r is the annual interest rate as a decimal,

n is the number of times interest is compounded per year,

t is the number of years the money is borrowed for.

In this case, P = $500, r = 6%, n = 1  and t = 4.

So, the formula becomes:

A = $500 x (1 + 0.06/1)^(1 x 4)

A = $500 x (1.06)⁴

A = $500 x 1.249536

A = $624.76

Therefore, you will pay a total of $624.76 after borrowing $500 for 4 years at an annual interest rate of 6%.

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Answer:

y = 350x + 225

It will cost $4425 for 12 credits

Step-by-step explanation:

From the two points shown in the graph, we can write the equation of the line.

(5, 1975), (8, 3025)

slope = m = (y_2 - y_1)/(x_2 - x_1) = (3025 - 1975)/(8 - 5) = 1050/3 = 350

y = mx + b

y = 350x + b

1975 = 350 × 5 + b

b = 225

The equation is

y = 350x + 225

For 12 credits, x = 12.

y = 350 × 12 + 225

y = 4425

Answer: It will cost $4425 for 12 credits

Answer:

x = 15.25

y = 71/6

Step-by-step explanation:

10x -9y = 46

-2x + 3y = 5

Time the second equation by 5

10x - 9y = 46

-10x + 15y = 25

6y = 71

y = 71/6

Now put 71/6 back in for y and solve for x

10x -9(71/6) = 46

10x -106.5 = 46

10x = 152.5

x = 15.25

Let's check

-2(15.25) +3(71/6) = 5

-30.5 + 35.5 = 5

5 = 5

So, x = 15.25 and y = 71/6 is the correct answer.

I would chose more initial zombies, but a slower growth rate because when they grow stronger, you get stronger so you have a better chance of survival if their development rate is gradual, giving you time to collect weapons and construct a shelter.

Growth rate refers to the percentage increase or decrease in a particular variable over a specific period of time. It is commonly used in finance, economics, and business to describe the rate of change of various economic indicators such as gross domestic product (GDP), population, revenue, profit, and so on.

To calculate the growth rate, you need to divide the difference between the final value and the initial value of the variable by the initial value, and then multiply the result by 100 to express it as a percentage. The formula for growth rate is as follows:

Growth rate = ((Final value - Initial value) / Initial value) x 100

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Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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The area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ) is 294π square units.

To find the area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ), we need to evaluate the integral for half of the area and then double the result.

The curve of the limacon has a loop when 0 ≤ θ ≤ π, so we integrate from 0 to π. The area can be calculated as follows:

A = 2 ∫₀^π 1/2 r² dθ

Using the equation for r given, we can substitute and simplify:

A = 2 ∫₀^π 1/2 (7 - 14sin(θ))² dθ

A = 2 ∫₀^π 1/2 (49 - 196sin(θ) + 196sin²(θ)) dθ

A = ∫₀^π (98 - 392sin(θ) + 392sin²(θ)) dθ

Using the trigonometric identity 1 - cos(2θ) = 2sin²(θ), we can simplify further:

A = ∫₀^π (98 - 392sin(θ) + 196 - 196cos(2θ)) dθ

A = ∫₀^π (294 - 392sin(θ) - 196cos(2θ)) dθ

Integrating with respect to θ:

A = [294θ + 392cos(θ)sin(θ) + 98sin(θ)]₀^π

Evaluating at the limits of integration, we get:

A = [294π + 0 + 0] - [0 + 392cos(0)sin(0) + 98sin(0)]

A = 294π - 0 - 0 = 294π

Therefore, the area inside the loop of the limacon r = 7 - 14sin(θ) is 294π square units.

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Answer: Let's call the number of bananas your character slipped on as "x". Then, the total points from slipping on bananas would be -3x. And since the total points from slipping on bananas during one race were at most -27, we can write an inequality to represent this:

-3x ≤ -27

Now we'll solve for x:

Divide both sides by -3:

x ≥ 9

So, the least number of bananas your character slipped on is 9.

To find the least number of seconds of race time, we need to multiply the number of bananas by 2 seconds per banana:

9 bananas * 2 seconds/banana = 18 seconds

So, the least amount of race time your character took to slip on bananas is 18 seconds.

Step-by-step explanation: