What are the domain and range of the function h(x) = –12 (x − 4)2 + 3? A.The domain is all real numbers and the range is y ≤ 3. B.The domain is x ≥ 4 and the range is y ≥ 3. C.The domain is all real numbers and the range is y ≥ 3. D.The domain is x ≥ −4 and the range is y ≤ −3.

Answer:

2

Step-by-step explanation:

From what I understand from the question,

you're looking for the difference between f(x) and f(x+4)

lets take the points f(-3) and f(1)

the difference is 0.5 - -1.5=2

Answer:

-18/13

Step-by-step explanation:

(x1,y1) = (-6,9)

(x2,y2) = (7,-9)

m= y2-y1 / x2-x1 =  -9-9 / 7-(-6)

-18/13

The probability that Team A wins the series in 3 games is 0.2745 (rounded to four decimal places).

To calculate the probability that Team A wins the series in 3 games, we need to consider the different possible scenarios. In order for Team A to win in 3 games, they must win the first three games of the series.

Since each game is independent and Team A has a probability of winning any given game with 0.65, the probability of Team A winning the first game is 0.65. If they win the first game, the probability of winning the second game is also 0.65. Similarly, if they win the second game, the probability of winning the third game is 0.65.

To find the probability of all these events occurring together (Team A winning the first, second, and third game), we multiply the individual probabilities. So the probability of Team A winning the series in 3 games is 0.65 * 0.65 * 0.65 = 0.2745.

Therefore, there is approximately a 27.45% chance that Team A will win the series in 3 games.

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The formula for the stopping distance in feet is

\(d=1.1v+0.055v^2\)

where \(v\) = Speed of the car in miles per hour.

The stopping distance for the car traveling at 15 mph is

\(d=1.1\times 15+0.055\times 15^2\\\Rightarrow d=28.875\approx 29\ \text{feet}\)

The stopping distance for the auto traveling at 15 mph is \(29\ \text{feet}\).

The stopping distance for the car traveling at 30 mph is

\(d=1.1\times 30+0.055\times 30^2\\\Rightarrow d=82.5\approx 83\ \text{feet}\)

The stopping distance for the auto traveling at 30 mph is \(83\ \text{feet}\).

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Answer: Let x be the number of nickels, and y be the number of pennies. Then we can write two equations based on the given information:

The total number of coins is 20: x + y = 20

The total value of the coins is $0.68: 0.05x + 0.01y = 0.68

We can solve this system of equations using any method we like, such as substitution or elimination. Here, we will use the elimination method.

To eliminate y, we can multiply the first equation by 100 to get 100x + 100y = 2000, and then subtract the second equation from it:

100x + 100y - 5x - y = 2000 - 0.68

Simplifying, we get:

95x + 99y = 1932

Now we have one equation with only x and y. We can use this equation to solve for one variable in terms of the other. For example, we can solve for y:

y = (1932 - 95x) / 99

To check if the solution is valid, we need to make sure that x and y are both non-negative integers, since we are dealing with coins. We can start by checking if x is an integer between 0 and 20 (inclusive). We can use a loop in a programming language, or we can simply try each integer one by one. If x is an integer between 0 and 20, we can plug it into the equation for y and check if y is a non-negative integer. If we find a pair of x and y that satisfy all the conditions, then Hannah's brother counted the money correctly. If we cannot find such a pair, then he made an error.

Alternatively, we can use the fact that y must be divisible by 1 cent (since it represents the number of pennies), and check if the expression (1932 - 95x) is divisible by 99 for any integer x between 0 and 20 (inclusive). If it is divisible, then the quotient is the number of pennies, and we can check if it is a non-negative integer. If it is not divisible for any x, then there is no solution.

Step-by-step explanation:

Answer:

15 and 270

Step-by-step explanation:

using the property of radicals

(\(\sqrt{x}\) )² = x and (\(\sqrt[3]{x}\) )³ = x

then

(\(\sqrt{5}\) )² × (\(\sqrt{3}\) )² = 5 × 3 = 15

(\(\sqrt[3]{9}\) )³ × (\(\sqrt{30}\) )² = 9 × 30 = 270

Answer: The fourth option. if you round, 200 * 20, 1800 is found out to be much too low.

Step-by-step explanation:

Answer:

Her estimate is too low because 200 * 20 = 4000

Step-by-step explanation:

Take 19 and round to 20

Take 212 and round to 200

20 * 200 =4000

Her estimate is low

Answer:

x= -3/2 or x=1.

Step-by-step explanation:

First, make the equation into a factorable form by subtracting 2 from each side to get 2x²+x-3=0. Then factor that into (2x+3)(x-1)=0. Then, you would do 2x+3=0, 2x=-3, x= -3/2. After that, do the second equation x-1=0, x=1.

(hope this helps :P)

Answer:

\( \frac{2}{35} \)

Step-by-step explanation:

\( \frac{ \binom{1}{1} }{ \binom{7}{1} } \times \frac{ \binom{2}{1} }{ \binom{5}{1} } = \frac{2}{35} \)

of course it can easily be simplified, but the logic is shown here!

first you have to draw 1 checker marble out of the seven marbles.

at the top is the ideal draw where you draw the one checker marble out of that one, and the bottom is all the options to draw 1 marble out of the 7 marbles.

3 is the prime number.

again, at the top you draw obe 3 out of the two, and the bottom is all the options to draw one out of the five numbers.

First, we have to acknowledge that the marble draw's outcome is independent from the card being drawn.  Because of this independence, we can multiply the two individual probabilities.

For the marble, there are 7 outcomes (7 marbles we could draw) and only 1 of which is checkered  We have a 1/7 chance of picking a checkered marble.

For the cards, there are 5 possible outcomes (5 cards we could drawa) and 2 are prime (there are two "3" cards).  We have a 2/5 chance of drawing a card with a prime number.

For the overall probability, since the two events are independent, we multiply the individual probabilities to find the overall probability:

   1/7 · 2/5 = 2/35

We have a 2/35 (about 5.714%) chance of drawing a checkered marble and then picking a card with a prime number.

Answer:

51.7%

Step-by-step explanation:

Because percent is out of 100, you multiply 0.517 by 100 and get 51.7, which is your percent.

In a case whereby letters in the word bubble are arranged in a row the number of unique arrangements that are there  in the letters is 120.

From the question we were given the word, bubble  which can be recognized as 6! arrangements  however we know that the  3 B’s are interchangeable, from the word which is to be arranged, and we can see that there are 6 letters all together in the word and can be arranged as;

6!/3!

= 720/6

= 120

Hence, we can conclude the arangement here is 120 unique wayas.

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Answer:

The probability of rolling a dice six time until a 7 is first seen is 0.059

Step-by-step explanation:

The probability of getting a seven is equal to \(\frac{1}{10}\)

The dice need to be rolled only six times.

This means that for the first 5 times the dice showed values other than 7 and in the last roll it displays 7

Hence the probability of rolling a dice six time until a 7 is first seen is

\((\frac{9}{10})^5 * (\frac{1}{10})^1\)

\(= \frac{9^5}{10^6} \\= 5.90\) % or 0.059

If the coefficient of determination is 0.94, we can say that ninety-four percent of the total variation of the dependent variable is explained by the independent variable. The correct answer is: ninety-four percent of the total variation of the dependent variable is explained by the independent variable.

This means that there is a strong positive relationship between the two variables. The coefficient of determination, represented as R², measures the proportion of the total variation in the dependent variable that is explained by the independent variable. In this case, an R² of 0.94 indicates that 94% of the total variation in the dependent variable can be explained by the independent variable. The coefficient of determination does not provide information about the direction or strength of the relationship. The correct answer therefore is ninety-four percent of the total variation of the dependent variable is explained by the independent variable.

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Answer:

288pi or approximately 904.32

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3 where r is the radius

V = 4/3 pi (6)^3

V = 288 pi

If we use the approximation for pi

V = 288(3.14)

V =904.32

Answer:

V = 288π units³

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³.

With r = 6 units, the volume of this sphere is V = (4/3)π(6 units)³, or

V = (4π/3)(216 units³), or V = 288π units³

Answer: 9 weeks

Step-by-step explanation:

Let x be the number of weeks

So the equation will be

1497 - 83x < 750

Subtract 1497 on both sides

-83x < -747

x < 9

So the answer is 9 weeks

By using combination, there are 24 possible ways to place 4 rooks on a 4 x 4 chessboard such that no two rooks can capture each other.

To place 4 rooks on a 4 x 4 chessboard such that no two rooks can capture each other, we can use the process of combination to place one rook in each row and column, so that no two rooks are in the same row or column.

We can start by placing the rook in the first row and first column. There are four options for where to place the rook in the second row, three options for where to place the rook in the third row, and two options for where to place the rook in the fourth row.

Therefore, there are 4 x 3 x 2 x 1 = 24 ways to place 4 rooks on a 4 x 4 chessboard such that no one rook can capture another rook.

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A vector is a mathematical object that represents both magnitude and direction. It is commonly used to represent physical quantities such as displacement, velocity, and force. In simple terms, a vector is an arrow that has a length (magnitude) and points in a specific direction.

To add vectors, we can use the "tip-to-tail" method. This involves placing the tail of the second vector at the tip of the first vector and drawing a new vector from the tail of the first vector to the tip of the second vector. The resulting vector, called the sum or resultant, is the vector that connects the tail of the first vector to the tip of the second vector.

Component styles are two common methods used to represent vectors: the Cartesian coordinate system and the polar coordinate system. In the Cartesian coordinate system, vectors are represented by their horizontal and vertical components. The polar coordinate system represents vectors using their magnitude and angle from a reference axis.

To decompose a vector into components, we use trigonometry. For example, in the Cartesian coordinate system, we can find the horizontal and vertical components of a vector by using the cosine and sine functions, respectively, along with the magnitude and angle of the vector.

When a vector is multiplied by a scalar (a real number), the vector's magnitude is scaled by the scalar value, and its direction remains unchanged. If the scalar is negative, the vector will reverse direction.

Graphically, we can arrange vectors by placing their tails at the origin of a coordinate system and drawing the vectors as arrows with their tips pointing to the desired location. Vector addition is represented by placing the tail of the second vector at the tip of the first vector, while vector subtraction is represented by placing the tail of the subtracted vector at the tip of the original vector, pointing in the opposite direction.

Overall, vectors provide a powerful mathematical tool for representing and manipulating quantities with both magnitude and direction. They are essential in many areas of science, engineering, and mathematics.

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In the trigonometric function, f(x) = 7cos[2π(x + 9)/7] + 1, the direction and how many units is is shifted vertically is 1 unit up

A trigonometric function is an equation containing a trigonometric ratio

Given the trigonometric function f(x) = 7cos[2π(x + 9)/7] + 1, we want to compare it with the trigonometric equation f(x) = acos[2π(x + c)/b] + d, to find the vertical shift of the graph. We proceed as follows

Since we know that the general equation of a trigonometric function is  f(x) = acos[2π(x + c)/b] + d where

Comaring both equations, we have that

So, we see that since d = + 1, we see that the function f(x) = 7cos[2π(x + 9)/7] + 1 is shifted vertically upwards by 1 unit.

So, the direction and how many units is is shifted vertically is 1 unit up

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(a) Using combination, the number of ways to choose 10 players to take the field is 286. (b) Using permutation, the number of ways to assign the 10 positions is 1037836800.

The softball team has 13 people for a game.

a) Since the sequence doesn't matter, there are a total of 13 ways to select 10 players, which results in the following combination:

₁₃C₁₀ = 13! / ( 13 - 10 )! 10!

₁₃C₁₀ = ( 13 × 12 × 11 ) / ( 3 × 2 )

₁₃C₁₀ = 13 × 2 × 11

₁₃C₁₀ = 286

b) The permutation of 13 players for 10 slots yields a total of possible positions that can be assigned by choosing 10 players:

₁₃P₁₀ = 13! / ( 13! - 10! )

₁₃P₁₀ = 13! / 3!

₁₃P₁₀ = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4

₁₃P₁₀  = 1037836800

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The 27 percent is equal to 27/100 as a fraction, 0.27 as a decimal and 27% as a percentage.

What is percentage?

A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or ratio of one number to another, usually with respect to a whole. A percentage is denoted by the symbol "%". It can be represented as a decimal or a fraction.

27 out of 100 students in 6th grade said they have one sibling.

As a fraction, this is 27/100.

As a decimal, this is 0.27

As a percentage, this is 27%

Hence, 27 percent is equal to 27/100 as a fraction, 0.27 as a decimal and 27% as a percentage.

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Answer:

It would look like that I think

Step-by-step explanation:

We find that it takes approximately 47 months to recover the initial investment.

To calculate the time it takes to recover the initial investment on a monthly basis, we need to consider the savings in fuel costs and the cost of funds over time.

First, let's calculate the monthly savings in fuel costs by subtracting the average natural gas cost from the fuel oil cost:

Savings in fuel costs = Fuel oil cost - Natural gas cost

= $145 - $60

= $85

Next, let's calculate the present value of the savings in fuel costs over the recovery period. Since the savings occur monthly, we can use the formula for the present value of an annuity:

Present value of savings = Savings in fuel costs * (1 - (1 + interest rate)^(-n)) / interest rate

Where:

Savings in fuel costs is $85 per month

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the savings using the given values:

Present value of savings = $85 * (1 - (1 + 0.0075)^(-n)) / 0.0075

Next, let's calculate the present value of the initial investment using the formula for present value:

Present value of initial investment = Initial investment / (1 + interest rate)^n

Where:

Initial investment is $2500

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the initial investment using the given values:

Present value of initial investment = $2500 / (1 + 0.0075)^n

To recover the initial investment, the present value of savings must equal the present value of the initial investment:

$85 * (1 - (1 + 0.0075)^(-n)) / 0.0075 = $2500 / (1 + 0.0075)^n

To solve for n, we can rearrange the equation and solve for n using trial and error or by using numerical methods.

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In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.

Given the demand equations and the total cost function:

Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1

Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2

Total Cost: TC = 120 + 4Q

To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:

MR1 = MC:

16 - 0.2Q1 = 4

0.2Q1 = 12

Q1 = 60

MR2 = MC:

10 - 0.1Q2 = 4

0.1Q2 = 6

Q2 = 60

Substituting the quantities back into the demand equations, we find:

P1 = 16 - 0.1(60) = 10

P2 = 10 - 0.05(60) = 7

The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:

TR = P1 * Q1 + P2 * Q2

TR = (10 * 60) + (7 * 60)

TR = 600 + 420

TR = 1020

The total cost (TC) is given by the total cost function:

TC = 120 + 4Q

TC = 120 + 4(60 + 60)

TC = 120 + 480

TC = 600

Finally, the profit (π) can be calculated by subtracting total cost from total revenue:

π = TR - TC

π = 1020 - 600

π = 420

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

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The mean of given data test is 66.

Let's use the standard notation for a normal distribution, which is \($N(\mu, \sigma)$\), where \($\mu$\) is the mean and \($\sigma$\) is the standard deviation.

We know that a score of 60 falls two standard deviations below the mean, so we can write:

\($60 = \mu - 2\sigma$\)

Similarly, we know that a score of 75 falls three standard deviations above the mean, so we can write:

\($75 = \mu + 3\sigma$\)

We can use these two equations to solve for the mean, \($\mu$\). Here's how:

First, we can isolate \($\mu$\) in the first equation by adding \($2\sigma$\) to both sides:

\($60 + 2\sigma = \mu$\)

Next, we can substitute this expression for \($\mu$\) into the second equation:

\($75 = (60 + 2\sigma) + 3\sigma$\)

Simplifying the right-hand side gives:

\($75 = 60 + 5\sigma$\)

Subtracting 60 from both sides:

\($15 = 5\sigma$\)

Dividing both sides by 5:

\($\sigma = 3$\)

Finally, substituting this value for \($\sigma$\) into the expression we found for \($\mu$\) earlier:

\($\mu = 60 + 2\sigma = 60 + 2\cdot 3 = 66$\)

Therefore, the mean of this test is 66.

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Answer:company b

Step-by-step explanation:

it would cost $75 to hire company b and $90 to hire company a.

The given function is f(x) = (4-x)/29. We need to find the x-values where f is not continuous and determine whether the discontinuities are removable or nonremovable.

For this function, there are no nonremovable discontinuities. The only type of discontinuity that could occur is a removable discontinuity. This occurs when a point is undefined, but the limit exists and is finite. In other words, the function can be made continuous by redefining it at that point.

To find any possible removable discontinuities, we need to find the values of x for which the denominator becomes zero, because division by zero is undefined. The denominator is always 29, which is never zero, so there are no values of x for which the denominator is zero. Therefore, there are no removable discontinuities.

In conclusion, the function f(x) = (4-x)/29 is continuous for all values of x, and there are no removable or nonremovable discontinuities.

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Ben can plot the residuals, create a histogram and Q-Q plot, or use statistical tests such as the Shapiro-Wilk test.

To test for the normality of residuals in a multiple regression model, Ben can use several methods. Here are a few options:

Plot the residuals: Ben can create a scatter plot of the residuals against the predicted values. If the residuals are normally distributed, they should be evenly scattered around the zero line. If there is a pattern or if the residuals are skewed, this indicates non-normality.

Histogram and Q-Q plot: Ben can create a histogram of the residuals and compare it to a normal distribution. He can also create a Q-Q plot (quantile-quantile plot), which compares the quantiles of the residuals to the quantiles of a normal distribution. If the residuals are normally distributed, they should fall along the diagonal line in the Q-Q plot.

Statistical tests: Ben can use statistical tests to formally test for normality of residuals. One commonly used test is the Shapiro-Wilk test, which tests whether the residuals are drawn from a normal distribution. If the p-value is greater than 0.05, Ben can conclude that the residuals are normally distributed.

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