Let g(x) = 5x^2 -9. . (a) Find the average rate of change from - 2 to 4. (b) Find an equation of the secant line containing (-2, g(-2)) and (4, g(4)). (a) The average rate of change from - 2 to 4 is (Simplify your answer.)

Answer:

\( - 16.9(.11) + 23.2 = 21.341\)

To the nearest hundredth, this percent efficiency is 21.34.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

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The correct option regarding the linear regression equation is:

No, the equation is not a good fit because the sum of the residuals is a large number.

To find the equation, we need to insert the points (x,y) in the calculator.

In possession of the equation, the residuals are given by the difference of the predicted values(with the equation) and the actual values.

The model represents a good fit if the sum of the residuals is close to 0.

For this problem, the sum of the residuals is given by:

90 - 50  - 100 - 100 + 150 - 50 = -60.

The sum is a large number, hence the model is not a good fit.

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Answer:

C

Step-by-step explanation:

supplementary angles sum to 180° , then

3x + 15 + 60 = 180 , that is

3x + 75 = 180 ( subtract 75 from both sides )

3x = 105 ( divide both sides by 3 )

x = 35

Answer:

There is no mode !

Step-by-step explanation:

Hello,

what is the mode of a set of data?

It is the value in the set that occurs most often.

To note that this is also possible to have a set of data with no mode.

in this example, let's order them

7, 8, 11, 12, 13, 14, 15, 20

There is no repetition, right? each value occurs only once.

So, there is no mode!

hope this helps

Answer

Step-by-step explanation:

Given the inequality function

2x < - 8

Divide through by 2

2x/2 < -8/2

x < -4

Answer:

d = 69° , e = 32° , f = 79°

Step-by-step explanation:

d and 69° are vertically opposite angles and are congruent , so

d = 69°

e and 32° are vertically opposite angles and are congruent , so

e = 32°

69° , e , f lie on a straight line and sum to 180° , that is

69° + 32° + f = 180°

101° + f = 180° ( subtract 101° from both sides )

f = 79°

Answer:

Solution,

\(f(x) = - 4 {x}^{2} + 5x \\ f(6) = - 4 \times {6}^{2} + 5 \times 6 \\ \: \: \: \: \: \: = - 4 \times 36 + 30 \\ \: \: \: = - 144 + 30 \\ \: \: \: - 114\)

hope this helps.

Good luck on your assignment..

Answer:

-114

Step-by-step explanation:

To find f(6), you need to plug in the value in parentheses wherever there is an x in the equation.

f(x) = -4x + 5x

f(6) = -4(6) + 5(6)

f(6) = -4(36) + 30

f(6) = -144 + 30

f(6) = -114

The answer is -114.

Answer:

700 feet per hour is the rate of descent

Step-by-step explanation:

3 hours is 2100 so 2100/3 is 700 which is per hour

The point (-5, -3, 2) can be represented in spherical coordinates as (ρ, θ, ϕ) = (6.2, 2.6, 1.0) approximately.

To convert the point (-5, -3, 2) to spherical coordinates, we need to determine the values of ρ (rho), θ (theta), and ϕ (phi).

The first step is to calculate ρ, which represents the distance from the origin to the point. It can be found using the formula ρ = sqrt(x^2 + y^2 + z^2). Plugging in the values, we get ρ = sqrt((-5)^2 + (-3)^2 + 2^2) = sqrt(34) ≈ 6.2.

Next, we need to find θ, which represents the azimuthal angle. It is the angle between the positive x-axis and the projection of the point onto the xy-plane. θ can be calculated using the formula θ = atan2(y, x), where atan2 is the four-quadrant inverse tangent function. Substituting the values, we have θ = atan2(-3, -5) ≈ 2.6.

Finally, we determine ϕ, which represents the polar angle. It is the angle between the positive z-axis and the line segment connecting the origin to the point. ϕ can be found using the formula ϕ = acos(z / ρ). Plugging in the values, we get ϕ = acos(2 / 6.2) ≈ 1.0.

Therefore, the spherical coordinates for the point (-5, -3, 2) are approximately (6.2, 2.6, 1.0).

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Answer:

23.6111

hehe

Step-by-step explanation:

Speed of 85 kilometers per hour in meters per second is 23.611 m/s.

The rate of change of position with respect to time is known as speed.

Given that,

Convert the speed of 85 km/ hour in meters per second.

Before this we know that in an hour, there are 60 minutes and in each minute, there are 60 seconds.

∴ 1 hour = 60 x 60 seconds

and

1 kilometer is equals to 1000 meters.

∴ 85 km/hr = (85 x 1000)/ (60 x 60) = 23.611 m/s

Hence the final result is 23.611 m/s.

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Correct answers are

<BDE

<EDF

Answer:

\(18x+32\)

Step-by-step explanation:

Perimeter is the total distance around a shape and can be found by calculating the sum of a shape's sides.

In this case, we are given a parallelogram, a quadrilateral with two pairs of parallel sides. Thus, the formula for a parallelogram's perimeter is as follows:

\(P=2(a+b)\)

Substitute the variables in the formula for the expressions on the parallel lines:

\(a=3x+6\)

\(b=6x+10\)

\(P=2(3x+6+6x+10)\)

Distribute the 2 into each term:

\(P=6x+12+12x+20\)

\(P=18x+32\)

Answer:

Step-by-step explanation:

Perimeter = 3x + 6 + 6x + 10 + 6x + 10 + 3x + 6

= 18x + 32...ans

Answer:

Step-by-step explanation:

Let's break this problem down step by step.

Start by defining a variable to represent the unknown number. Let's call it "x".

Translate the given sentence into an inequality:

"The sum of a number and 19" means "x + 19"

"is at least" means "≥"

"8.2" means "8.2"

So the inequality is:

x + 19 ≥ 8.2

Solve the inequality for x:

x + 19 ≥ 8.2

Subtract 19 from both sides:

x ≥ 8.2 - 19

Simplify:

x ≥ -10.8

So the solution is:

x ≥ -10.8

This means that any number that is greater than or equal to -10.8 will make the original sentence true.

Answer:

D its 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = y = 4x + 7

Solve for "x"

4x + 7 = y ⇒ x = \(\frac{1}{4}\) y - \(\frac{7}{4}\)

Exchange the places "x" and "y"

\(f^{-1}\)(x) = \(\frac{1}{4}\) x - \(\frac{7}{4}\)  

or \(f^{-1}\) (x) = \(\frac{x-7}{4}\)

Answer: 2(x+2)=(y+3)^2

Step-by-step explanation:

Answer:

A. 2(x+2) = (y+3)²

Step-by-step explanation:

Edge

The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.

The check register shows a balance of $500, while the bank statement shows a balance of $510.

In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.

A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.

For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.

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Answer: D is incorrect

Step-by-step explanation:

Answer:

f rxddx6fxyfxtxd5dx5xdc5rcf5cf55fccf5ctfctd5dx5dxx5rx5tex5erx7gx

ygyvuhUhws

Step-by-step explanation:

6x + 2y = -8

-6x -6x

2y = -6x - 8

y = (-6/2)x - 8/2

y = -3x -4

subtraction addition  is commutative for rational numbers Class 8

LHS means left-hand side of the equation and RHS means right-hand side of the equation

3c(-5) = (-5)3c

The LHS of the above expression can also be written as 3 * c * (-1) * 5

The RHS of the above expression can also be written as (-1) * 5 * 3 * c

Since, this expression involved multiplication, it will definitely represent a multiplicative property. Since the order of the numbers that are being multiplied has been changed between LHS and RHS, and it is yielding the same result, it indicates that this is the commutative property of multiplication. This property states that a group of numbers can be multiplied in any order. Hence, the answer is C.

8+3.4=3.4+8

In the above, the order of the numbers being added has been changed across RHS and LHS, but is yielding the same result, it is representing the commutative property of addition. This property states that a group of numbers can be added in any order. Hence, the correct answer is C.

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When finding local maxima and minima from the graph of a derivative, we need to identify the points where the derivative changes sign. These points represent the locations of local maxima and minima on the original function.

When finding local maxima and minima from the graph of a derivative, we need to understand the relationship between the original function and its derivative. The derivative of a function represents the rate of change of the function at any given point. Local maxima and minima occur where the derivative changes sign from positive to negative or from negative to positive. At these points, the slope of the original function changes from increasing to decreasing or from decreasing to increasing.

By following these steps, we can identify the local maxima and minima from the graph of a derivative.

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Identify the critical points, Determine the intervals, Analyze the sign changes and Check the endpoints

To find the local maximum and minimum points from the graph of a derivative, you can follow these steps:

Identify the critical points: These are the points where the derivative is either zero or undefined. Find the values of x where f'(x) = 0 or f'(x) is undefined.

Determine the intervals: Divide the x-axis into intervals based on the critical points and any other points of interest. Each interval represents a section of the graph where the derivative is either positive or negative.

Analyze the sign changes: Within each interval, observe the sign of the derivative. If the derivative changes sign from positive to negative, there is a local maximum at that point. If the derivative changes sign from negative to positive, there is a local minimum at that point.

Check the endpoints: Also, check the derivative's sign at the endpoints of the graph. If the derivative is positive at the leftmost endpoint and negative at the rightmost endpoint, there is a local maximum at the left endpoint. Conversely, if the derivative is negative at the leftmost endpoint and positive at the rightmost endpoint, there is a local minimum at the left endpoint.

By following these steps and analyzing the sign changes of the derivative within intervals, as well as checking the endpoints, you can identify the local maximum and minimum points from the graph of the derivative.

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Answer:

126

Step-by-step explanation:

The probability is 90/500 = 18%

So, from 700 customers,

700 * 18%  = 700 * 18/100 = 126

Therefore, 126 customers will be selected on saturday.

The measures of the angle is 56 degree and 34 degree. The sum of their measurement is 90 degree.

Let the measure of the angle be x degrees. According to the given information, the measure of its complement will be (90 - x) degrees. The difference between the angle and its complement is 22 degrees.

Let's assume the measure of the angle is x degrees. The complement of the angle is defined as (90 - x) degrees since the sum of an angle and its complement is always 90 degrees for a right angle. According to the given information, the difference between the angle and its complement is 22 degrees. Mathematically, we can express this as:

x - (90 - x) = 22

Simplifying the equation, we get:

x - 90 + x = 22

Combining like terms, we have:

2x - 90 = 22

Adding 90 to both sides:

2x = 112

Dividing both sides by 2:

x = 56

Therefore, the measure of the angle is 56 degrees. By substituting this value into (90 - x), we can find the measure of its complement, which is 90 - 56 = 34 degrees.In conclusion, the angle measures 56 degrees, and its complement measures 34 degrees

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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

11 minutes. 1/4 of 44 is 11

The value of ? and X are 24 and 32 respectively

A triangles is 2D shape with three sides and angles.

From the given diagram, the ratio of similar sides is equal to a constant as shown;

15/20 = 9+15/20+x

Cross multiply

15/9+15 = 20/20+x

15/24 = 20/20+x

Comparing with the given ratio

? = 24

X = 20+x

Find x

15(20+x) = 480

300 + 15x = 480

15x = 180

x =12

X = 20 +x

X= 32

Hence the value of ? and X are 24 and 32 respectively

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The option that is not characteristic of the t-test is "The Student t distribution has mean of t = 0 and a standard deviation of 5 = 1". The correct answer is option A.

The t-test is a statistical test that uses the Student t-distribution. The Student t-distribution has a mean of 0, but its standard deviation is not equal to 1. The standard deviation of the t-distribution varies depending on the degrees of freedom, which is determined by the sample size. Therefore, the statement in option A is not true. The correct answer is option A.

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Answer:

-40

Step-by-step explanation:

Given that,

c = -6

d = 2

To find the value of the given expression, replace c & d with 6 & 2 respectively.

Let us solve it now.

10c - cd + d³

( 10 × -6 ) - ( -6 × 2 ) + 2³

- 60 - ( -12 ) + 8

- 60 + 12 + 8

- 40

Therefore , the solution of the given problem of linear equation comes out to be conan needs one more tube to put away the remaining 2 tennis balls.

A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The previous line is usually referred to as a "math equation mixing numerous variables," even though y / y represent independent components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations.

Here,

We know that Conan has 5 tubes, and that 2 tennis balls are left unfilled. This means that he has already filled up 5 - 1 = 4 tubes.

Each tube can hold a certain number of tennis balls, so we need to know how many tennis balls each tube can hold. Once we know that, we can figure out how many tubes are needed to hold the remaining 2 tennis balls.

Let's say each tube can hold n tennis balls. Then, the 4 filled tubes have a total capacity of 4n tennis balls. We also know that there are 2 tennis balls left unfilled. Therefore, we can set up the following equation:

4n + 2 = 5n

Simplifying this equation, we get:

2 = n

So each tube can hold 2 tennis balls. Therefore, Conan needs one more tube to put away the remaining 2 tennis balls.

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