which of the following represents the average rate of change to the function g(x) = 3/2x + 1 over the interval -2 < x < 8

The slope of as per the given points will be equal to 3/2. Hence, option B is correct.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the information given in the table,

The points are (-14, -18) and (-10, -12)

Use the equation given below to find the slope,

m = (y₂ - y₁)/(x₂ - x₁)

Substitute values in above equation,

m = (-12 - (-18))/(-10 - (-14))

m = (-12 + 18)/(-10 + 14)

m = 6/4

m = 3/2

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A logarithmic function is defined by f(x) = [tex]log_a[/tex]x(r) y = [tex]log_a[/tex]x, where a > 0 and y = [tex]log_a[/tex]x. It is the inverse of the exponential function [tex]a^{y}[/tex] = x.

During the 16th century, Scottish mathematician, scientist, and astronomer John Napier discovered logarithms. The technique is widely used in astronomical and scientific calculations involving huge numbers. As an inverse of exponential functions, logarithmic functions are closely related to exponential functions. By transforming [tex]a^{x}[/tex] = N into [tex]log_a[/tex] N = x, the exponential function is transformed into a logarithmic function.

Let's say that y=[tex]10^{\log x}[/tex]

see this, 100=[tex]10^2[/tex],

then [tex]log _{10}[/tex] 100 = 2

therefore, [tex]log _{10}[/tex] y=[tex]\log _{10}[/tex] xy = x

[tex]10^{\log x}[/tex] = x

Hence, proved.

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Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.  

A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.

Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.

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The edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. Hence, the rate of change of the volume of the cube at that instant will be 2178  [tex]inches^3[/tex] /s.

The volume of the cube V = [tex]a ^ 3[/tex]

where 'a' is the edge.

Rate of increase of volume = dV / dt = 3a^2 da/dt.

da/dt = 6 inches /s

dV / dt = 3 [tex]a^2[/tex] da/dt.

When a = 11 inches.

dV /dt = 3 x [tex]11 ^2[/tex] x 6

           = 3 x 121 x 6

           = 2178  [tex]inches^3[/tex] /s

Hence, the rate of change of the volume of the cube at that instant will be 2178  [tex]inches^3[/tex] /s.

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Answer:You consume 14 pounds of turkey annually. At a discount store, the price of turkey is $0.99 less per pound than at a supermarket. How much would you save annually, in dollars, if you bought all of your turkey at the discount store?

Step-by-step explanation:

The value of the given function f (x) is 10

[tex]f (x) = \left \{ {{2 \text{ for x} < 3} \atop {x- 1 \text { for x } \geq 3} \right. \\\\[/tex]

Integrating the given functions,

[tex]\int\limits^5_1 {f(x)dx = \int\limits^3_1 2dx + \int\limits^5_3 (x- 1)dx[/tex]

[tex]\int\limits^5_1 {f(x)dx =2x + [\frac{x^{2}} {2} - x][/tex]

Applying the limits,

[tex]\int\limits^5_1 {f(x)dx =[2(3)-2(1)]+ [\frac{5^{2}} {2} - 5-\frac{3^{2}} {2} + 3][/tex]

[tex]\int\limits^5_1 {f(x)dx =[6- 2]+ [\frac{25} {2} - 5-\frac{9} {2} + 3][/tex]

[tex]\int\limits^5_1 {f(x)dx = 4 + 6[/tex]

[tex]\int\limits^5_1 {f(x)dx = 10[/tex]

The value of the given function on integrating using the limits is 10

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Answer: -5/4

Step-by-step explanation:

The slope is rise/run or y2 - y1/ x2 - x1

The two points are (-6,-3) (-2, -8)

The y decreases by 5 and the x increase by 4

So the slope is -5/4

The cost when the two plans are the same is  $1802. The number of sessions where the plans would be the same is 27.

The linear equation that represents the total cost of the first plan: initial consultation + charge per session x number of sessions)

= $74 + $64s

The linear equation that represents the total cost of the second plan: $20 + $66s

When the two plans are the same, the two linear equations would be the same.

$20 + $66s = $74 + $64s

In order to determine the value of s, take the following steps:

Combine similar terms:

$66s - $64s = $74 - $20

Add similar terms:

$2s = $54

Divide both sides of the equation is $2

s = $54 / 2

s = 27

Total cost when s is 27: $20 + $66(27)

$20 + 1782 = $1802

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the integral by reversing the order of integration. Double integrate e^x^2 dxdy= 1/3x e^x^3 + C

The integral can be written as:

∫ ∫ e^x^2 dx dy

∫ ∫ e^x^2 dy dx

Applying the formula for double integrals, the answer is:

∫ e^x^2 dy × ∫ dx

Since the inner integral is a constant, it is simply equal to x.

The answer is therefore:

∫ e^x^2 dy × x = x × ∫ e^x^2 dy

The outer integral is a standard antiderivative, and is equal to:

1/3e^x^3 + C

Therefore, the final answer is:

1/3x e^x^3 + C

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Answer:

its 3

Step-by-step explanation:

the rate is 3

Answer: 18%

Step-by-step explanation:

I gogled

The probability of waiting more than 0.5 minutes to get the next inquiry call is .165 seconds.

Probability is given by the number of possible outcomes ÷ number of total outcomes

Rate of phone calls = 3.6 per minute

Total number of calls between 2:00 p.m and 4:00 p.m (120 minutes) = 3.6 × 120 = 432

Number of calls in 0.5 minutes = 3.6 × 0.5 = 1.8

The probability that the number of calls in 0.5 minutes = 1.8/432 = 1/240.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X=x) =[/tex] e^-μ *  μ^[tex]x[/tex]

                        [tex]x[/tex]!

In which

x is the number of successes

e = 2.71828 is the Euler number

μ is the mean in the given time interval.

The probability of waiting more than 0.5 minutes to get the next inquiry call is according to a Poisson process.

Each minute has 60 seconds.

Rate of phone calls = 3.6 per minute

So a rate of 1 call every 50/3 seconds.

The probability that it takes more than 0.5 minutes for the first inquiry to arrive is approximate.

Mean of 1 call every 50/3 seconds, so for 0.5 minutes, μ = 0.5*60/50/3 = 1.8.

This probability is P(X = 0).

[tex]P(X=x) =[/tex] e^-μ *  μ^[tex]x[/tex]

                        [tex]x[/tex]!

P(X=0) = e^-1.8 * 0.03^0

                      0!

= 0.165

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Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0

The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The standard deviation, which is proportional to the square root of variance, is calculated by comparing the variance of each data point to its mean.

Here,

The null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0

Alternate hypothesis , [tex]H_{A}[/tex]= [tex]u_{d}[/tex] ≥ 0

thus,

[tex]d^{'}[/tex]=(14 + 11 + 7 + 11 -2 + 5 + 0 +5)/9

[tex]d^{'}[/tex]=4.44

[tex]S_{d}[/tex]=6.747

t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex]

Putting values in above equation

[tex]d_{f}[/tex]=9-1=8

α=0.10 => t(0.1,8)

t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex] = 1.397

Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0

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The algebraic form of the statement is b/4 + 7 = 2 and the value of b is -20.

Given the statement; the quotient of a number b and four plus seven is two.

First, we convert the statement into an algebraic equation.

Now, combine the terms and equality sign.

b/4 + 7 = 2

Next, solve for the numerical value of b.

b/4 + 7 = 2

Subtract 7 from both sides

b/4 + 7 - 7  = 2 - 7

Simplify the left-hand side

b/4 = 2 - 7

Subtract 7 from 2

b/4 = -5

Next, multiply both sides by 4

b/4 × 4 = -5 × 4

b = -5 × 4

b = -20

Therefore, the numerical value of b is -20.

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Equation which represents the m(x) and n(x) are inverse functions given by Option B.

3[7x/(3 - x)] / [ ( 7x / 3 - x ) + 7 ] =7[3x/(x + 7)] / [ 3 - ( 3x / x + 7 )  ] =x.

As given in the question,

Given functions are

m(x) = 3x /(x+7) and n(x) = 7x/ (3 - x)

Let y = m(x)

y = 3x /(x+7)

Now replace x by y and vice versa:

x = 3y / (y + 7) __(1)

Now substitute (1) in n(x)

n(x) = 7x/ (3 - x)

      = 7[3y / (y + 7)] / [ 3 - 3y / (y + 7) ]  __(3)

      = y

Now n(x) = y

y = 7x/ (3 - x)

Replace x by y and vice versa

x = 7y /( 3 - y )  __(2)

Now , substitute (2) in m(x)

m(x) = 3x /(x+7)

       = 3[7y /( 3 - y ) ] / [ 7y /( 3 - y )  + 7 ]  __(4)

       = y

Replace y by x in (3) and (4)

Equation representing m(x) and n(x)  as inverse functions:

3[7x/(3 - x)] / [ ( 7x / 3 - x ) + 7 ] =7[3x/(x + 7)] / [ 3 - ( 3x / x + 7 )  ] =x.

Therefore, equation representing m(x) and n(x) as inverse function is given by :

Option B. 3[7x/(3 - x)] / [( 7x / 3 - x ) + 7] =7[3x/(x + 7)] /[3 - ( 3x / x + 7 )] =x.

The complete question is :

Marin write the functions m(x) = 3x /(x+7) and n(x) = 7x/ (3 - x).

Which equation must be true for m(x) and n(x) to be inverse functions?.

Options are shown in attachment.

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Answer:

y = 21

Step-by-step explanation:

You need to find k

y = x

54 = 9k  Divide both sides by 9

6 =k

y = 6(3.5)

y = 21

The lump-sum distribution includes employer securities and the payer reported an amount in box 7.

A lump-sum distribution is when all of a plan participant's remaining balance from all of the employer's eligible plans of one kind are distributed or paid to them in one tax year (for example, pension, profit-sharing, or stock bonus plans).

The net unrealized appreciation (NUA) in employer securities is typically not subject to tax until you sell the securities, even if the lump-sum distribution includes employer securities and the payer reported a sum in box 7 of your Form 1099-R, Distributions From Pensions, Annuities, Retirement or Profit-Sharing Plans, IRAs, Insurance Contracts, etc. for NUA in employer securities. You may, however, decide to include the NUA in your income in the year that you receive the securities.

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The value of a for which v is a linear combination is given as follows:

a = -8.

How to obtain the value of a?

A vector generated by adding two or more vectors (with various orientations) and multiplying by scalar values is known as a linear combination of two or more vectors.

v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.

From the vectors, the system is defined as follows:

-x = -1.

2x - y = 4.

5x + 4y - 3z = -6.

-x + 3y - z = a.

From the first equation, the value of x is obtained as follows:

-x = -1

x = 1.

From the second equation, the value of y is obtained as follows:

2x - y = 4

2 - y = 4

y = 2 - 4

y = -2.

From the third equation, the value of z is obtained as follows:

5x + 4y - 3z = -6.

5 - 8 - 3z = -6

3z = 3

z = 1.

Then the value of a needed for the linear combination is of:

a = -x + 3y - z

a = -1 - 6 - 1

a = -8.

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The smallest possible composite, positive, integer x and y such that x/y=5 are x=20, y=4.

The result of multiplying two smaller positive integers is a positive integer known as a composite number. It is, in other words, an integer that is positive and has at least one divisor besides itself and 1. The composite numbers are exactly the numbers that are not prime and not a unit, since every positive integer is either composite, prime, or the number 1.

Because it is the result of the two smaller integers 2 and 7, for instance, the number 14 is a composite number. The integers 2 and 3 are also not composite numbers because they can only be divided by one another and themselves.

The smallest possible composite, positive, integers are

4 and 20

20/4=5

So, x=20 and y=4

Therefore, the smallest possible composite, positive, integer x and y such that x/y=5 are x=20 and y=4.

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The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).

Given that,

a to b is translated by the vector (4/-3)

We have to find what is the vector converting b to a.

We know that,

Quantities with both magnitude and direction are referred to as vectors. Additionally, it refers to the type of the quantity.

Here,

We have a vector,

ab=(4/-3)

Its direction will be reversed to translate the vector in the other way,

For

ba=-(4/-3)

ba=4/3

Therefore, The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).

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Answer:

The second one

Step-by-step explanation:

The first graphic would be correct if the connector was "AND" instead of "OR"

"AND" --> Both conditions must ALWAYS be fulfilled

"OR" ---> It's only necessary that one of the conditions is fulfilled

The points of intersection of the system formed by the circle (x - 2)² + (y - 3)² = 16 and the ellipse (x - 2)² / 16 + (y - 3)² / 64 = 1 are (x₁, y₁) = (- 2, 3) and (x₂, y₂) = (6, 3).

Herein we get a system formed by two conics, the former represents a circle and the latter represents an ellipse. There are different methods to solve the system, the use of graphing tools offers a quick though reasonable approach to find that. First, write the equations corresponding to the conics:

Circle

(x - 2)² + (y - 3)² = 16

Ellipse

(x - 2)² / 16 + (y - 3)² / 64 = 1

Second, plot the two graphs of the functions. (Please see the image attached below)

Third, write the points of intersection:

(x₁, y₁) = (- 2, 3), (x₂, y₂) = (6, 3)

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The value of x in the triangle is 22.

The angles in the triangle are 22, 29 and 127.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees. A scalene triangle is a triangle that has three different angles.

x + (x + 7) + 127 = 180

In order to determine the value of x, take the following steps:

2x + 134 = 180

2x = 180 - 134

2x = 44

x = 44/2

x = 22

x + 7 = 22 + 7 = 29

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The perimeter of the equilateral triangle is 48 cm

equilateral triangle

An equilateral triangle is a type of triangle in which all three sides are equal in length and all three angles are also equal, measuring 60 degrees each.

Given that: the area of an equilateral triangle is 64√3 cm²

The formula for the area of an equilateral triangle is given by:

A = (√3)/4  ×  a²

Where a is the length of the side

64√3 = (√3)/4  ×  a²

4 × 64√3 = (√3) ×  a²

4 × 64 = a²

a² = 4 × 64

a² = 256

a = √256

a = 16 cm

Perimeter of the equilateral triangle = a + a + a = 3a

Perimeter of the equilateral triangle = 3 × 16 = 48 cm

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If 5 dollars can be exchanged for 7.7095 units of some foreign​ currency, the unit of that currency that can be obtained for 6 ​dollars will be

5 dollars can be exchanged for 7.7095 units. This means that 1 dollar equals to:

5 dollars / 5 = 7.7095 units / 5

1 dollar = 7.7095 units / 5

1 dollar = 1.5419 units.

Now, for 6 ​dollars, the foreign currency that can be obtained is:

= 6 * 1.5419 units

= 9.2514 units. Therefore, 9.2514 unit of the foreign​ currency can be obtained for 6 ​dollars.

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I have earned 10 college credit hours before end of my high school graduation date.

A credit hour is an approach to estimating how much credit an understudy gets for going to a course which relates to the hours out of each week spent in that course. Dissimilar to numerous conventional secondary school courses that expect understudies to go to class consistently, school courses may just meet a few times each week.

Each hour that an understudy spends in the class regularly compares to a credit hour. For instance, on the off chance that an understudy signs up for a class that meets for one hour on Monday, Wednesday, and Friday, that course would be worth three credit hours, which is normal of numerous school courses.

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Answer:

100 metere is 1 km

Thanks for the question

a) A random family is chosen and then a random child within that family is chosen the mean is 1.45 and the variance is 0.38.

b) A random child is chosen in the town, the mean is 1.579 and the variance is 0.454.

For part A:

A random family is chosen and then a random child within that family.

P(X=1)= P(X=1 | family with one child). P(family with one child)

             + P(X=1 | family with two children).P(family with two children)

             +P(X=1 | family with three children).P(family with three children)

           = 1.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 37/60

P(X=2)=P(X=2 | family with one child). P(family with one child)

             + P(X=2 | family with two children).P(family with two children)

             +P(X=2 | family with three children).P(family with three children)

           = 0.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 19/60

P(X=3)=P(X=3 | family with one child). P(family with one child)

             + P(X=3 | family with two children).P(family with two children)

             +P(X=3 | family with three children).P(family with three children)

           = 0.30/100 + 0 . 50/100 + 1/3 . 20/100 = 4/40

hence, using these probabilities we can find,

E(X) = 1(37/60) + 2(19/60) + 3(4/60) = 1.45,

therefore, Var(x) = 149/60 − [tex]1.45^{2}[/tex] = 457/1200 ≈ 0.38

hence, the mean of the child's birth is 1.45 and the variance of the child's birth ranks 0.38.

For part B,

When a random child is chosen in the town with equal probabilities.

There are 1 x 30 + 2 x 50 + 3 x 20 = 190 children in the town where 100 of them are first born, 70 of them are second born, and 20 of them are third born. Let X be a random variable that marks the birth rank of a child.

Hence,

E(X) = 1(100/190) + 2(70/190) + 3(20/190) ≈ 1.579

and

Var(X) = 2.947 − [tex]1.579^{2}[/tex] ≈ 0.454

For a random child chosen, the mean of the child's birth is 1.579 and the variance of the child's birth ranks 0.454.

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Answer:

27.21 to nearest hundredth

Step-by-step explanation:

You find the lengths of the 4 sides and add them.

AB = 4 - (-2) = 6

BC = 4 - (--1) = 9

CD = √(-1-(-5)^2 + (-2-4)^2)

     = √(16 + 36)

     = √52

AD = 5

So, the perimeter

= 6 + 9 + 5 + √52

= 20 + √52

= 27.21 to nearest hundredth.