Are the following two functions inverses of each other? Use function composition to explain your answer.

Answer:

15 ×3e rd=12. &$.!&!_$_-,!&-.$_$,'

Answer: 154.08$

Step-by-step explanation:

Answer:

two real, equal roots

Step-by-step explanation:

Start by finding the discriminant, b^2 - 4ac.  The coefficients of this quadratic are a = 49, b = 42 and c = 9.  The discriminant is therefore

(42)^2 - 4(49)(9) = 0.  Rule:  If the discriminant is zero (0), then the quadratic has two real, equal roots.

1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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f(x) = 4²ˣ, this is an exponential function. Then the correct option is E.

Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as

y = aˣ + b

The exonentuial functions are given below.

a. f(x)=x³ + 2x²² -6, this is not an exponential function.

b. f(x) = 5/x, this is not an exponential function.

c. f(x) = 5x + 2, this is not an exponential function.

d. f(x) = 4x², this is not an exponential function.

e. f(x) = 4²ˣ, this is an exponential function.

Then the correct option is E.

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Answer:

1.0625 seconds

Step-by-step explanation:

Given that:

Initial velocity of Belinda, \(v_0=17\ ft/sec\)

Height in feet of Belinda above the trampoline is given as the formula:

\(d(t) = v_0t-16t^2\)

Where \(t\) is the time in seconds.

To find:

Time taken by Belinda to come back to trampoline = ?

Solution:

When Belinda will come back to trampoline, the height will be zero.

Putting \(d(t) =0\)

We have the equation as:

\(0 = 17t-16t^2\\\Rightarrow 16t^2-17t=0\\\because t\neq0\\\Rightarrow 16t=17\\\Rightarrow t=\dfrac{17}{16}\\\Rightarrow t =1.0625\ seconds\)

Therefore, the answer is: 1.0625 seconds

Answer: 8/3

Step-by-step explanation:

Answer: I THINK ITS THE SENCOND ONE

Step-by-step explanation:

To find the z-score for a sales associate who earns $37,500, we can use the formula:

z = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, $37,500),

μ is the mean of the distribution (in this case, $32,500), and

σ is the standard deviation of the distribution (in this case, $2,500).

Substituting the given values into the formula, we have:

z = (37,500 - 32,500) / 2,500

z = 5,000 / 2,500

z = 2

Therefore, the z-score for a sales associate who earns $37,500 is 2.

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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.

The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.

We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:

Z = (Value - Mean) / Standard Deviation

So, the z-score for an associate earning $37,500 would be:

Z = ($37,500 - $32,500) / $2,500

This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.

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The calculated value of the surface area of the cube is 294 mm^2

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

The cube

The side length of the cube is

Length = 7 mm

The surface area of the cube is calculated as

Surface area = 6 * Length^2

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

Surface area = 6 * 7^2

Evaluate

Surface area = 294 mm^2

Hence the surface area is 294 mm^2

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Answer:

22+c=54

Step-by-step explanation:

22 + his age =54

Answer: 13

Step-by-step explanation:

2k = 26

k= 26/2

13

Answer:

125 is a rational number because it can be expressed as the quotient of two integers: 125 ÷ 1.

hope this helps you

Step-by-step explanation:

Answer:

it is a cube number

Step-by-step explanation:

because 5^3 is 125

hope this is what you meant :)

Answer:135

Step-by-step explanation:

bcs 45x60 is 2700 ÷20= 135

Answer:

D

Step-by-step explanation:

you divide 1 by 7 to get a decimal that's what you need it's your precent , then you take that decimal and multiply it by 36 which is both of the guys makings an hour which gives you a decimal 5.14... which you would just round to 5.14 to get her making hoped this helped

Solution

Event 1: Probability is 8/16 = 1/2

Event 2: Probability is 1(certain to happen)

Event 3: Probability is 0(Impossible). There are no white slices in Spinner A

Event 4: Probability is 9/20

Answer:

AB is longer than FD

Step-by-step explanation:

I took the quiz on edge

Answer:

Step-by-step explanation:

Answer:

Y'all playing with me........right???

Answer:

5/3

Step-by-step explanation:

z = (Distributed score - Mean)/Standard deviation= (80-70)/6 = 5/3

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (80 - 70)/6 = 10/6 = 5/3 = 1.666666... ≈ 1.67

as most z-tables round the z-scores to hundredths.

not to forget : the sign matters. so, don't worry, if you have e.g. a specific score of 60 :

(60 - 70)/6 = -10/6 = -5/3 = -1.666666... ≈ -1.67

you did not do anything wrong. that is all ok and valid.

Answer:

5

Step-by-step explanation:

Sketch the diagram

AE is equal to the other half of the diagonal EC

3x + 12 = 27

Subtact 12 from both sides

3x = 15

Divide both sides by 3

X = 5

Answer:

x = 13     smaller integer

x + 2 = 15  the other integer

Step-by-step explanation:

x = the smaller integer

x + 2 = the next integer          

7(x) = 61 + 2(x + 2)

7x = 61 + 2x +4

5x = 61 + 4

5x  = 65

x = 13     smaller integer

x + 2 = 15  the other integer

An expression for the product √15x * √21x³ without a perfect square

factor in the radicand is: 3x²√35

The number or expression written under a root symbol or radical sign is known as a radicand in math. It is an expression of which we are taking a root.

A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system. Examples of Numbers that are Perfect Squares. 25 is a perfect square

√15x * √21x³

The product of roots with the same index is equal to the root, so

√(15x * 21x³)

Calculate the sum inside the radical

√315x⁴

Then, you can simplify the radical expression and move the variable + exponent to get:

3x²√35

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Complete question is:

Write an expression for the product √(15x) * √(√21x³) without a perfect square factor in the radicand.

Answer:

Since the sample size is n=10 we can find the first quartile taking in count the first 5 observations from the data set ordered and we have this:

33  60  62  63  69

\( Q_1 =62\)

We can find the third quartile taking in count the last 5 observations from the data set ordered and we have this:

70  74  79 107 119

\( Q_3 =79\)

And finally the median can be calculated with the average of the two moddlie values and we got:

\( Median= \frac{69+70}{2} =69.5 \)

And the IQr would be:

\( IQR = 79-62= 17\)

Step-by-step explanation:

Assuming that 2 is not part of the data we have:

74, 63, 69, 62, 33, 79, 70, 60, 107, 119

We can sort the values on increasing order and we got:

33  60  62  63  69  70  74  79 107 119

Since the sample size is n=10 we can find the first quartile taking in count the first 5 observations from the data set ordered and we have this:

33  60  62  63  69

\( Q_1 =62\)

We can find the third quartile taking in count the last 5 observations from the data set ordered and we have this:

70  74  79 107 119

\( Q_3 =79\)

And finally the median can be calculated with the average of the two moddlie values and we got:

\( Median= \frac{69+70}{2} =69.5 \)

And the IQr would be:

\( IQR = 79-62= 17\)

Step-by-step explanation:

hope it helps correct me if wrong pa brainliest please

Answer:

set none

Step-by-step explanation:

Question 11

The slope is 7/2 (so the line is increasing), and the y-intercept is 3.

Question 12

The slope is -8/3 (so the line is decreasing), and the y-intercept is -5.

Answer:

4x + x = 145,                            x=29 (shorter piece)

5x=145

x=145/5 = 29

Step-by-step explanation:

Answer:the slope of a line it the angle/slope that that line is at

Step-by-step explanation: slope times width

The expression for the length of the rectangular prism is L = 9x² + 7x - 2

Given data ,

Let the length of the rectangular prism be L

Let the volume of the rectangular prism be V = 36x³ - 28x + 8

Let the height of the prism be H = 3x - 1

Let the width of the prism be W = 4

And , Volume of Rectangle = Length x Width x Height

On simplifying , we get

36x³ - 28x + 8 = L ( 3x - 1 ) ( 4 )

L ( 12x - 4 ) = 36x³ - 28x + 8

By long division , we get

       -----9x² + 7x - 2--------------------------------------

4(3x - 1) | 36x³ - 28x + 8

                  - (36x - 9x)

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

                           7x - 2

                           - (7x - 2)

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

                                          0

Hence , the length of the prism is L = 9x² + 7x - 2

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we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

The sample provides information about the favorite snack of a random sample of people, but we need to use this information to make a prediction about the whole population of 2600 people.

First, we can calculate the proportion of the sample who chose pretzels or cookies as their favorite snack:

proportion = (number of people who chose pretzels + number of people who chose cookies) / total number of people in the sample

proportion = (16 + 54) / (30 + 16 + 54 + 64)

proportion = 70 / 164

proportion ≈ 0.4268

Next, we can use this proportion to estimate the number of people who will choose pretzels or cookies as their favorite snack out of the whole population:

predicted number of people = proportion × total number of people in the population

predicted number of people = 0.4268 × 2600

predicted number of people ≈ 1110.8

Rounding to the nearest whole number, we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

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