f(x) =
2-x
x+1
g(x) = 18 - 3x
(fog)(x) =

[tex]$W(\mathbf{x})$[/tex]is a linear transformation. it is not onto .The given statement is false.

The objective is to determine whether the following statement is true or false.

"If [tex]$$T_1(\mathbf{x})$ and $T_2(\mathbf{x})$[/tex] are onto linear transformations from [tex]$\mathbf{R}^n$[/tex] to [tex]$\mathbf{R}^m$[/tex] then [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex] is an onto linear transformation."

To check whether [tex]$W(\mathbf{x})$[/tex] is a linear transformation or not:

For a, b ∈ R and for x, y ∈ [tex]$\mathbf{R}^n$[/tex],

[tex]$$\begin{aligned}W(a \mathbf{x}+b \mathbf{y})= & T_1(a \mathbf{x}+b \mathbf{y})+T_2(a \mathbf{x}+b \mathbf{y}) \quad\left(\text { Since } W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})\right) \\= & {\left[a T_1(\mathbf{x})+b T_1(\mathbf{y})\right]+\left[a T_2(\mathbf{x})+b T_2(\mathbf{y})\right] } \\& \quad\left(\text { Since } T_1(\mathbf{x}) \text { and } T_2(\mathbf{x}) \text { are onto linear transformations }\right) \\\end[/tex]

[tex]= & a\left[T_1(\mathbf{x})+T_2(\mathbf{x})\right]+b\left[T_1(\mathbf{y})+T_2(\mathbf{y})\right] \\\\= & a W(\mathbf{x})+b W(\mathbf{y})\end{aligned}$$[/tex]

Therefore, [tex]$W(\mathbf{x})$[/tex] is a linear transformation.

To check whether [tex]$W(\mathbf{x})$[/tex] is onto:

Define the linear transformations:

[tex]$$T_1: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_1(\mathbf{x})=\mathbf{x}$[/tex]

[tex]$$T_2: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_2(\mathbf{x})=-\mathbf{x}$[/tex]

Then, [tex]$T_2(\mathbf{x})=-\mathbf{x}=-T_1(\mathbf{x}) \Rightarrow T_2(\mathbf{x})=-T_1(\mathbf{x})$[/tex]

The range of both functions [tex]$T_1, T_2$ is $\mathbf{R}$[/tex] This is same as the co-domain of [tex]$T_1, T_2$[/tex]. So, they are onto functions.

If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called the onto function.

Therefore, [tex]$T_1, T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex]are onto linear transformations.

And, [tex]$W=T_1+T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex] is a mapping.

Now, [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex]

[tex]$$\begin{aligned}& =T_1(\mathbf{x})-T_1(\mathbf{x}) \\& =0\end{aligned}$$[/tex]

So, the range of [tex]$$W(\mathbf{x})$ is $\{0\} \neq \mathbf{R}($[/tex] co-domain of [tex]$W(\mathbf{x}))$[/tex]

Then, is [tex]$W(\mathbf{x})$[/tex] not onto.

So, the given statement is false.

Hence, the correct answer is 5th option

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The number of independent pieces of information used to calculate a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. I

Itbis determined by subtracting the number of restrictions from the sample size. Subtract the number of relations from the number of observations to determine degrees of freedom. You need to deduct one (1) from the total number of observations, n, in order to calculate the degrees of freedom for a sample mean or average.

The degrees of freedom for the chi-square are calculated as df = (r-1)(c-1) where

r = the number of rows

c = the number of columns.

If the observed chi-square test statistic is greater than the critical value, the null hypothesis can be rejected.

Note that an overview was given as the information you gave is incomplete.

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There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.

What does the math term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.              

                     Statistics is the study of events that follow a probability distribution.

Given that:

Mean = 56, standard deviation = 4, For 50:

z = (50 - 56) / 4 = -1.5

For 44:

z = (55 - 56) / 4 = -0.25

P(50 < x < 55) = P(z < -0.25) - P(z < -1.5) = 0.4013 - 0.0668 = 33.45

There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.

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The tower is 24 feet tall.

To solve this problem, we need to use the formula for the volume of a rectangular prism, which is V = l × w × h, where l and w are the length and width of the base and h is the height.

We are given that the side length of the base of the building is 100 feet less than the height of the building, so the height of the building is h = l + 100, where l is the side length of the base. We can substitute this expression for h into the formula for the volume of the building:

V = l × w × (l + 100) = 2 million cubic feet

Since the building is 25 times as tall as the tower, the height of the tower is h = (1/25) × h = (1/25) × (l + 100). Substituting this expression for h into the formula for the volume of the building, we get:

V = l × w × (1/25) × (l + 100) = 2 million cubic feet

Solving this equation for l, we find that l = 500 feet. This is the side length of the base of the building, so the height of the building is h = l + 100 = 500 + 100 = 600 feet. The tower is (1/25) × 600 = 24 feet tall.

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The ordered pair -2,2 makes the inequalities y < –x + 1 and y > x true. Therefore, option B is true.

Inequality is the absence of an equality link between two expressions or values. An ordered pair is made up of the x and y coordinates, with two values stated in a certain order inside parenthesis.

Substitute the values from the given ordered pair one by one to check whether the given inequalities are true.

Substituting (-2,2) in y < –x + 1 and y > x,

For,  y < –x + 1

2<2+1

2<3

For, y > x

2>-2

This ordered pair (-2,2) makes the given inequalities true.

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Answer:

500 grams

Step-by-step explanation:

you doubled the people, so you would need to double the flour.

Answer:

98 yd²

Step-by-step explanation:

diagonal = 7 · 2 = 14 yd

side = x² + x² = 14²

2x² = 196

x² = 196/2

x² = 98

x = √98

area = √98² = 98 yd²

Answer:

Below

Step-by-step explanation:

The change rate at the top of the mt is given as - 2.5 ° / hr

 at the base it is 1/5th of this number

1/5 * -2.5   =  - 0.5 °C  per hour

Answer:

The answer is x = -6 and y = -5.

Step-by-step explanation:

To solve this problem, we can use substitution. Let's first solve one of the equations in terms of the variable y, and then substitute this value into the other equation.

4x = 3y - 9

3y = 4x + 9

Since the term "3y" is present in the other equation given, we can substitute the right side of this equation (4x + 9) into the other equation for 3y. This is shown below.

6x - 3y = -21

6x - (4x + 9) = -21

6x - 4x - 9 = -21

We can simplify the left side of the equation and solve for x.

2x - 9 = -21

2x = -12

x = -6

Now, we can substitute this value for x into one of our equations to solve for y.

4x = 3y - 9

4(-6) = 3y - 9

-24 = 3y - 9

-15 = 3y

y = -5

Therefore, the correct answer is x = -6 and y = -5.

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i'm kind of sure it's -4.7

Your query has an answer of Extras charges = $999.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula's percentage?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Detailed explanation:

Data

Total cost: $11.325

8% state tax

$53 for license plates

$40 for an emissions inspection.

Process

1.- Determine the 8% of the car's cost.

11325 ———————— 100%

x ———————- 8%

x = (8 x 11325)/100

x = 90600/100

x = $1,066.16 in state taxes

2. Determine the entire cost.

Charges total $906 plus $53 plus $40.

= $ 999

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The multiplicative rate of change of the exponential function is 1.5

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The general form of the geometric sequence is an=a1r(n−1),

where r is the common ratio

a1 is the first term

n is the placement of the term

Now, use the geometric sequence formula to solve for the rate:

an=a1r^(n-1)

6.75=4.5r^(2-1)

6.75=4.5r

6.75/4.5=r

r= 1.5

and if you want to make sure just multiply each number by 1.5 and see if it gets you the next number

4.5 4.5×1.5=6.75 (holds true)

6.75 6.75×1.5=10.125 (holds true)

10.125 10.125×1.5=15.1875 (holds true)

15.1875

1.5 is the multiplicative rate.

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141.472 N of drag force is applied in 1.6m wide and 1.4m high car travelling at 10m/s

Drag force is the net force in the direction of flow experienced by any item moving through a fluid and is caused by pressure and shear stress forces acting on the surface of the object.

Formula of drag force is given by:

[tex]F_d = \frac{1}{2}C_dAPv^2[/tex]

where

[tex]F_d[/tex] = drag force (N)

[tex]C_d[/tex] = drag coefficient (1.05 for moving car)

P = density of fluid (1.2 kg/m3 for air at NTP)

v = flow velocity (m/s)

A = characteristic frontal area of the body

A = height * width

=> 1.6*1.4

so A=2.24 [tex]m^2[/tex]

and v=10 m/s

so [tex]F_d[/tex] = 1/2* 1.05 * 2.24 *( 1.2 *10*10)

=> 0.5*1.05*2.24 *122

=> 143.472 N

so [tex]F_d[/tex]  = 143.472 N

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Answer:

32

Step-by-step explanation:

The factorization of y²+7y-8 is (y+8)(y-1).

y²+7y-8

=y²+8y-y-8

=y(y+8)-1.(y+8)

=(y+8)(y-1)

The factors are (y+8), (y-1).

The method we are following here is factorize by grouping.

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The correct question is-

Factor y²+7y-8.

The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable).

It is denoted by r-squared and typically takes values between 0 and 1. A value of 0 indicates that the independent variable does not explain any of the variance in the dependent variable, while a value of 1 indicates that the independent variable explains all of the variance in the dependent variable. The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable). A higher R-squared value indicates a stronger regression relationship between the two variables.

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Answer:

  368

Step-by-step explanation:

You want the 41st term of the arithmetic sequence that starts 8, 17, 26.

The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

for first term a1 and common difference d.

The difference between terms is ...

  d = 17 -8 = 9

The first term is a1 = 8, so the 41st term is ...

  a41 = a1 +d(41 -1) = 8 +9(41 -1) = 368

The 41st term of the sequence is 368.

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I would prefer leaving the answer as a radical number as √5 since it is a shorter form and exact form of the answer.

My reasons for leaving it as a radical form or a decimal approximation are;

1) If we are trying to find an exact answer, then we should leave it as √5. For example, if we are told a square has an area of 5 square units, then it means that the exact length of the side is √5 units.

2) If √5 is the length of an object that has to be made to that specific length, then we would require an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then we will definitely need an approximation of √5 ft = 2.24 ft, which would help us make each side of the cardboard square in the length of 2.24 ft.

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Answer:

To calculate the total interest that Lucy will have to pay, we need to use the formula for simple interest: I = P * R * T, where I is the interest, P is the principal (the amount borrowed), R is the interest rate (as a decimal), and T is the time in years. Using this formula, we can calculate the total interest that Lucy will have to pay as follows:

I = P * R * T

I = $4000 * 0.05 * 2

I = $400

Therefore, the total interest that Lucy will have to pay is $400.

________________________________________________________

To calculate the total repayment amount (including interest), we need to add the total interest to the original amount borrowed, which in this case is $4000. Therefore, the total repayment amount will be $4000 + $400 = $4400. This is the amount that Lucy will have to pay back to her parents at the end of the two-year period.

Step-by-step explanation:

Answer:

Total interest = $400

Total repayment (including interest) = $4,400

Step-by-step explanation:

Simple Interest Formula

[tex]\large\boxed{ \sf I = Prt}[/tex]

where:

Given:

To find the total interest, substitute the given values into the formula and solve for I:

[tex]\implies \sf I=4000 \cdot 0.05 \cdot 2[/tex]

[tex]\implies \sf I=200 \cdot 2[/tex]

[tex]\implies \sf I=400[/tex]

Therefore, the total interest Lucy has to pay is $400.

The total repayment amount is the sum of the principal and the interest:

[tex]\implies \sf A=P+I[/tex]

[tex]\implies \sf A=4000 +400[/tex]

[tex]\implies \sf A=4400[/tex]

Therefore, the total repayment (including interest) is $4,400.

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

y-intercept is when the line hits the y-axis, or when the x=0 on a line.

Look at the test below the axis.

y-axis = heartrate (resting)

for

x-axis = hrs of exercise per week

When x = 0, (0 hours of exercise,)  y = 80, (average resting heart rate.)Telling us the average resting heartrate pf people who do not exercise.

The correct option is A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.

The given function is;

f(x) = StartRoot x EndRoot , which is written as;

f(x) = √x  

Domain for the  x   = [ 0 , ∞ )

x     f(x)

-1   undefined

0     0

1      1

4     2

The reflection over x-axis.

f(x) ---->  - f(x)

x     f(x)

-1   undefined

0     0

1      -1

4     -2

Thus, the correct option is; A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.

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The complete question is-

Which represents the reflection of f(x) = StartRoot x EndRoot over the x-axis?

A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.

B: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries 1, 0, undefined, undefined.

C: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (negative 4, negative 2).

D: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the right through (2, negative 4).

Answer:

D

Step-by-step explanation:

Edge 2023

Amal has seven CDs, whereas the Jacksons have eleven, with the Jacksons owning four more than Amal. They have a total of 18 CDs.

Given that,

4 more CDs belong to Jackson than Amal. They have 18 CDs altogether.

We have to find what number of CDs does Amal own and Jackson has how many CDs.

We know that,

Let amount of CD Jackson have x.

Let Amal have CD has y.

So,

x=y+4

x-y=4 ----->equation(1)

x+y=18 ------>equation(2)

So, now we have to solve the equations.

Adding equation(1) and equation(2)

x-y=4

x+y=18

-----------

2x=22

x=22/2

x=11

So, substitute x=11 in equation(1)

11-y=4

-y=4-11

-y=-7

y=7

Therefore, Amal have 7 cd and the Jackson have 11 cd when 4 more CDs belong to Jackson than Amal. They have total 18 CDs altogether.

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The equation in slope-intercept form to model the cooking time in minutes, y, for x patties is y = (3/2)x + 1.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given,  On a box of chicken patties state that one patty should be cooked for 2.5 minutes in the microwave.

If more than one patty is cooked, an additional 1.5 minutes should be added per patty.

So,  The equation in slope-intercept form to model the cooking time in

minutes, y, for x patties.

If we write this as y = 1.5x + 2.5 and put x = 0 , y = 2.5 which is not satisfying the given statement.

∴ y  = 1.5x + (2.5 - 1.5). (the additional patty cooking time).

y = 1.5x + 1.

y = (3/2)x + 1.

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Answer:

You are going send Christmas cards to 100 of your friends. Each box of Christmas cards contains 15 cards and the cost per box is $17.00. You are going to purchase enough Forever stamps from the post office to mail 100 cards. How much will it cost in total?

1box - 15 card - $17

100/15 = 6.67     (round off to 7 box since u cant buy 6.67 box)

7 * $17 = $119

Therefore, you will spend $119 to buy 7 box with a total of 105 cards.

Step-by-step explanation:

[tex]17 - \frac{9}{7} j[/tex]

[tex]14 - 4 - \frac{6}{7} j - \frac{3}{7} j[/tex]

[tex]17 - \frac{6}{7} - \frac{3}{7}j [/tex]

[tex]17 - \frac{9}{7} j[/tex]

The answer is A

It's multiples by 8 each time

Answer:

.

Step-by-step explanation:

If both bouquets have 6 tickseeds, the first bouquet ( roses + tickseeds) has more flowers.

The problem can be solved using ratio.

Bouquet 1 :

Every 2 tickseeds there are 7 roses

Hence, the ratio

Tickseed : rose = 2 : 7    

If there are 6 tickseeds, then

2 : 7 = 6 : rose

rose = (6/2) x 7 = 21

Number of flowers = 6 tickseeds + 21 roses = 27 flowers

Bouquet 2 :

Every 3 tickseeds there are 4 daisies

Hence, the ratio

Tickseed : daisy = 3 : 4

If there are 6 tickseeds, then

3 : 4 = 6 : daisy

daisy = (6/3) x 4 = 8

Number of flowers = 6 tickseeds + 4 daisies = 10 flowers

Hence, if there are 6 tickseeds in each bouquet, the first bouquet contains more flowers.

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