Consider the function f(x) = (x - 3)².
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.

The standard deviation for the given data is 5

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Given that,

the data,

X            Xₙ - X₀            (Xₙ - X₀)²

18            -7                      49

21             -4                      16

24            -1                        1

24            -1                        1

25             0                       0

31              6                      36

32            7                     49  

175                                  152

X₀  = 175/7 = 25

Variance  =    (Xₙ - X₀)²/(n-1)

                 =  152/(7-1)

                 =   25.33

Standard deviation =  √Variance

                                =  √25.33

                                =   5.03

Hence, the standard deviation is 5

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Answer:

-63

Step-by-step explanation:

Write the problem as a mathematical expression.

\(f(x)=-x^2+1\)  \(for\) \(x =3-9\) \(4-4-8\)

Simplify  4−4−8  to substitute in f(x)=−x^2+1

Subtract  4  from 4

\(0-8\)

Subtract  8  from 0

\(-8\)

Replace the variable  x  with  −

8  in the expression

\(f(-8)=-(-8)^2+1\)

Simplify

\(f(-8)=-64+1\)

\(f(-8)=-63\)

Answer = -63

Plz give me Brainliest if you can, hope this helps.

Answer:

D -8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Required function would be:

Answer:

the smallest r is the 4r and the biggest r is the r^2

VERTEX (-2,-64)

Step-by-step explanation:

Answer:

smaller r = -10

larger r = 6

The ordered pair for the vertex of the parabola is \((-2,-64)\)

Step-by-step explanation:

We have the function \(f(r)=r^2+4x-60\)

In order to factor this quadratic equation, we need to look for two numbers that will

Add together to get 4

Multiply together to get -60

Lets look for the numbers that multiply to give us -60.

-1 and 60

1 and -60

2 and -30

-2 and 30

3 and -20

-3 and 20

4 and -15

-4 and 15

5 and -12

-5 and 12

6 and -10

-6 and 10

Now, we just need to determine which of these numbers will add together to get us 4.

Those two numbers would be -6 and 10.

This means that our factored form of this equation will be

\(f(r)=(r-6)(r+10)\)

From this, we can find our roots, which are the solutions to the equation when it is equal to 0.

\((r-6)(r+10)=0\\\\r=-10, r=6\)

These are our r values.

The vertex of a parabola will always be directly between the two roots.

The number that is between -10 and 6 is \(r=-2\)

To find the y-value of the coordinate pair, we just need to plug -2 into our function.

\(f(-2)=(-2)^2+4(-2)-60\\\\f(-2)=4-8-60\\\\f(-2)=-64\)

This means that the ordered pair for the vertex of the parabola is \((-2,-64)\)

The relationship between corresponding terms in the two patterns is B(n) = 2A(n) where the A(n) and B(n) is the nth terms of the pattern A and pattern B.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have Pattern A starts at 0 and has the rule "add 3"

Pattern A:

0, 3, 6, 9, 12.....and so on

Pattern B starts at 0 and has the rule "add 6."

Pattern B:

0, 6, 12, 18, 24, 30.... and so one

In the pattern A we can find the nth term:

First term = 0, common difference = 3

A(n) = 0 + (n-1)3 = 3(n-1)

Similarly in the pattern B we can find the nth term

First term = 0, common difference = 6

B(n) = 0 + (n-1)6 = 6(n-1)

The relation can be derived between the nth term of pattern A and pattern B as follows:

B(n) = 2A(n)

Thus, the relationship between corresponding terms in the two patterns is B(n) = 2A(n) where the A(n) and B(n) is the nth terms of the pattern A and pattern B.

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The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.

What is a right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Given that, in △BCD

BD = 24 m

DC = 10 m

BC = 26 m

△BCD is a right angle triangle.

The trigonometry ratio of sine is ratio of height to hypothenuse.

With respect to C, the height of △BCD is 24m and hypothenuse is 26m.

sin C = height/hypothenuse

sin C = 24/26

C = 67.38°

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The solution to the equation 10x = 8 + 18 is x = 2.6

The equation is given as

10x = 8 + 18

Evaluate the sum of 8 and 18

10x = 26

Divide both sides of the equation by 10

10x/10 = 26/10

Evaluate the quotient

x = 2.6

Hence, the solution to the equation 10x = 8 + 18 is x = 2.6

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The equations are given

x(t)=t+5, y(t)=3t^2−4, where t is on the interval [−4,0].

To find the rectangular form of parametric equations

Substitute the value of t from x in y.

Then ,

The rectangular form of parametric equations is

The interval where x fall is

Answer:

over the five years Mr. Amari will have gained 30$

Step-by-step explanation:

The standard deviation is 2.24 if the sum of squares for a sample containing 101 items equals 500 option (C) is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{n-1}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

∑(x(i) - X)² = 500

n = 101

SD = √(500/101-1)

SD = √5

SD = 2.236 ≈ 2.24

Thus, the standard deviation is 2.24 if the sum of squares for a sample containing 101 items equals 500 option (C) is correct.

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The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

The optimal solution for the given linear programming problem using the Big-M method is x₁ = 4, x₂ = 2, with a maximum value of Z = 22.

To solve the given linear programming problem using the Big-M method, we first convert it into standard form by introducing slack, surplus, and artificial variables.

The objective function is to maximize Z = 4x₁ + 3x₂. The constraints are 2x₁ + x₂ ≥ 10, -3x₁ + 2x₂ ≤ 6, x₁ + x₂ ≥ 6, and x₁, x₂ ≥ 0.

We introduce slack variables s₁, s₂, and s₃ to convert the inequalities into equalities. The initial Big-M tableau is set up with the coefficients and variables, and the artificial variables are introduced to handle the inequalities. We set a large positive value (M) for the artificial variables' coefficients.

In the first iteration, we choose the most negative coefficient in the Z-row, which is -4 corresponding to x₁. We select the s₂-row as the pivot row since it has the minimum ratio of the RHS value (6) to the coefficient in the pivot column (-3). We perform row operations to make the pivot element 1 and other elements in the pivot column 0.

After multiple iterations, we find that the optimal solution is x₁ = 4, x₂ = 2, with a maximum value of Z = 22. This means that to maximize the objective function, x₁ should be set to 4 and x₂ should be set to 2, resulting in a maximum value of Z as 22." short

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The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.

The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;

Step 1; cos x = cos(2x + x)

Step 2; cos(2x) cosx - sin(2x) sinx

Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx

Step 4; cosx - 2sin²x cosx - 2sin²x cosx

Step 5; cosx - 4sin²x cosx

Step 6; cosx( 1 - 4sin²x)

Step 7; cosx{1 - 4(1 - cos²x)}

Step 8; cosx{-3 + 4cos²x}

Step 9; 4cos³x - 3cosx

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Answer:

C. -4x² + 5x - 28

Step-by-step explanation:

1. Expand -7(x² + 4):

-7x² - 28

3x² + 5x -7x² - 28

2. Group like terms:

-4x² + 5x -28

hope this helps :)

Bristol is the cheapest city and Paul can drop from his plans to stay under budget.

To determine which city Paul can drop and still stay under budget, we need to find the total cost of visiting all four cities and compare it to Paul's budget of £300.

We do not have information about the cost of sightseeing in each city, so we will assume that the cost is the same for each city. In that case, the cost of visiting all four cities is:

Cost of visiting all cities = Cost of visiting one city x 4

Let's call the cost of visiting one city "x". Then:

Cost of visiting all cities = x * 4

To stay under budget, the cost of visiting all cities must be less than or equal to £300. So we can write the following inequality:

Simplifying this inequality, we get:

x ≤ £75

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The answer is (c) Bristol, as it has the highest cost among the remaining cities and dropping it would leave Paul with 224 pounds, which is still within his budget.

A budget is whenever one plans on how to spend an estimated income. All the income should be considered as well as all the expenses. In other words, it is an expending plan.

The total cost of visiting all cities is:

76 + 66 + 91 + 60 + 72 = 365

To stay under budget, Paul must drop at least one city. To determine the cheapest city to drop, we can calculate the cost of the trip to each city if visited individually and compare it to the remaining budget:

- Bristol: 76 pounds

 Remaining budget: 300 - 76 = 224 pounds

- Leicester: 66 pounds

 Remaining budget: 300 - 66 = 234 pounds

- Glasgow: 91 pounds

 Remaining budget: 300 - 91 = 209 pounds

- Leeds: 60 pounds

 Remaining budget: 300 - 60 = 240 pounds

- Belfast: 72 pounds

 Remaining budget: 300 - 72 = 228 pounds

The city that Paul can drop while staying under budget is the one with the lowest cost.

Therefore, the answer is (c) Bristol, as it has the highest cost among the remaining cities and dropping it would leave Paul with 224 pounds, which is still within his budget.

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Answer:

13.4445 I think.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

9-5=4

Answer:

4

Step-by-step explanation:

9-5 is 4

Answer:

Oslo

Step-by-step explanation:

It's colder in Oslo by 7 degrees.

hope this answer helps!

Y = -1/8X +2

When X is 1, Y = -0.125+2, or 1.875

When X is -5, Y = 0.625+2, or 2.625

When X is -9, Y = 1.125+2, or 3.125

When X is -2, Y = 0.25+2, or 2.25

When X is -4, Y = 0.5+2, or 2.5

---

hope it helps

Answer:

35 dollars.

Step-by-step explanation:

The clerk likely just changed the price as a whole to 30 rather than add 30% to the original bought price.

Answer:

$35.10

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

that's hard but you'll figure it out so don't worry

Answer:

3/11

Step-by-step explanation:

3/11 equals 0.272727273 which is a repeating decimal.

Answer:

3/11 is C

Step-by-step explanation:

Answer:

F(t) = 1.8 - 0.04t

Step-by-step explanation:

Given that :

Length of trail = 1.8m

Walking speed = 0.04 miles per minute

Distance left, t minutes after one statues walking :

Total distance covered after t minutes = speed * time = 0.04t

Distance left after t minutes :

Initial distance - distance covered

Hence,

F(t) = 1.8 - 0.04t

The estimated outside diameter of the cyclone is approximately 101.01 microns. The estimated volumetric flow rate through the cyclone is approximately 6.434 × 10^(-8) cubic meters per second.

To estimate the outside diameter of the cyclone for a given cut diameter and inlet velocity, we can use the concept of cyclone efficiency. The cyclone efficiency (η) is the ratio of the actual cut diameter to the theoretical cut diameter. It is typically expressed as a percentage.

(a) Estimate the outside diameter of the cyclone:

To determine the outside diameter (D) of the cyclone, we can rearrange the formula for cyclone efficiency as follows:

η = (Dc / D) * 100

Where Dc is the cut diameter. Rearranging the formula, we have:

D = (Dc / η) * 100

We have that the cut diameter (Dc) is 1 micron and the desired cyclone efficiency (η) is 99%, we can calculate the outside diameter (D) as follows:

D = (1 micron / 0.99) * 100 = 101.01 microns

Therefore, the estimated outside diameter of the cyclone is approximately 101.01 microns.

(b) Estimate the volumetric flow rate:

To estimate the volumetric flow rate through the cyclone, we can multiply the inlet velocity (V) by the cross-sectional area of the cyclone (A).

Volumetric flow rate = V * A

Given that the inlet velocity (V) is 20 m/s, and assuming the cross-sectional area is circular, we can use the formula for the area of a circle:

A = π * (D^2) / 4

Substituting the estimated outside diameter (D) of 101.01 microns into the formula, we convert it to meters:

D = 101.01 microns = 0.00010101 meters

A = π * (0.00010101^2) / 4 = 3.217 × 10^(-9) square meters

Now we can calculate the volumetric flow rate:

Volumetric flow rate = 20 m/s * 3.217 × 10^(-9) m^2 = 6.434 × 10^(-8) cubic meters per second

Therefore, the estimated volumetric flow rate through the cyclone is approximately 6.434 × 10^(-8) cubic meters per second.

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The two intrinsic parameters associated with Cepheid variables are their period (the time it takes for one pulsation cycle) and their luminosity (the total amount of energy emitted).

Cepheid variables are a type of pulsating stars that exhibit regular variations in their brightness. The two intrinsic parameters associated with Cepheid variables are their period (the time it takes for one pulsation cycle) and their luminosity (the total amount of energy emitted).

The significant feature lies in the relationship between these two parameters. By measuring the period, which can be done relatively easily from observational data, it becomes possible to determine the luminosity of the Cepheid variable.

This relationship, known as the period-luminosity relationship, allows astronomers to estimate the absolute luminosity of Cepheid variables based on their observed periods. This information is crucial for determining distances to celestial objects and studying the properties of the universe.

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The statement \(log_{2} 4 + log_{2} 8 = 5\) is true.

We have been given two logarithm terms that is the first term is \(log_{2} 4\) and second term is \(log_{2} 8\).

The properties of logarithm that we are going to use are

          \(log a^{m} = m *log a\)  and \(log_{a} a = 1\)

First we will find the value of the two terms by operating the above mentioned properties of logarithm to obtained the values of the logarithm.

Thus,

                          \(log_{2} 4 = log_{2} 2^{2} \\ = 2* log_{2} 2\\ = 2*1\\ = 2\)

Similarly,    

                            \(log_{2} 8 = log_{2} 2^{3} \\ = 3* log_{2} 2\\ = 3*1\\ = 3\)        

Now adding both the terms by substituting its respective values which we have calculated above, we get

                   \(log_{2} 4 + log_{2} 8 = 2+3 = 5\)  

Thus,  we have proved that    R.H.S = L.H.S  

Hence the statement is  \(log_{2} 4 + log_{2} 8 = 5\) is true.

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