The function f(x) is given in the graph below. Find its average rate of change between the followin
points. Show the calculations that lead to your answer.
(a) x=-6 to x = 4
(b) x=-2 to x=2.

Answer:

Step-by-step explanation:

a) 100cm 1m so, 320/100=3.2m, 1200/100=12m

b) 3.2+3.2+12+12= 6.4+24=30.4

c) 3*12=36m squared

d) 3.2*12= 3*12+0.2*12=36+2.4=38.4m squared

e) My estimate in d) was reasonable

f) This is because 36 and 38.4 are really close to each other they only have a difference of 2.4 and that is because instead of multiplying the estimate with 3 and a 0.2 I just multiplied it with a 3. 0.2*12=2.4 so the difference is reasonable.

Answer:

14.5 feet

Step-by-step explanation:

     To make the subject as 'w', isolate w.

              2L + 2W =P

                      2W = P - 2L

                        [tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]

   P = 37 feet

   L = 4 feet

           [tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]

                = 18.5 - 4

           W = 14.5 feet

a) The margin of error associated with a 95% confidence interval is 4.

b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)

a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.

The formula for margin of error is Z  = zα/2 σ √ n

Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96

So, the value of error margin is  zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04

= 4

b) We know from part a that margin of error is 4.

Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77

The value of confidence interval for population mean is,

x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)

Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)

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Answer:

Any equation that has the same slope as this line will be parallel to it. The slope is -1/4, so whichever equation has -1/4 x in it will be parallel to the line.

Answer:

-3.5

Step-by-step explanation:

-4x-1+1≤ 13+1

-4x/-4 ≤ 14/-4

x≤ -3.5

The person who runs fastest is Zach.

Ron runs 9 feet per second: 9 ft/s

Zach runs 410 feet in 49 seconds:

410/49 ft/s

=8.36 ft/s

= 8.4 ft/s (Approximately)

Katie runs 1 mile in 412 seconds:

1 mile = 5280 ft

5280/412 ft/s

=12.8 ft/s

Noah  runs 870 feet in 1 minute:  

= 870/60 ft/s

= 14.5 ft/s

Hence,

Ron 9 feet per seconds

Zach 8.4 feet per seconds

Katie  12.8 feet per seconds

Noah 14.5 feet per seconds

So, Zach is the fastest.

Therefore the fastest is Zach.

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The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.

What is Linear Function?

A straight line on the coordinate plane is represented by a linear function.

The linear function formulas are:

Here, we have

The given functions are f(0)=2 and f(3) = -1

For f(0) = 2

Coordinate: (0,2)

y-intercept, c: 2

For f(3) = -1

Coordinate: (3,-1)

gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1

=( y₂-y₁)/(x₂-x₁)

= ( -1 -2)/(3 - 0)

= -3/3

= -1

The linear equation is in the slope-intercept form, y=mx+c

f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.

Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.

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Answer:

2x2x3x5= 60

I hope you like it

Answer:

2 X 2 X 3 X 5

Step-by-step explanation:

We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.

Answer: the answer would be 2

Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.

2x3=6-4=2

The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that  opposite angles of a parallelogram are congruent.

We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.

Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.

Thus, angle G is congruent to angle T and angle L .

Therefore, ∠L ≅ ∠T

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Answer:

By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Step-by-step explanation:

got it right on edge2

Caelan must spend a total cost of $ 17 for 10 bowling games.

The total cost consists in the sum of a fixed cost, represented by rent of shoes, and a variable cost, represented by the number of bowling games, whose model is presented below:

c' = c + r · n

Where:

First, construct the system of equations related to Kai and Jack:

Kai

c + 3 · r = 6.50

Jack

c + 5 · r = 9.50

Second, solve the system of linear equations by numerical methods:

(c, r) = (2, 1.5)

Third, write the resulting function:

c' = 2 + 1.5 · n

Fourth, evaluate the function for the situation of Caelan:

17 = 2 + 1.5 · n

1.5 · n = 15

n = 10

Caelan rents 10 bowling games for $ 17.

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Step-by-step explanation:

so the ticket booth had $150 so $1254 -$150=$1104

so $1104 ÷ by $3 each person = to 368 people paid the admission

Had: $150

Tickets :368

Total :$1254

For the period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.

According to the specified question-

Rate of change = (final number - initial number)/(final year - initial year)

Rate of change = (12,458 - 968)/(2010 - 2005)

Rate of change = -11490/5

Rate of change = -2298 fishes per year.

Negative sign shows there is a decline in the number.

Thus, for the time period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.

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Utilizing multiplication to find relationships and predicting that value of one  "Linear regression" is a quantity derived from the value of another.

The relationship in between magnitude of one parameter and that of a second is modeled by simple linear regression.

Thus, finding correlations via multiplication and assuming that the value of one "Linear regression" is a number obtained as from value of another

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The arrangement of the points in increasing order of the slopes are (27, 2) and (243, 18),  (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40),  (12, 32) and (18, 48), (18, 63) and (24, 84)

Slope is defined as the change in y divided by the change in x. Mathematically:

Slope = (y2 - y1) / (x2 -x1)

To arrange the pair of points. You need to find the slope:

For (15, 30) and (20, 40):

x1 = 15, y1 =30 and x2 =20, y2=40

slope = (40-30)/(20-15) = 10/5 =2

For (12, 32) and (18, 48):

slope = (48-32)/(18-12) = 16/6 = 2.67

For (27, 12) and (72, 32):

slope = (32-12)/(72-27)  = 20/45 = 0.44

For (45, 15) and (60, 20):

slope = (20-15)/(60-45) = 5/15 = 1/3 = 0.33

For (27, 2) and (243, 18):

slope = (18-2)/(243-27) = 16/216 = 0.07

For (18, 63) and (24, 84):

slope = (84-63)/(24-18) = 21/6 = 7/2 = 3.5

For (63, 9) and (84, 12):

slope = (12-9)/(84-63) = 3/21 = 1/7 = 0.14

Therefore, the pairs of points in increasing order of the slopes are (27, 2) and (243, 18),  (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40),  (12, 32) and (18, 48), (18, 63) and (24, 84)

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2/216 or 1/108 is the probability of rolling a number .

How does probability explain work?

The great thing about this question is that all three of those rolls are Independent Scenarios.

The probability of the first roll does not effect the outcome of the second or third roll

   1/6 ( we want a 1, and there are 6 options.)

1/6 ( We want a 3, and there are 6 options

2/6 ( We want a 5 or 6, and there are 6 options)

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The rationalization of the denominator of the given fraction gives 8 -2√3

From the question, we are to rationalize the denominator of the given fraction

The given fraction is

26 / (4+√3)

To rationalize the given expression, we will multiply both the numerator and the denominator of the fraction by the conjugate of the denominator.

The denominator is 4+√3

Thus,

The conjugate of the denominator is 4-√3

Now, multiply the numerator and the denominator by the conjugate.

That is,

(26 × (4-√3)) / ((4+√3) × (4-√3))

(104 - 26√3) / (16 - 3)

(104 - 26√3) / 13

= 104/13 - (26√3)/13

= 8 - 2√3

Hence,

The result of rationalizing is 8 -2√3

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Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

The  residual value is 0.6.

The estimated value of a fixed asset at the conclusion of its useful life or lease term is known as the residual value, also known as salvage value. In lease agreements, one of the lessor's main methods for figuring out how much the lessee must pay in periodic lease payments is the residual value.

Given:

y = 1.416x − 0.76

For (7, 8):

As, residual value = Measured value - Predicted value

or, residual value = (actual y-coordinate of the point) - (value of y from the

                                                                                                       equation)

When x = 10:

So, the value of y from the equation,

[tex]y_1[/tex] = 1.416 x 10 - 0.76

[tex]y_1[/tex]=  14.16 - 0.76

[tex]y_1[/tex]= 13.4

and, actual y-coordinate of the point, [tex]y_2[/tex]= 14

Residual value = 14 - 13.4

Residual value = 14 - 13.4

Residual value = 0.6

Hence, the residual value is 0.6

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Answer:

0.6

Step-by-step explanation:

im taking the test rn

The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven

Let the number of days be d.

Let the number of miles be m.

The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.

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Based on the given ratio of modern and classical songs learned, the number of modern songs learned if 9 classicals have been learned is 15

If the choir has learned 9 classical songs;

Equate the ratio of the number of modern songs to the number of classical songs

5 : 3 = x : 9

5/3 = x/9

5 × 9 = 3 × x

45 = 3x

divide both sides by 3

x = 45/3

x = 15

In conclusion, the number of modern songs they have learned if they learn 9 classical songs is 15

Complete question:

Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.

If the choir has learned 9 classical songs, how many modern songs have they learned?

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Answer:

Step-by-step explanation:

Hi Mia,  are you aware that the last name Hamilton is a famous math person?  :)    anyway,  

The triangle in the picture is an isosceles triangle,  we know that b/c the angle of the one is 45° meaning the other side must also be a 45° angle.  So we know the two sides are the same length.

side n = 7 [tex]\sqrt{2}[/tex] / 2

then use Pythagoras to find m

[tex]c^{2}[/tex] = ( 7 [tex]\sqrt{2}[/tex] / 2)^2  + ( 7 [tex]\sqrt{2}[/tex] / 2)^2

[tex]c^{2}[/tex] = 49*2/4  + 49*2/4

[tex]c^{2}[/tex] = 49/2  + 49/2

[tex]c^{2}[/tex] = 98/2

[tex]c^{2}[/tex] = 49

c = 7

side m = 7   :)  nice, huh ?

a) Sin X = O/H

Sin 45 = [tex]7\sqrt{2}[/tex]/2/H

H= [tex]7\sqrt{2}[/tex]/2/ Sin 45

m= 7

b) cos X = A/H

   cos 45= A/7

A= cos45*7

n= 4.95

Graph of f(x) = 3x - sin 4x is using method of adding y-coordinates is attached below.

What is graphing method by adding ordinates?

The function y = 3x - sin 4x is actually the sum of two functions, y = 3x and y = - sin 4x.

For every value in the domain, there is a corresponding value in the range so that the point (x, 3x - sin 4x) is on the graph of y = 3x - sin 4x.

According to the given question:

Follow these steps to graphing the function:

1. Open an Excel file. Label the first column "x-coordinates," the second column "y = 3x," the third column "y = -sin 4x," and the fourth column "y = 3x - sin 4x." Set each column to round to four decimal places.

2. Set up the first column to range from -2pi to 2pi by intervals of pi/4.

3. Fill in the second and third columns by utilizing the equations y = 3x and y = - sin 4x, respectively.

4. Fill in the fourth column by simply adding the second and third columns.

5. Graph y = 3x - sin 4x  by using the x-coordinates from column A and the y-coordinates from column D.

Check the attachment below for the required graph obtained after plotting the points.

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Answer:

200 at 9% simple interest for 2 years

Answer:

a

Step-by-step explanation:

Hope it helps and have a nice day!!!! :)

Step-by-step explanation:

OR

Answer:

Step-by-step explanation:

The value of the equation y(t) at y(25) is 150

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Equations can be linear, quadratic or polynomials.

if y(t) = -14t + 500

The y(25)  means substitute t = 25 into the equation

y(25) = -14(25) + 500

y(25) = -350 + 500

y(25) = 150

In conclusion, the value of y(25) is 150

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Answer:

10 days

Step-by-step explanation: