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Given:

Consider the given function is:

[tex]f(x)=x^2-8x+13[/tex]

To find:

The average rate of change of the function over the interval [tex]-1\leq x\leq 6[/tex].

Solution:

The average rate of change of the function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

We have,

[tex]f(x)=x^2-8x+13[/tex]

At [tex]x=-1[/tex],

[tex]f(-1)=(-1)^2-8(-1)+13[/tex]

[tex]f(-1)=1+8+13[/tex]

[tex]f(-1)=22[/tex]

At [tex]x=6[/tex],

[tex]f(6)=(6)^2-8(6)+13[/tex]

[tex]f(6)=36-48+13[/tex]

[tex]f(6)=1[/tex]

Now, the average rate of change of the function f(x) over the interval [tex]-1\leq x\leq 6[/tex] is:

[tex]m=\dfrac{f(6)-f(-1)}{6-(-1)}[/tex]

[tex]m=\dfrac{1-22}{7}[/tex]

[tex]m=\dfrac{-21}{7}[/tex]

[tex]m=-3[/tex]

Therefore, the average rate of change of the function f(x) over the interval [tex]-1\leq x\leq 6[/tex] is -3.

Answer:

5e+14

Step-by-step explanation:

999,999,999,999.99 x 500=5e+14

hope i helped

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The exponential function y = -3× 2⁽ˣ⁻⁴⁾ shows an exponential decay in the graph.

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. The graphs of exponential functions are nonlinear because their slopes are always changing, like curves, not straight lines

In the function given, we have that

y = -3× 2⁽ˣ⁻⁴⁾

This can be represented on a graph which shows an exponential decay of the function.

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Answer:

r=5  O(1;-12)

Step-by-step explanation:

x² + y² -2x + 24y +120 = 0

⇒ x²-2x+1+ y²+ 24y+144-145+120 = 0

⇒ (x-1)²+ (y+12)²=25   and    (x-h)² + (y-k)² =r²

so, h=1          k=-12       r=√25=5

center is O(h;k)   O(1;-12)

Answer:

70$ profit

8.75 per hour

Step-by-step explanation:

Ole's profit was $70 and Ole made $8.75 per hour fixing and selling the snowmobile.

percentage, a relative value indicating hundredth parts of any quantity.

To find the profit, we need to subtract the total cost of buying and fixing the snowmobile from the amount he sold it for:

Profit = Selling Price - Total Cost

Total Cost = Purchase Price + Cost of Parts

Total Cost = $600 + $430 = $1030

Profit = $1100 - $1030 = $70

Therefore, Ole's profit was $70.

b. To find the money Ole made per hour, we need to know how much time he spent fixing the snowmobile.

He spent 8 hours fixing it, so his hourly rate would be:

Hourly Rate = Profit / Time

Hourly Rate = $70 / 8 hours

Hourly Rate = $8.75 per hour

Therefore, Ole made $8.75 per hour fixing and selling the snowmobile.

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Answer:

gev5y

Step-by-step explanation:

Answer:

x<-2

Step-by-step explanation:

5x + 3 < -7

5x  < -7-3

5x<-10

x<-10/5

x<-2

Answer:

Step-by-step explanation:

2+b/ b pretend this is a fraction

The critical value of t has probability 0.10 to the right with 8 degrees of freedom is 1.3968.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

The t-distribution with 8 degrees of freedom has probability 0.10 to the right of t.

That is, df = 8,

α = 0.10 by using these values, the critical value of t is obtained.

From the t-distribution table:

The critical value is 1.3968.

The critical value of t has probability 0.10 to the right with 8 degrees of freedom is 1.3968.

Therefore, the critical value of t has probability 0.10 to the right with 8 degrees of freedom is 1.3968.

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Answer:

B - ∠b and ∠f

Step-by-step explanation:

Corresponding angles are the angles in matching corners of the intersections in the traversal. Since ∠b and ∠f are in the same position relative to the intersection, they are corresponding.

Answer:

80 miligrams

Step-by-step explanation:

100 / 250 = 0.4

0.4 * 200 = 80

Answer:

3 factors.

Step-by-step explanation:

When we have a product of some numbers A, B and C

A*B*C

(here I used 3, but the number does not matter, is just for the example)

To find the number of factors of the product, we first need to find the number of factors for each one of the numbers that is being multiplicated.

Here you need to remember that every integer number can be written as a product of prime numbers.

For example, 15 can be written as:

15 = 2*3*5

So the number 15 has 3 factors.

In the case of prime numbers, like 7, we have:

7 = 7

So 7 has only one factor in its decomposition.

In our case, our numbers are:

7, 11, and 13.

We can see that the 3 numbers are prime numbers.

Then each number has only one factor in its decomposition.

Then we have 3 factors in the multiplication, it is:

7*11*13

Answer:

D

Step-by-step explanation:

to get average you need to add everything and divide by the number of the datas there are, which is the mean

Answer:

the answer is c 253.5

Step-by-step explanation:

6.5×6.5+6.5×6.5+6.5×6.5+6.5

×6.5+6.5×6.5+6.5×6.5

=253.5

Answer:

25.35

Step-by-step explanation:

Area of the shaded portion = Area of semicircle - Area of the right triangle

Area of semicircle = πr²/2

Area of semicircle = 3.14(6)²/2

Area of semicircle = 3.14 * 18

Area of semicircle = 56.52

Area of triangle = 1/2 * base * height

Get the height using the SOH CAH TOA identity

sin 60 = H/12

H = 12sin60

H = 12(0.8660)

H = 10.39

Get the base

12² = b²+10.39²

144 = b²+108

b² = 144 - 108

b² = 36

b = 6

Area of triangle = 1/2 * 6 * 10.39

Area of triangle = 3 * 10.39

Area of triangle = 31.17

Area of shaded portion = 56.52 - 31.17

Area of shaded portion = 25.35

Answer:

( 2m - n + p )² - ( 2m + n - p )² = 4m² + n² + p² - 4mn + 4mp - 2np - ( 4m² + n² + p² + 4mn - 4mp - 2np ) = 4m² + n² + p² - 4mn + 4mp - 2np - 4m² - n² - p² - 4mn + 4mp - 2np = -8mn + 8mp

Answer:

h

Step-by-step explanation:

Answer:

Your answer is (6x−1)(3x−2)

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

It would have to be 13, because if you look at the top of the shape, you see the little 45 degrees. You can also see the 90 degrees right angle. Triangles no matter what add up to 180 degrees.

(a is the unknown angle in the bottom right)

90+45+a=180

45+a=90

a=45

now that we have that , we know that it has to be symmetrical.

so it can only be 13

hope this helps!

Answer:

121.21 people per square mile

Step-by-step explanation:

area = 1/2(12 + 21)(14) = 231 mi²

28,000/231 = 121.21 people per square mile

Answer

False

Step-by-step explanation:

The max number is 1 and so the unlikelier the number, the less value the number will be.

For example: The likelyhood of fliping a coin and landing on heads: 0.5

Hopes this makes sense!

Answer:

They are the same.

Step-by-step explanation:

12 divided by 15 = .8 and 8 divided by 10= .8

.8=.8

Hope this helps!

Answer:

Yes, and see below for sentences.

Step-by-step explanation:

Yes, they do have the same value. If you create equivalent fractions for each of them with a common denominator, you can compare the numerators to each other.

12/15 is equal to 24/30 when you multiply numerator and denominator by 2, and 8/10 is equal to 24/30 when you multiply numerator and denominator by 3.

Please let me know if you have any questions.

Answer: 23 feet

Step-by-step explanation:

The question simply means that we should calculate the radius of the circle. In this case, the area has been given to be 1661ft².

Area of a circle = πr²

πr² = 1661ft²

3.14(r²) = 1661

r² = 1661 / 3.14

r² = 528.98

r = ✓528.98

r = 23

The solution is 23 feet.

Answer:

The answer is B.

Step-by-step explanation:

As you can see, box plot A is symmetrical so that applies to answers A and B. However, box B is very skewed to the right which makes it positively skewed so answer B is the only one that matches the correct description of the two box and whisker plots.

We can conclude that the distribution for town A is symmetric, but the distribution for town B is positively skewed.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

The distribution for town A is symmetric, but the distribution for town B is positively skewed.

We can determine the skewness of the distributions by comparing the position of the median with respect to the quartiles.

In town A,

The median (30) is located at the center of the box, and the first and third quartiles (20 and 40, respectively are equidistant from the median.

This indicates a symmetric distribution.

In town B,

The first and third quartiles (20 and 30, respectively) are closer to the median (25) on the left-hand side of the box than on the right-hand side. This indicates a positively skewed distribution.

Therefore,

We can conclude that the distribution for town A is symmetric, but the distribution for town B is positively skewed.

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Answer:

[tex]\sqrt{6\cdot \:216}=\sqrt{1296}[/tex]

[tex]=\sqrt{36^2}=36[/tex]

Answer:

60%

Step-by-step explanation:

30            60

----     =     ----         =  60%

50            100

Answer:

A. there must be a vertical asymptote at x=c

Step-by-step explanation:

Answer: A

Step-by-step explanation:

got it right edge 2022