Given f ( x ) = 1 x + 10 , find the average rate of change of f ( x ) on the interval [ 8 , 8 + h ] . Your answer will be an expression involving h .

The regression equation is given by [tex]\overline{y}=50-0.01x[/tex]

We have given that,

The scatter plot shows the relationship between the mass of a tree and the total mass of the vegetation within 100 square meters of the tree.

The slope =change in y/change in x

We have given the two points (100,40) and (25000,2)

Therefore the slope of the given point is,

[tex]=\frac{25-40}{2500-1000} \\=-0.01[/tex]

The y-intercept is the value of y when x=0 this implies that y=50

Therefore the regression equation is given by

[tex]\overline{y}=50-0.01x[/tex]

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Answer:

Step-by-step explanation:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

⇒  The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.

Answer:

range = 18 and SD = 6

Step-by-step explanation:

range = max - min

= 228 - 210

= 18

FOR STANDARD DEVIATION * USE A SCIENTIFIC CALCULATOR THEY WON'T PENALIZE YOU*

follow these steps:

1. press mode then STAT

2. then press 1-VAR

3. put all the numbers on the table in ascending order

4 after press AC

5. press shift then 1

6. you will see many things but we are only interested in standard deviation, press *Var*

7. then select the standard deviation sign and press the equal sign

The profit-maximizing price of​ e-books relating to​ do-it-yourself topics is $5.35 and the average total cost of producing​ e-books is $4.35.

​

a. Profit-maximizing price

The maximum that the firm can earn is $35,000 at a quantity of 35,000 copies

Fixed cost FC = $140,000

Variable cost vc=$0.35 per book

Total Revenue TR =P XQ

Total Revenue TR= P x 35,000

Total Cost TC = FC + VC XQ

Total Cost TC = 140,000 + (0.35×35,000)

Total Cost TC = 140,000 +$12,250

Total Cost TC = $152,250

Profit = TR- TE

35,000 = 35,000P- $152,250

35,000P=187,250

P=187,250/35,000 copies

P=$5.35

b. Average total cost

Average total cost=Total cost/Quantity

Average total cost= $152,250/35,000 copies

Average total cost=$4.35

Therefore the profit-maximizing price of​ e-books relating to​ do-it-yourself topics is $5.35 and the average total cost of producing​ e-books is $4.35.

​

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The complete question is:

A firm that sells​ e-books - books in digital form downloadable from the Internet​ - sells all​ e-books relating to​ do-it-yourself topics​ (home plumbing,​ gardening, and so​ on) at the same price. At​ present, the company can earn a maximum annual profit of ​$35,000 when it sells 35,000 copies within a​ year's time. The firm incurs a 35​-cent expense each time a consumer downloads a​ copy, but the company must spend ​$140,000 per year developing new editions of the​ e-books. The company has determined that it would earn zero economic profits if price were equal to average total​ cost, and in this case it could sell 40,000 copies. Under marginal cost​ pricing, it could sell 120,000 copies.

In the short​ run, to the nearest​ cent, what is the​ profit-maximizing price of​ e-books relating to​ do-it-yourself topics? ​

At the​ profit-maximizing quantity, to the nearest​ cent, what is the average total cost of producing​ e-books?

39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:

We can write a mixed fraction in a fraction:

6 1/2 = 13/2

8 1/2  = 33/2

7 3/4 = 31/4

8 1/12 = 97/12

8 5/12 = 101/12

Adding all the fractions:

[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]

[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]

[tex]=23+\dfrac{64}{4}[/tex]

= 39 hours

Thus, 39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

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Answer:

Area of the minor segment = 2.505324230749 cm²

Step-by-step explanation:

Area of the minor segment

= Area of the sector ABC - Area of the triangle ABC

……………………………………………………………………………………

• Area of the sector ABC

= Area of the whole circle ÷ 8

= (π×8²) ÷ 8

= 8π

______

•• Area of the triangle ABC

= (1÷2) × CA × CB × sin(45)

= (1÷2) × 8 × 8 × (√2/2)

= 16√2

______

Thus

Area of the minor segment

= 8π - 16√2

= 2.505324230749

The reflected function is g(x) = √(-x).

And the correct option is the third one.

Remember that for a function f(x), a reflection across the y-axis gives:

g(x) = f(-x).

In this case, the original function was:

f(x) = √x

Then we have:

g(x) = √(-x).

So we can only evaluate this function in values of x such that:

x ≤ 0.

Then the correct option is:

"On a coordinate plane, a graph starts at (0, 0) and goes to the left through (negative 4, 2)."

As when we evalute g(x) in -4, we get:

g(-4) =  √(-(-4)) = √4 = 2

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Answer:

C

Step-by-step explanation:

Answer:

y = 5x + 11

Step-by-step explanation:

We are given that a line passes through (-2, 1) and also it contains a slope of 5

We want to write the equation of this line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y axis

As we are already given the slope, we can immediately substitute it into the formula

Replace m with 5 in y=mx+b:

y = 5x +  b

Now we need to find b

As the equation passes through the point (-2, 1), we can use its values to help solve for b.

Substitute -2 as x and 1 as y:

1 = 5(-2) + b

Multiply

1 = -10 + b

Add 10 to both sides

11 = b

Substitute 11 as b in the equation

y = 5x + 11

Topic: finding the equation of the line

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The value of x for the missing lengths in the given chords in the circle is; x = 4

The intersecting chords theorem  is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle.

Thus, for two chords AC and BD intersecting in a point S the following equation holds: AS * SC = BS * SD

Thus, for this question;

8(x + 2) = 12x

8x + 16 = 12x

12x - 8x = 16

4x = 16

x = 16/4

x = 4

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Answer:yw

Step-by-step explanation:

The only true statement is A:

"The data show a negative linear relationship."

On the graph, we can see how the car's vale decreases almost linearly with the age of the car.

Where the response variable would be the one on the y-axis, which is the car's value.

For that linear behavior, we know that there is a correlation coefficient different than zero. So options B, C, and D are false.

Finally, we already saw the linear behavior (decreasing, so the slope is negative). Then we conclude that the only true statement is A.

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Answer:

Step-by-step explanation:The answer is 45

Answer:

See below

Step-by-step explanation:

Longest is the down tube.....it is opposite the largest angle (95°) angle in the triangle .    This is a SCALENE triangle ( all sides of different length)

The longest tube that we have here is the down tube. The triangle that is formed id the scalene triangle

A scalene triangle is a type of triangle where all three sides have different lengths. In other words, no two sides of a scalene triangle are equal in length. Additionally, the angles of a scalene triangle are also different from each other.

The term "scalene" comes from the Greek word "skalenos," which means "uneven" or "unequal." This name reflects the defining characteristic of the scalene triangle, which is the absence of any equal sides or angles.

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Answer:

Since we want to find radius and the diameter is 28 we will divide by two = ²⁸/2 which gives a radius of 14

since the radius is 14cm. we move on to the volume .

WE SUBSTITUTE

⁴/3× ²²/7× 14 equals 58.2cm²

therefore radius; 14cm

volume; 58.2cm

The foci of the hyperbola represented by (0, –6) and (0, 6). Then the correct option is B.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

The equation of the parabola is given below.

5y² – 4x² – 80 = 0

Then the equation can be written as

y² / 4 – x² / 5 – 4 = 0

  y² / 16 – x² / 20 = 1

Then the value of eccentricity will be

a² = 16 and b² = 20

Then we have

e = √[1 + (b² / a²)]

e = √[1 + (20 / 16)]

e = 1.5

Then the focus of the parabola will be

⇒ (0, ±ae)

⇒ (0, ± 4 x 1.5)

⇒ (0, ±6)

⇒ (0, –6) and (0, 6)

Then the correct option is B.

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Answer:

======================================================

Explanation:

Let's solve for y to get the equation into y = mx+b form, aka slope intercept form.

4x-8y= -6

-8y= -6-4x

y = (-6-4x)/(-8)

y = -6/(-8) + (-4x)/(-8)

y = 3/4 + (1/2)x

y = (1/2)x + 3/4

This is now in y = mx+b form

m = 1/2 = slope

b = 3/4 = y intercept

We'll ignore the y intercept and focus on the slope only.

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

Rule: If the slope of a line is a/b, then the perpendicular slope is -b/a

Flip the fraction and flip the sign.

In this case, the original slope 1/2 has a perpendicular slope of -2/1 or simply -2.

The original slope multiplied with the perpendicular slope yields -1. So (1/2)*(-2/1) = -1

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

Another rule: Two parallel lines always have equal slopes, but different y intercepts.

The original slope is 1/2, so the parallel slope is also 1/2.

Answer:

see explanation

Step-by-step explanation:

using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

[tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

then

[tex]\sqrt{500}[/tex]

= [tex]\sqrt{100(5)}[/tex]

= [tex]\sqrt{100}[/tex] × [tex]\sqrt{5}[/tex]

= 10 × 2.24

= 22.4

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

[tex]\sqrt{0.5}[/tex]

= [tex]\sqrt{\frac{50}{100} }[/tex]

= [tex]\frac{\sqrt{50} }{\sqrt{100} }[/tex]

= [tex]\frac{\sqrt{50} }{10}[/tex]

= [tex]\frac{7.07}{10}[/tex]

= 0.707

Answer:54

Step-by-step explanation:

There are quicker ways to solve this but a simple and easy way to do this would be by dividing your number by the percent so 288/80 and with this, you would get your number for 1 percent or 3.6. Now you can multiply that number by the percent your need to find so 15. And 15 x 3.6 is = 54.

The real-life problem will be:- The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression is:-

[tex]24\times \dfrac{1}{3}[/tex] = 8

The real-life problem will be given the as:-The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

Hence the number of chocolates in each box will be 8.

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Answer:

61

Step-by-step explanation:

the question is asking to find the number of element of set b that are not in set a

to find this one must know the common elements

the question has given the common elements to be 5

now subtract the number of elements in set b with the common elements

i.e. 66-5

=61

The solution of the given equation 4(3x - 4) - 7( 2x + 3) = 3 is -20.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is;

4(3x - 4) - 7( 2x + 3) = 3

To solve;

4(3x - 4) - 7( 2x + 3) = 3

Solve the parentheses using the distributive property;

12x - 16 - 14x - 21 = 3

we need to get the like terms together;

12x - 14x -16 - 21 = 3

-2x - 37 = 3

Add 37 both sides, we get;

-2x = 40

Divide both sides by -2

x = -20

Hence, the solution of the given equation is -20.

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Using translation concepts, the equation for the graph is given as follows:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have a cosine function(zero at pi/2, this is zero at the origin), shifted pi/2 units to the right and 1 unit up(as the standard amplitude is between -1 and 1, here is between 0 and 2).

Hence the rule is given by:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

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We will see that we have a shift of 9 units to the left and 6 units upwards

For any given function H(x), we define a vertical shift of N units as:

g(x) = H(x) + N.

While a horizontal shift is written as:

g(x) = H(x + N).

Here we know that:

f(x) = 3*|x + 9| + 6

If the original function was:

H(x) = 3*|x|

Then we can write:

f(x) = H(x + 9) + 6

So we have a shift of 9 units to the left and 6 units upwards.

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Answer: [tex](-\infty, -8) \cup (-8, \infty)[/tex]

Step-by-step explanation:

I'm assuming you meant [tex]f(x)=\frac{x-9}{x+8}[/tex]

For this function, we need to make sure the denominator is not equal to 0, because if it was, then the fraction would be undefined.

Thus, [tex]x+8 \neq 0 \longrightarrow x \neq -8[/tex]

In interval notation, this is [tex](-\infty, -8) \cup (-8, \infty)[/tex]

The probability that both are smokers is 6903/180000

The given parameters are:

Male smoker = 177

Female smoker = 78

Total student = 78 + 522 = 600

The probability of a male smoker is

P(Male) = 177/600

The probability of a female smoker is

P(Female) = 78/600

The probability that both are smokers is

P(Smoker) =P(Male) *P(Female)

So, we have:

P(Smoker) = 177/600 * 78/600

Simplify

P(Smoker) = 177/600 * 39/300

Evaluate the product

P(Smoker) = 6903/180000

Hence, the probability that both are smokers is 6903/180000

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Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.

It is given by, after t years:

[tex]A(t) = 14(2.71)^{-0.016t}[/tex]

It will reach an amount of 7 parts per million when A(t) = 7, hence:

[tex]A(t) = 14(2.71)^{-0.016t}[/tex]

[tex]7 = 14(2.71)^{-0.016t}[/tex]

[tex](2.71)^{-0.016t} = 0.5[/tex]

[tex]\log{(2.71)^{-0.016t}} = \log{0.5}[/tex]

[tex]-0.016t\log{(2.71)} = \log{0.5}[/tex]

[tex]t = -\frac{\log{0.5}}{0.016\log{2.71}}[/tex]

t = 43.5.

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The regular price is $22.5 if everything in a store is 20% off, and the discounted price of an item is $18.00

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

If everything in a store is 20% off, and the discounted price of an item is $18.00

Let's suppose the regular price is x

(100-20)% of x = 18

80x/100 = 18

x = $22.5

Thus, the regular price is $22.5 if everything in a store is 20% off, and the discounted price of an item is $18.00

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