Fine the average rate of change for f(x) on the interval [-1,3]

Given

A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. the graph shows the height above the surface of the ground, y, in feet the hammer is x seconds after being thrown from the roof

Solution

The final answer

Option C

The equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

Let

Since the rectangular plot of ground is 30 meters longer than it is wide, we have that

L = W + 30

Since the area of the rectangular plot is A = LW where

Since A = 20,000 m², we have that

LW = 20,000

(W + 30)W = 20,000

W² + 30W = 20,000

W² + 30W - 20,000 = 0

Using the quadratic formula, we have that

[tex]W = \frac{-30 +/- \sqrt{30^{2} - 4 X (-20000)} }{2 X 1} \\W = \frac{-30 +/- \sqrt{900 + 80000} }{2} \\W = \frac{-30 +/- \sqrt{80900} }{2} \\W = \frac{-30 +/- 284.43}{2} \\W = \frac{-30 +/- 284.43}{2}\\W = \frac{-30 - 284.43}{2} or \frac{-30 + 284.43}{2}\\W = \frac{-314.43}{2} or \frac{254.43}{2}\\W = -157.22 or 127.23\\[/tex]

Since W cannot be negative, we have W = 127.23

Since L = W + 30

L = 127.23 + 30

L = 157.23

So, the dimensions are

So, the equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

Learn more about rectangular plot here:

https://brainly.com/question/28828287

#SPJ1

The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.

Given,

The exponents; 3^6 and 3^5.

We have to simplify this into a single power of 3.

In multiplication;

That is,

aᵇ . aⁿ = a^(b + n)

a^b . c^d = a x c ^ (b + d) = ac^bd

So,

3⁶ . 3⁵ = 3^(6 + 5) = 3¹¹

That is,

The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.

Learn more about simplification of exponents here:

https://brainly.com/question/28339931

#SPJ1

If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras

The distance traveled by Mr. Giordano = 4.5 miles

The time taken = 5 minutes

Speed = Distance / Time

Substitute the values in the equation

Speed = 4.5/5

= 0.9 miles per minutes

The distance traveled by Mr. Baras = 6.3 miles

The time taken = 8 minutes
Speed = Distance / Time

Substitute the values in the equation

Speed = 6.3/8

= 0.78 miles per minutes

Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras

Learn more about speed here

brainly.com/question/7359669

#SPJ1

The expected number of juniors in the committee is 1.3

The question is incomplete, the complete question is given below:

A committee of 3 members is selected from a club made up of 13 juniors members and 17 senior members. What is the expected number of juniors in the​ committee?

The expected number of juniors in the committee is computed here as:

Juniors in the committee=13

Seniors in the committee=17

Total number of members=(13+17)=30

Fraction of juniors in total members=13/30

So expected number of juniors in the committee:

=Fraction of juniors in total members*Total number of members to be selected

=(13/30)*3

=1.3

Therefore 1.30 is the expected number of juniors in the committee

Learn more about probabilities here:

https://brainly.com/question/26814883

#SPJ4

Step-by-step explanation:

[tex]area \: of \: circle = \pi\:r^{2} \\ \pi \times6.5^{2} - \pi \times {2.3}^{2} = 36.96\pi = 116.113... {cm}^{2} [/tex]

Answer:

116.129 cm²

Step-by-step explanation:

       [tex]\boxed{\bf Area \ of \ circle = \pi r^2}[/tex]

Area of outer circle:

    R = 6.5 cm

   Area =3.142 * 6.5 * 6.5

             = 132.75 cm²

Area of inner circle:

 r = 2.3 cm

       Area of inner circle =3.142 * 2.3 *2.3

                                        = 16.621 cm²

Area of shaded area = area of outer circle - area of inner circle

                                    = 132.75 - 16.621

                                    =  116.129 cm²

Explanation

Given the function;

We are asked to find the population of the bacteria after 7 days.

Given that t represents the number of days, we can find the population by substituting 7 into the formula. This can be seen below.

Answer: 4374

Answer:

first plot the positive 2 on the y axis

plot (0,2)

Then from (0,2) go up 2 and right 2.

Answer in attached image

An equation which represents the proportional relationship between the x and y-values is: C. y = 2x​.

A direct variation represents two variables that are directly proportional to each other, which simply means as one variable increases, the other variable also increases and vice-versa.

Mathematically, a proportional relationship can be represented by the following equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) based on the data points given:

k = y/x

k = 20/10

k = 2

Therefore, the required equation is as follows:

y = 2x

Read more on proportionality here: brainly.com/question/20167968

#SPJ1

Complete Question:

As the x-value increases by 20, the y-value increases by 10. Which of the following equations represents the relationship between the x and y-values?

A. y = 2 + x

B. y = 2 - x

C. y = 2x​

Answer:16

Step-by-step explanation:

x-[tex]\sqrt{x}[/tex]=12

x=16

Given the formula for the circumference of a circle:

C = 2πr

Let's find the circumference of a circle with a diameter of 4 ft.

Where r is the radius.

To find the radius, we have:

The radius of the circle is 2 ft.

Take π = 3.14

Hence, to find the circumference of the circle, C, substitute 2 for r, 3.14 for π, and evaluate.

Thus, we have:

Therefore, the circumference of the circle is 12.56 ft

ANSWER:

C. 12.56 ft

Answer:

4.24ms-²

Step-by-step explanation:

S: x. write suvat and sub in values

u:4.2

v:14.8

a:?

t:2.5

use correct equation

v=u+at

sub values in

14.8=4.2+2.5a

rearrange to get a

10.6/2.5= a

a=4.24

Answer:

C. 152

Step-by-step explanation:

8 × 10 + 6 × 12 = 80 + 72 = 152

Given

The table,

The sample size is 27.

To find:

The mean weight of these 27 babies.

Explanation:

It is given that,

That implies,

The mean weight of 27 babies is,

Hence, the mean weight of 27 babies is 6.1 pounds.

The width of the house driveway in the scale drawing is 4 inches.

Scale drawing is drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale).

Therefore, he measured a house and its lot and made a scale drawing.

The scale of the drawing was 1 inch : 5 feet.

The houses driveway is 20 feet wide in real life.

Therefore,

5 feet = 1 inch

20 feet = ?

cross multiply

Therefore,

width of the driveway on the scale drawing =  20 × 1 / 5

width of the driveway on the scale drawing =  20 / 5

width of the driveway on the scale drawing =  4 inches.

learn more on scale drawing here: https://brainly.com/question/28729500

#SPJ1

Answer:744

Step-by-step explanation:

800-7%=744

Answer:

$56

Step-by-step explanation:

The number of tiny toys that Toby's Tiny Toys need to sell to reach its break-even point is 13,475.

The break-even point is the production and sales units that will ensure that Toby's Tiny Toys does not incur a loss or generate a profit.

At the break-even point, the total revenues are equal to the total costs (fixed and variable).

Selling price per unit = $16.50

Variable expenses per unit = $12.50

Contribution margin per unit = $4 ($16.50 - $12.50)

Fixed expenses = $53,900

Break-even point in units = Fixed costs/Contribution margin per unit

= 13,475 ($53,900/$4)

Thus, we can conclude that Toby’s Tiny Toys needs to sell 13,475 to break even.

Learn more about the break-even point at brainly.com/question/15281855

#SPJ1

The number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.

The overall revenues and entire costs are equal at the break-even point (fixed and variable).

The production and sales units that will verify that Toby's Tiny Toys does not suffer a loss or make a profit are the break-even point.

$16.50 is the selling price per unit.

Variable costs amount to $12.50 per unit.

The contribution margin = $16.50 - $12.50 = $4 per unit equals

Fixed costs is $53,900.

Break-even point = Fixed costs / Contribution margin

Break-even point = $53,900/$4

Apply division operation to get

Break-even point = 13,475

Thus, the number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.

To learn more about the break-even point here:

https://brainly.com/question/13680956

#SPJ1

Answer:

Step-by-step explanation:

You want the ratios (red to blue), of perimeter and area, given that corresponding sides have the ratio red to blue = 5 to 8.

The ratio of perimeters is the ratio of corresponding side lengths:

  red to blue = 5 / 8

The ratio of areas is the square of the ratio of corresponding side lengths:

  red to blue = (5 to 8)² = 25 / 64

__

Additional comment

Ratios are customarily expressed in any of three equivalent forms:

The length of the scraps of wood when placed side by side is 53 inches.

A line plot is a graph that is made up of a number line and check marks above the numbers on the number line. The check marks above the number line represents the frequency of the data. For example, there are two checkmarks above 7. This means that there are two scraps of woods that measure 7 inches.

In order to determine the approximate length of the scraps of wood if they are placed side by side, add the length of each scrap of wood together.

Addition is a mathematical operation that is used to determine the sum of two or more numbers. The sign that is used to denote addition is +.

[tex]5\frac{1}{2} + 6 + (6\frac{1}{2}. 3) + (7. 2) + 8[/tex] =

[tex]5\frac{1}{2} + 6 + 19\frac{1}{2} + 14 + 8[/tex] = 53 inches

Please find attached the complete question. To learn more about addition, please check: https://brainly.com/question/19628082

#SPJ1

Answer:

In second week there is percentage limit (-ve sign) of 20% in people traveling examine to first week.

In 0.33 week there is proportion increase of 50% in human beings traveling compare to 2nd week.

In fourth week there is share limit of 75% in humans visiting evaluate to 1/3 week.

a) The total mass of sugar used is 1.7 kg.

b)The mass of sugar he has left is 0.3 kg.

A fraction is a numerical value that represents a piece of a total in mathematics. The total can be any number, a specific value, or a single item. Fractions are denoted by the symbol p/q.

Given:

Total mass of sugar Mr tan has = 2 kg

Fraction of sugar used to make dessert = 1/4 kg

Fraction of sugar used to bake some cakes = 3/5 kg

The total mass of sugar used is determined as,

= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes

Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg

Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg

Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg

Mass of sugar left with him =  Total mass of sugar - Total mass of sugar used

= 2 kg - 1.7 kg  = 0.3 kg

To learn more about fractions visit:

brainly.com/question/11979743

#SPJ13

The complete question is: "Mr tan had 2 kg of sugar. He used 1/4 kg of sugar to make dessert and 3/5 kg of sugar to bake some cakes.

(a) What was the total mass of sugar used?

(b) How much sugar did he have left?"

Answer:

  2.7 - h < 2.3

Step-by-step explanation:

You want an inequality to represent the relationship described by "Stella wants to know the number of hours (h) by which she must reduce her 2.7 hour half-marathon time to run in under 2.3 hours."

If h is the number of hours by which the time is reduced, Stella wants ...

  2.7 -h < 2.3 . . . . . . . . . representative inequality

__

Additional comment

The solution would be h > 0.4. Stella must reduce her time by more than 0.4 hours.

<95141404393>

The formula to find the surface area of a cylinder is:

In this case, we have:

B. 140π units²

After four years, the investment is worth £8934.34.

The interest you earn on interest is known as compound interest. For instance, if you start with $100 and it generates 5% interest annually, you will conclude the first year with $105 in your account. You'll have $110.25 after the second year is over.

We employ the formula approach to determine the entire amount,

A = P(1+r)^n

The amount invested, or principal(P), is £8,000.

Interest rate r is 2.8%, or 0.028.

n = 4 years have passed.

Now, immediately enter these values into the formula, A = P(1+r)n.

A = 8000 * (1 + 0.028) ^ 4

= 8000 * 1.028 ^ 4

= 8934.34

Consequently, the investment's value after four years is £8934.34.

To read more about compound interest

https://brainly.com/question/28020457

#SPJ9

Answer: 3 hours

Let john take x hours to finish the work

Let nelly take y hours to finish the work

given, y =x+3

Portion of work done by john alone in one hour = 1/x

Portion of work done by Nelly alone in one hour = 1/y

∴Portion of work done by both john and nelly in one hour = 1/x + 1/y

[tex]= \frac{1}{x} + \frac{1}{x+3}\\=\frac{x+3+x}{x*(x+3)}\\=\frac{2x+3}{x^2+3x}[/tex]

Total time taken by John and nelly to finish the work = 2 hours

[tex]\therefore [2(2x+3)]/[x^2 + 3x] = 1\\= > 4x + 6 = x^2 + 3x\\= > x^2 -x -6 =0\\= > x^2 - 3x + 2x -6 =0\\= > x(x-3) + 2(x-3)=0\\= > (x+2)(x-3)=0[/tex]

Hence either x = -2 or x = 3

Since x is time taken, it cannot be negative, hence x = 3

∴Time taken by john to finish the work = 3 hours

Read a similar work-time answer:

https://brainly.com/question/17146782

Answer:

65

Step-by-step explanation:

2:26

1:x

26/2 = x = 13

The heli uses 13 gallons per hour.

5:y

13x5 = y = 65

Hope that helps

Answer: 2

Step-by-step explanation:

      We will use the slope formula to find the slope of the line going through these two points.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\displaystyle \frac{0-2}{-5--4} =\frac{-2}{-5+4} =\frac{-2}{-1} =2[/tex]

      The slope of this line is 2.

Read more about finding the slope here: https://brainly.com/question/17879149

Linear equations - The team can bring its 24 players

What do you mean by linear equations with one variable?

A linear equation with one variable is one that can be written as ax+b = 0, where a and b are two integers, and x is a variable. This type of problem only has one solution. For instance, the linear equation 4x+4=8 only has one variable.

We are given that,

the total money raised by the lacrosse team is given to be $2863.50

bus rented at a cost of $1087.50

meal budget per person is calculated to be $74

let us assume the number of players the team can bring to the tournament to be "x".

bus rent + (meal budget * number of players) = total money raised

= 1087.50 + (74*x) = 2863.50

= 1087.50 + 74x = 2863.50

= 74x = 2863.50 - 1087.50

= 74x = 1776

= x = 1776 ÷ 74

= x = 24

Thus the team can bring its 24 players.

to learn more about linear equations visit:
https://brainly.com/question/2030026
#SPJ13