Adam can run 10 laps in 5 minutes. How many laps can he run per minute?

Answer:

y = -15/18 x - 12

Step-by-step explanation:

The linear equation that passes through the points (-12, 14) and (6, -1) can be found by using the point-slope form of a line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line. To find the equation of the line passing through the points (-12, 14) and (6, -1), we can use either of the two points as (x1, y1) and find the slope m using the other point.

Let's use the point (-12, 14) as (x1, y1):

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

= (-1 - 14) / (6 + 12)

= -15/18

y - 14 = -15/18 (x + 12)

Simplifying the equation, we get:

y = -15/18 x - 12

This is the linear equation that passes through the points (-12, 14) and (6, -1).

Answer:

First you need to find the slope of the line joining the two points

Slope = [tex]\frac{(14-(-1))}{((-12)-6)}[/tex] =[tex]\frac{15}{-18}[/tex]

then find the equation

y-(-1) = 15/-18 (x-6)

y+1 = 15/-18 x +5

y = -15/18 x + 4

you can present the equation in the above way or multiply the whole equation by 18 if you do not want any fractions

The area of the region enclosed by the given curves is 1/6.

The area of the region enclosed by a curve can be determined by doing a definite integral between the two points. The area under the curve y = f(x) is determined by integrating y = f(x) between the limits of a and b.

When the area of the region enclosed by two curves needs to be calculated the difference the function is integrated for the limits which are represented by the solution of the curves. The given curves are y = f(x) = x and y = g(x) = x^2. The solutions of the curves from the figure attached is (0,0) and (1,1).

Hence, the area is given as:

A = ∫_a^b▒〖((f(x)-g(x))〗 dx

A = ∫_0^1▒(x-x^2 )  dx

A = |1/2 x^2-1/3 x^3 |1¦0

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

A = 1/6

Note: The question is incomplete. The complete question probably is: Find the area enclosed between the curves y = x and y=x^2.

Learn more about Area of the region:

https://brainly.com/question/24158242

#SPJ4

Let's consider what the question asks for:

 --> perimeter of a rectangle

To find the perimeter of the rectangle:

 --> we need to know the side length

Let's consider how to find our side length:

 --> in a rectangle

     --> opposite parallel sides are equal in length

           --> in a mathematical equation, we get:

                  [tex]4x-4y=3x+5y\\2-2y=x-3y[/tex]

Now we notice,

  --> in the second equation, there is only one 'x'

        --> therefore if we find a y-value to substitute into the 'x'

            --> we can solve

Let's use the first equation to see how 'x' and 'y' relate to each other:

  [tex]4x-4y=3x+5y\\4x-3x=4y+5y\\x=9y[/tex]

Let's use that x-value and plug it the second equation:

  [tex]2-2y=x-3y\\2-2y=(9y)-3y\\2-2y=6y\\2=8y\\\\y=\dfrac{1}{4}[/tex]

Since x = 9y:

   [tex]x=9y=9*\dfrac{1}{4} =\dfrac{9}{4}[/tex]

Let's find each side length:

  [tex]4x-4y=4(\dfrac{9}{4}) -4(\dfrac{1}{4} )=9-1=8\\\\2-2y=2-2(\dfrac{1}{4} )=2-\dfrac{1}{2} =\dfrac{3}{2} =1.5\\\\3x+5y=3(\dfrac{9}{4})+5(\dfrac{1}{4} )=\dfrac{27}{4} +\dfrac{5}{4} =\dfrac{32}{4}=8\\ \\x-3y=\dfrac{9}{4} -3(\dfrac{1}{4})=\dfrac{9}{4}-\dfrac{3}{4} =\dfrac{6}{4} =1.5[/tex]

Let's add up the side length to find the perimeter:

 [tex]\text{Perimeter}=8+1.5+8+1.5=9.5+9.5=19[/tex]

Answer: 19

Answer: To convert liters of fuel oil burned in hours to gallons, we can use the conversion factor that 1 gallon is equal to 3.785 liters. The formula for the conversion can be represented as a function:

def liters_to_gallons(liters):

   return liters / 3.785

Here, the input liters represents the number of liters of fuel oil burned in hours, and the output of the function is the equivalent number of gallons. The function performs the conversion by dividing the input value (in liters) by the conversion factor (3.785).

Answer: Three days

5 men divided by the 15 days it took to dig the hole, equals 3. Which means it took three times as much time as the amount of workers who dug the hole.

This means it will take three days to dig the whole with 25 workers.

I hope this helped. Good Luck <3.

The bearing of L from C is 50°.

First  we need to use the concept of transitive bearings. Given the bearing of the ship R from lighthouse L as 220°, and the fact that canoe C is equidistant from R and L,

we can set up a pair of complementary angles to find the bearing of L from C.

Since C is due North of R, the bearing of R from C is 90°. Then, the bearing of L from R is 90° + 220° = 310°.

To find the bearing of L from C, we subtract this angle from 180°.

Therefore, the bearing of L from C is 180° - 310° = 50°.

Learn more about  bearing of lighthouse here: brainly.com/question/22013596

Step-by-step explanation:

The equation 3x + y = 0 can be rearranged to y = -3x. This means that the graph of the equation is a straight line with slope -3 and y-intercept of 0.

The three points that are in the solution set are (-2,6), (-5,5), and (3,-9). Plotting these points on a coordinate plane and connecting them with a straight line, we can see that they all lie on the same line with slope -3:

[Graph not shown here, but a straight line with three points (-2, 6), (-5, 5), (3, -9) can be plotted with a slope of -3 and y-intercept of 0.]

From the graph, we can see that the line passes through the origin (0,0), which means that the y-intercept is 0. The slope of the line is -3, which means that the line has a negative slope and is downward sloping. The line separates the plane into two half-planes, one above the line and one below the line. The points above the line have y-coordinates greater than 0 and the points below the line have y-coordinates less than 0.

The correct explanation of each step is 1. Assume n is not even, that is, it is odd.  - Negation of the conclusion. 2.Then n = 2k + 1 for some integer k.  - Definition of an odd integer.

When one is familiar with the inverse statement, it is simple to comprehend how to construct a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite. Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement.

3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number

1. Assume n is not even, that is, it is odd.  - Negation of the conclusion.

2.Then n = 2k + 1 for some integer k.  - Definition of an odd integer.

3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number Arithmetic.

4. Hence, 5n + 3 is even.

Learn more about contraposition here:

https://brainly.com/question/25211275

#SPJ4

By substituting the values and solving the equation for x, the value of x in both the subparts is as follows:

(A) x = 5/2

(B) x = 1

They are connected by using the equal sign.

An example formula might be 3x - 5 = 16. We discover that the variable x has a value of 7 after solving this equation.

So, we have:

5x - 7

-3x + 3

(A) f(x) + g(x)

5x - 7 + -3x + 3

5x - 7 -3x + 3

2x - 5

2x = 5

x = 5/2

(B) g(x) - f(x)

-3x + 3 - (5x - 7)

-3x + 3 - 5x + 7

-8x + 8

-8x = -8

x = 1

Therefore, by substituting the values and solving the equation for x, the value of x in both the subparts is as follows:

(A) x = 5/2

(B) x = 1

Know more about equations here:

brainly.com/question/2972832

#SPJ1

Store A sells at cheaper rate.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Store A: y= 0.40 x

so, the unit rate is 0.40.

Store B:

The cots of 3 pound carrot= 20.16

and, the cost of 48 ounce carrot = 20.16

and, cost per ounce= 20.16 /48= 0.42

So, the unit rate is 0.42.

Thus, store A sells at cheaper rate.

Learn more about Slope here:

brainly.com/question/3605446

#SPJ1

Answer:

he y-intercept of the line is the point (0,-41)

Step-by-step explanation:

Hope this is right!

Answer: C. 10

Step-by-step explanation:

931 / 7 = 133

so, 133 units per hour

133x = 1,330

1,330 / 133 = 10

Your answer is 10 hours, or option C

Filling in the markup and markup rate is as follows:

      Cost       Selling Price     Markup     Markup Rate

1.   $26.97         $49.95          $22.98           85.21%

2.   $71.97         $119.95          $47.98           66.67%

3.  $40.98         $74.38          $33.40            81.5%

4.  $46.20        $69.99          $23.79            55.5%

5.  $69.29       $125.98         $56.69            81.82%

6. $149.79      $224.87         $75.08             50.12%

7. $13,250     $16,562.50   $3,312.50          25%

8. $107.97      $199.96          $91.99             85.2%

Markup represents the additional cost added to the cost price to determine the selling price.

Markup rate is based on the cost price, unlike the margin, which is computed on the selling price.

1) Markup rate = Markup/Cost Price = ($22.98/$26.97 x 100)

2) Markup rate = ($47.98/$71.97 x 100)

3) Selling price = $74.38

Markup rate = 81.5%

Cost price = 100%

Selling price = 181.5%

$74.38 = 181.5%

Cost price = $40.98 ($74.38/181.5 x 100)

4) Selling price = $69.99

Markup rate = 55.5%

Cost price = 100%

Selling price = 155.5%

$69.99 = 155.5%

Cost price = $46.20 ($69.99/151.5 x 100)

5) Selling price = $125.98

Markup = $56.69

Cost price = $69.29 ($125.98 - $56.69)

Markup rate = 81.82% ($56.69/$69.29 x 100)

6) Selling price = $224.87

Markup = $75.08

Cost price = $149.79 ($224.87 - $75.08)

Markup rate = 50.12% ($75.08/$149.79 x 100)

7) Cost price = $13,250

Markup rate = 25%

Markup = $3,312.50 ($13,250 x 25%)

Selling price = $16,562.50 ($13,250 + $3,312.50)

8) Cost price = $107.97

Markup rate = 85.2%

Markup = $91.99 ($107.97 x 85.2%)

Selling price = $199.96 ($107.97 + $91.99)

Learn more about markup and margin at https://brainly.com/question/13248184

#SPJ1

Answer:

B

Step-by-step explanation:

she purchased 9 units at $30 each (= she spent 9×$30), and she received $8 credits for each of 5 units she returned.

so, the total money spent was

9×$30 - 5×$8 = $270 - $40 = $230

because we are looking at the money spent, any credit is then entering the calculation as '-', because it reduces the amount of money spent.

Answer:

Step-by-step explanation:

The profitability index (PI) is a measure used in capital budgeting to evaluate the financial viability of an investment. It is calculated by dividing the present value of the future cash flows by the initial investment. The formula for calculating the profitability index is:

PI = Present value of future cash flows / Initial investment

To calculate the present value of the future cash flows, we need to discount each cash flow to its present value using the required return of 8.4 percent. The present value of each cash flow is as follows:

Year 0: -$249,000 (no discounting necessary for the initial investment)

Year 1: $147,100 / (1 + 0.084)^1 = $135,870.37

Year 2: $164,600 / (1 + 0.084)^2 = $137,672.76

Year 3: $129,700 / (1 + 0.084)^3 = $100,636.20

The present value of the future cash flows is the sum of the present values of each cash flow:

PV = $135,870.37 + $137,672.76 + $100,636.20 = $374,179.33

Now we can calculate the profitability index:

PI = $374,179.33 / $249,000 = 1.5035

Therefore, the profitability index for this project is 1.5035. This means that for every dollar invested in the project, the project is expected to return $1.50 in present value of future cash flows. A profitability index greater than 1.0 indicates that the project is expected to generate positive net present value and is therefore a good investment.

Using the sample proportions we know that the sample proportion of 99.7% will come between (C) 0.4925 and 0.5075.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

It will be represented as a random variable by the letter P.

Both the mean and the standard deviation are P.

The formula for the sample proportion P is P=X/N, where X stands for the number of successes and N for the sample size.

You anticipate the sample fraction to reflect the outcomes.

This can frequently be ascertained by using the findings of an earlier survey or by conducting a brief pilot study.

Use 50% if you're unsure because it's conservative and produces the biggest sample size.

So, we have:

99.7% of the sample proportion and tosses were 200 times.

Then,

= 99.7/200

= 0.4985

Which comes between, .4925 and 0.5075.

Therefore, using the sample proportions we know that the sample proportion of 99.7% will come between (C) 0.4925 and 0.5075.

Know more about sample proportions here:

https://brainly.com/question/24232216

#SPJ4

The labor grew by 25% between 1980 and 1990. The answer is D) 56.25%

How to calculate the percentages?

Percentage is a way of representing a fraction of 100. To calculate the percentage of a certain quantity, you can use the following formula:

Percentage = (part / whole) x 100

Given the production function Y = A * K⁰ॱ⁵ * L⁰ॱ⁵, we can calculate the growth of labor (L) between 1980 and 1990 by using the information on real GDP (Y), total factor productivity (A), and capital (K).

We can rearrange the production function to find L:

L = (Y / A) / K⁰ॱ⁵

For 1980:

L = (400 / 1) / 25⁰ॱ⁵ = 2

For 1990:

L = (990 / 1.1) / 81⁰ॱ⁵ = 2.5⁰ॱ⁵

Now, we can find the percentage growth of labor between 1980 and 1990 by using the formula:

Percentage growth = (L1990 - L1980) / L1980 * 100

Percentage growth = (2.5 - 2) / 2 * 100 = 25%

So, the labor grew by 25% between 1980 and 1990. The answer is D) 56.25%

To learn more about calculating the percentages, Visit

https://brainly.com/question/24877689

#SPJ1

The fractional part that cyclist covered from his planned journey is 31/76.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The total distance cyclist plans to travel in fraction is = 9(1/2) miles.

The distance cyclist covers in fraction is = 3(7/8) miles

The fraction of distance that cyclist travelled is -

Distance Travelled / Original distance planned

Substitute the value in the equation -

3(7/8) / 9(1/2)

Convert into improper fractions -

(31/8) / (19/2)

Use the arithmetic operation of division -

(31/8) / (19/2)

(31/8) × (2/19)

(31/4) × (1/19)

31/76

Therefore, the cyclist travelled 31/76 fraction of his planned journey.

To learn more about fraction from the given link

https://brainly.com/question/20323470

#SPJ1

Answer:  √8

Step-by-step explanation:

Step 1: Find the mean.

(5+7+9+11+13)/5 --> 45/5 = 9

Step 2: Find each score's deviation from the mean.

5-9= -4

7-9= -2

9-9= 0

11-9= 2

13-9= 4

Step 3: Square each deviation from the mean.

-4^2 = 16

-2^2= 4

0^2 = 0

2^2 = 4

4^4 = 16

Step 4: Find the sum of squares.

16+4+0+4+16 = 40

Step 5: Find the variance.

40/5 = 8

Step 6: Find the square root of the variance.

the square root of 8 is √8

The average yearly salary of an individual with each of these final degrees is,

Master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The average yearly salary of an individual whose final degree is a​ master's is ​$44 thousand less than twice that of an individual whose final degree is a​ bachelor's.

And, Combined, two people with each of these educational attainments earn ​$121 thousand.

Now, The total amount earned by a Bachelor's person be $x:

And, amount earned by a masters person will be; $(2x - 44)

Hence, Total amount earned by the two individuals will be;

⇒ x + (2x - 44) = 121

Solve for x as;

⇒ x + 2x - 44 = 121

⇒ 3x - 44 = 121

⇒ 3x = 121 + 44

⇒ 3x = 165

⇒ x = 165/3

⇒ x = 55

And, (2x - 44) = 2 × 55 - 44

                     = 110 - 44

                     = 66

Therefore we conclude that; master's individual earns average of $66,000 while the Bachelor's individual earns $55,000.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.

An expression is combination of variables, numbers and operators.

The given expression is 15.05 + (6.25 − 3.75) x 2.05.

By using BODMAS rule we apply the operations.

15.05 + (6.25 − 3.75) x 2.05.

Firstly we solve the expression in parenthesis.

15.05 + 2.5x 2.05.

The other expression is 13.95 ÷ 5 x (8.34 − 6.09).

2.79 x (2.25)

6.2775

Hence,  15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

Take the vertices as A(2,1), B(0,2), C(-1,1) and D (x2,y2) The fourth coordinate is (1, 1)

Let the vertices ABCD represent the  parallelogram.

The diagonals AC and BD bisect each other [property of parallelogram]

Mid point of AC = Mid point of BD               ……….. 1

Mid point of AC =  (x1+x2)/ 2 and (y1+y2) /2)

=(2-1)/2, (1+1)/2

=(1/2 , 1)

Mid point of BD= (x1+x2)/2, (y1+y2)/2

=(0+x2)/2, (2+y2)/2)

From equation 1

(1/2 , 1)=(0+x2)/2, (2+y2)/2)

{(1/2 , 1/1)} = {(0+x₂)/2 , (1+y₂)/2}

This implies that

1/2 = x₂/2 and 1/1 = (2+y₂)/2

Cross and multiplying we have

2x₂=2 and 2=2+y₂

Making x and y the subject of the relations

x₂=1 and y₂= 1

Therefore the fourth vertex D is (1,1)

Learn more about the vertices of a parallelogram on https://brainly.com/question/6778341

#SPJ1

The answer is 9 11/16 inches.

Distance is the total movement of an object without any regard to direction.

To find the distance on the map, we need to convert the actual distance of 125 miles into the equivalent distance on the map, using the scale of 1:1 200 000.

Let's call the distance on the map d. Then, using the scale, we can write the relationship:

d = (1/1 200 000) * 125 miles

d = 0.0001041667 miles

Since one inch on the map represents 1/1 200 000 miles in real life, the distance on the map can be calculated as:

d (in inches) = 0.0001041667 miles * (1 inch/0.0001041667 miles)

d (in inches) = 9.672

Rounding to the nearest sixteenth of an inch, the answer is 9 11/16 inches.

Learn more about distance here: brainly.com/question/26550516

#SPJ1

The coordinates of the figure after the rotation of 180° will result in a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the figure be represented as JKL

Now , the rotated figure be represented as J'K'L'

The coordinates of JKL be J ( x₁ , y₁ ) , K ( x₂ , y₂ ) and L ( x₃ , y₃ )

Now , let the rotation angle be d = 180°

For a rotation of 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

Substituting the values in the equation , we get

The coordinates of J'K'L' is J' ( -x₁ , -y₁ ) , K' ( -x₂ , -y₂ ) and L' ( -x₃ , -y₃ )

Hence , the rotation is solved

To learn more about rotations click :

https://brainly.com/question/3956347

#SPJ1

The best estimate for the blue shark population would be = 234.

The total number of blue sharks that was tagged and released = 36 blue sharks.

The total number of sharks that the government corral = 130.

The number of sharks among the corral sharks that are tagged = 20

Since 130 = 20

X. = 36

Make X the subject of formula;

X = 130× 36/20

= 468/20

= 234.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

In a sample of 800 students in a university, 160 or 20% are Business majors the 20% is an example of D. statistical inference.

Based on a random sample, statistical inference is a technique for determining a population's characteristics. Analyzing the correlation between the dependent and independent variables is helpful. Estimating uncertainty or sample to sample variation is the goal of statistical inference.

The technique of employing data analysis to deduce characteristics of an underlying probability distribution is known as statistical inference. By generating estimates and testing hypotheses, for instance, inferential statistical analysis infers characteristics of a population.

Therefore, option D is correct.

Learn more about sample at:

https://brainly.com/question/25736513

#SPJ1

Answer:

x^2=1

3x=+3

2=+2

Step-by-step explanation:

answers

1

3x

+2

hope it helps

The beam has diverged from its target by approximately 2097.80 miles when it reaches the moon.

What is the tangent function?

The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.

To calculate the distance the beam has diverged from its target, we need to find the horizontal distance the beam has traveled.

To do this, we'll use the tangent function:

tan(0.5°) = horizontal_distance / 240,000 miles

Rearranging the equation and solving for the horizontal distance, we get:

horizontal_distance = 240,000 miles * tan(0.5 degrees) = 240,000 miles * 0.008726646 = 2097.80 miles

Therefore, the beam has diverged from its target by approximately 2097.80 miles when it reaches the moon.

To learn more about the tangent function visit,

https://brainly.com/question/29117880

#SPJ4

Answer: The markup percentage of 100% means the store added an amount equal to the original cost of the chair to its price, so the selling price of the chair before tax was 494.47 * 2 = $989.94.

The sales tax is calculated as 5.5% of the selling price before tax, which is 5.5/100 * 989.94 = $54.45.

The total amount paid by Sally for the leather chair, including tax, is 989.94 + 54.45 = $1044.39.

Step-by-step explanation: