Sarah and John are running clockwise around a circular track with radius 25 meters. They start at the same position, and Sarah runs at 2.7 m/s while John runs at 2.2 m/s. How far away from their starting point are they when Sarah catches up and passes John for the first time after the start?

Answer:

[tex]\frac{3}{4}[/tex] miles

Step-by-step explanation:

Total length of the trail = [tex]4\frac{1}{2}[/tex] miles = [tex]\frac{9}{2}[/tex] miles

She ran the first [tex]\frac{2}{3}[/tex] of the distance i.e.

The distance for which she ran = [tex]\frac{2}{3} \times \frac{9}{2} = 3\ miles[/tex]

Remaining distance = Total length of trail minus the distance for which she has already run = [tex]\frac{9}{2} - 3 = \frac{3}{2}[/tex] miles

Given that: After running, Annie has to walk due to steep nature of the trail, So, Annie walked for [tex]\frac{1}{2}[/tex] of the remaining distance.

The distance for which Annie walked = [tex]\frac{1}{2} \times[/tex] Remaining distance

The distance for which Annie walked = [tex]\frac{1}{2} \times[/tex] [tex]\frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] miles

So, the answer is: [tex]\frac{3}{4}[/tex] miles

Answer:

0.285

Step-by-step explanation:

To do this, divide 28 1/2% by 100%, obtaining:

28.5%

---------- = 0.285

100%

A.) linear,weak

just got it right on edge 2020

The best describes the association of this scatterplot will be linear, and weak. Then the correct option is A.

Scatter plots are graphs that show how two variables in a data collection relate to one another. On a two-dimensional plane or in a Cartesian system, it represents data points.

In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are created to plot data points on both horizontal and vertical axis.

A set of dots plotted on an azimuth and elevation axis is known as a scatter plot. Given that they can demonstrate the degree of connection, if any, in between values of measured quantities or events, scatter plots are crucial in statisticians (called variables).

The best describes the association of this scatterplot will be linear, and weak. Then the correct option is A.

More about the scatter plot link is given below.

https://brainly.com/question/13984412

#SPJ2

Answer:

Axis of Symmetry: x = -4

Vertex: (-4, 54)

Step-by-step explanation:

We use a graphing calc.

Answer:

the equation of the axis of symmetry is [tex]x=-4[/tex]

Step-by-step explanation:

Recall that the x-value of the vertex of a parabola of the form:

[tex]y=ax^2+bx +c[/tex]

is given by the expression:

[tex]x_{vertex}=-\frac{b}{2\,a}[/tex]

therefore, in our case the x-position of the vertex becomes;[tex]x_{vertex}=-\frac{b}{2\,a}=\frac{32}{-8} =-4[/tex]

and since the equation of the axis of symmetry is [tex]x=x_{vertex}[/tex]

Then, the equation of the axis of symmetry is [tex]x=-4[/tex]

Answer:

3 a^(-2)

3 / a^2

Step-by-step explanation:

(3a) (a^-3)

Multiply

3 a^1 * a^-3

Since we are multiplying, we add the exponents

3 a^ ( 1-3)

3 a^(-2)

If  you are not supposed to leave a negative exponent

x^-b = 1 / x^b

3 / a^2

Answer:

2a-6b+6c

Step-by-step explanation:

Combine like terms

Answer: -2a + 2c

Step-by-step explanation:

The situation is saying that subtract  4a-3b+2c from 2a-3b+4c.

(2a-3b+4c) - (4a - 3b +2c) Subtract by terms

-2a + 2c

Answer: LOL

Step-by-step explanation:

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So the "back" of the arrow is on/above -20.

The arrow points to -12.

You added something to -20 to get to -12.

So the first number is -20. You added ? to get -12. -12 is the last number / the answer to the equation.

So the equation from what you have so far is -20 + ? = -12

You need to isolate the ? so that you know what it is.

So to get rid of the -20 (make it 0), you have to add 20. -20 plus 20 equals 0, which basically means it is gone. You also have to add 20 to -12. 20 plus -12 equals 8.

Now the equation is ? = 8.

So you know that the second number is 8.

The equation makes sense; -20 + 8 = -12.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

Answer:

See graph attached

Step-by-step explanation:

Our life is simple because the equation [tex]y=2x+2[/tex] is already put in slope-intercept form.

This form is called slope-intercept because it states exactly what it's called: The number multiplied by [tex]x[/tex] (the constant of proportionality, in this case, 2) is the slope - and the y-intercept is what is being added to the equation (in this case, also 2, since there is a +2 at the end.)

With this info, we can start graphing.

We know that the y-intercept is 2, meaning one point will be (0,2).

We also know that the slope is 2, meaning every time x increases by 1, y will increase by 2. So the next point is (1, 4), the next is (2, 6), and so on.

Hope this helped!

The graph of the function y = 2x + 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 2x + 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ6

Answer: The answer is 7 ( x + 3 ).

Step-by-step explanation:

So we are given in word-form this equation:

seven times the sum of a number and three

We can rewrite this as:

7 times ( number + 3)

This number can be rewritten as a variable. Take any variable of your pick. I'll use x because that's one of the most used variables.

7 ( x + 3 )

There you go! Finished.

Answer:

[tex]77\div.77\cdot1[/tex]

Step-by-step explanation:

What we're basically looking for here are ways to get 100 using these numbers.

My immediate first thought was "can we divide the 7's by some 7's to get 100?"

I know that [tex]7 \div .7=10[/tex], so I had the idea to make it [tex]77 \div .77 = 100[/tex]. This means that we can use the number 7 four times in the equation [tex]77 \div .77=100[/tex].

However, we're still missing a 1 that we need to include. This is easy, we can just multiply [tex]77 \div .77[/tex] by 1.

So in conclusion, we get [tex]77 \div .77\cdot1[/tex]

Hope this helped!

Answer:

177 - 77 = 100

Step-by-step explanation:

there are basically 4 7s

77-77 = 00

177 - 77 = 100

hope this helps （＾▽＾）

Answer:

The weekly profit function P(x,y) = 72x  - 0.01x² -0.005xy + 38y -  0.005xy -0.015y²  - 10000

3.5 oz bars = 3560

5 oz bars = 80

The maximum weekly profit = 119680

Step-by-step explanation:

Given that:

the demand functions are p and q

the variable cost of x = 8x and the variable cost of y = 12y

Since the  fixed cost attributed to the division is exist 10,000/week

∴ the total cost C = 8x + 12y + 10000

R(x,y) = p(x) + q(y)

where ;

xp(x) = 80x -0.01x² -0.005y

yqz(y) = 50 -0.005x -0.015y²

R(x,y) = 80x -0.01x² -0.005xy +  50y -0.005xy -0.015y²

The weekly profit function P(x,y) = R(x,y) - C

P(x,y) = 80x -0.01x² -0.005xy + 50 -0.005xy -0.015y² - ( 8x + 12y + 10000)

P(x,y) = 80x -0.01x² -0.005xy + 50 - 0.005xy -0.015y² - 8x -12y - 10000

P(x,y) = 72x  - 0.01x² -0.005xy + 38y -  0.005xy -0.015y²  - 10000

(b) How many of the 3.5-oz size bars and how many of the 5-oz bath size bars should the division produce per week to maximize its profit?

profit will be  maximized if:

[tex]\dfrac{\partial P}{\partial x} =0 \ and \ \dfrac{\partial P}{\partial y} =0[/tex]

given  that:

[tex]\dfrac{\partial^2 P}{\partial x^2} < 0 \ and \ D >0[/tex]

where;

D = Px Py -Pxy²

Now;

[tex]\dfrac{\partial P}{\partial x} =(-0.02 x -0.01 y +72)[/tex]

[tex]\dfrac{\partial P}{\partial y} =(-0.03 x -0.01 y +38)[/tex]

[tex]\dfrac{\partial P}{\partial x} =0 \to 2x+y = 7200[/tex]

[tex]\dfrac{\partial P}{\partial y} =0 \to x+3y = 3800[/tex]

2x + y   = 7200

2x + 6y = 7600  

5y = 400

y = 400/5

y = 80

From

x + 3y = 3800

x + 3(80) = 3800

x = 3800 - 240

x =  3560

∴ 3.5 oz bars = 3560

5 oz bars = 80

What is the maximum weekly profit?

The maximum weekly profit = 72x  - 0.01x² -0.005xy + 38y -  0.005xy -0.015y²  - 10000

The maximum weekly profit = 72(3560)  - 0.01(3560)² -0.005(3560)(80) + 38(80) -  0.005(3560)(80) -0.015(80)²  - 10000

The maximum weekly profit =  256320 - 126736 - 1424  + 3040 -  1424 -96  - 10000

The maximum weekly profit = 119680

Answer:

a)after 1,000 years?

1 meter

b) 10 million years?

10,000 meters

c) 50 million years?

50,000 meters

Step-by-step explanation:

We are told in the question that mountains rise 1 mm per year.

a) After 1000 years

1 year = 1 mm

1000 years =

Cross Multiply

1000 × 1 mm

= 1000mm

Converting to meters

1 mm = 0.001 m

1000 mm =

1000 × 0.001m

= 1 meter

b) After 10 million (10,000,000) years

1 year = 1 mm

10000000years =

Cross Multiply

10000000 × 1 mm

= 10,000,000mm

Converting to meters

1 mm = 0.001 m

10,000,000mm =

10,000,000 × 0.001m

= 10,000 meters

c) After 50 million years(50,000,000)

After 50,000,000 years

1 year = 1 mm

50,000,000years =

Cross Multiply

50,000,000 × 1 mm

= 50,000,000mm

Converting to meters

1 mm = 0.001 m

50,000,000mm =

50,000,000 × 0.001m

= 50,000 meters

Answer:

See below.

Step-by-step explanation:

Triangle:

The area for a triangle is given by the formula:

[tex]A=\frac{1}{2}bh[/tex]

Where b is the length of the base and h is the vertical height.

We can see that the base length is (2x+4) and the height is (x+3). So, the expression for the area would be:

[tex]\frac{1}{2}(2x+4)(x+3)[/tex]

Rectangle:

The perimeter of a rectangle is given by the formula:

[tex]P=2l+2w[/tex]

Where l is the length and w is the width.

We can see that the length is 2x-1 and the width is 3x+2. Thus, the perimeter is:

[tex]2(2x-1)+2(3x+2)[/tex]

For the area, the formula is:

[tex]A=lw[/tex]

So, the expression for area would be:

[tex](2x-1)(3x+2)[/tex]

Rectangular Prism:

The volume for a rectangular prism is given by the formula:

[tex]V=lwh[/tex]

The length is (x+2), the width is (x), and the height is (2x+1). Thus:

[tex]x(x+2)(2x+1)[/tex]

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

y = 4/3x - 5

Comparing with the general equation above

Slope/ m = 4/3

Since the lines are parallel their slope are also the same

So we have

Slope of parallel line = 4/3

Equation of the line using point (−6,−5) and slope 4/3 is

We have the final answer as

Hope this helps you.

Answer:

c) (0.40)(0.35)x + (0.45)(0.64)y = 1200

Step-by-step explanation:

Profit on each tulip bulb is:

Profit on x amount of tulip bulbs:

Similarly, profit on y amount of daffodil bulbs is:

Since the target is $1200, the required equation is:

Correct answer option is C)

Answer:

A

Step-by-step explanation:

12x-8/4 divide

12x/4 = 3x

-8/4 = -2

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{3x - 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ \frac{12x - 8}{4} }[/tex]

Factor out 4 from the expression

⇒[tex] \sf{ \frac{4(3x - 2)}{4} }[/tex]

Reduce the fraction with 4

⇒[tex] \sf{3x - 2}[/tex]

Hope I helped!

Best regards! :D

Answer:

the reciprocal of the slope of f(x) is the same as the slope of f⁻¹(x)

Step-by-step explanation:

To find the equation of a line given two points, we use the formula:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

The standard equation of a line is given by:

y = mx + c; where m is the slope of the line and c is the intercept on the y axis

For the function f(x), we have to select two points, let us select (-6, 9) and (0, 27)

Hence the equation of the line f(x) is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-9=\frac{27-9}{0-(-6)}(x-(-6))\\ \\y-9=\frac{18}{6} (x+6)\\\\y-9=3(x+6)\\\\y-9=3x+18\\\\y=3x+18+9\\\\y=3x+27\\[/tex]

Comparing y = 3x + 27 with y = mx + c, we can see that the slope (m) = 3 and the y intercept is 27

For the inverse function f⁻¹(x), let us use the points (-3, -10) and (0, 9)

Hence the equation of the line f⁻¹((x) is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-(-10)=\frac{-9-(-10)}{0-(-3)}(x-(-3))\\ \\y+10=\frac{1}{3} (x+3)\\\\y+10=\frac{1}{3}x+1\\\\y=\frac{1}{3}x+1-10\\\\y=\frac{1}{3}x-9\\[/tex]

To find the x intercept put y = 0

0 = (1/3)x - 9

(1/3)x = 9

x = 27

Comparing y = (1/3)x - 9 with y = mx + c, we can see that the slope (m) = 1/3 and the y intercept is -9

Hence, the reciprocal of the slope of f(x) is the same as the slope of f⁻¹(x) (i.e reciprocal of 3 = 1/3)

Answer: A

The reciprocal of the slope of f(x) is the same as the slope of f–1(x).

Step-by-step explanation:

Answer:

K-273=C

Step-by-step explanation:

K=C+273

Subtract 273 from each side

K-273=C+273-273

K-273=C

Answer:

Step-by-step explanation:

The time for each canoe is 3.5 hours

The total distance traveled by the first canoe is not known. Nor is the distance for the second canoe. We do know that the difference is 5.25 miles.

So let the rate of the slower canoe = x

Let the rate for the second canoe = 2x

The first canoe goes a distance of 2*x * 3.5 = 7x

The second canoe goes a distance of 3.5x

The difference = 7x - 3.5x = 5.25

3.5x = 5.25                                       divide by 3.5

x = 5.25/3.5

x = 1.5 which is the rate of the slower canoe

2x = 3  which is the rate of the faster canoe    

Answer: Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other

Hope it helps:) I got it right on my test btw

Step-by-step explanation:

Answer:

10) -1

11) 1/2 or 0.5

12) -1/5 or -0.2

13) -13/6 or -2.166666666

14) -1/8 or -0.125

15) 1/2 or 0.5

hope it helps;)

good luck!

Answer:

13 playing cards

Step-by-step explanation:

Thomas = 19 playing cards

Brother = 6 playing cards (which give Thomas)

Thomas = 19 playing cards - 6 playing cards = 13 playing cards

Answer:

[tex]\huge\boxed{\sf 13\ cards}[/tex]

Step-by-step explanation:

Thomas has total = 19 playing cards

He gave away = 6 cards

Thomas have now:

=> 19-6

=> 13 cards

Answer:

3x+3

plz mark brainliest

Answer:

3x + 3

Step-by-step explanation:

Combine like terms. Like terms are terms with the same amount of variables.

10x - 7x + 3

(10x - 7x) + 3

Subtract:

10x - 7x = 3x

Remember to bring the constant down.

3x + 3 is your answer.

~

Answer:

15

Step-by-step explanation:

if 6/10 = 9 gal. then we can divide 9 by 6 and then multiply that answer by ten

Answer:

D): 15

Step-by-step explanation:

if 6/10 = 9 gal. then we can divide 9 by 6 and then multiply that answer by ten

Answer:

$35.2

Step-by-step explanation:

I’m assuming you meant the total of the dress after tax.

1. 32 * 1.1 = 35.2

OR

1. 32 * 0.1 = 3.2

2. 32 + 3.2 = 35.2

You could do it either way.

Answer:

22.4cm

Step-by-step explanation:

Opposite side of the triangle is x

Adjacent side of the triangle is 10

Tangent 20° = x/10

2.237 = x/10

x = 2.237 × 10

x = 22.37cm

x = 22.4cm to the nearest tenth

Peter weighs 156 pounds, but he would like to wrestle in a lower weight class.He loses 4 pounds one week, gains back 2 pounds the next, loses 5 pounds the third week and loses 3 pounds the fourth week.How much does 

Peter weigh now?