Three runners competed in a race data were collected at each mile mark for each runner If the runner ran at a constant paste the data would be linear a regression line was fitted to their data Use the residual plots to decide which data set is best fit by regression line and then identify the runner that kept the most consistent pace

Answer:

120 Miles

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We want to solve the equation:

[tex]5\sin(2x)=3\cos(x)[/tex]

To do so, we can rewrite the equation.

Recall the double-angle identity for sine:

[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]

By substitution:

[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]

Distribute:

[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]

We can subtract 3cos(x) from both sides:

[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]

And factor:

[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]

Hence, our answer is A.

*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.

Answer:

A. cosx(10sinx-3)=0

Step-by-step explanation:

5(2sinxcosx)=3cosx

10sinxcosx-3cosx=0

cosx(10sinx-3)=0

Answer:

We say that a function is increasing on an interval if the function values increase as the input values increase ...

Step-by-step explanation:

Answer:

The volume of a prism is the area of the base times the height, V=Bh. The volume of a rectangular prism is the length times width times height, V=lwh. The volume of a cube is the length of one side cubed, V=s3.

Step-by-step explanation:

if you don't get it, then i'll just answer.

Answer:

Step-by-step explanation:

There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:

P = 2w + l; solving for l and filling in our length of fencing gives us:

l = 148 - 2w

The area then for this will be:

A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:

[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:

[tex]A=-2w^2+148w[/tex]

The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.

To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:

[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:

[tex]-2(w^2-74w)=0[/tex]

The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:

[tex]-2(w^2-74w+1369)=...[/tex]

But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:

[tex]-2(w^w-74w+1369)=-2738[/tex]

The left side can be simplified down to a perfect square binomial:

[tex]-2(w-37)^2=-2738[/tex]

Now we'll add over the -2738:

[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.

Answer:

C = 4.94   M = 18.38

Step-by-step explanation:

the easiest way is to graph both equaitons and see where they intersect,

see the image

or solve by substitution

6C + 47M=893.50           C = (893.50 - 47M)/6

25C + 22M=527.86

25((893.50 - 47M)/6)  + 22M = 527.86

25/6 [(893.50) - 47M] + 22M = 527.86

25/6 [ - 47M] + 22M = 527.86 - 25/6 [(893.50)

22M - 25(47M)/6  = -3195.06

22M - 195.83M  = -3195.06

      -173.83M   =   -3195.06

                 M  =  18.38

C = (893.50 - 47(18.38)/6

C = 4.94

Answer:

1078in

Step-by-step explanation:

Surface area =2(wl+hl+hw)

2·(17·19+6·19+6·17)=1078in

Answer:

The car gets 35 miles per gallons.

Step-by-step explanation:

Answer:

since r > 0.361

we reject H₀

Therefore, Yes, It does suggest that  there is a linear relation between student task persistence and achievement score, since r  [0.883 ] is greater than critical value for 30 [ 0.361 ]

Step-by-step explanation:

Given the data in the question;

n = 41

r = 0.883

H₀ : population correlation coefficient = 0 ( both are independent )

Hₐ : population correlation coefficient ≠ 0 ( there is a linear relation between student task persistence and achievement score )

critical value for n = 30 is 0.361

that means, for n = 41, critical value will be less than 362

now, since r > 0.361

we reject H₀

Therefore, Yes, It does suggest that  there is a linear relation between student task persistence and achievement score, since r  [0.883 ] is greater than critical value for 30 [ 0.361 ]

Answer:

72. If the second 3cm has some relevance, leave a note and I'll come back and modify my answer.

Step-by-step explanation:

Givens

L = 6 cm

W = 3 cm

H = 2 cm

I don't know what the extra 3 cm is for.

Formula

SA = 2*L*W + 2*L*H + 2*H*W

SA = 2*6*3 + 2*6*2 + 2*2*3

SA = 36 + 24 + 12

SA = 72

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  A) down

  B) 25 m; 200 m/s

  C) (20.41, 2065.82)

Step-by-step explanation:

When you are first introduced to equations for ballistic motion, you may be told that the formula is ...

  h(t) = -4.9t² +v₀t +h₀ . . . . . height in meters at time t seconds

where v₀ is the initial upward velocity in meters per second, and h₀ is the initial height in meters.

When you are first introduced to quadratic equations, and the vertex form in particular, you may be told that the form is ...

  f(x) = a(x -h)² +k . . . . . . . vertex (h, k) and vertical scale factor 'a'

When the scale factor (or leading coefficient) is negative the graph of the parabola opens downward. When it is positive, the graph opens upward.

Knowing these things, you are prepared to match the given equation to these patterns.

__

Part A: We observe that the leading coefficient of the function (-4.9) is negative, so the parabola opens down.

__

Part B: The constant in the first given equation is 25, so the initial height is 25 meters.

The coefficient of t in the first given equation is 200, so the initial velocity of the rocket is 200 m/s.

__

Part C: The vertex can be read from the second equation as ...

  (h, k) = (20.41, 2065.82)

Answer:

3,268,584

Step-by-step explanation:

1^12 is 1

Answer:

y = -x + 8

Step-by-step explanation:

m = -1  ; x1 = 3 ; y1 = 5

Slope point form: y - y1 = m(x -x1)

y - 5 = -1(x - 3)

y -  5 = -1x - 3 *(-1)

y - 5 =-x + 3

    y =  -x + 3 + 5

     y = -x + 8

Answer:

10/15

Step-by-step explanation:

The probability is 10/15 or 67% chance

Answer:

Is 3(b+c) equivalent expressions?

A. True

Answer:

The top number in a fraction. Shows how many parts we have. (The bottom number is the Denominator and shows how many equal parts the item is divided into.)

Step-by-step explanation:

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

The scale factor is the ratio of corresponding dimensions:

  (6 cm)/(9 cm) = 2/3

-4× = 16 answer: -4

Step-by-step explanation:

-4 × -4 = 16

Answer:

600000Ω

Step-by-step explanation:

1μA = 10⁻⁶ A

200μA = 0.0002 A

Potential difference = V = 120 V

Current = I = 0.0002 A

Resistance = R

R = V / I

  = 120 / 0.0002

  = 600000Ω

Answer: 8*5

Step-by-step explanation: Because the comutative property says you can like, switch up the orders of the numbers in a thing and it is still trye. So 5*8=8*5.

The expression using the commutative property is

5 x 8 = 8 x 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The commutative property states that,

a x b = b x a

Now,

Using the commutative property,

5 x 8 is equal to 8 x 5.

Thus,

5 x 8 = 8 x 5

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

1/100 (1471 z + 2100)

0.01 (1471 z + 2100) the result I got

and the Factorization over the splitting field:

14.71 z + 21

9514 1404 393

Answer:

  14

Step-by-step explanation:

Use the formula with n=3.

  h(3) = h(3-2) +h(3-1)

  h(3) = h(1) +h(2)

  h(3) = -6 +20 . . . . . substitute the given values

  h(3) = 14

there should be a cross multiplication

3(8x)=2

expanding bracket

24x=2

multiple both sides by 24

x=1/12

Answer:

299 square feet

Step-by-step explanation:

Area of a parallelogram = base × height

Base = 23 ft

Height = 13 ft

Note: the other length, 15 ft is not needed in calculating area of the parallelogram. All we need is just the length of the base and the height.

Area of the parallelogram shown = 23 × 13

Area = 299 ft²

80m, you kind of distribute so 8 times 10m is 80m