A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table.

The amount of hot chocolate served daily is inversely correlated with the temperature of the city, with more cups being sold once the temperature is between 40 and 50 F.

When two variables change in tandem, the relationship is said to be direct. The variable y increases as the variable x increases. A linear relationship denoted by the equation y = kx is directly proportional.

There is a direct correlation between a circle's radius and area, meaning that when the radius is increased or decreased, the area correspondingly changes. If one variable increases while the other declines or vice versa, the relationship between the two variables is inverse.

For given question-

Jordan created the graph below to illustrate the correlation between a city's temperature and the daily sales of hot chocolate.

As we can see that - when the temperature increases the demand for the ice cream also increases which is the direct relation.

Thus, the amount of hot chocolate served daily is inversely correlated with the temperature of the city, with more cups being sold once the temperature is between 40 and 50 F.

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The diagram for the question is attached:

Answer:

3:23

Step-by-step explanation:

Answer:

12:13 - 01:13=1 hour

01:13-01:13= 1 hour

02:13-03:13= 1 hous

03:13-03:23= 10 minutes

12:13-03:23= 3hr 10min

Answer:

Step-by-step explanation:

f(x) = 5x² - x + 2

Using the remainder theorem

To find the reminder substitute the value of x into the above function and solve

That's

x + 1 = 0

x = - 1

So we have

f(-1) = 5(-1)² - ( - 1) + 2

f(-1) = 5 + 1 + 2

f(-1) = 6 + 2

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Let's just say this circle has value x.

x increases by 5%, or 0.05 of x.

x + 0.05x = 1.05x

1.05x now increases by 5% again:

1.05x + 0.05(1.05x) = 1.1025x

The total increase is equal to (1.1025-1)*100 = 10.25%

Hope this helps!

Answer:

Below

Step-by-step explanation:

Circumf = pi * 2 r

Circumf/(2pi ) = r

area = pi r^2

       = pi * (circumf/2pi)^2    

        = circumf^2 / 4 pi =

                24^2 / (4 pi) = 45. 8  units^2  

Answer:

45.84 units^2

Step-by-step explanation:

A car is on a slope of 10degree above the horizontal . a force 1000N is applied to the car up the line of the slope. the car has amass of 500 kg . what is the acceleration of the car

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer:

15

Step-by-step explanation:

you can't divide 4/15 down to have a denominator of 5 since 4 cant divide by 3 evenly

you can't divide 15 by something to get 10

so the only answer is 15

so 1/5 would turn into 3/15 by multiplying the top and bottom by 3

You have to work in factors of 5 because thats what they have in common

Answer:

15

Step-by-step explanation:

1/5+4/15=3/15+4/15

We have our common denominator.

We have to multiply the numerator with the denominator.

We multiplied 5 by 3 to get to 15, so we do the same to 1:

3/15+4/15=7/15

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Answer:

Perimeter of square:   4*side

Let's take the side to be 'x'

4x = 40

x = 10

Therefore, EACH SIDE = 10ft.

Answer:

-8n+16. You can also put 16-8n

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

F1 + F2 = ΣF' is the simultaneous equation that relates the two forces F1 and F2 in kilonewtons acting on a structure, based on the principle of equilibrium.

If two forces F1 and F2 in kilonewtons are acting on a structure, the simultaneous equation that relates the two forces can be derived using the principle of equilibrium. The principle of equilibrium states that for a structure to be in equilibrium, the sum of all the forces acting on it must be zero.

Mathematically, the principle of equilibrium can be expressed as:

ΣF = 0

where ΣF represents the sum of all the forces acting on the structure.

For the two forces F1 and F2, we can express their vector sum as:

F = F1 + F2

where F is the resultant force of the two forces.

Now, for the structure to be in equilibrium, the vector sum of the two forces must be equal and opposite to the vector sum of all the other forces acting on the structure. This can be expressed as:

-F = ΣF'

where ΣF' represents the sum of all the other forces acting on the structure.

Equating the two expressions for F and -F, we get:

F1 + F2 = ΣF'

This is the simultaneous equation that relates the two forces F1 and F2 in kilonewtons acting on a structure, based on the principle of equilibrium.

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Answer:

rational

Step-by-step explanation:

Answer:

Side AC corresponds to side FD

Angle BAC corresponds to angle BFD

Answer: 15cm and 5cm

Step-by-step explanation:

A rectangle's area is the product of the length and width

Given length x and width y, 2x+2y = 40 and x*y = 75.

Verifying my answer:

2(15)+2(5) = 40

30+10 = 40

40 = 40

15*5 = 75

75= 75

This is a week late so I hope this helped.

The length and the width of the rectangle​ are 15cm and 5cm respectively

The given parameters are:

Area (A) = 75

Perimeter (P) = 40

The area of a rectangle is LW, while the perimeter is 2(L + W)

So, we have:

LW = 75

2(L + W) = 40

Divide by 2

L + W = 20

Make L the subject

L = 20 - W

Substitute L = 20 - W in LW = 75

(20 - W)W = 75

Expand

20W - W^2 = 75

Rewrite as:

W^2 - 20W + 75 = 0

Expand

W^2 - 15W - 5W + 75 = 0

Factorize

(W - 15)(W -5) = 0

Split

W - 15 = 0 or W - 5 = 0

Solve for W

W = 15 or W = 5

Recall that:

L= 20 - W

So, we have

L = 20 - 15 or L = 20 - 5

This gives

L = 5 or L = 15

Hence, the length and the width of the rectangle​ are 15cm and 5cm respectively

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Answer:

A is the correct answer

Step-by-step explanation:

(9 -4)/ 5

5/5

=1

Answer:

The area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Step-by-step explanation:

From this study,

The surface area of f(x,y) is expressed by:

\(A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA\)

where

\(0 \leq x \leq 2 \ and \ 0 \leq y \leq 2\)

Given that:

f(x,y) = 9 - x²

Thus, \(f_x = -2x\) and   \(f_y = 0\)

However, the area becomes:

\(A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy\)

\(A = \iint_R \sqrt{1+4x^2} \ dxdy\)

From above, replacing x with \(\dfrac{1}{2} \ tan \ u\)

then \(dx = \dfrac{1}{2} sec^2 \ udu\)

∴

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu\)

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu\)

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)\)

Hence;

\(\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}\)

\(\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Therefore, the area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Answer:

14

Step-by-step explanation:

7*2y+27

14y+27

14 is coefficient of variable y

Step-by-step explanation:

y = 3x_______equation1

3x + 2y = 12_____equation2

sub y into equation 2

3x+2(3x)=12

3x+6x=12

9x=12

x=3/4

sub X into equation 1

y=3x

y=3(3/4)

y=9/4

y=9/4 x=3/4

I hope this helps

Answer:

volume of contaber= 4*4*5

=80cm cube

volume of box=4*2*1

=8cm cube

she can pack box in contaner= volume of continer/ volume of box

=80/8

=10 box

Answer:

10

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

10 and 25 can both be divided by 5

10 divided by 5 equals 2

25 divided by 5 equals 5

1. When you travel 3 miles in New York City, the cost of The Red Cabs and The Green Cabs would be the same.

2. The difference in cost between the two companies if you need to travel 8 miles is $5.

3. It is cheaper to travel with Red Cabs than Green Cabs if the total distance is more than 3 miles.

First, for the costs of both companies to be equal, we set the two cost equations to be equal to each other and solve for the unknown variable (miles).

Based on the equations for the two companies, we can determine the total costs of using any option.

The difference between the total costs is obtained by subtracting.

Let cost of Green Cab = 2 + 2m

Let cost of Red Cab = 5 + m

For the two companies costs to be equal, 2 + 2m = 5 + m

= 2m - m = 5 - 2

m = 3

Green Cab = 2 + 2m

= 2 + 2(8)

= 18

= $18

Red Cab = 5 + m

= 5 + 8

= 13

= $13

The difference in cost = $5 ($18 - $13)

Thus, based on the solution to the cost equations, cost-conscious travelers should prefer Red Cabs to Green Cabs when they travel in New York City for a distance exceeding 3 miles.

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The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³

Given data ,

The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis

The formula for Area under definite integral is

∫ₐᵇ f ( x ) = f ( b ) - f ( a )

Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x

The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)

Using these expressions for r and h, we can write the volume of each cylindrical shell as:

V(x) = 2πx[f(x + Δx) - f(x)]Δx

V = ∫₀² 2πx[f(x + Δx) - f(x)]dx

As Δx approaches zero, this integral becomes:

V = ∫₀² 2πx√(1 + (f'(x))²) dx

where f'(x) is the derivative of f(x), which is:

f'(x) = x/√(x² + 9)

Substituting this expression for f'(x) into the integral, we get:

V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx

This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:

V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx

V = [4/5 π(x² + 9)^(5/2)]₉¹³

V = 44.46 units³

Hence , the volume of the solid is 44.46 units³

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Answer:

Because they are both base angles of isosceles triangles

Answer:

Shown in Step-By-Step, written in bold text.

Step-by-step explanation:

16) x : 1      y: -3

         2          0

         3          9

3x - 6

3(1) - 6 = -3

3(2) - 6 = 0

3(3) - 6 = 9

17) x: 1        y: -10

        2           -12

        3           -14

-2(x + 4) = -2x - 8

-2(1) - 8 = -10

-2(2) - 8 = -12

-(3) - 8 = -14

Step-by-step explanation:

Given that :

Total length of the track = 630 m

Distance covered by Sweeti by walking = 2/7 of the running track

2/7 of 630 m

⇛ (2/7)×630

⇛ (2×630)/7

⇛ 1260/7

⇛ 180 m

Distance covered by walking = 180 m

Remaining distance =

Total distance - Distance covered by walking

⇛630 m - 180 m

⇛ 450 m

The total distance covered by running by Sweeti is 450 m.

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You can burn about 450 calories if you run 5 miles. How many miles will you need to run to burn 630 calories? Justify your reasoning.....

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