What is the volume of a cube with a side length of 11 inches? A. 33 in3 B. 10,648 in3 C. 1331 in3 D. 121 in3

Answers

Answer 1

Answer: $s= 11 \ inches \n \nV=s^3 \n \n V=11^3 = 11*11*11 = 1331 \ in^3 \n \n Answer : \ C. 1331 in3$

Answer 2

Answer: The volume of a cube is s^3
v=s^3
v=11^3
v=1331

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The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 72 miles due north of the warehouse.A truck traveled from the warehouse to the airport and then to the factory. What is the total number of miles the truck traveled?

54 miles
72 miles
144 miles
162 miles

Answers

Answer:

C. 144 miles

Step-by-step explanation:

We have that the truck traveled from the warehouse to the airport and then to factory.

First we will find the distance between the warehouse and the airport using the 'Distance formula'.

'Distance Formula' gives the distance between two points $(x_(1),y_(1))$ and $(x_(2),y_(2))$ by $\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}$ .

As, from the graph, we have,

Warehouse is located at (27,-36) and Airport is located at (-27,36).

So, the distance between them is,

$\sqrt{(-27-27)^(2)+(36-(-36))^(2)}$

i.e. $\sqrt{(-27-27)^(2)+(36+36)^(2)}$

i.e. $\sqrt{(-54)^(2)+(72)^(2)}$

i.e. $√(2916+5814)$

i.e. $√(8100)$

i.e. $90$

So, the distance from warehouse to the airport is 90 miles.

Moreover, as the truck further traveled to the factory which is 72 miles north of the warehouse.

So, the factory is located at (27,72-36) i.e. (27,36).

Then, the distance from the airport (-27,36) to the factory is (27,36) is,

$\sqrt{(27+27)^(2)+(36-36)^(2)}$

$\sqrt{54^(2)+0^(2)}$

$√(2916)$

$54$

So, the distance from airport to the factory is 54 miles.

Thus, the total distance traveled by the truck is 90 + 54 = 144 miles.

Hence, option C is correct.

The paths of two runners cross at a stop sign. One runner is heading south at a constant rate of 6.5 miles per hour while the other runner is heading west at a constant rate of 7 miles per hour. How fast is the distance between them changing after 10 minutes?

Answers

Answer:

The distance between them changing after 10 minutes will be 9.553 mph.

Step-by-step explanation:

The paths of two runners cross at a stop sign (O). One runner is heading south at a constant rate of 6.5 miles per hour towards A while the other runner is heading west at a constant rate of 7 miles per hour towards B.

So, after 10 minutes the first runner covers a distance of $6.5 * (10)/(60) = 1.083$ miles and the second runner covers a distance of $7 * (10)/(60) = 1.167$ miles.

Therefore, after 10 minutes their distance will be $\sqrt{(1.083)^(2) + (1.167)^(2)} = 1.592$ miles.

Now, the distance between them is given by

AB² = OA² + OB²

Now, differentiating this equation with respect to time t (in hours) we get

$2(AB) (d(AB))/(dt) = 2(OA) (d(OA))/(dt) + 2(OB) (d(OB))/(dt)$

⇒ $(AB) (d(AB))/(dt) = (OA) (d(OA))/(dt) + (OB) (d(OB))/(dt)$

⇒ $1.592 * (d(AB))/(dt) = 1.083 * 6.5 + 1.167 * 7 = 15.208$

⇒ $(d(AB))/(dt) = 9.553$ mph.

Therefore, the distance between them changing after 10 minutes will be 9.553 mph. (Answer)

Final answer:

The distance between the two runners is not changing after 10 minutes.

Explanation:

To find the rate of change of the distance between the two runners, we can use the concept of relative velocity. The distance is changing due to the motion of both runners, so we need to find the rate at which each runner is approaching or moving away from the other. Since one runner is heading south and the other is heading west, their velocities are perpendicular to each other. We can use the Pythagorean theorem to find their combined velocity and then calculate the rate of change of the distance between them.

Let's consider the southward runner as Runner A and the westward runner as Runner B. The velocity of A is 6.5 miles per hour, and the velocity of B is 7 miles per hour. After 10 minutes, the distance traveled by A can be calculated as (6.5 miles/hour) * (10/60) hours = 1.083 miles. The distance traveled by B can be calculated as (7 miles/hour) * (10/60) hours = 1.167 miles.

Using the Pythagorean theorem, we can calculate the distance between the two runners after 10 minutes:

Distance = sqrt((1.083 miles)^2 + (1.167 miles)^2) ≈ 1.563 miles

To find the rate of change of the distance between them, we can differentiate the equation for the distance with respect to time:

d(Distance)/dt = (1/2)*((2*(1.083 miles)*(0))/(sqrt((1.083 miles)^2 + (1.167 miles)^2))) + (1/2)*((2*(1.167 miles)*(0))/(sqrt((1.083 miles)^2 + (1.167 miles)^2))) = 0

Therefore, the distance between the two runners is not changing after 10 minutes.

Learn more about Relative velocity here:

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(-14) (divide sign)7+2

Answers

Answer:

(-14)/7 +2

PEMDAS

Division:

[-14/7] + 2

= -2 +2

Addition:

Step-by-step explanation:

Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painting. Calculate the area of the isosceles trapezoid.Isosceles trapezoid with top base 16 feet, bottom base of 24 feet, and height of 10 feet.
A. 140 ft2
B. 160 ft2
C. 180 ft2
D. 200 ft2

Answers

Answer:

Option D is the correct answer.

Step-by-step explanation:

Refer the figure given below

Area of isosceles trapezoid = Area of 2 triangles + Area of rectangle.

$\texttt{Area of isosceles trapezoid =}(1)/(2)* (1)/(2)* (b-a)* h+(1)/(2)* (1)/(2)* (b-a)* h+ah\n\n\texttt{Area of isosceles trapezoid =}(1)/(2)* (b-a)* h+ah$

We have

a = 16, b = 24 and h = 10

Substituting

$\texttt{Area of isosceles trapezoid =}(1)/(2)* (24-16)* 10+16* 10=200feet^2$

Option D is the correct answer.

A=(a+b)×h÷2
=(16+24)×10÷2
= 200 ft2

Erin ran 1/4 the distance that Carolyn ran. Erin ran a total of 1.5 miles. How far did Carolyn run? (Please explain)

Answers

1.5 ×4 will get u 6. so there fore 6 divided by 4 equals 1.5

Put the following events in order from least to most likely. Please help me in this

Answers

Answer:

Colorado Bronze wins

I Am Pat wins

Good Legs Lance wins

Step-by-step explanation:

Put them all as decimals and THEN put them in order. Hope this helps :)

Final answer:

When ordering events from least to most likely, you rank them based on their probabilities which typically range from 0 (impossible event) to 1 (certain event). The event with the smallest value is considered the least likely and the event with the largest value is considered the most likely.

Explanation:

Without specific events provided in your question, I'm unable to put them in order from least to most likely. However, to help you understand how to do this yourself: probabilities of events typically range from 0 (impossible event) to 1 (certain event). Let's use an example. Say we have the following events and their probabilities: A: It will rain tomorrow (0.9), B: A tossed coin will land heads (0.5), C: Drawing a red card from a deck (0.5), and D: Winning the lottery (0.0000001).

You arrange these from least to most likely as follows: D (least likely), B and C (equally likely), and A (most likely).

Learn more about Probability here:

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