Simplify: (27)^1/3•(27)^2/3

Answer:

Check: He used an incorrect time ratio converting hours to minutes

Check: He incorrectly concluded that she is not running fast enough

Do not check: His units do not cancel

Do not check: He used an incorrect distance ratio converting miles to feet

Do not check: He cannot determine her average rate in miles per hour after only 15 minutes

Step-by-step explanation:

You're welcome bud :)

To write an equation for a vertical translation, subtract the amount of the translation from the original equation. In this case, the equation y = 1/2x becomes y = 1/2x - 18, representing a vertical translation of 18 units downwards.

To write an equation for the vertical translation, we start with the equation y = 1/2x. Since we need to shift the graph 18 units down, the equation becomes y = 1/2x - 18. This equation represents a vertical translation of 18 units downwards.

To drag the coach at a constant speed, each player needs to apply a force of approximately 583.89 N to counteract the friction force of 1140 N on the sled, calculated using trigonometry and Newton's Second Law of Motion.

The key concept in this question involves Newton's Second Law of Motion and the dynamics of forces acting at angles. The friction force on the sled is given as 1140 N, and since the football coach is moving at a steady speed, we can infer that the net force is zero, implying that the pulling forces balance out the friction force.

To find the force each player must exert, we first determine the total force needed to overcome friction. Since the rope's angle is 25.0° (half the angle between the ropes), the total horizontal force exerted by the two players (F-total) needs to match the friction force. Using trigonometry, the force each player exerts (F-player) can be expressed as:

F-player = F-total / (2 × cos(25.0°/2)) = 1140 N / (2 × cos(12.5°))

So, we calculate the force:

F-player = 1140 N / (2 × cos(12.5°)) = 1140 N / (2 × 0.9763) = 1140 N / 1.9526 = 583.89 N

Therefore, each player needs to exert approximately 583.89 N to drag the coach at a steady speed of 2.30 m/s.

The probability that the three marbles drawn are all the same color is 64/3375.

To find the probability that all three marbles drawn are the same color, we need to consider two cases:

1. The probability of drawing three red marbles
2. The probability of drawing three white marbles

For the first case, the probability of drawing one red marble from the bag is 4/15. After replacing the marble, the probability of drawing another red marble is still 4/15. So, the probability of drawing three red marbles is (4/15) * (4/15) * (4/15).

For the second case, the probability of drawing one white marble from the bag is 5/15. After replacing the marble, the probability of drawing another white marble is still 5/15. So, the probability of drawing three white marbles is (5/15) * (5/15) * (5/15).

Adding the probabilities of the two cases, we get (4/15) * (4/15) * (4/15) + (5/15) * (5/15) * (5/15), which simplifies to 64/3375.

Actually I believe that Coach Link is incorrect in saying that he can only make 91 teams of 1 or 1 team of 91.

To find the number of teams he can make, we have to find the whole number that can divide 91 and give also a whole number answer. In this case, I found it to be 7.

91 / 7 = 13

So this means that Coach Link can also make 7 teams of 13 or 13 teams of 7.

To find the height of the cloud cover, we use the tangent of the 45° elevation angle, which equals 1. Since the distance is 590 m, the height of the cloud cover is also 590 m.

To calculate the height of the cloud cover, we can use trigonometry. The problem describes two angles and a distance between the spotlight and the observer, which forms a right-angled triangle on the ground and a triangle from the observer to the light on the cloud. The two angles in use are 75° (the angle of the spotlight from the horizontal) and 45° (the angle of elevation from the observer to the light). Using the tangent function, which is the ratio of the opposite side over the adjacent side in a right-angled triangle, we can find the height of the cloud cover (h).

Since the angle of elevation from the observer to the light on the cloud is 45°, the tangent of this angle is 1. This means that for every unit distance from the observer to the point directly underneath the cloud cover, there is one unit of rise. As we are given that the distance (d) is 590 m ,, using the tangent relationship (tan(45°) = h/d), we find that the height of the cloud cover (h) is equal to the distance to the observer (d).

The calculations are as follows:

Therefore, the height of the cloud cover is 590 meters.

To maximize the atrium area with a 756-ft perimeter, the dimensions should be 189 ft x 189 ft, with an area of 35,721 sq ft.

To find the dimensions that will maximize the area of the rectangular atrium, we need to set up an equation based on the given perimeter and then use calculus to find the dimensions that maximize the area.

Let's denote the length of the atrium as "L" and the width as "W."

The perimeter of a rectangle is given by the formula:

Perimeter = 2L + 2W

In this case, the perimeter is 756 ft, so we have:

2L + 2W = 756

Divide both sides of the equation by 2 to solve for L:

L + W = 378

Now, we can express L in terms of W:

L = 378 - W

The area of a rectangle is given by the formula:

Area = L * W

Substitute the expression for L in terms of W:

Area = (378 - W) * W

Area = 378W - W^2

To maximize the area, we need to find the critical points.

Take the derivative of the area formula with respect to W and set it equal to zero:

d(Area)/dW = 378 - 2W = 0

Solve for W:

2W = 378

W = 189

Now, we can find the corresponding value of L using L = 378 - W:

L = 378 - 189

L = 189

So, the dimensions that will maximize the area of the atrium are:

Length (L) = 189 ft

Width (W) = 189 ft

The maximum area of the atrium will be:

Area = L * W

Area = 189 ft * 189 ft

Area = 35,721 square feet.

For similar question on perimeter.

https://brainly.com/question/19819849

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Final answer:

To find the number of large bags of dog food Doug bought, use the given prices and total spent in the store.

Explanation:

Doug bought 3 large bags of dog food.

To solve this problem, we can set up the equation: $57x + $9 = $180. From here, we can find x by rearranging the equation to solve for x.

Therefore, Doug bought 3 large bags of dog food, as each large bag costs $57 and he spent $180 in total.

Answer:

Distribute the 3 to each term in the parentheses by multiplying.

Step-by-step explanation:

3(2x – 6 – x + 1)^2 – 2 + 4x

In Step 1 she simplified within the parentheses.

The expression becomes [tex]3(x-5)^2 - 2 + 4x[/tex]

In Step 2 she expanded the exponent.

After expanding the exponent (x-5)^2 it becomes (x^2-10+25)

[tex]3(x^2-10+25)  - 2 + 4x[/tex]

In the next step we distribute 3 inside the parenthesis in order to remove the parenthesis .

Answer: Distribute the 3 to each term in the parentheses by multiplying.

The value of this expression is [tex] 3 x 10^{6} [/tex]

In order to find this, you divide each term separately. First we'll start with the numbers in the front.

[tex] \frac{4.8}{1.6} = 3 [/tex]

Now that we have the first number, we look to the 10s and the powers they are raised to. Since we are looking at powers of the same number, we can use the properties of exponents to simply subtract the numbers they are raised to.

[tex] \frac{10^{9}}{10^{3}} = 10^{6} [/tex]

Then we put the two back together for the final answer.

[tex] 3 x 10^{6} [/tex]

Answer:

[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex] in simplest form would be [tex]2x^{10}y^{12}.[/tex]

Step-by-step explanation:

Given expression [tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex].

Let us simplify given rational expression in smaller parts.

[tex]\frac{60}{30} = 2[/tex]

[tex]\frac{x^{20}}{x^{10}} = x^{20-10} = x^{10}[/tex]

[tex]\frac{y^{24}}{y^{12}} = y^{24-12} = y^{12}.[/tex]

Combining all terms together, we get

[tex]2x^{10}y^{12}.[/tex]

Therefore,

[tex]\frac{60x^{20}y^{24}}{30x^{10}y^{12}}[/tex] in simplest form would be [tex]2x^{10}y^{12}.[/tex]

1 mile = 5280 feet

45 x 5280 = 237,600 feet per hour

Answer:

D.

Step-by-step explanation:

The range is the (y) value. And you never repeat a number when finding the relation or domain (x).  Therefor the best answer would be D.

Its not A because the numbers are for the domain (X value; First column)

Not B because its also for the Domain and it repeats -1 twice

Not C because it repeats 2 twice

Making D the reasonable answer

I hope this helps :))

Final answer:

To find the height h, divide the area A (96) by the base b (12) to get h = 8.

Explanation:

The problem statement A = bh is a formula to calculate the area of a rectangle, where A is the area, b is the base or width, and h is the height. You're given that the area A is 96 and the base b is 12; you need to find the height h. You can rearrange the formula to solve for h by dividing both sides by b:

h = A / b.

Plug in the values that you know:

h = 96 / 12 = 8.

So, the height h equals 8.

Answer:

To change from one unit to another in the metric system, multiply or divide by multiples of 10.

Step-by-step explanation: