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2 years ago

Which expression is equivalent to 3 256x^10y^7

1 answer:

3 0

$3 \sqrt{256 \ \times x^{10} y^{7} }$

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square root of 256 is 16 :
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$= 48 \sqrt{x^{10} y^{7}}$

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√10¹⁰ = 10⁵ :
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$= 48x^5 \sqrt{ y^{7}}$

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√y⁶ = y³ :
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$= 48x^5y^3 \sqrt{ y}}$

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klemol [59]

Answer:

P-value = 0.0455

Step-by-step explanation:

In this question, we are concerned with calculating the P- value in a test.

Mathematically we know that;

P-value = 2 * P(Z > |z|)

Please check attachment for complete solution and by step explanation

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2 years ago

It shipped traveled for a total of 85 miles over the course of five hours heading west the ship travels and average of 14 mph an

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complete question:

A ship traveled for a total of 85 miles over the course of 5 hours. Heading west, the ship traveled at an average speed of 14 miles per hour, and heading north, it traveled at an average speed of 19 miles per hour. For how many hours was the ship heading north?

Answer:

The ship heading north traveled for 3 hours

Step-by-step explanation:

A ship travels for a total of 85 miles over the course of 5 hours journey. The speed of the journey can be calculated below.

speed = distance/time

total distance = 85

total time = 5 hours

speed = 85/5

speed = 17 miles/hr

West direction

Heading west the ship traveled at an average speed of 14 miles per hour. The speed can be represented for this journey as follows.

speed = distance/time

14 = dist/time

let

a = time traveled west

distance = 14a

North direction

speed = dist/time

19 = dist/time

time travel north = 5 - a

distance = 19(5 - a)

distance = 95 - 19a

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a = -10/-5

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The ship heading north will travel for 5 - 2 = 3 hours

5 0

2 years ago

Read 2 more answers

A child wanders slowly down a circular staircase from the top of a tower. With x,y,zx,y,z in feet and the origin at the base of

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Answer:

a) The tower is 90 feet tall

b) She reaches the bottom at t = 18 minutes.

c) Her speed at time t is 5 \sqrt[]{5} ft/minute

d) Her acceleration at time t is 10 ft/minute^2

Step-by-step explanation:

Consider the path described by the child as going down the tower to have the following parametrization $\gamma(t) = (10\cos t, 10 \sin t, 90-5t)$

a) Assuming that the child is at the top of the tower when she starts going down, we have that at the initial time (t=0) we will have the value of the height of the tower. That is z = 90-5*0 = 90 ft.

b) The child reaches the bottom as soon as z =0. We want to find the value of t that does that. Then we have 0 = 90-5t, which gives us t = 18 minutes.

c) Given the parametrization we are given, the velocity of the child at time t is given by $\frac{d\gamma}{dt}= (\frac{d}{dt}(10\cos t), \frac{d}{dt} (10 \sin t ), \frac{d}{dt}(90-5t)) = (-10 \sin t, 10 \cos t, -5)$ . The speed is defined as the norm of the velocity vector,

so, the speed at time t is given by $v = \sqrt[]{(-10 \sin t)^2+(10 \cos t)^2+(-5)^2} = \sqrt[]{100(\sin^2 t + \cos^2 t)+25} = \sqrt[]{125}= 5 \sqrt[]{5}$

d) ON the same fashion we want to know the norm of the second derivative of $\gamma$ .

We have that $\gamma ^{''}(t) =(-10\cost t, -10 \sin t , 0)$ so the acceleration is given by $\sqrt[]{100(\cos^2 t+ \sin^2 t )} = 10$

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1 year ago

On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2.

koban [17]

Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

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So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

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1 year ago

Carla can choose two of her three pairs of sneakers to take to a track meet. If the pairs of sneakers are called A, B, and C, wh

Semenov [28]

Number of ways of choosing two pair of sneakers from three pairs named A, B, C is given by 3C2 (3 combination 2) = 3! / 2!(3 - 2)! = 3! / (2! x 1!) = (3 x 2) / (2 x 1) = 3.

Therefore, the sample space is given by S = {AB, AC, BC}

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2 years ago

Read 2 more answers