Total area of the shape.

Using synthetic division, what is the quotient (3x3 + 4x − 32) ÷ (x − 2)?

Wewaii [24]

The question is set up in the following way:

2] 3 0 4 -32

_____________

Here the 2 is from when x-2 is set equal to zero and then solved for x, the rest is from the the number being divided with zero taking the place of the x^2.

Then the following happens:

2] 3 0 4 -32
6 12 32
______________
3 6 16 0

Here the following happens:
1. We drop down the first coefficient, which is 3
2. We take this coefficient and multiply it by the two in the corner and get 6.
3. We place this six under the second coefficient (0) and add them together and get 6.
4. We take this 6 and multiply it by the two in the corner and get 12.
5. We take this 12 and put it under the third coefficient (4), add them together and get 16.
6. We take the 16 and multiply it by the two in the corner and get 32.
7. We take the 32 and place in under the forth coefficient and get zero.

This gives us the coefficients of the final answer in the order 3, 6 and 16 with no remaninders which gives us 3x^2+6x+16.<span />

5 0

3 years ago

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Find the missing angle.

Svetlanka [38]

Answer:

85 degrees

Step-by-step explanation:

All angles in a triangle add up to 180 degrees

50 + 45 is 95

95 + 85 = 180

3 0

3 years ago

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Combine the like terms to create an equivalent expression. 12p + p

svet-max [94.6K]

I'm pretty sure the answer is 13p

3 0

3 years ago

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Tompkins Associates reports that the mean clear height for a Class A warehouse in the United States is 22 feet. Suppose clear he

coldgirl [10]

Given Information:

Mean clear height = μ = 22 feet

Standard deviation of clear height = σ = 4 feet

Required Information:

a) P(X > 16) = ?

b) P(X < 14) = ?

c) P(25 < X < 30) = ?

Answer:

a) P(X > 16) = 93.12%

b) P(X < 14) = 2.27%

c) P(25 < X < 30) = 20.39%

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

a) We want to find out the probability that the clear height is greater than 16 feet.

$P(X > 16) = 1 - P(X < 16)\\\\P(X > 16) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 16) = 1 - P(Z < \frac{16 - 22}{4} )\\\\P(X > 16) = 1 - P(Z < \frac{-6}{4} )\\\\P(X > 16) = 1 - P(Z < -1.5)\\\\$

The z-score corresponding to -1.5 is 0.0668

$P(X > 16) = 1 - 0.0668\\\\P(X > 16) = 0.9312\\\\P(X > 16) = 93.12 \%$

Therefore, the probability that the clear height is greater than 16 feet is 93.12%

b) We want to find out the probability that the clear height is less than 14 feet

$P(X < 14) = P(Z < \frac{x - \mu}{\sigma} )\\\\P(X < 14) = P(Z < \frac{14 - 22}{4} )\\\\P(X < 14) = P(Z < \frac{-8}{4} )\\\\P(X < 14) = P(Z < -2)\\\\$

The z-score corresponding to -2 is 0.02275

$P(X < 14) = 0.02275\\\\P(X < 14) = 2.27 \%$

Therefore, the probability that the clear height is less than 14 feet is 2.27%

c) We want to find out the probability that the clear height is between 25 and 30 feet.

$P(25 < X < 30) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(25 < X < 30) = P( \frac{25 - 22}{4} < Z < \frac{30 - 22}{4} )\\\\P(25 < X < 30) = P( \frac{3}{4} < Z < \frac{8}{4} )\\\\P(25 < X < 30) = P( 0.75 < Z < 2 )\\\\$

The z-score corresponding to 0.75 is 0.7734 and 2 is 0.9773

$P(25 < X < 30) = P( Z < 2 ) - P( Z < 0.75 ) \\\\P(25 < X < 30) = 0.9773 - 0.7734 \\\\P(25 < X < 30) = 0.2039\\\\P(25 < X < 30) = 20.39 \%$

Therefore, the probability that a child spends more than 4 hours and less than 8 hours per day unsupervised is 20.39%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.50 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

6 0

3 years ago

The length of an arc of a circle is 6/5 pi feet long and the diameter is 10 feet. What is the measure of the central angle?

Nadusha1986 [10]

Answer:

4.377°

Step-by-step explanation:

3 0

3 years ago

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