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Dahasolnce [82]
3 years ago
10

Part A: Determine if the expression is one of our special products. If so, identify it by its general form:

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
8 0

Answer:

1.

Part A: Yes, it is (a - b)².

Part B: a² - 2ab + b² => (x - 6)² = x² - 12x + 36.

Part C: x² - 12x + 36.

2.

Part A: Not a special product.

Part B: Binomial distribution => (x + 8)(x + 1) = x² + 9x + 8.

Part C: x² + 9x + 8.

3.

Part A: Yes, it is (a + b)²

Part B: a² + 2ab + b² => (3x + 2)² = 9x² + 12x + 4.

Part C: 9x² + 12x + 4.

4.

Part A: Yes, it is (a + b)(a - b), a difference of squares.

Part B: a² - b² => 4x² - 49

Part C: 4x² - 49.

5.

Part A: Not a special product.

Part B: Binomial distribution => (x - 5)(2x - 5) = 2x² - 15x + 25.

Part C: 2x² - 15x + 25.

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Answer: Choice C

Vertex = (5, -2)

===============================================

Explanation:

Vertex form is y = a(x-h)^2 + k where the vertex itself is located at (h,k)

As the name implies, we can very quickly pull out the coordinates of the vertex without doing much math at all.

In the case of choice C, we have y=  \frac{1}{2}(x-5)^2 - 2 which is the same as y = \frac{1}{2}(x-5)^2 + (-2) and we can see that h = 5 and k = -2. Therefore, the vertex is located at (h,k) = (5, -2)

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2 years ago
X=<br> A) 80<br> B) 90<br> C) 100
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X= A) 80 I believe you double 120 to 240 and divide by the 4 quarters.
6 0
3 years ago
Read 2 more answers
Mr. Clark claims that he has a coin that is weighted so that the probability of heads is 40%. To test this, his students flip th
Brrunno [24]
While I'm unsure what the word choices were, his claim is likely to be true. 

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3 years ago
Assume that the empirical rule is a good model for the time it takes for all passengers to board an airplane. The mean time is 4
slamgirl [31]

Answer:

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 48, \sigma = 4.

Which interval describes how long it takes for passengers to board the middle 95% of the time?

This is between the 2.5th percentile and the 97.5th percentile.

So this interval is the value of X when Z has a a pvalue of 0.025 and the value of X when Z has a pvalue of 0.975

Lower Limit

Z has a pvalue of 0.025 when Z = -1.96. So

Z = \frac{X - \mu}{\sigma}

-1.96 = \frac{X - 48}{4}

X - 48 = -1.96*4

X = 40.16

Upper Limit

Z has a pvalue of 0.975 when Z = 1.96. So

Z = \frac{X - \mu}{\sigma}

1.96 = \frac{X - 48}{4}

X - 48 = 1.96*4

X = 55.84

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

7 0
3 years ago
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