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dmitriy555 [2]
3 years ago
8

Replace ∗ by a monomial so that the trinomial may be represented by a square of a binomial: 25a^2 + * + 1/4b^2

Mathematics
1 answer:
TEA [102]3 years ago
7 0

Answer:

Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial: 36–12x + ∗, and 25a^2+ ∗ + .25 b^2

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A line goes through the point (6,–2) and has a slope of –3.
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Y = mx + b
slope(m) = -3
(6,-2)...x = 6 and y = -2
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New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today
Simora [160]

Answer:

a) 0.3520 = 35.20% probability that a hotel room costs $225 or more per night.

b) 0.1038 = 10.38% probability that a hotel room costs less than $140 per night.

c) 0.4878 = 48.78% probability that a hotel room costs between $200 and $300 per night.

d) $251.

Step-by-step explanation:

Problems of normally distributed samples are 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 = 204, \sigma = 55

a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)?

This probability is 1 subtracted by the pvalue of Z when X = 225. So

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

Z = \frac{225 - 204}{55}

Z = 0.38

Z = 0.38 has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

0.3520 = 35.20% probability that a hotel room costs $225 or more per night.

b. What is the probability that a hotel room costs less than $140 per night (to 4 decimals)?

This probability is the pvalue of Z when X = 140. So

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

Z = \frac{140 - 204}{55}

Z = -1.16

Z = -1.16 has a pvalue of 0.1038.

0.1038 = 10.38% probability that a hotel room costs less than $140 per night.

c. What is the probability that a hotel room costs between $200 and $300 per night (to 4 decimals)?

This probability is the pvalue of Z when X = 300 subtracted by the pvalue of Z when X = 200. So

X = 300

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

Z = \frac{300 - 204}{55}

Z = 1.75

Z = 1.75 has a pvalue of 0.9599.

X = 200

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

Z = \frac{200 - 204}{55}

Z = -0.07

Z = -0.07 has a pvalue of 0.4721.

0.9599 - 0.4721 = 0.4878

0.4878 = 48.78% probability that a hotel room costs between $200 and $300 per night.

d. What is the cost of the 20% most expensive hotel rooms in New York City?

This is X when Z has a pvalue of 1-0.2 = 0.8. So X when Z = 0.84

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

0.84 = \frac{X - 204}{55}

X - 204 = 0.84*55

X = 250.2

Rounding to the next dollar.

$251.

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3 years ago
Graph this function using intercepts:<br> 5x–3y=30
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Answer:

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Step-by-step explanation:

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2 years ago
Brenda received 3 times as many grades as Robert. Timothy received half as many 85s as Brenda. How many grades of 85 did Brenda,
Diano4ka-milaya [45]

Answer:

11 grades of 85 did Brenda, Robert, and Timothy receive altogether.

Step-by-step explanation:

Let 6x be the number of 85 received by Brenda.

The number of 85 received by Robert is 1/3 of Brenda= 2x

The number of 85 received by Timothy is 1/2 of Brenda= 3x

Then according to the given conditions

6x+ 2x+ 3x

= 11x

So  the number of total 85s received by all the three is 11.

11 grades of 85 did Brenda, Robert, and Timothy receive altogether.

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3 years ago
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