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3 years ago

The area of this rectangle is at most 400 square centimeters. Write and solve an inequality to represent the

Mathematics

1 answer:

Lelu [443]3 years ago

6 0

Answer:

1ft≤h≤25ft

Step-by-step explanation:

The area of a rectangle is expressed as;

Area = Length * height

A = Lh

If the area of a rectangle is at most 400 square centimeter, this is expressed as;

A ≤400

≤ means at most that is the area of the rectangle cannot be greater than 400

Substitute the given value into the inequality expression

Lh ≤ 400

Given

L = 16

16h ≤ 400

Divide both sides by 16

16h/16 ≤ 400/16

h ≤ 400/16

h ≤ 25

Hence the possible values of the height are with the range 1ft≤h≤25ft since we cannot have a negative value for the dimension

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Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 61 miles/hour. The hig

cricket20 [7]

Answer:

The standard deviation of the speeds of cars travelling on California freeway is 6.0088 miles per hour.

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

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

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 This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 61 miles/hour. This means that $\mu = 61$ .

The highway patrol's policy is to issue tickets for cars with speeds exceeding 75 miles/hour. The records show that exactly 1% of the speeds exceed this limit. This means that the pvalue of Z when $X = 75$ is 0.99. This is $Z = 2.33$

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

$2.33 = \frac{75 - 61}{\sigma}$

$2.33\sigma = 14$

$\sigma = \frac{14}{2.33}$

$\sigma = 6.0088$

The standard deviation of the speeds of cars travelling on California freeway is 6.0088 miles per hour.

6 0

3 years ago

Please solve 5 ≤ y + 2 ≤ 11

Ostrovityanka [42]

Answer: 3 < y < 9

Please mark me brainliest

5 0

3 years ago

At a certain gas station, 40% of the customers use regulargas(A1), 35 % use plus gas (A2) and 25 % usepremium (A3). Of those cus

Lady_Fox [76]

Answer:

a) 21%

b) 45.5%

c) 26.4%

Step-by-step explanation:

Given the supplied information, a table of probabilities can be constructed. (See the attachment.) The numbers across the bottom reflect the given ratios of customers selecting the different gas types. The numbers in the cells are those bottom numbers multiplied by the percentage that fill the tank (or not). The numbers on the right are the sums of the numbers in each row.

a) The top center cell in the table answers this question. It it the product ...

p(plus)×p(fill | plus) = 0.35×0.60 = 0.21 = 21%

b) The sum on the right answers this question:

p(fill) = 45.5%

c) The ratio of the first column number (12%) to the row sum for Fill (45.5%) answers this question:

p(regular | fill) = 12%/45.5% ≈ 26.4%