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The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible val

Dvinal [7]

Let width be W

Then length = 5W

P=2L+2W

P< 96cm

Then the Perimeter of the rectangle is equal to

(2L+2W)< 96

2*(5W)+2W)≤96

Therefore, 2w+2⋅(5w)≤96

should be your answer

8 0

4 years ago

What is 12 divided by 8

Alina [70]

Answer:

1.5

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius r Arc Length s 1

Maslowich

Answer:

The radian measure of the central angle of the given circle is $\frac{7}{19} rad$

Step-by-step explanation:

The radian measure of the central angle θ of a circle of radius r that intercepts an arc of length s can be calculated from the formula given below

s =rθ

where s is the length of arc

r is radius of the circle

and θ is the central angle in rad (radian)

From s = rθ, Then

θ = s / r

From the question,

Radius r = 19 feet

and Arc length s = 7 feet

Hence,

θ = s / r becomes

θ = 7 / 19

∴ θ $= \frac{7}{19} rad$

This means the radian measure of the central angle of the given circle is $\frac{7}{19} rad$

5 0

3 years ago

A group of 18 people ordered soup and sandwiches for lunch. Each person in the group either ordered one soup or one sandwich . T

kkurt [141]

Let's say a = number of ordered soups, b = number of ordered sandwiches.

Then 4.5a + 7.75b = 113.50, and a and b are integers between 0 and 18 inclusive.

How do we tackle this? If all ordered soup, the cost would be $81, so we'll have at least 4 sandwiches. If all ordered sandwich, the cost would be $139.5, so at most 15 sandwiches were ordered. You also know an even number of sandwiches was ordered, to let the price end at 50 cent.

If you brute-force from 4,6,8,10,12 to 14 sandwiches, you find the answer at 10 sandwiches and 8 soups.

10*7.75 + 8*4.50 = 113.50

8 0

4 years ago

Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$