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3 years ago

The length of a rectangle bus 2 cm less than 7 times the width the perimeter is 156 cm what is the length and width

Mathematics

1 answer:

svetoff [14.1K]3 years ago

3 0

length = 68 cm and width = 10 cm

let w represent the width then length = 7w - 2

perimeter = 2(length + width) = 2(7w - 2 + w)= 2(8w - 2) = 16w -4

we are given perimeter = 156 thus

16w - 4 = 156 → (solve for w)

add 4 to both sides

16w = 156 + 4 = 160

divide both sides by 16

w = $\frac{160}{16}$ = 10

thus width = 10 cm and length = (7 × 10) - 2 = 70 - 2 = 68 cm

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Svetach [21]

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3 years ago

Read 2 more answers

A sample of size 126 will be drawn from a population with mean 26 and standard deviation 3. Use the TI-84 calculator.

GenaCL600 [577]

Answer:

1. The probability that x will be more than 25 is 0.6305.

2. The 55th percentile is 26.38.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean 26 and standard deviation 3.

This means that $\mu = 26, \sigma = 3$

1 Find the probability that x will be more than 25.

This is 1 subtracted by the p-value of Z when X = 25. So

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

$Z = \frac{25 - 26}{3}$

$Z = -0.333$

$Z = -0.333$ has a p-value of 0.3695.

1 - 0.3695 = 0.6305.

The probability that x will be more than 25 is 0.6305.

2 Find the 55th percentile of x.

This is X when Z has a p-value of 0.55, so X when Z = 0.125.

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

$0.125 = \frac{X - 26}{3}$

$X - 26 = 0.125*3$

$Z = 26.38$

The 55th percentile is 26.38.

7 0

2 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$