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Nadusha1986 [10]

2 years ago

8

Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Whi

ch is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter.
A.) 2.72 meters

B.) 3.06 meters

C.) 9.16 meters

D.) 10.18 meters

2 answers:

liubo4ka [24]2 years ago

6 0

sandbox 1 area = 5*5 = 25 square m

sandbox 2

25=w*(3w+1)=

3w^2+w-25=0

w=2.7248 (round to 2.72 m)

2.72*3=8.16+1 = 9.16

Longest side = 9.16 meters

gavmur [86]2 years ago

3 0

Answer:

C.) 9.16 meters

Step-by-step explanation:

We are given that the two sandboxes have same area and the equation is given by 25 = w*(3w+1).

Now, we simplify this equation in order to find the value of unknown variable 'w'.

i.e. 25 = 3 $w^{2}$ +w

i.e. 3 $w^{2}$ +w-25=0

The two factors of this quadratic equation are w=2.72 and w= -3.05.

But, as 'w' represents the length of the box, so it cannot be negative.

Therefore, w = 2.72

So, the longest side of the box is (3w+1) = 3*2.72+1 = 9.16 meter

Hence, the length of longest side to the nearest hundredth is 9.16 meter.

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dolphi86 [110]

Let the price of 1 shirt be represented by = s

A pair of pants costs twice as much as a shirt, then the cost of pants is = 2s

The total cost of 1 pair of pants and 1 shirt is $18 , means : $s+2s=18$

Solving this we get,

$3s=18$

$s=6$

So, the price of 1 shirt is $6 and price of 1 pair of pants is = 2s = 2*6 = $12.

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2 years ago

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If y = 8x − 2, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?

Nataly [62]

You just need to try with all of the pair f.ex
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So set 1
1 and 6: 8*1-2=6 ok
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1 year ago

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A rectangle that is x feet wide is inscribed in a circle of radius 25 feet. Express the area of the rectangle as a function of x

Viefleur [7K]

Answer:

$A(x)=x(\sqrt{2500-x^{2} } )$ is the area expressed as function of x,

and x: >0, <50 is the domain of the function.

Step-by-step explanation:

Draw an appropriate figure and then express the area of the rectangle as a function of x.

We know that the diagonal of a rectangle inscribed in a circle, will be equal to the diameter of the circle. 50 feet

let w = the width of the rectangle

therefore

$x^2 + w^2 = 50^2\\w^2 = 2500 - x^2\\w = \sqrt{2500-x^{2} }$

recall

Area = x*w

replace w

$A(x)=x(\sqrt{2500-x^{2} } )$ is the area expressed as function of x

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7 0

2 years ago

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

Sati [7]

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

Step-by-step explanation:

When the distribution is normal, we use 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.

If X is two standard deviations from the mean or more, it is considered unusual.

In this question:

$\mu = 128, \sigma = 23$

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

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

$Z = \frac{135 - 128}{23}$

$Z = 0.3$

$Z = 0.3$ has a pvalue of 0.6179

1 - 0.6179 = 0.3821

38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the pvalue of Z when X = 141.

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

$Z = \frac{141 - 128}{23}$

$Z = 0.565$

$Z = 0.565$ has a pvalue of 0.7140

71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So

X = 125

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

$Z = \frac{125 - 128}{23}$

$Z = -0.13$

$Z = -0.13$ has a pvalue of 0.4483

X = 120

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

$Z = \frac{120 - 128}{23}$

$Z = -0.35$

$Z = -0.35$ has a pvalue of 0.3632

0.4483 - 0.3632 = 0.0851

8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

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

$1.28 = \frac{X - 128}{23}$

$X - 128 = 1.28*23$

$X = 157.44$

So

157.44mmHg

6 0

2 years ago

On march 12, klein company, inc. sold merchandise in the amount of $7,800 to babson company, with credit terms of 2/10, n/30. th

Assoli18 [71]

Given:
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</span><span>march 15 - Babson returns some of the merchandise. the selling price of the merchandise is $600
march 20 - Babson pays the invoice and takes the appropriate discount.

Since March 20 is still within the 10-day discount from date of purchase, Babson is entitled to 2% discount.

7,800 - 600 = 7,200 sales invoice
7,200 * 2% = 144 sales discount
7,200 - 144 = 7,056 net sales

Babson will pay the amount of $7,056</span>

6 0

1 year ago