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leonid [27]
3 years ago
12

Which expression can be used for the missing side length of the rectangle?

Mathematics
1 answer:
hram777 [196]3 years ago
3 0

Answer: Length = 2x✓15

Step-by-step explanation:

A rectangle has a width of 2x inches and a diagonal length of 8x inches. We are told to find the length of the rectangle. The square of the diagonal is the addition of the square of the length and square of the width.

Adjacent² = length² + width²

(8x)² = length² + (2x²)

Length² = 64x² - 4x²

Length² = 60x²

Length = ✓60x²

Length = ✓4 × ✓15 × ✓x²

Length = 2 × ✓15 × x

Length = 2x✓15

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For babysitting, Angie charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitti
Ghella [55]

Answer:

C=5h+3 when h=5

C=28

Step-by-step explanation:

She charges $5 per hour (5h)

and a flat fee of $3 (+3).

Replace the h (the number of hours babysitting) with 5 (the amount of hours you want to find for).

Then you multiple 5 and 5, then add 3.

Which gives you an answer of $28.

Hope this helped!

7 0
3 years ago
The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to d
Hoochie [10]

Answer:

Step-by-step explanation:

Hello!

X: number of gypsy moths in a randomly selected trap.

This variable is strongly right-skewed. with a standard deviation of 1.4 moths/trap.

The mean number is 1.2 moths/trap, but several have more.

a.

The population is the number of moths found in traps places by the agriculture departments.

The population mean μ= 1.2 moths per trap

The population standard deviation δ= 1.4 moths per trap

b.

There was a random sample of 60 traps,

The sample mean obtained is X[bar]= 1

And the sample standard deviation is S= 2.4

c.

As the text says, this variable is strongly right-skewed, if it is so, then you would expect that the data obtained from the population will also be right-skewed.

d. and e.

Because you have a sample size of 60, you can apply the Central Limit Theorem and approximate the distribution of the sampling mean to normal:

X[bar]≈N(μ;σ²/n)

The mean of the distribution is μ= 1.2

And the standard deviation is σ/√n= 1.4/50= 0.028

f. and g.

Normally the distribution of the sample mean has the same shape of the distribution of the original study variable. If the sample size is large enough, as a rule, a sample of size greater than or equal to 30 is considered sufficient you can apply the theorem and approximate the distribution of the sample mean to normal.

You have a sample size of n=10 so it is most likely that the sample mean will have a right-skewed distribution as the study variable. The sample size is too small to use the Central Limit Theorem, that is why you cannot use the Z table to calculate the asked probability.

I hope it helps!

6 0
3 years ago
The municipality of Waterloo needs $915,000 from property tax to meet its budget. The total value of assessed property in Waterl
levacccp [35]

Answer: <em>Tax rate per dollar =  .06536</em>

Given:

Amount needed from property tax = $915000

Value of assessed property  = $14000000

Therefore, we'll compute tax rate per dollar as:

Tax rate per dollar = \frac{Property\ tax\ amount}{Value\ of assessed\ property}

= \frac{915000}{14000000}

= .06536

4 0
3 years ago
Question 11
Blababa [14]

Answer:

283

Step-by-step explanation:

6 0
3 years ago
Simplify. <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B8m%7D%20%7B%7D%5E%7B3%7D%20" id="TexFormula1" title=" \sqrt[
olya-2409 [2.1K]

\sqrt[3]{8m}^3

  • Set up

(8m^{\frac{1}{3}})^3

  • Convert the radical into a fractional exponent using \sqrt[n]{x^m} = x^{\frac{m}{n}}

8m^{(3 \cdot \frac{1}{3})}

  • Use the property that (x^a)^b = x^{(a \cdot b)}

8m

  • Simplify

The simplification would be 8m.



7 0
3 years ago
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