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Anuta_ua [19.1K]

4 years ago

10

A triangle is cut from a piece of fabric. The triangle has a height of 8 inches in an area of 120 in.². What is the length of th

e base of the triangle A triangle is cut from a piece of fabric. The triangle has a height of 8 inches in an area of 120 in.². What is the length of the base of the triangle?

1 answer:

andreyandreev [35.5K]4 years ago

8 0

Answer: 30 inches

Step-by-step explanation:

Given:

ABC-tringle

BH= 8 in - height

S= 120 in^2

AC-?

Solution:

S=1/2ab

120in=1/2a*8in

120=4a

4a=120

a=30 in

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Find tan(450-a), If <br><img src="https://tex.z-dn.net/?f=%20%5Ctan%28a%29%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20" id="TexFormula1"

Inessa05 [86]

Answer:

$tan(450-a)=5\sqrt{3}-8$

Step-by-step explanation:

We know that:

$tan(a-b)=\frac{tan(a)-tan(b)}{1+tan(a)tan(b)}$

$tan(450-a)=\frac{tan(450)-tan(a)}{1+tan(450)tan(a)}$

Remember:

450°=360°+60°

and:

$tan(a)=\frac{1}{2}$

Thus:

$tan(450-a)=\frac{tan(60)-tan(a)}{1+tan(60)tan(a)}\\\\$

Then:

$tan(450-a)=5\sqrt{3}-8$

4 0

3 years ago

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

4 0

3 years ago

Brian needs to buy some pencils bread I had a pack of 12 pencils for 298 when we has a pack of a pack of 18 pencils for 499 find

AlekseyPX

Answer:

The pack of 12 pencils for 298 is better as it has a lower unit price.

Step-by-step explanation:

To be able to find the answer, you have to calculate the unit price for each brand by dividing the price of the pack by the number of pencils in the pack.

-298/12=24.83

-499/18=27.72

According to this, the answer is that the pack of 12 pencils for 298 is better as it has a lower unit price.

8 0

4 years ago

I need help with question 5 and its solve by subtitution

Bingel [31]

Y = 3x + 15
y = 2x + 8

3x + 15 = 2x + 8
-2x -2x
——————-
x + 15 = 8
-15 -15
—————-
x = -7

4 0

4 years ago

Apply the distributive property to factor out the greatest common factor.

Sauron [17]

Answer:

$\large\boxed{25p+50q=25(p+2q)}$

Step-by-step explanation:

$\text{The distributive property}\\\\a(b+c)=ab+ac\\\\25p=\boxed5\cdot\boxed5\cdot p\\\\50q=2\cdot\boxed5\cdot\boxed5\cdot q\\\\GCF(25p,\ 50q)=\boxed5\cdot\boxed5=25\\\\25p+50q=25\cdot p+25\cdot2q=25(p+2q)$

3 0

3 years ago