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3 years ago

Help finding volume

Mathematics

1 answer:

grin007 [14]3 years ago

7 0

Volume = 150.9 cubic units

Explanation:

(First, we need to find the side opposite to 40 degrees)
Let the side be ‘s’
tan(40) = s/6 (Opposite/Adjacent)
tan(40) x 6 = s
s ≈ 5.03 units

Area of triangle base = 1/2 x Base x Height = 1/2 x 6 x 5.03 = 15.09 square units

Area of prism = Base Area x Height = 15.09 x 10 = 150.9 cubic units

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3 years ago

Which linear equation best represents the line of best fit for the scatterplot?

Lena [83]

Answer:

$y = -\frac{1}{3}x$

Step-by-step explanation:

The scatter plot trends downward from left-> right, meaning that it is negative. Next, use two points to solve for the value for the slope.

In this case, I will use (-3 , 1) & (0 , 0)

Use the following equation. m = slope:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let:

$(x_1 , y_1) = (0 , 0)\\(x_2 , y_2) = (-3 , 1)$

Plug in the corresponding numbers to the corresponding variables:

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Your answer will be:

$y = -\frac{1}{3}x$

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2 years ago

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krek1111 [17]

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Step-by-step explanation:

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3 years ago

Read 2 more answers

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is <u>n for which M = 0.04.</u>

There is no estimate, hence $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

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2 years ago

I certain brand of coffee comes into sizes a 10.5 ounce package cost $3.24 I 30.6 ounce package cost $9.88 find the unit price f

Fofino [41]

Unit price: divide each coffee's total cost by the total package weight.
First Coffee= $3.24 ÷ 10.5 oz= $0.3085 per oz= $0.31 per oz rounded

Second Coffee= $9.88 <span>÷ </span>30.6 oz= $0.3228 per oz
= $0.32 per oz rounded

ANSWER: The first coffee is a better buy at only $0.31 cents per ounce. The second coffee has a higher price per ounce, so it is not a better buy.
Hope this helps! :)

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3 years ago