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ZanzabumX [31]
3 years ago
9

The Orchard Cafe has found that about 3% of the diners who make reservations don't show up. If 83 reservations have been made, h

ow many diners can be expected to show up? Find the standard deviation of this distribution. (Round your answers to two decimal places.) μ = σ =
Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Answer:

\mu = 80.51\\\sigma = 1.56

Step-by-step explanation:

We are given the following information in the question:

Percentage of of the diners who make reservations don't show up = 3%

Number of reservations = 83

Thus, we are given a binomial distribution with n = 83 and p = 0.97

X\sim \text{ Binom}(p = 0.97, n = 83)

\mu = np = (83)(0.97) = 80.51

Around 81 people  can be expected to show up.

\sigma = \sqrt{np(1-p)} = \sqrt{(83)(0.97)(1-0.97)} = 1.5541 \approx 1.56

The standard deviation of this distribution is 1.56

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Volume of prisms just 3 problems
Vladimir79 [104]

Answer:

2.  18 cubic cm.

3. 27 cubic cm

5. 90 cubic m

Step-by-step explanation:

2. Triangular prism

So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4.  We'll take the triangle shape as the base.

Like for any prism, the volume is the base multiplied by the height.

So, the area of the base is found with the regular formula: base x height:

so, 3 x 1.5 = 4.5 sq cm for the base.

Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.

3. Trapezoidal prism

Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.

The area of a trapezoid is calculated with the formula:

A = h/2 * (a + b) where a and b represent the short and long sides respectively.

So, for our given trapezoid:

A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.

Then we multiply the base area by the height to get the volume:

V = 4.5 * 6 = 27 cubic cm

5. Triangular prism 2

The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.

But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:

hypotenuse² = sideA² + sideB²

In our case, we have:

13² = x² + 5²

169 = x² + 25

x² = 144

x = 12

Now we can calculate the area of the triangle easily:

A = (b x h)/2 = (5 x 12)/2 = 30 sq m

Then multiply by the thickness of the prism....

V = 30 x 3 = 90 cubic m

4 0
3 years ago
2/3 4/5 3/4 1/8 put in order from greatest to least
m_a_m_a [10]
2/3, 4/5, 1/8 is the correct order from greatest to least.
3 0
3 years ago
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suppose an amount increases by 100% then decreases by 100%. find the final amount. Would the situation change if the original in
denpristay [2]
The first amount would be the original amount as the answer because you are adding and then subtracting the same number. If the increase was 150% then the answer would be 50% more because 150%-100%=50%.
4 0
3 years ago
Jennifer sold 57 pieces of art if she sold twice as many paintings as sculptures how many painting did she sell??
Westkost [7]

so we know she has sculptures and paintings, if she sold twice as many paintings as sculptures, that means that for every 2 paintings, she sold 1 sculpture, so the paintings and sculptures are on a 2:1 ratio.

we know she sold a total of 57, so we'll need to split 57 in a 2:1 ratio, we'll simply divide the whole amount of 57 by (2+1) and distribute accordingly.

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3 0
3 years ago
Simplify (2x-1/x^2-2x-3) + (1/x-3)<br> Please provide a step by step
topjm [15]

Answer:

(3x - 9)/(x² - 5x + 12)

Step-by-step explanation:

Answer attached, please refer it.

<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em> </em><em>:</em><em>)</em>

8 0
2 years ago
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