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zvonat [6]
4 years ago
11

The lengths of plate glass parts are measured to the nearest tenth of a millimeter. The lengths are uniformly distributed with v

alues at every tenth of a millimeter starting at 590.2, and continuing through 590.8. Determine the mean and variance of the lengths. (a) mean (in tenths of millimeters) Round your answer to two decimal places (e.g. 98.76). (b) variance (in tenths of millimeters2) Round your answer to three decimal places (e.g. 98.765).
Mathematics
1 answer:
yarga [219]4 years ago
4 0

Answer:     \text{Mean length}=590.5\ mm\\\\\text{Variance of the lengths}=0.03\ mm

Step-by-step explanation:

The mean and variance of a continuous uniform distribution function with parameters m and n is given by :-

\text{Mean=}\dfrac{m+n}{2}\\\\\text{Variance}=\dfrac{(n-m)^2}{12}

Given : m=590.2\ \ \ n=590.80

\text{Then, Mean=}\dfrac{590.2+590.8}{2}=590.5\ mm\\\\\text{Variance}=\dfrac{(590.8-590.2)^2}{12}=0.03\ mm

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(2h3 + 6h) + (3h3 - 7h - 3) standard form sum or difference.​
worty [1.4K]

Answer:

5h^3- h - 3

Step-by-step explanation:

Given

(2h^3 + 6h) + (3h^3 - 7h - 3)

Required

Standard form

We have:

(2h^3 + 6h) + (3h^3 - 7h - 3)

Remove bracket

(2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 6h + 3h^3 - 7h - 3

Collect like terms

(2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 3h^3+ 6h  - 7h - 3

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3 0
3 years ago
It takes 1 1/2 cups of flour, 1 1/4 cups of sugar, and 1/2 cup of butter to bake fifteen shortbread cookies. If Ramon has 5 cups
Stolb23 [73]
Short answer 48 cookies
Remark

This is an extremely valuable question if you are going to take chemistry at some point. You have to calculate all three to see what the limiting ingredient is.

Flour
Assuming that all of the flour will be used, you set up a proportion to find out how many cookies will be produced.

1.5 cups of flour / 15 cookies = 5 cups of flour / x     Cross multiply
1.5 x  = 15 * 5
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Sugar
Now you must do the same thing with the sugar
1.25 pounds sugar/15 cookies = 4 / x      Cross multiply
1.25 x = 4 * 15
1.25 x = 60                         Divide both sides by 1.25
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x = 48               cookies possible with 4 pounds of sugar.

Butter
0.5 pounds of butter/15 cookies = 1.75 pounds of butter /x   Cross Multiply
0.5 * x = 15 * 1.75
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Conclusion
The limiting ingredient is the sugar. You can only make 48 cookies with that amount of sugar. 

So you will have left over flower. You will have left over butter (even if you round down). But you will use all your sugar. It is the least amount.
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