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3 years ago

15

Suppose you roll a standard number cube once. Are rolling a 4 and rolling a 3 mutually exclusive events? Explain.

1 answer:

Anuta_ua [19.1K]3 years ago

3 0

Yes, they are. They cannot happen both. Every time that you roll a cube you can get only one number, then if you roll a 4 you cannot roll a 3 at the same tiem, and if you roll a 3 you cannot roll a 4 at the same time.

Mutually exclusive events cannot happen at the same time.

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Simplify the expression (-5)(4)(-2)(-3)

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(-20)(6)
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3 years ago

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The focal length F of a lens made by combining two lenses of focal length U and V is given I/F=I/U+I/V

jolli1 [7]

Answer:

a). $V=\frac{U.F}{U-F}$

b). V = 15 units

Step-by-step explanation:

Focal length F of a lens made by combining two lenses of different focal lengths U and V will be,

$\frac{1}{F}=\frac{1}{U}+\frac{1}{V}$

A). By solving the given formula,

$\frac{1}{V}=\frac{1}{F}-\frac{1}{U}$

$\frac{1}{V}=\frac{U-F}{U.F}$

$V=\frac{U.F}{U-F}$

B). If F = 6 and U = 10 then we have to find the value of V.

By substituting the given values in the formula,

$V=\frac{6\times 10}{10-6}$

$V=\frac{60}{4}$

V = 15 units

Therefore, focal length (V) of the lens = 15 units

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3 years ago

What are the slope and y-intercept of the linear function<br> graphed to the left?

laila [671]

Answer:

Slope -1/2 y-intercept 1

Step-by-step explanation:

The line crosses through the y-axis at 1

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3 years ago

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4 years ago

A 13ft board is to be cut into three pieces, two equal length ones and the third 9in shorter than each of the other two. If cutt

vaieri [72.5K]

Answer:

The pieces are 55 inches, 55 inches and 46 inches long

Step-by-step explanation:

A 13ft board is to be cut into three pieces consisting of two equal length ones. The third one is 9in shorter than each of the other two.

Let us first convert the length of the board to inches:

1 ft = 12 inches

13 ft = 12 * 13 = 156 inches

Let the length of each of the other two pieces be x.

Therefore, the length of the third piece is (x - 9)

Therefore, the sum of the lengths of the three pieces is equal to 156 inches. This means that:

x + x + (x - 9) = 156

x + x + x - 9 = 156

=> 3x = 156 + 9

3x = 165

x = 165 / 3 = 55 inches

Each of the first two pieces are 55 inches long.

The length of the third piece will be:

55 - 9 = 46 inches

The pieces are 55 inches, 55 inches and 46 inches long.

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3 years ago