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2 years ago

What is the length of MN

Mathematics

1 answer:

rusak2 [61]2 years ago

3 0

Answer:

C. 5

Step-by-step explanation:

∆LMN kid an isosceles triangles because it has two base triangles that are equal to each other. Therefore, the sides opposite the base triangles would also be equal to each other.

Thus:

3x = x + 10

Solve for x. Subtract x from each side

3x - x = 10

2x = 10

Divide both sides by 2

x = 5

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An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What

galina1969 [7]

Answer:

Part A:

The probability that all of the balls selected are white:

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

$P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

$P(D_i)=\frac{1}{6}$ for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

$P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}$

$P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}$

$P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}$

$P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}$

$P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}$

$P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0$

Part A:

The probability that all of the balls selected are white:

$P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)$

$P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\ P(A)=\frac{5}{66}=0.075757576$

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find $P(D_3|A)$

The data required is calculated above:

$P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516$

7 0

2 years ago

What is the rang for the equation y=2x-3

a_sh-v [17]

Answer:

The range for the equation is all real numbers.

Step-by-step explanation:

The range of an equation is the set of y-values that you can get by plugging in all possible x-values.

Another way to put it is, when you graph the equation, whatever y-values the line produces, is its range.

Graphing y=2x-3, you can see it is a graph with a positive slope that extends from negative infinity y-value to positive infinity x-value.

4 0

3 years ago

Estimate the square root of 0.39 to the nearest 10th Place

Marta_Voda [28]

Answer:

0.62

Step-by-step explanation:

3 0

3 years ago

Can someone help me graph these?

Neporo4naja [7]

Answer:

see below

Step-by-step explanation:

x ≤ 3

There is a closed circle at 3 because of the equals sign

the lines goes to the left since it is less than

x < 3

There is a open circle at 3 because there is no equals sign

the lines goes to the left since it is less than

3 0

3 years ago

PLEASE HELP QUICK!!! WILL GIVE BRAINLIEST!!

Lera25 [3.4K]

Answer:

$\boxed{\bold{112}}$

Step By Step Explanation:

Follow PEMDAS Order Of Operations

Calculate Within Parenthesis: $\bold{120+\left(12\div \:3\cdot \:30\right): \ 240}$

$\bold{240\div \:20+10^2}$

Calculate Exponents: $\bold{10^2: \ 100}$

$\bold{240\div \:20+100}$

Divide: $\bold{240\div \:20: \ 12}$

$\bold{12+100}$

Add

$\bold{112}$

➤ $\boxed{\bold{Mordancy}}$

4 0

2 years ago