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Lapatulllka [165]
3 years ago
9

A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have accepta

ble voltages. Suppose that 80% of all batteries from a certain supplier have acceptable voltages. Among fifteen randomly selected flashlights, what is the probability that at least fourteen will work? (Round your answer to three decimal places.)
Mathematics
1 answer:
VikaD [51]3 years ago
4 0

Answer: Our required probability is 0.167.

Step-by-step explanation:

Since we have given that

n = 15

Probability of success p = 80% = 0.8

Probability of failure q = 20% = 0.2

We need to find the probability that at least fourteen will work.

So, by Binomial distribution, we get that

P(X\geq 14)=P(X=14)+P(X=15)\\\\P(X\geq 14)=^{15}C_{14}(0.8)^{14}(0.2)+^{15}C_{15}(0.8)^{15}\\\\P(X\geq 14)=0.167

Hence, our required probability is 0.167.

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Step-by-step explanation:

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Probability of letter b tiles: 10/20= 1/2

How to get the denominator?

4+6=10

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10+10=20

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It's because a tenth means that you've divided it by 10. So if it's 20, it means you're multiplying tenths by 20, leaving you with 2 wholes.

For example, you have 2 cakes and you cut each into 10 slices, the slices are each one tenth of the whole cake, and in total there are 20 tenths.

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2 years ago
Given: A, B, and C What is the value of X in the matrix equation AX + B = C?
Ksju [112]

Answer:

Option (2)

Step-by-step explanation:

Given expression is, AX + B = C

A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}

B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}

C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}

AX + B = C

AX = C - B

C - B = \begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}-\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix} = \begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}

C - B = \begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}

Let  X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}

AX = \begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}\times \begin{bmatrix}a & b\\ c & d\end{bmatrix}

     = \begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}

Since AX = C - B

\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}

Therefore, a = 1, b = 5

(-3a - 4c) = -35

3(1) + 4c = 35

3 + 4c = 35

4c = 32

c = 8

And (-3b - 4d) = -11

3(5) + 4d = 11

4d = -4

d = -1

Therefore, Option (2). X = \begin{bmatrix}1 & 5\\ 8 & -1\end{bmatrix} will be the answer.

7 0
3 years ago
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