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4 years ago

A quarter of the sum of a number and 20 is equivalent to 30. Find the number.

Mathematics

1 answer:

Alisiya [41]4 years ago

4 0

Answer:

X = 100

Step-by-step explanation:

X + 20 over 4 = 30

1/4x + 5 = 30

-5 -5

1/4x = 25

multiply both sides by 4

x = 100

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The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a m

Mazyrski [523]

Answer:

The probability that the instrument does not fail in an 8-hour shift is $P(X=0) \approx 0.8659$

The probability of at least 1 failure in a 24-hour day is $P(X\geq 1 )\approx 0.3508$

Step-by-step explanation:

The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:

$P(X)=\frac{e^{-\mu}\mu^x}{x!}$

Let X be the number of failures of a testing instrument.

We know that the mean $\mu = 0.018$ failures per hour.

(a) To find the probability that the instrument does not fail in an 8-hour shift, you need to:

For an 8-hour shift, the mean is $\mu=8\cdot 0.018=0.144$

$P(X=0)=\frac{e^{-0.144}0.144^0}{0!}\\\\P(X=0) \approx 0.8659$

(b) To find the probability of at least 1 failure in a 24-hour day, you need to:

For a 24-hour day, the mean is $\mu=24\cdot 0.018=0.432$

$P(X\geq 1 )=1-P(X=0)\\\\P(X\geq 1 )=1-\frac{e^{-0.432}0.432^0}{0!}\\\\P(X\geq 1 )\approx 0.3508$

3 0

3 years ago

The product of 5 and a number y

zysi [14]

Answer: 5y

Step-by-step explanation:

Product means the multiplication of, so taking the product of 5 and y we simply have;

5*y=5y

8 0

3 years ago

Read 2 more answers

How to do factor each expression 63 + 81

Katyanochek1 [597]

Answer:

$9(7 + 9)$

Step-by-step explanation:

To factor an expression you have to first find the highest common factor (HCF) of the numbers in the expression. You divide them by their HCF, bracket it and place the HCF outside the bracket.

$63 + 81 = \\ 9(\frac{63}{9} + \frac{81}{9}) = \\ 9(7 + 9)$