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2 years ago

Simplify 12x to the power of 7 y to the power of 3 divided by 6x to the power of 3 y

Mathematics

1 answer:

Galina-37 [17]2 years ago

7 0

Answer:

2x⁴y²

Step-by-step explanation:

The question gives us the expression;

12x⁷y³ ÷ 6x³y

We are supposed to simplify the expression;

First we could divide the digits;

12 ÷ 6 = 2

Then we divide the like terms;

x⁷ ÷ x³

This means;

$=\frac{x*x*x*x*x*x*x }{x*x*x}$

$= x*x*x*x$

$=x^4$

y³ ÷ y

That is;

$=\frac{y*y*y}{y}$

$=y*y$

$=y^2$

Therefore, the simplified expression will be 2x⁴y²

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2 years ago

General Hospital has noted that they admit an average of 9 patients per hour.

serious [3.7K]

Answer:

(a) The probability that during the next hour less than 3 patients will be admitted is 0.00623.

(b) The probability that during the next two hours exactly 8 patients will be admitted is 0.00416.

Step-by-step explanation:

The complete question is: General Hospital has noted that they admit an average of 8 patients per hour.

(a) What is the probability that during the next hour less than 3 patients will be admitted?

(b) What is the probability that during the next two hours exactly 8 patients will be admitted?

The above situation can be represented through Poisson distribution as it includes the arrival rate of the pattern. So, the probability distribution of the Poisson distribution is given by;

$P(X = x) = \frac{e^{-\lambda} \times \lambda^{x} }{x!} ; x = 0,1,2,......$

Here X = Number of patients admitted in the hospital

$\lambda$ = arrival rate of patients per hour = 9 patients

So, X ~ Poisson( $\lambda$ = 9)

(a) The probability that during the next hour less than 3 patients will be admitted is given by = P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= $\frac{e^{-9} \times 9^{0} }{0!} + \frac{e^{-9} \times 9^{1} }{1!} + \frac{e^{-9} \times 9^{2} }{2!}$

= $e^{-9} +(e^{-9} \times 9)+ \frac{e^{-9} \times 81}{2}$

= 0.00623

(b) Here, $\lambda = 9 \times 2$ = 18 because we have to find the probability for the next two hours and we are given in the question of per hour.

So, X ~ Poisson( $\lambda$ = 18)

Now, the probability that during the next two hours exactly 8 patients will be admitted is given by = P(X = 8)

P(X = 8) = $\frac{e^{-18} \times 18^{8} }{8!}$

= 0.00416

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2 years ago

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The mixed number is 4 5/12.

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2 years ago

Simplify 26/5(5/13b+10/26) .

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The answer is 2b+2 hope this will help

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2 years ago

A bottle of white wine at room temperature (68°f) is placed in a refrigerator at 4 p.m. its temperature after t hr is changing a

Nat2105 [25]

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2 years ago

Read 2 more answers