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3 years ago

Which expression is equivalent to 4√⋅3√⋅5√ ?

Mathematics

1 answer:

likoan [24]3 years ago

5 0

Answer:

$2\sqrt{15}$

Step-by-step explanation:

To multiply radicals with the same root, you just need to multiply the numbers or expressions inside the root retaining the same root and then simplify the result.

In this case: $\sqrt{3} \sqrt{4} \sqrt{5} = \sqrt{60} = 2\sqrt{15}$

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According to a survey, 65% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed

monitta

Answer:

a) $P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421$

b) $P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714$

$P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502$

$P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319$

And adding these values we got:

$P(36 \leq X \leq 38)= 0.1535$

c) We can find the expected value given by:

$E(X) = np =50*0.65 = 32.5$

And the standard deviation would be:

$\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373$

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

$\mu -2\sigma = 32.5- 2*3.373 = 25.75$

And then we can consider a value of 18 as unusual lower for this case.

Step-by-step explanation:

Let X the random variable of interest "number cleared by arrest or exceptional", on this case we can model this variable with this distribution:

$X \sim Binom(n=50, p=0.65)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

We want this probability:

$P(X=41)=(50C41)(0.65)^{41} (1-0.65)^{50-41}=0.00421$

Part b

We want this probability:

$P(36 \leq X \leq 38)$

We can find the individual probabilities:

$P(X=36)=(50C36)(0.65)^{36} (1-0.65)^{50-36}=0.0714$

$P(X=37)=(50C37)(0.65)^{37} (1-0.65)^{50-37}=0.0502$

$P(X=38)=(50C38)(0.65)^{38} (1-0.65)^{50-38}=0.0319$

And adding these values we got:

$P(36 \leq X \leq 38)= 0.1535$

Part c

We can find the expected value given by:

$E(X) = np =50*0.65 = 32.5$

And the standard deviation would be:

$\sigma = \sqrt{np(1-p)} \sqrt{50*0.65*(1-0.65)}= 3.373$

We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:

$\mu -2\sigma = 32.5- 2*3.373 = 25.75$

And then we can consider a value of 18 as unusual lower for this case.

6 0

3 years ago

Use formula A=LW to find the length of a rectangle when the width is 35 ft and the area is 1,750 sq ft

Ludmilka [50]

Answer:

the length of the rectangle is 50 ft

Step-by-step explanation:

A-LW

1,750=L(35)

divide both sides by 35

L= 50

6 0

2 years ago

The revenue, cost, and profit functions for a line of cell phone cases is shown. Identify the location on the profit function wh

grigory [225]

Answer:

Im pretty sure the profit location is at the center of the rise

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

PLEASE HELP !!! ILL GIVE YOU 10 POINTS IF YOU GET THIS CORRECT FOR MY TEST!!!!

kherson [118]

Answer:

Last one. I am 100% positive cause I'm good at this kind of math. If you need help on anything else, let me know

Step-by-step explanation:

6 0

3 years ago

Why does a square with an area 20² not have a whole number side length.

Klio2033 [76]

Answer:

This is because the number '20' is not a perfect square.

Step-by-step explanation:

If you find $\sqrt{20}$ , you will be getting 4.4721935955... which is not a whole number, thus 20 is not a perfect square.

5 0

3 years ago