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Arturiano [62]
3 years ago
5

Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 49 day

s and a standard deviation of 10.2 days. Find the probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days.
Mathematics
1 answer:
zimovet [89]3 years ago
3 0

Answer:

The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.

Step-by-step explanation:

In this case, we have a population lifetime normally distributed with mean 49 and standard deviation 10.2.

We take a sample of size n=64.

Then, we can calculate the z-score for a sample mean M=54, in order to calculate P(M>54):

z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{54-49}{10.2/\sqrt{64}}=\dfrac{5}{1.275}=3.922\\\\\\P(M>54)=P(z>3.922)=0.00004

The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.

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A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately h
strojnjashka [21]

Answer:

C

Step-by-step explanation:

If we were to draw a horizontal line from the bottom of the ladder to the bottom of the tree and then draw a vertical line from the bottom of the tree to the top of the ladder, we'd get a right triangle with legs as the distance between the bottom of the tree and the bottom of the ladder and the height of the ladder, and the hypotenuse is the length.

Here, we know the hypotenuse is 10 feet and that the bottom of the ladder is 4 feet away from the bottom of the tree, so use the Pythagorean Theorem to find the height:

h = \sqrt{10^2-4^2} =\sqrt{84} ≈ 9.2 feet

The answer is C.

7 0
3 years ago
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The diagonal of the floor of a square room is 6 meters.what is the length of a side of the room? round to the nearest tenth.
shutvik [7]
Side of the room = x.
From the right triangle, where sides of the square are legs of the right triangle, and the diagonal of the square is a hypotenuse of the right triangle.
x²+x²=6²
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4 0
3 years ago
Simplify: 6y + 5z + 8y – 3z
mezya [45]
Combine like terms. 6y + 8y is 14y. 5z - 3z is 2z. so the answer is 14y + 2z.
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3 years ago
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Dan buys a car for £2100.
SVETLANKA909090 [29]

Answer:

£1837.5

Step-by-step explanation:

Given data

Cost of car P=  £2100.

Rate r= 2.2%

Time t= 6 years

Now we want to find the  worth after 6 years, let us apply the compound interest expression but this time for depreciation

A= P(1-r)^t

Substitute

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Hence the amount of the car after 6 years is £1837.5

8 0
3 years ago
What is the least common denominator of the rational expressions below?
Lyrx [107]

Answer:

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12/(x^2 - 11x+30) - 43/(x^2-6x)

12/((x - 5) (x - 6)) - 43/x(x-6) [Factoring the denominator]

Both have x-6 common in the denominator,

4 0
3 years ago
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