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3 years ago

There are 4 prime numbers

Mathematics

1 answer:

amid [387]3 years ago

4 0

Answer:

Step-by-step explanation:

As you go to larger numbers, there are more possibilities of factors for them.

For example, the internal from 20 to 30 contains only two prime numbers (23 and 29) and the interval from 90 to 100 contains only one prime (97).

However, the number of prime numbers in an interval varies. There are four prime numbers between 100 and 110 (101, 103, 107, 109).

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Mrs. johnson's and mr. wei's classes are participating in the Meridian School arts and crafts exhibit. Their spaces will be next

Nat2105 [25]

Answer:

See explanation

Step-by-step explanation:

Ms. Johnson space has 48 carpet squares.

Mr. Wei space has 36 carpet squares.

Factorize these two numbers:

$48=2\cdot 2\cdot 2\cdot 2\cdot 3\\ \\36=2\cdot 2\cdot 3\cdot 3$

All common factors are 1, 2, 3, 4, 6, 12

<u>All possibilities:</u>

1. If Ms. Johnson space width and Mr. Wei space width is 1 carpet, then Ms. Johnson space length is 48 carpets and Mr. Wei space length is 36 carpets.

2. If Ms. Johnson space width and Mr. Wei space width is 2 carpets, then Ms. Johnson space length is 24 carpets and Mr. Wei space length is 18 carpets.

3. If Ms. Johnson space width and Mr. Wei space width is 3 carpets, then Ms. Johnson space length is 16 carpets and Mr. Wei space length is 12 carpets.

4. If Ms. Johnson space width and Mr. Wei space width is 4 carpets, then Ms. Johnson space length is 12 carpets and Mr. Wei space length is 9 carpets.

5. If Ms. Johnson space width and Mr. Wei space width is 6 carpets, then Ms. Johnson space length is 8 carpets and Mr. Wei space length is 6 carpets.

6. If Ms. Johnson space width and Mr. Wei space width is 12 carpets, then Ms. Johnson space length is 4 carpets and Mr. Wei space length is 3 carpets.

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The function C(h)=(2h^2+5h)/(h^3+8) models the concentration of medication in the bloodstream (as a percent) h hours after its i

salantis [7]

Answer:

h ≥ 0
C = 0; concentration eventually decays to nothing
(0, 0) is the only intercept in the domain. It means the concentration in the bloodstream is zero at the time the drug is injected.
1.95 hours

Step-by-step explanation:

1. a. The domain of the function in the context of this problem is h ≥ 0. The maximum value of h will correspond to the time at which the concentration is considered to be negligible. If that time is when the concentration decays to 1% of its peak value, then perhaps the suitable domain is 0 ≤ h ≤ 180.

b. The equation of the vertical asymptote of this function is where the denominator of C(h) is zero, that is ...

h^3 +8 = 0

h = ∛(-8)

h = -2 . . . . the equation of the vertical asymptote

This is not a concern for a medical professional because it is outside the domain of the function.

2. As h gets large the value of the function approaches 2/h, which is to say the horizontal asymptote is C = 0. It means the concentration of medication in the blood eventually decays to zero.

3. C(0) = 0 is the only intercept in the domain of the function. (h, C(h)) = (0, 0)

In the context of this problem, it means the blood concentration of medication is zero at the time of the injection.

4. About 1.95 hours after injection, a maximum concentration of the drug occur in the bloodstream. This value is easily found using a graphing calculator.

Taking the derivative of the function gives you ...

C'(h) = -2(h^4 +5h^3 -16h -20)/(h^3 +8)^2

This has two real zeros and two complex zeros. The positive real zero is near h = 1.94527, about 1.95.

That is, the concentration in the bloodstream reaches a maximum about 1.95 hours after injection into the muscle.