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fiasKO [112]
3 years ago
6

Write the prime factorization of 20 using exponents

Mathematics
1 answer:
otez555 [7]3 years ago
4 0
Here you go

2 to the second power times 5
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A box contains 17 transistors three of which are defective. If three are selected find the probability that
Fiesta28 [93]

Answer:

I think the answer is A

7 0
3 years ago
Suppose that the population​ P(t) of a country satisfies the differential equation dP/dt = kP (600 - P) with k constant. Its pop
jeka94

Answer:

The country's population for the year 2030 is 368.8 million.

Step-by-step explanation:

The differential equation is:

\frac{dP}{dt}=kP(600 - P)\\\frac{dP}{P(600 - P)} =kdt

Integrate the differential equation to determine the equation of P in terms of <em>t</em> as follows:

\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}

At <em>t</em> = 0 the value of <em>P</em> is 300 million.

Determine the value of constant C as follows:

\frac{P}{600-P} = Ce^{600kt}\\\frac{300}{600-300}=Ce^{600\times0\times k}\\\frac{1}{300} =C\times1\\C=\frac{1}{300}

It is provided that the population growth rate is 1 million per year.

Then for the year 1961, the population is: P (1) = 301

Then \frac{dP}{dt}=1.

Determine <em>k</em> as follows:

\frac{dP}{dt}=kP(600 - P)\\1=k\times300(600-300)\\k=\frac{1}{90000}

For the year 2030, P (2030) = P (70).

Determine the value of P (70) as follows:

\frac{P(70)}{600-P(70)} = \frac{1}{300} e^{\frac{600\times 70}{90000}}\\\frac{P(70)}{600-P(70)} =1.595\\P(70)=957-1.595P(70)\\2.595P(70)=957\\P(70)=368.786

Thus, the country's population for the year 2030 is 368.8 million.

3 0
4 years ago
Pls halp due today &gt;_&lt; thank you!
d1i1m1o1n [39]

Answer:

It is the first option: -\sqrt{25}, -\frac{22}{4}, -560%, -2\pi

3 0
3 years ago
Which expression both gives the average rate of change of the function h(x)
liubo4ka [24]

Answer:

D

Step-by-step explanation:

The average rate of change of a function over an interval a ≤ x ≤ b is found by:

\frac{f(b)-f(a)}{b-a}

Here, a is 0 and b is 3, so: \frac{f(3)-f(0)}{3-0}=\frac{f(3)-f(0)}{3}

Just plug in 3 for the first term and 0 for the second term in the numerator:

- First term: \frac{1}{2} (3^{3+\frac{1}{2} })+3=\frac{1}{2} (3^{3\frac{1}{2} })+3

- Second term: \frac{1}{2} (3^{0+\frac{1}{2} })+3=\frac{1}{2} (3^{\frac{1}{2} })+3

So, the final answer is:

\frac{[\frac{1}{2} (3^{3\frac{1}{2} })+3]-[\frac{1}{2} (3^{\frac{1}{2} })+3]}{3}

Thus, the answer is D.

Hope this helps!

5 0
3 years ago
the perimeter of a rectangle is 40m. one of the lengths or the sides is 5m. find the lengths of the other 3 sides.​
Annette [7]

The perimeter of a rectangle is 40m and one side of it is 5m. What is the length of the other side using an equation?

Perimeter of the rectangle =2(l+ b)=40m

If one of its side b=5, then l = (40/2)-5

= 20–5

= 15 m Therefore

Length= 15 cm

Breadth =5 cm

4 0
3 years ago
Read 2 more answers
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