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Sliva [168]
3 years ago
8

A town has 5000 residents. A survey finds that 81 residents

Mathematics
1 answer:
fomenos3 years ago
8 0

Answer:

448-848

Step-by-step explanation:

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Show that 1n^ 3 + 2n + 3n ^2 is divisible by 2 and 3 for all positive integers n.
Dmitry_Shevchenko [17]

Prove:

Using mathemetical induction:

P(n) = n^{3}+2n+3n^{2}

for n=1

P(n)  = 1^{3}+2(1)+3(1)^{2} = 6

It is divisible by 2 and 3

Now, for n=k, n > 0

P(k) = k^{3}+2k+3k^{2}

Assuming P(k) is divisible by 2 and 3:

Now, for n=k+1:

P(k+1) = (k+1)^{3}+2(k+1)+3(k+1)^{2}

P(k+1) = k^{3}+3k^{2}+3k+1+2k+2+3k^{2}+6k+3

P(k+1) = P(k)+3(k^{2}+3k+2)

Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also

divisible by 2 and 3.

Hence, by mathematical induction, P(n) = n^{3}+2n+3n^{2} is divisible by 2 and 3 for all positive integer n.

3 0
3 years ago
Jess owns 4 red shirts, 5 blue shirts, and 3 white shirts. She chooses a shirt to wear at random. What is the probability that s
xxTIMURxx [149]
D is the answer because in total she has 12 shirts and 3 out of the twelve shirts are white. so find the percentage of 3/12 which i belive is 1/4 
7 0
3 years ago
The equation P=4s represents the perimeter P of a square with side length s. What is the perimeter of a square with a side lengt
PilotLPTM [1.2K]

Answer:

20 feet

Step-by-step explanation:

s= side

P= 4s

I our case, s is 4, so 4*5 is 20.

Hence,

P=20

Hope this helps!

6 0
2 years ago
What is the interquartile range of the following data set? 3,8, 14, 19, 22, 29, 33, 37, 43, 49. A. 26 B. 23 C. 19 D. 18
Fynjy0 [20]

Answer:

I think the answer is B.23

8 0
3 years ago
Write an equation of a line that passes through (-12,-14) with slope 6
shusha [124]
Fill in the slope and that point in y=mx+b

-14=6(-12) + b

-14= -72 + b

b= 58

Y=6x + 58
7 0
3 years ago
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