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DENIUS [597]
3 years ago
7

Is 7.5 a integer or rational or whole number

Mathematics
2 answers:
melomori [17]3 years ago
8 0
7.5 is a rational number
ivann1987 [24]3 years ago
5 0

It is a rational number

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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
(Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to
RUDIKE [14]

Answer:

\%Change = 8.8\%

Step-by-step explanation:

Given

Initial = 51\ cents

Final = 55.5\ cents

Required

Determine the percentage change

Percentage change is calculated as;

\%Change = \frac{Final - Initial}{Initial} * 100\%

\%Change = \frac{55.5 - 51 }{51 } * 100\%

\%Change = \frac{4.5}{51} * 100\%

\%Change = \frac{4.5* 100\%}{51}

\%Change = \frac{450\%}{51}

\%Change = 8.8\%

<em>Hence, the percentage change is approximately 8.8%</em>

6 0
2 years ago
a number has a 4 in the thousands place the number also has a digit whose value is 10 times the value of the 4 on the thousands
maks197457 [2]
Well I can still answer that question without the following and it will be 44,000
3 0
3 years ago
You have 1240 acres of land, and each acre is worth $52. How much is your land worth in total?
murzikaleks [220]
If one acre is $52, you would multiply 1240 by 52. Your land in total is worth $64,480.
5 0
3 years ago
Thanks in advance if you help me!
8090 [49]
D) Definition of Equilateral Triangle
e) Vertical Angles
f1) ΔTVS <span>≅ </span>ΔUVR
f2) Side Angle Side Postulate
g) Definition of Congruent Triangles

Hope that helps!
4 0
3 years ago
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