All categories

3 years ago

Need help with 13 14 and 15

Mathematics

1 answer:

ad-work [718]3 years ago

6 0

Answer:

njbvi3brfjkncdoewkmdrfrj

Step-by-step explanation:

gagagagagaggag

You might be interested in

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

Please solve the math problem for me... I will mark you brainliest

natali 33 [55]

Answer:

$x=34$

Step-by-step explanation:

*it's kind of hard to read the number in parenthesis though but i think it's 5

both angles have to add up to 180º because they are co-exterior angles on parallel lines.

$2(x+5)+102=180\\2(x+5)=78\\2x+10=78\\2x=68\\x=34$

6 0

3 years ago

David, a high school senior was wondering if the cost of attending college is worth the

expeople1 [14]

Answer:

Step-by-step explanation:

<u>Explanation for part 1.</u>

To find the mean, find total then divide by number of data set

For college salaries

Sum=41+67+53+48+45+60+59+55+52+52+50+59+44+49+52=786

Number of samples=15

Mean= 786/15 =52.4 * $1000=$52400

For High school salaries

Sum=23+33+36+29+25+43+42+38+27+25+33+41+29+33+35=492

Number of samples =15

Mean= 492/15 = 32.8 *$1000= $32800

College grads make more money according to the means.

<u>Explanation for part 2.</u>

Treat the data as part of coordinates and graph then on the same scale and axis to visualize the trend and make comparison.In this case, the graph for the line of best fit is linear as attached.

3 0

3 years ago

PLEASE HURRY!!!

11Alexandr11 [23.1K]

Answer:

so the 2 questions i see are surveys so... you have to answer them with truth on your own self

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

14. A pitcher contains quart of lemonade.

Sergio039 [100]

Answer:

1/9 quart in each glass

Step-by-step explanation:

2/3) / 6

(2/3) * (1/6) = 2/18 = 1/9 quart in each glass

3 0

3 years ago