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2 years ago

Since only 2 of the 50 states are not connected to the mainland, what percentage of the states ARE on the mainland?

Mathematics

1 answer:

Nitella [24]2 years ago

6 0

Answer:

96%

Step-by-step explanation:

too easy for me

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Real numbers are (closed/not closed) under multiplication.

Sveta_85 [38]

thanks tho

<u>next time use ur head</u> Step-by-step explanation:

7 0

2 years ago

What inequality the number line represents.

nordsb [41]

Answer:

B hope this helps:)

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

1*5*665*5665*5545*5665

sergiy2304 [10]

Answer:

thats long just use calcukator

5 0

2 years ago

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

2 years ago

Write an equation of the line perpendicular to the line 8x+15y=12 and containing the point (11,17) write the answer in standard

jek_recluse [69]

The slope of a line perpendicular to another line has a slope which is the negative reciprocal of that line or:

m1 = -1/m2

First, we convert the given equation into slope-intercept form of a line: y = mx + b

8x + 15y = 12

15y = -8x + 12

y = (-8/15) x + 0.8

m1 = -8 / 15

Therefore the slope of the perpendicular line is:

m2 = 15 / 8

Since the perpendicular line crosses the point (11, 17), therefore using the slope formula:

m = (y2 – y1) / (x2 – x1)

15 / 8 = (y2 – 17) / (x2 – 11)

1.875 (x2 – 11) = y2 – 17

1.875 x2 – 20.625 = y2 – 17

y2 = 1.875 x2 – 3.625

y = (15/8) x – 3.625

multiplying both sides by 8:

8y = 15x – 29

rewriting in standard form:

<span>15x – 8y = 29 (ANSWER)</span>

3 0

2 years ago