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2 years ago

1. There are always twice as many girls as boys in school. Mathematical expression

Mathematics

2 answers:

Airida [17]2 years ago

8 0

Answer:

Boys x 2 = Girls

Step-by-step explanation:

If there are twice as many girls in school as boys than take the number of boys and multiply that by 2. For example if there are 400 boys in school and there are twice as many girs your equation would, 400 x 2 = 800 girls.

posledela2 years ago

5 0

Girls x 2 = boys because 2 girls make a boy

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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.

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2 years ago

To find the area of a triangle, you can use the expression b × h ÷ 2, where b is the base of the triangle and h is its height. W

rosijanka [135]

Answer:

Step-by-step explanation:

first multiply 6 and 4.

then divide by 2.

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2 years ago

Carol is given a 10% pay decrease. Her new wage is £306 per week. What would be her weekly wage if, instead, she had received a

svetlana [45]

the answer would be 374.00

the original value before any increase or decrease is 340.00

so...

340.00 X 1.10 = 374.00

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2 years ago

Read 2 more answers

Please help,thank you

expeople1 [14]

Answer:

No, It is not a function!

Step-by-step explanation:

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2 years ago

Given the equation y − 3 = 1/2 (x + 6) in point-slope form, identify the equation of the same line in standard form. )

Doss [256]

Answer:

a: x − 2y = −12

Step-by-step explanation:

the standard form of a line is is usually given as Ax + By = C, so just by deduction you can tell that the correct answer is a.

If you want to do the procedure it would be:

y − 3 = 1/2 (x + 6)

y − 3 = 1/2 x + 3

y - 1/2 x = 3 + 3

y - 1/2 x = 6

(y - 1/2 x = 6) * 2 to get rid of the fraction

2y - x = 12 rearrenge the terms

x - 2y = -12

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2 years ago