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erma4kov [3.2K]
3 years ago
10

A company rents out 12 food booths and 22 game booths at the county fair. The fee for a food booth is $75 plus $7 per day. The f

ee for a game booth is $80 plus $10 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
Mathematics
1 answer:
dem82 [27]3 years ago
4 0

Answer:

sry yaar not understandable

Step-by-step explanation:

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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.

3 0
2 years ago
What is 0.326 in expanded form
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0.300 + .020 + 0.006 would be 0.326 in expanded form.
3 0
3 years ago
Can someone please help me with this problem
pychu [463]
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5 0
3 years ago
Solve 2/3+5/6 and put answer in simplest form <br>A)3/2<br>B)9/6<br>C)7/6<br>D)2/3
Mice21 [21]
It would be 9/6 which simplifies to 3/2
5 0
3 years ago
(will give brainliest!)
Flura [38]

Answer:

D) cot(C) = 1/2.

Step-by-step explanation:

We can go through each choice and examine is validity.

Choice A)

We have:

\displaystyle \sec B=\frac{3}{7}

Recall that secant is the ratio of the hypotenuse to the adjacent.

With respect to B, the adjacent is 6 and the hypotenuse is 7.

Therefore, sec(B) should be 7/6 instead.

A is incorrect.

Choice B)

We have:

\displaystyle \cot B=\frac{3}{2}

Cotangent is the ratio of the adjacent side to the opposite.

With respect to B, the adjacent side is 6 and the opposite side is 3.

Therefore, cot(B) = 6/3 = 2.

B is incorrect.

Choice C)

C is incorrect for the reasons listed in A.

Choice D)

We have:

\displaystyle \cot C=\frac{1}{2}

Again, cotangent is the ratio of the adjacent side to the opposite.

With respect to C, the adjacent side is 3 and the opposite side is 6.

So, cot(C) = 3/6 = 1/2.

Therefore, D is the correct choice!

8 0
3 years ago
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