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2 years ago

What is the midpoint of coordinates (6, 1) and (9, -3)?

Mathematics

1 answer:

ZanzabumX [31]2 years ago

4 0

Answer:

(7.5, -1)

Step-by-step explanation:

hope this helps you!

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What is -3/5 x -10/21?

sammy [17]

The answer would be 2/7!

7 0

3 years ago

Reviewing Imaginary Numbers. Simplify I^12

melamori03 [73]

Answer:

Step-by-step explanation:

$i^{12}= i^{2} *i^{2} *i^{2} *i^{2} *i^{2} *i^{2}$

Remember that $i^{2}=-1$

Plug it in:

$i^{12}= (-1)^{2} *(-1)^{2} *(-1)^{2} *(-1)^{2} *(-1)^{2} *(-1)^{2}$

$=1*1*1*1*1*1$

$=1$

6 0

3 years ago

Use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2 2^n+1 + 100

anastassius [24]

The given Statement which we have to prove using mathematical induction is

$5^n\geq 2*2^{n+1}+100$

for , n≥4.

⇒For, n=4

LHS

$=5^4\\\\5*5*5*5\\\\=625\\\\\text{RHS}=2.2^{4+1}+100\\\\=64+100\\\\=164$

LHS >RHS

Hence this statement is true for, n=4.

⇒Suppose this statement is true for, n=k.

$5^k\geq 2*2^{k+1}+100$

-------------------------------------------(1)

Now, we will prove that , this statement is true for, n=k+1.

$5^{k+1}\geq 2*2^{k+1+1}+100\\\\5^{k+1}\geq 2^{k+3}+100$

LHS

$5^{k+1}=5^k*5\\\\5^k*5\geq 5 \times(2*2^{k+1}+100)----\text{Using 1}\\\\5^k*5\geq (3+2) \times(2*2^{k+1}+100)\\\\ 5^k*5\geq 3\times (2^{k+2}+100)+2 \times(2*2^{k+1}+100)\\\\5^k*5\geq 3\times(2^{k+2}+100)+(2^{k+3}+200)\\\\5^{k+1}\geq (2^{k+3}+100)+3\times2^{k+2}+400\\\\5^{k+1}\geq (2^{k+3}+100)+\text{Any number}\\\\5^{k+1}\geq (2^{k+3}+100)$

Hence this Statement is true for , n=k+1, whenever it is true for, n=k.

Hence Proved.

4 0

3 years ago

I need help with 43-45

Lena [83]

43. 300 customers per day is the median of the distribution, so half of the measurements of customers per day are 300 or less. We could say, about half the time.

44. The quaritles of the distribution for Store A are evenly spaced, so we can say the distribution is symmetrical and nearly uniform.

For Store B, the longer distances between quartiles on the right and the long right-side "whisker" mean the distribution is skewed to the right.

45. The average and median are likely very close to the same for Store A, at about 300 customers per day. The average for Store B is likely slightly above its median of 350, so is more than 350 customers per day. The worst days for Store B are not as good as the best days for Store A, but, on average, Store B has more customers.

8 0

3 years ago

You purchased your car for $28,000. The value of the car depreciates by 9% per year. How much will the car be worth in 5 years?

Westkost [7]

Answer:

Worth after 5 years is $12423.75.

Step-by-step explanation:

Current worth is C=$28000. Depreciation rate is D=15%. Time in years is T=5. Worth (W) after 5

8 0

2 years ago