MATHEMATICS COLLEGE

What is the square root of 64y16?
o 44
O 4y
o 8
o gy

Answers

Answer 1
Answer:

Answer:

B is the answer of the question
Answer 2
Answer:

Answer:

The answer is 4y8

Step-by-step explanation:

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Sketch the region R defined by 1 ≤ x ≤ 2 and 0 ≤ y ≤ 1/x^3 .a. Find (exactly) the number a such that the line x = a divides R into two parts of equal area.
b. Then find (to 3 decimal places) the number b such that the line y = b divides R into two parts of equal area.

Answers

For part (a), you're looking to find a such that

\displaystyle\int_1^a(\mathrm dx)/(x^3)=\int_a^2(\mathrm dx)/(x^3)

You have

\displaystyle\int_1^a(\mathrm dx)/(x^3)=-\frac1{2x^2}\bigg|_(x=1)^(x=a)=-\frac12\left(\frac1{a^2}-1\right)

and

\displaystyle\int_a^2(\mathrm dx)/(x^3)=-\frac1{2x^2}\bigg|_(x=a)^(x=2)=-\frac12\left(\frac14-\frac1{a^2}\right)

Setting these equal, you get

\displaystyle-\frac12\left(\frac1{a^2}-1\right)=-\frac12\left(\frac14-\frac1{a^2}\right)\implies a=2√(\frac25)

For part (b), you have

y=\frac1{x^3}\implies x=\frac1{\sqrt[3]y}

and you want to find b such that

\displaystyle\int_0^(1/8)\mathrm dy+\int_(1/8)^b(\mathrm dy)/(\sqrt[3]y)=\int_b^1(\mathrm dy)/(\sqrt[3]y)

You have

\displaystyle\int_0^(1/8)\mathrm dy+\int_(1/8)^b(\mathrm dy)/(y^(1/3))=\frac18+\frac32y^(2/3)\bigg|_(y=1/8)^(y=b)=-frac14+\frac32b^(2/3)

and

\displaystyle\int_b^1(\mathrm dy)/(y^(1/3))=\frac32y^(2/3)\bigg|_(y=b)^(y=1)=\frac32-\frac32b^(2/3)

Setting them equal gives

-\frac14+\frac32b^(2/3)=\frac32-\frac32b^(2/3)\implies b=\frac7{24}√(\frac73)\approx0.446

Point R is on line segment QS. Given RS = 2 and QS = 10, determine the length QR

Answers

Answer: QR=12

Step-by-step explanation:

10+2=12

Joe and Susan are both 40 years old and hope to have enough money saved to retire by the time they're 65. They deposit $6,000 eachyear into an account that pays 4% interest compounded annually. Use this information to complete the table.
Formula to Use
Account Balance in 20 years
Total Interest Earned
present value of an annuity
future value of a lump sum
future value of an annuity
$99,875
$112,253
$149,875
$249,875
$286,363

Answers

Account balance In 20 years is $249,875 and total interest earned is $99,875.

What is the future value?

The FV formula assumes a constant rate of growth and a single up-front payment left untouched for the duration of the investment. The FV calculation can be done one of two ways, depending on the type of interest being earned.

We have,

P = $6,000

r = 0.04

n = 1

t = 25

We know the formula for future value

​FV= PV (1 + r)^(n).

where:

P=Investment amount

R=Interest rate

T=Number of years

According to the question​​

FV=$6,000×(1+0.04

FV = $249,875

To find the total interest earned, first find the total value of the deposit payments:$6,000 annual payments for 25 years = 6,000 × 25= $150,000

Total interest earned = FV - annually payment for 25 year = $249,875 - $150,000 = $99,875

To learn more about future value from here

brainly.com/question/14860893

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Answer:

Formula: Future value of annuity

In 20 years: $249,875

Total Interest: $99,875

Step-by-step explanation:

Use the formula for future value:

FV =

P = $6,000

r = 0.04

n = 1

t = 25

FV =

FV = $249,875

To find the total interest earned, first find the total value of the deposit payments:

$6,000 annual payments for 25 years = 6,000 • 25

= $150,000

(I copied that explanation from somewhere else so its a little messed up. I just couldn't explain it properly. Hope this helps!)

Estimate the product by rounding 4×472

Answers

4*500=2000

Answer = 2000

Answer:

i think it would be 2000

Step-by-step explanation:

An airline company is considering a new policy of booking as many as 354 persons on an airplane that can seat only 330. (Past studies have revealed that only 88% of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 354 persons, not enough seats will be available

Answers

Title:

See the explanation.

Step-by-step explanation:

It is given that, if 100 persons book their seats, then only 88 passengers come.

The probability of 1 passenger to come is (88)/(100) = 0.88.

There will not be enough seats only when, 331 or more than 331 passengers will come.

The probability of 1 passenger will not come is (1 - 0.88)= 0.12.

Out of 354 passengers the probability that n passengers will come is ^(354)C_n (0.88)^n (0.12)^(354 - n).

The required probability is ∑^(354)C_n (0.88)^n (0.12)^(354 - n), where 331\leq n \leq 354.

What is The greatest common factor of 42 and 96 I’ll give you brainliest

Answers

The greatest common factor of 42 and 96 is 6.

What is greatest common factor?

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

42 = 2 x 3 x 7

96 = 2 x 2 x 2 x 2 x 2 x 3

Greatest common factor = 2 x 3 = 6

Learn more about greatest common factor here

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Answer:

6

Step-by-step explanation:

42 and 96

first we will find the factors of 42:

2 21

3 7

7 7

hence, factors of 42 are 2,7 and 3

then, we will find the factors of 96:

2 96

2 48

2 24

2 12

2 6

3 3

1

hence, factors of 96 are 2,2,2,2,2 and 3

Common factors are: 2 and 3

Highest common factor: 6
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