What is the exact volume of a cylinder with a height of 30 inches and radius of 13 inches

Answer:

6root(2)/25

Step-by-step explanation:

5^-2 = 1/25

3(root(8)) = 6(root(2))

so you get 6(root(2))(1/25)

= 6(root(2))/25

The required simplified value of the given expression is 0.34 or  6√2 / 25.

Given that,
Expression to simply ios given,
5⁻² x 3√8

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Simplification =>
= 5⁻² x 3√8
= 1/ 5⁻² x 3 x 2 √2
= 6√2 / 25
= 0.34

Thus, the required simplified value of the given expression is 0.34 or  6√2 / 25.

Learn more about arithmetic here:

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Answer:

Uncle is 34. Nephew is 10.

Step-by-step explanation:

Let u equal the age of the uncle, and n equal the age of the nephew.

First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:

[tex](u-2)+(n-2)=40[/tex]

[tex]u+n-4=40[/tex]

[tex]u+n=44[/tex]

Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:

[tex]u+2=3(n+2)[/tex]

We now have a system of equations and can solve accordingly.

First, from the first equation, we can determine that:

[tex]u=44-n[/tex]

We can substitute this into the second equation.

[tex](44-n)+2=3(n+2)[/tex]

[tex]46-n=3n+6[/tex]

[tex]40=4n[/tex]

[tex]n=10[/tex]

Thus, the nephew's age is 10.

And the uncle's age is 44-10 or 34.

Hey there! :)

Answer:

y = 4x + 48

Step-by-step explanation:

Original equation:

y = 1/4x -12

Switch 'x' and 'y' to solve for the inverse:

x = 1/4y - 12

Add 12 to both sides:

x + 12 = 1/4y - 12 + 12

x + 12 = 1/4y

Multiply both sides by 4:

4(x+12) = y

4x + 48 = y

The inverse is y = 4x + 48

Answer:

4x + 48

Step-by-step explanation:

f(x) = 1/4x - 12

y = 1/4x - 12

Add 12 to both sides.

y + 12 = 1/4x

Multiply both sides by 4.

4y + 48 = x

Switch variables.

4x + 48 = y

Answer:

-1, 1

Step-by-step explanation:

what is 1/3 of -3 and 3

Answer:

  [tex]\textbf{A. }4\sqrt{6}[/tex]

Step-by-step explanation:

The hypotenuse of the isosceles right triangle is √2 times the length of one leg, so is 6√2.

The hypotenuse of the 30°-60°-90° right triangle is 2/√3 times the length of the longer leg.

  [tex]x=\dfrac{2}{\sqrt{3}}\cdot 6\sqrt{2}\\\\=\dfrac{(2\sqrt{3})(6\sqrt{2})}{3}\quad\text{rationalize the denominator}\\\\\boxed{x=4\sqrt{6}}[/tex]

Answer:

(B)21+3a

Step-by-step explanation:

An expression is said to be distributive when:

[tex](a+b)c=a \cdot c+b \cdot c[/tex]

Given the algebraic expression: (7 + a)3

Applying the distributive property

[tex](7 + a)3 = 7 \cdot 3+a \cdot 3\\=21+3a[/tex]

An equivalent expression is 21+3a.

The correct option is B

Hey there! :)

Answer:

C) 74 units.

Step-by-step explanation:

MT is congruent to KT because the diagonals of a quadrilateral bisect each other. Therefore:

8y + 18 = 12y - 10

Subtract 8y from both sides:

18 = 4y - 10

Add 10 to both sides:

28 = 4y

Divide both sides by 4:

28/4 = 4y/4

y = 7 units. Plug this into the equation for MT:

8(7) + 18 = 74 units.

Answer:

74

Step-by-step explanation:

Set up the equations

8y + 18 = 12y -10

Combine like terms

28 = 4y

Divide each side by 4

y=7

Plug in the value of y in the equation of 8y + 18 since that's the value for MT

8(7) + 18 = 74

Hope this helps!

Hey there! :)

Answer:

0.3.

Step-by-step explanation:

Looking at the row for "Less than 80° F", the column for "Rain" shows a 0.3 probability in the table. Therefore:

The probability of rain on a day less than 80°F is 0.3.

Answer:B

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

Let's first and try to isolate x.

-2x < 5

(Divide by -2)

x > -5/2 ( < changes to > b/c it was divided by a negative)

x > -2.5

Since x is all values greater than -2.5, -6 is not within those bounds.

Thus, -6 is not a solution to the inequality.

Hope that helps!

Answer:

x12

Step-by-step explanation:

When multipling  numbers that are the same with exponent you can just add the exponents.

so x5*x7=x12

(It would be subtraction if there was division)

Hope this helped you and feel free to ask questions!

Answer:

x^12

Step-by-step explanation:

When multiplying exponents, the rule below is followed.

[tex]x^a * x^b= x^{a+b}[/tex]

Basically, the base remains the same, but the numbers in the exponents are added.

We are given:

[tex]x^5*x^7[/tex]

We leave the base (x)as is, and add the numbers in the exponents (5 and 7).

[tex]x^5*x^7\\[/tex]

[tex]x^{5+7[/tex]

[tex]x^{12}[/tex]

The expression [tex]x^5*x^7\\[/tex] can be simplified as: [tex]x^{12{[/tex]

The question is not typed properly! Complete question along with answer and step by step explanation is provided below.

Question:

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .

You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to

a. 118

b. 118/100=1.18

c. 118/√100= 11.8

d. cannot be determined

Answer:

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Step-by-step explanation:

From the given information,  

The population mean SAT critical reading score is

[tex]\mu = 495[/tex]

The population standard deviation is

[tex]\sigma = 118[/tex]

You choose an SRS of 100 students and average their SAT Critical Reading score.

[tex]n = 100[/tex]

Since the sample size is quite large then according to the central limit theorem,

The mean sample will be the same as the population mean  SAT critical reading score.

[tex]\bar{x} = \mu = 495[/tex]

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Answer:

answer is b). y = 100+ 0.05x

Step-by-step explanation:

Answer:

x = 6/5

y = 8/5

Step-by-step explanation:

3x - y = 2

2x + y = 4

Add the equations, cancelling y.

5x = 6

x = 6/5

Put x as 6/5 in the second equation and solve for y.

2(6/5) + y = 4

12/5 + y = 4

y = 4 - 12/5

y = 8/5

Answer: 168 hours

Step-by-step explanation:

There are 24 hours in a day.  Thus, simply multiply 7*24 to get 168.

Hi there! Hopefully this helps!

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Answer: There are 168 hours in 7 days.

Since there 24 hours in a day, Multiply 24 times 7 and you get 168.

Example : 24 x 7 = 168.

Answer:

101.58 in

Step-by-step explanation:

The ramp r is the hypotenuse of a right triangle with the ground and 28 in height being the legs.

The angle of elevation 16° is the angle inside the triangle opposite the 28 in height.

Using the sine ratio in the right triangle, then

sin16° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{28}{r}[/tex] ( multiply both sides by r )

r × sin16° = 28 ( divide both sides by sin16° )

r = [tex]\frac{28}{sin16}[/tex] ≈ 101.58 in

Answer:

The 3rd answer

Step-by-step explanation:

Answer:

He will have 13 packages containing 3 pairs of headphones and 1 music player each.

Step-by-step explanation:

He has 39 pairs of headphones and 13 music players.

He wants to sell both set of items in identical packages.

To do this he has to divide them in such a way that the same number of both set of objects are in every box.

Let us find the ratio of the pairs of headphones to music players:

39 : 13 = 3 : 1

Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.

So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.

Answer:

(0, 6)

Step-by-step explanation:

The solution is the point of intersection of the lines.

(0, 6)

Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

Answer:

B

Step-by-step explanation:

Since the diagonals of a rhombus bisect each other, that means P is the midpoint of LN. Therefore, LP = 1/2 * LN = 1/2 * 30 = 15.

There isn't an obvious question to this problem but with the given we can assume what is to be asked. I think we are to find the total cost of a certain poultry seasoning. The poultry seasoning would have a total weight of 4+2=6 ounces. The total cost will then have to be 4(4) + 2(3) = 22 dollars. 

Answer:

D. 6

Step-by-step explanation:

Got it correct on edg2020

Answer:

  -63

Step-by-step explanation:

Compare ...

  f(x) = x^2 -3x +18

to the standard form ...

  f(x) = ax^2 +bx +c

and you will see that ...

  a = 1, b = -3, c = 18.

__

The value of the discriminant is ...

  d = b^2 -4ac

  d = (-3)^2 -4(1)(18) = 9 -72 = -63

The discriminant is -63.

Answer:

The answer is B.

Step-by-step explanation:

2y = -2x - 10

y =    2x + 2 (combine like terms using addition)

_________

3y = -8

Answer:

Required angle measures 39°

Step-by-step explanation:

Let's say, x measures the angle between the hypotenuse and the common base of two triangles.

Sin(x) = 5/8

x = 39°

This angle is complementary to the angle other than theta (let's say y) in the required triangle.

90 - x = y and 90 - theta = y

>>> Theta = x

Best Regards!

Answer:

a)16      (2*2*2*2= 16)

b)16  (-4*-4-16)(-+-=+)

c)500 (5*5*5=125        125*4=500)

d)0.49  (0.7*07)

e)480  (4^=16     9^=81  121^0=1          16+81 -1 =96     96*5=480)

f)5^2  or 25 (a^m/ a^n=a^m-n)

g) 11^14 (reason same as the f one)

h)8.20

i) 4(-4*16=64)

j)900

Answer:

0.865

Step-by-step explanation:

To solve for the probability we would be using the formula:

F(x) = 1 - e^−λx

Therefore, P(x > 2000) = F(x) = 1 - e^−λx

Mean = 1000 hours

λ = 1/mean = 1/1000 hours

x= 2000 hours

F(x) = 1 - e^−(1/1000)2000

F(x) = 1 - e^−2

= 0.8646647168

Therefore, the probability the the circuit will last at least 2000 hours = 0.865

Answer:

18.84 meters.

Step-by-step explanation:

The formula for a circle is πr^2.

πr^2 = 28.26

3.14 * r^2 = 28.26

r^2 = 9

r = plus or minus 3.

But since this deals with the area of a circle, there is no way a radius can be negative. So, the radius is 3 meters.

The formula for the circumference is 2πr.

2 * 3.14 * 3 = 6 * 3.14 = 18.84.

So, the circumference of the circle is 18.84 meters.

Hope this helps!

Answer:

A ≈ 3215.36

Step-by-step explanation:

A = πr²

Radius - D/2

Radius - 64/2 → 32

A = 3.14(32)²

A = 3215.36

Hope this helps! :)

Answer:

3215.36 um²

Step-by-step explanation:

d = 2r => r = d/2 = 64/2 = 32 um

A = π·r²

= 3.14·32²

= 3.14·1024

≈ 3215.36 um²

Answer:

y = (x-.5)^2 -12.25

Step-by-step explanation:

first, find the vertex

x from (x,y) = -b/2a

ax^2-bx - c

1x^2-1x -12

-1/2(-1) = -1/-2 - 1/2

(1/2,y) then use x value to find y value

y = 1/2^2 - 1/2 - 12

y = .25 -.5 - 12    = -12.25

(.5,-12.25) input values into this formula:

y = a(x-h)^2 + k where h = x-value and k = y-value. use same a value = 1

y = (x-.5)^2 -12.25