If a/b = 2/3, then 3a = ___.

Given:

Principal = $400

Rate of interest = 6% compounded monthly

Time = 5 years.

To find:

The amount in the bank after 5 years.

Solution:

The formula for amount is:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is principal, r is the rate of interest, n is the number of time interest compounded in an year and t is the number of year.

Interest compounded monthly. So, [tex]n=12[/tex].

Putting [tex]P=400, r=0.06, n=12[/tex] and [tex]t=5[/tex], we get

[tex]A=400\left(1+\dfrac{0.06}{12}\right)^{12(5)}[/tex]

[tex]A=400\left(1+0.005 \right)^{60}[/tex]

[tex]A=400\left(1.005 \right)^{60}[/tex]

[tex]A\approx 539.54[/tex]

Therefore, the amount of money in the bank after 5 years is $539.54.

Answer:

The thickness of the new dirt cover is 0.144 yards.

Step-by-step explanation:

Dimension of garden = 25 feet by 25 feet.

Volume of soil bought = 10 cubic yards

Volume = length x width x height

But,

1 foot = 0.333333 yard

So that,

25 feet = 25 x 0.333333

            = 8.33333 yards

The new dimension of the garden = 8.33333 yards by 8.33333  yards.

Let the thickness of the new dirt cover be represented by h.

Thus,

Volume = 8.33333 x 8.33333 x h

10 = 69.44439 x h

h = [tex]\frac{10}{69.44439}[/tex]

  = 0.144

h = 0.144 yards

The thickness of the new dirt cover is 0.144 yards.

Answer:

Cost of each book = 14.5

Step-by-step explanation:

Given:

Total amount spend = 52.50

Cost of calendar = 9

Number of books = 3

Assume;

Cost of each book = a

Find:

Cost of each book

Computation:

Total amount spend  = Cost of calendar + Number of books(Cost of each book)

52.50 = 9 + 3(a)

Cost of each book = 14.5

Answer:

B.

Step-by-step explanation:

V = (pi)r^2h

V = 3.14 * (8 m)^2 * 28 m

V = 5626.9 m^3

Answer: B.

Answer:

-8x^2 + 14x -6

Step-by-step explanation:

Answer:

- 8x² + 14x - 6

Step-by-step explanation:

Given

(- 8x² + 10x + 4) - (- 4x + 10)

Distribute the parenthesis, noting to distribute the second one by - 1

= - 8x² + 10x + 4 + 4x - 10 ← collect like terms

= - 8x² + 14x - 6

Hello! The area of square KLMN is 25 cm²

Make sure to read an explanation for better understanding to the problem.

Any questions about my answer and explanation can be asked through comments.

Step-by-step explanation:

Since the square has same length for both sides. We can proceed side × side formula. Our side is 5 because if we count these small squares or grids, we'd get 5 for both sides.

Therefore 5 × 5 = 5² = 25 cm².

We can also use Calculus to solve the problem by using Integration.

Because both lines are horizontal, they are constant function. That means they are in the form of y = b where b is a constant.

A line that passes through (a,4) where a is all real numbers. The equation is y = 4

A line that passes through (c,-1) where c is all real numbers. The equation is y = -1

Therefore,

[tex] \large{ \int^{b}_a f(x) dx+ \int^{b}_a g(x)dx} \\ \large{ \int^{2}_{ - 3} (4)dx+ \int^{2}_{ - 3} ( - 1)dx}[/tex]

Because y = -1 is below x-axis. Therefore,

[tex] \large{ \int^{2}_{ - 3} 4 dx+ \int^{2}_{ - 3} 1dx} \\ \large{ (4x)^{2}_{ - 3} + (x)^{2}_{ - 3} } \\ \large{8 - ( - 12) + 2 - ( - 3)} \\ \large{8 + 12 + 2 + 3 = 25}[/tex]

Answer:

1 cup of milk = 3cups of brown sugar

Answer:

It's 3

Step-by-step explanation:

Because...

When we see the table we can find that it is given 2×3=6, 6×3=18, .... and so on so if we multiply 3 with 1 cup of milk then

3×1=3

So from this the answer is 3

Hope you understood!!

Answer:

a. f(-12) = 10

b. f(0) = 1

c. f(4) = -2

Step-by-step explanation:

In order to find the function of each of these numbers, you just need to replace them in the function as x and then solve:

a. f(-12) = 1 - 3/4(-12)

 - f(-12) = 1 - (-36/4)

 - f(-12) = 1 + 9

 - f(-12) = 10

b. f(0) = 1 - 3/4(0)

 - f(0) = 1 - 0

 - f(0) = 1

c. f(4) = 1 - 3/4(4)

 - f(4) = 1 - 12/4

 - f(4) = 1 - 3

 - f4) = -2

Answer:

x=34

Step-by-step explanation:

132-64=

68/2=

34

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Answer: Check the screenshot below!

Explanation:

I hope this helped!

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Answer:

35x^2y^2

Step-by-step explanation:

just multiply and combine like terms

Answer: x squared equals y

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of a cone is pie times radius square times height divided by 3

So it will be 3.14 x (4x4)x 9/3= 150.72

Answer:

3^-5

Step-by-step explanation:

x^-3=1/x^3

this rule applies to all negative exponents lol

Answer:

A or C  Sorry!

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

Just multiply then divide:

55 x 32 = 1760

1760 ÷ 32 = 55

Or just easier like:

55 x 32 ÷ 32 = 55

Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

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Step-by-step explanation:

5x-2y=10

x-y=-1

Addition method

multiply the second equation by -2 and add it to the first one

5x-2y=10

-2x+2y=2

Total 3x=12

Divide by sides by 3

x=4

Now multiply the second equation by -5 and add it to the first one

5x-2y=10

-5x+5y=5

3y=15

Divide both sides by 3

y=5

Solutions are x=4 and y=5

2nd method

if x-y=-1, so x=y-1

bring the value of x in the first equation

5(y-1)-2y=10

5y-5-2y=10

put the similar term together

3y=15

Divide both sides by 3

y=5

now bring the value of y in one of the equation

x-y=-1

so x-(5)=-1

x=-1+5

x=4

Solutions are x=4; y=5

Answer:

1/10

Step-by-step explanation:

We are to determine the difference between the miles walked Tasha already and the total number of miles to school

[tex]\frac{7}{10} - \frac{3}{5}[/tex]

[tex]\frac{7-6}{10}[/tex] = [tex]\frac{1}{10}[/tex]

Answer:

R' = (0,7)

Step-by-step explanation:

The anwer is 62 degrees

Step-by-step explanation:

angle x and the angle with a measure of 62 degrees are alternate exterior angles therefore they are congruent

Answer:

126 miles

Step-by-step explanation:

If I remember right, you'll have to multiply 30 by 4.2 and get 126 miles since each hour is 30 miles.

Answer:

10, -10

Step-by-step explanation:

Take the sqrt(100)

What number times itself = 100

10*10 = 100

-10*-10 = 100

sqrt(100) = +10 or -10