you deposit $5000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?

Note: Round your answer to the nearest cent.

Answer:

Kindly check attached picture for sample space design

45 ways

Step-by-step explanation:

Number of qualified candidates to be chosen = 2

Number of candidates to be interviewed = 10

Combination formula :

nCr = n! / (n-r)! r!

10C2 = 10! ÷ (10 - 2)!2!

10C2 = 10*9 / 2 * 1

10C2 = 90/2

10C2 = 45 different samples

Our sample space will contain 45 different samples

Answer:

x=0

Step-by-step explanation:

-4(2x+6) = -24

distribute the -4 to the parentheses

-8x-24 = -24

add the 24 over

-8x=0

divide both sides by -8

x=0

Answer:

x=7.5

Step-by-step explanation:

\(\frac{8}{5} =\frac{12}{x}\)

\(8x=60\)

\(x=7.5\)

When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation

To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.

The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.

In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':

2a + c = 162.97

Rearrange the equation to isolate 'c':

c = 162.97 - 2a

Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.

For example, let's say we choose 'a' = 10:

c = 162.97 - 2(10)

c = 162.97 - 20

c = 142.97

So, when 'a' is 10, 'c' is approximately 142.97.

You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.

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Answer:

y=6

Step-by-step explanation:

Answer:

The answer is 15

Answer: 545

Step-by-step explanation:

Answer:

454

Step-by-step explanation:

Hope This Helps

Have A Great Day

Answer:

20+m

Step-by-step explanation:

Answer:

20+m=?

Step-by-step explanation:

if moore already has 20 songs and his freind brought m more books then we would need to find the total amount of books more has now.

The length of each side of the square is 16 cm, the perimeter is 64 cm, and the area is 256 cm^2.

Let's solve the problem step by step. We have a square ABCD, and we need to find the length of its sides when the diagonal is 16√2 cm long.

In a square, the diagonal forms a right triangle with the sides. The sides of a square are equal in length, so let's assume the length of one side of the square is 'x' cm.

Using the Pythagorean theorem, we can find the relationship between the side length and the diagonal:

x^2 + x^2 = (16√2)^2

2x^2 = 512

Dividing both sides by 2, we have:

x^2 = 256

Taking the square root of both sides:

x = √256

x = 16 cm

So, the length of each side of the square is 16 cm.

To find the perimeter of the square, we simply multiply the length of one side by 4 since all sides are equal:

Perimeter = 4 * 16 cm = 64 cm

To find the area of the square, we square the length of one side:

Area = (16 cm)^2 = 256 cm^2

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Note the complete question is:

Find the length of side of square ABCD when diagonal is 16√2 cm long. Also find the perimeter and area of the square?

Answer:

Fill the blank with \(\frac{8}{3}\)

Step-by-step explanation:

Given

\(9xy * (\frac{2}{3}x)^3 = (--/--)x^4y\)

Required

Fill in the gaps

\(9xy * (\frac{2}{3}x)^3 = (--/--)x^4y\)

Open Brackets

\(9xy * \frac{2^3}{3^3}x^3 = (--/--)x^4y\)

\(9xy * \frac{8}{27}x^3 = (--/--)x^4y\)

Multiply xy and x^3

\(9 * \frac{8}{27}x^4y = (--/--)x^4y\)

\(\frac{9 * 8}{27}x^4y = (--/--)x^4y\)

Divide fraction by 9/9

\(\frac{8}{3}x^4y = (--/--)x^4y\)

By comparison, the blank will be filled with:

\(\frac{8}{3}\)

Hence, the solution to the question is: \(9xy * (\frac{2}{3}x)^3 = \frac{8}{3}x^4y\)

Answer:

2

Step-by-step explanation:

PEMDAS says to do the equations in parentheses first

(14-4) = 10

PEMDAS then says to do multiplication or division, whichever comes first in the equation, which is multiplication in this case

(10)2 = 20

20 ÷ 10 = 2

Answer:   \(\frac{5}{6}\) of a yard

=========================================================

Explanation:

The longest is \(\frac{6}{6}\) yard and the shortest is \(\frac{1}{6}\) of a yard.

This is because 6 is the largest numerator and 1 is the smallest numerator.

Subtract the two fractions:

\(\frac{6}{6} - \frac{1}{6} = \frac{6-1}{6} = \frac{5}{6}\)

We subtract the numerators while the denominator stays the same at 6 the entire time.

This is the difference between the longest and shortest ribbon, and the unit is in yards.

Answer:

C 2.0

Step-by-step explanation:

x-1.4 =0.6

add 1.4 to both sides

x=2.0

Answer:

x=3, = -2

Step-by-step explanation:

Answer:

Step-by-step explanation: Inverse property of addition

Answer:

So let's take a look into the question, "Mrs. Grudman bought a dishwasher at a special sale. The dishwasher regularly sold for

$912. No down payment was required. Mrs. Grudman has to pay $160 for the next six months. What is the average amount she pays in interest each month?"

Step-by-step explanation:

So, " Mrs. Grudman has to pay $160 for the next six months" they want us to multiply, $160

              x

                    6

              _______

                  960

So, 960 is your answer. Hope this helps!    

The average amount she pays in interest each month will be $8.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The dishwasher regularly sold for $912.

No down payment was required.

Mrs. Grudman has to pay $160 for the next six months.

Now,

The total amount pay by Mrs. Grudman = 6 x $160

                                                             = $960

Thus, The average amount she pays in interest each month is;

= (960 - 912) / 6

= $8

Thus, The average amount she pays in interest each month will be $8.

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Answer:

Vertical movement: Move up 3 units

or

Horizontal movement: Move left 3 units

Step-by-step explanation:

If your parent equation is \(f(x) = 4(2)^{x}\) and your child equation is \(f(x) = 4(2)^{x} + 3\), then it has vertically moved up 3 units.

If your parent equation is \(f(x) = 4(2)^{x}\) and your child equation is \(f(x) = 4(2)^{x+3}\), then it has moved horizontally left 3 units.

Answer:

Translation upwards of 3 units.

Step-by-step explanation:

The + 3 moves the whole graph up 3 units.

f(x) ---> f(x) + 3.

( I have assumed that The + 3 is not part of the exponent).

Answer:

Step-by-step explanation:

Probably D,  he's measuring voltage across the wire.. and then across the light bulb,   there would be very little across the wire and a lot across the light bulb

Answer:

  24

Step-by-step explanation:

Let d represent the number of dimes. Then (57-d) is the number of quarters, and the total value (in cents) is ...

  10d +25(57 -d) = 1065

  -15d +1425 = 1065 . . . . . . simplify

  -15d = -360 . . . . . . . . . . subtract 1425

  d = -360/-15 = 24 . . . divide by the coefficient of d

There are 24 dimes in the jar.

Answer:

33°

Step-by-step explanation:

you add the two numbers together and subtract from 180° to get your answer

Answer:

∠A = 22°

Step-by-step explanation:

complementary angles is either of two angles whose sum is 90°

∠A + ∠B = 90°

m∠B = 68°

∠A + 68° = 90°

subtract 68 from both sides

∠A + 68° - 68 = 90° - 68

∠A = 22°

Answer:

22°

Step-by-step explanation:

M<A+M<B= 90° ( complementary angles)

M<A+ 68° = 90°

M<A = 90-68= 22°

M<A= 22°

Answer:

512.04

Step-by-step explanation:

first you need to find out how many miles it goes in 1 hour so 320 divided by 7.5 which is 42.67

then take 42.67 and multiply it by 12

hope this helps!!

Answer:450

Step-by-step explanation:

The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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Answer:

1023/4

Step-by-step explanation:

shown in the picture

True

Note that:

\(secant \theta = \frac{1}{cos\theta}\)

The graph of sine and cosine functions are very similar. They only have a shift in the x -axis.

That is,  sin x  =  cos (90  -  x)

Since there is a great similarity between the sine and cosine graphs, and the secant graph is an inverse of the cosine graph, the graph of sine can be used to construct the graph of the secant function

Mathematically:

since  sec x  =  1 / cos x

and, cos x = sin (90 - x)

therefore, sec x = 1 / sin (90 - x)

The graphs of the sine and secant functions are attached to this solution

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The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

Based on the information, dy/dx + 3y = 2x³ e^(-3x)

The integrating factor is e^(∫3 dx) = e^(3x),

e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)

d/dx (e^(3x) y) = 2x^3

e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C

C is an arbitrary constant of integration.

y = (1/2) x^4 e^(-3x) + C e^(-3x)

The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

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Answer:

36

Step-by-step explanation:

Area of a triangle = (bh)/2

Where b = base length and h = height

Given base length: 18ft

Given height: 4ft

This being known let's define the variables

b = 18

h = 4

Now to find the area we simply plug in these values into the formula

Area = (18)(4)/2

Simplify multiplication 18 * 4 = 72

Area = 72/2

Simplify division

Area = 36

The inverse of the equation is determined as \(y = \log_{6}(-3x)\).

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

\(-3x = 6^y\)

Take the logarithm of both sides of the equation with base -6:

\(\log_{6}(-3x) = y\)

Finally, replace y with x to obtain the inverse equation as follows;

\(y = \log_{6}(-3x)\)

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