Regan deposited $20 in a savings account earning 5% interest, compounded annually.

To the nearest cent, how much interest will she earn in 3 years?

Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

Steps to solve:

4x - 12 + 3x + 9

~Combine like terms

(4x + 3x) + (-12 + 9)

~Simplify

7x - 3

Best of Luck!

Answer:

X = 3/7

Step-by-step explanation:

4X - 12 + 3X + 9 = 0 (separate them)

4X + 3X = 12 - 9 (add)

7X = 3 (divide 7 on both sides)

X = 3/7

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Compound amount formula is given by:

Where:

P = $55000

r = 2% = 0.02

t = 2022 - 2013 = 9 years

n = 1

Therefore, Substituting the given values:

And solve:

Answer: the salary do you need to make is $65730.09

Answer:

A(-3,-4)

B(-1,1)

C(3,5)

D(2,-5)

Step-by-step explanation:

if you have any questions about it dont hesitate to ask me

Simplifying the logarithm expression 7 log 3 k + 6 log 3 m - 9 log 3 n, we have log3(k^7m^6/n^9)

From the question, we have the following parameters that can be used in our computation:

7 log 3 k + 6 log 3 m - 9 log 3 n.

Apply the power rule of logarithm

So, we have

log3k^7 + log3m^6 - log3n^9

Apply the product rule of logarithm

So, we have

log3(k^7m^6/n^9)

Hence, the solution is log3(k^7m^6/n^9)

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Answer:

We will find the value of each of the option to see which one is different

a) The opposite of 8

the opposite of 8 is -8

b) The distance between 5 and -3

distance is a scalar value and can NEVER be negative

So, distance = 8

c) The absolute value of 8

the absolute value of 8 is the modulus of 8

|8| = 8

d) The opposite of -8

the opposite of -8 is 8

From the above, we can see that the second, third and fourth options are equal except the first option

Answer:

\(y - 60 = 72(x-2)\)

Step-by-step explanation:

We need slope, an x coordinate, and a y coordinate for a tangent line.

Slope: f'(x) will give us the slope, so f'(2) = m = 9(2)\(\sqrt{3(2)^2 +4}\) = 18(\(\sqrt{16}\)) = 18(4) = 72

X coordinate: 2, given by the question.

Y coordinate: For the Y coordinate, we need to find f(2). To find f(x), we will use integration by substitution \(u = 3x^2\)      \(du =6x dx\)

\(\int\ {\frac{9}{6}\sqrt{u} } \, du\)

Apply Linearity

\(\frac{3}{2} \int\sqrt{u} } \, du\)

Integrate

\(u^{\frac{3}{2}} + C\)

Undo substitution

\((\sqrt{3x^2 + 4^}})^3 + C\)

Plug in x = 0 and solve for C

\(4 =\sqrt{(3(0)^2 + 4)^3} + C \\4 = \sqrt{64} + C\\4 = 8 + C\\C = -4\)

Now solve for f(2)

\((\sqrt{3(2)^2 + 4^}})^3 - 4\)

\((\sqrt{16}})^3 - 4\\64 - 4\\60\)

Fill in point slope form

\(y - 60 = 72(x-2)\)

Answer:

Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Average cumulative debt of recent college graduates is about $22,500, standard deviation of $7,000.

This means that \(\mu = 22500, \sigma = 7000\)

Proportion more than 30000.

1 subtracted by the pvalue of Z when X = 30000. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{30000 - 22500}{7000}\)

\(Z = 1.07\)

\(Z = 1.07\) has a pvalue of 0.8577

1 - 0.8577 = 0.1423

Approximately how many recent college graduates have accumulated a student loan of more than $30,000?

0.1423 out of 1.8 million.

0.1423*1.8 = 0.25614 million = 256,140

Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.

Answer:c

Step-by-step explanation:

Answer:

none, because all of them are greater than -3

Answer:

GCF = 7

hope this helps

Answer:

:)

Step-by-step explanation:

21 = 3 • 7,  35 = 5 • 7, 49 = 72

go add the snap carmel.bratz

The number of hydrogen atoms present in the sculpture of earth if the mass of earth is 829 kg is 4.145 × 10²⁹.

Given that,

Mass of the sculpture of the earth = 829 kg

We know that,

Mass of an hydrogen atom = 2 × 10⁻²⁷ kg

Number of hydrogen atoms = Mass of earth / Mass of hydrogen atom

                                              = 829 / 2 × 10⁻²⁷

                                              = 414.5 × 10²⁷

                                              = 4.145 × 10²⁹

Hence the required number of atoms is 4.145 × 10²⁹.

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Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

Answer: The equation of the line is y=-3/4x+1/4

Step-by-step explanation:

In order to find the equation of a line you can use the following form

y-y0=m(x-x0)

M in this case is our slope

For the line in this problem we know that our slope or m is = -3/4ths

While (x0,y0) = (-5,4)ths or the cordinates of the point

From here we subsitute the previous numbers into the equation

y - 4= -3/4ths (x-(-5))

Simply rearange the equation and you get the answer

The next digit in the quotient of 438 ÷ 6 after 7 is 3

The missing information in the question is added at the end

Caleb's workings is given as

   7

6  438

    42

---------------

      18

To determine the next digit we simply divide 18 by 8

18 divided by 6 is 3

So, we have

   73

6  438

    42

---------------

      18

      18

---------------

     0

The quotient has been calculated as 73

So, the next digit is 3

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Complete question

Caleb uses the standard algorithm to find 438 ÷ 6.

Part of his work is shown.

   7

6  438

    42

---------------

      18

What is the next digit in the quotient?

a) The sum of the measures of the interior angles of the regular nonagon is given by S₉ = 1260°

b) The measure of each interior angle of the regular nonagon is a = 140°

c) The measure of each exterior angle of the regular nonagon​ is b = 40°

Given data ,

Sum of the measures of the interior angles of a regular nonagon:

The Polygon Interior Angle Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is given by the formula:

Sum of interior angles = (n - 2) * 180°

For a nonagon, which has 9 sides, we can plug in n = 9 into the formula:

Sum of interior angles = (9 - 2) * 180

Sum of interior angles = 7 * 180

Sum of interior angles = 1260°

So, the sum of the measures of the interior angles of a regular nonagon is 1260°

Measure of each interior angle of a regular nonagon:

Since a regular nonagon has 9 sides, we can divide the sum of the interior angles (which we calculated as 1260 degrees) by the number of sides to find the measure of each interior angle:

Measure of each interior angle = Sum of interior angles / Number of sides

Measure of each interior angle = 1260 / 9

Measure of each interior angle = 140°

So, the measure of each interior angle of a regular nonagon is 140°

Measure of each exterior angle of a regular nonagon:

The Polygon Exterior Angle Sum Theorem states that the sum of the measures of the exterior angles of a polygon with n sides is always 360°

Since a regular nonagon has 9 sides, we can divide 360 degrees by the number of sides to find the measure of each exterior angle:

Measure of each exterior angle = 360 / Number of sides

Measure of each exterior angle = 360 / 9

Measure of each exterior angle = 40°

Hence , the measure of each exterior angle of a regular nonagon is 40°

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Answer:

Interest rate

Step-by-step explanation:

The amount owed is called the principal and the price of borrowing money is called interest. Some people spend a day's pay (or more) per week repaying the interest and principal owed on car loans, credit card bills, student loans, and other consumer debts.

Answer:

1. x = 15 in

2. x = 8 m

Step-by-step explanation:

1. Given:

length = 10 in

width = 3 in

height = x in

surface area of the rectangular prism = its volume

Required:

Value of x

Area = 2(wl + hl + hw)

Volume = l*w*h

Therefore:

2(3*10 + x*10 + x*3) = 10*3*x

2(30 + 10x + 3x) = 30x

2(30 + 13x) = 30x

60 + 26x = 30x

Subtract 26x from both sides

60 + 26x - 26x = 30x - 26x

60 = 4x

Divide both sides by 4

60/4 = 4x/4

15 = x

x = 15 in

2. Given:

length = 8 m

width = 4 m

height = x m

surface area of the rectangular prism = its volume

Required:

Value of x

Area = 2(wl + hl + hw)

Volume = l*w*h

Therefore:

2(4*8 + x*8 + x*4) = 8*4*x

2(32 + 8x + 4x) = 32x

2(32 + 12x) = 32x

64 + 24x = 32x

Subtract 24x from both sides

64 + 24x - 24x = 32x - 24x

64 = 8x

Divide both sides by 8

64/8 = 8x/8

8 = x

x = 8 m

Answer:

A. 6 = 36

8 = 64

10 = 100

12 = 144

14 = 196

B. 340

C. 582

D.6= 36

7 =49

8 = 64

9= 81

10= 100

Answer:

Step-by-step explanation:

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Answer:

The first one is 3/5 & The second one is 3/8 & The the third one is 1/8

Step-by-step explanation:

Hope this helps :)

Answer:

28,000 milligrams is your answer

Answer:

The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 0 0 . All lines that are parallel to y=−15 y = - 1 5 have the same slope of 0 .

Answer:

No

Step-by-step explanation:

the reason why i said nonis cause 96+123+106+72=397 which means he still needs 13 more

Answer:

A.

The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.