Samantha invested $1000 in an account that pays 5% interest
compounded annually. Assuming no deposits or withdrawals are
made, find how much money Samantha would have in the account 18
years after her initial investment. Round to the nearest tenth (if
necessary).

Answer:2,300

Step-by-step explanation:

The value of tan(m - p), where the value of sin(m) = -(4/5), and the value of cos(p) = -(15/17) using trigonometric identities is; [tex]tan(m - p) = \dfrac{36}{77}[/tex]

Trigonometric identities are equations that involve trigonometric functions which are true for all values of the input variables.

The information in the question are;

Therefore;

[tex]cos(m) = \sqrt{1- \left(-\dfrac{4}{5}\right)^2} =\pm\dfrac{3}{5}[/tex]

The location of m is in Quadrant III, therefore;

[tex]cos(m) =-\dfrac{3}{5}[/tex]

[tex]sin(p) = \sqrt{1- \left(-\dfrac{15}{17}\right)^2} =\pm\dfrac{8}{17}[/tex]

The angle p is located in Quadrant III, therefore;

[tex]sin(p) = -\dfrac{8}{17}[/tex]

180° ≤ Angle ∠m ≤ 270°; definition of angles in Quadrant III

180° ≤ Angle ∠p ≤ 270°; definition of angles in Quadrant III

Therefore;

270° - 270° ≤ |∠m - ∠p| ≤ 270° - 180°
0° ≤ |∠m - ∠p| ≤ 90°

The trigonometric identity for tan(m - p) is presented as follows;

[tex]tan(m - p) = \dfrac{tan(m) -tan(p)}{1+tan(m)\cdot tan(p)}[/tex]

[tex]tan(m - p) = \dfrac{\dfrac{sin(m) }{cos(m) } -\dfrac{sin(p) }{cos(p) } }{1+\dfrac{sin(m) }{cos(m) } \cdot \dfrac{sin(p) }{cos(p) } }[/tex]

Therefore;

[tex]tan(m - p) = \dfrac{\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) -\left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) }{1+\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) \times \left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) } }= \dfrac{36}{77}[/tex]

[tex]tan(m - p) = \dfrac{36}{77}[/tex]

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The coordinates along the directed line segment is (-4, -6)

The points are given as:

A  = (-7, -4)

B = (2, -10)

The ratio on the segment can be represented as;

m : n = 1 : 2

So, we have the coordinates of the point that lies along the directed line segment to be

Point = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

So, we have:

Point = 1/(1 + 2) * (1 * 2 + 2 * -7, 1 * -10 + 2 * -4)

Evaluate

Point = (-4, -6)

Hence, the coordinates of the point is (-4, -6)

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Answer:

-1/3

Step-by-step explanation:

Substituting into the slope formula, the slope is [tex]\frac{-6-(-5)}{-6-(-9)}=-\frac{1}{3}[/tex]

Step-by-step explanation:

9 < 2(x - 7)

hope this helpful

Answer:

96

Step-by-step explanation:

Area of a triangle

A = (1/2) × base × height

A = (1/2) × 12 × 16

A = (1/2) × 192

A = 96 units²

I hope this helps!

According to the given temperature function, the substance will not be in liquid state in range is written as the inequality -30.874 < x < 566.121.  

Function:

Function refers the special relationship where each input has a single output. It is often written as "f(x)" where x is the input value.

Given,

Matter in a liquid state when it’s temperature is between it’s melting point and boiling point. Suppose that some substance has a melting point of -34.93 degrees Celsius and a boiling point of -332.29 degrees Celsius.

Here we need to find the range of temperatures in degrees Fahrenheit for which this substance is not in liquid state.

Here we have the following details

Melting point = -34.93C°

Boiling point = -332.29C°

Function = C = 5/9 (F - 32)

n order to find the inequality of the function we have to apply the value of  boiling and melting point in it,

First, we have to apply the value of melting point, then we get,

=> -34.93 = 5/9 (F - 32)   Distribute

=> -34. 93 = 5/9 F - 160/9    Multiply both sides by 9

=> -314.37 = 5F - 160   Add 160 on both sides

=> -154.37 = 5F     Divide both sides by 5

=> -30.874= F

Therefore, the melting point in F= -30.874.

Similarly, for the boiling point it can be calculated as,

=> -332.29 = 5/9 (F - 32)   Distribute

=> -332.29 = 5/9 F - 160/9    Multiply both sides by 9

=> -2990.61 = 5F - 160   Add 160 on both sides

=> -2830.61 = 5F     Divide both sides by 5

=> -566.121= F

Therefore, the boiling point in F= -566.121

So, the resulting inequality is -30.874 < x < 566.121.

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Answer:

y = - 3x - 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute (- 4, - 2 ) into the partial equation

- 2 = 12 + c ⇒ c = - 2 - 12 = - 14

y = - 3x - 14 ← equation of line

Answer:

Step-by-step explanation:

360

The value of the investment at the end of 5 years be $ 15,281.012.

Given, 10400 dollars are invested at an interest rate of 8%.

We have to find the value of the investment at the end of 5 years.

Now, on using the compound interest formula, we get

Amount = P(1 + r/100)^t

Amount = 10400(1 + 8/100)^5

Amount = 10400(1.08)^5

Amount = 10400(1.469)

Amount = 15,281.012

Hence, the value of the investment at the end of 5 years be $ 15,281.012.

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Answer:

19

Step-by-step explanation:

add it all up its easy

Step-by-step explanation:

Shelby buys 3 barrettes...

2*3=6

and 1 comb

1*1=1

she spent $7 in total

6+1=7

Kendra buys 2 barrettes...

2*2=4

and 4 combs

1*4=4

so Kendra spent $8 in total

4+4=8

the amount spent from the to girls was...

8+7=15

Answer:

The two graphs have the same shape, but the second graph shifted 3 units left.

The equation that generate the table in slope intercept form is y = 2 / 5 x + 4

The equation of a linear table can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Therefore, let's represent the equation of the table of money spent and pounds of food.

using slope intercept form,

y = mx + b

where

Therefore, let's find the slope using (0, 4) and (20, 12)

m = slope = 12 - 4 / 20 - 0

slope = 8 / 20

slope = 2 / 5

Therefore, let's find the y-intercept using (0, 4)

4 = 2 / 5(0) + b

b = 4

Therefore, the equation is y = 2  /5 x + 4

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Answer:

It is positive and increasing

Step-by-step explanation:

After the graph, it becomes positive as it passes the y-axis, the line which is where y=0. Also, the graph is headed up and to the right(after c), so as the value of x increase, the value of the function does as well. This would mean the answers is "It is positive and increasing"

The solution of the inequality -1 > 6x + 9 is x < -1.67, therefore -1, -4 and -6 are the solutions of inequality

The inequality is

-1 > 6x + 9

The inequality is the mathematical statement that shows the relationship between two expression with and inequality sign. The inequality relationships are less than, less than or equal, greater than, greater than or equal etc. The equal sign will not be a part of inequality

The inequality is

-1 > 6x + 9

Rearrange the terms

6x + 9 < -1

Subtract both sides by 9

6x + 9 - 9 < -1 - 9

6x < -10

Divide both sides by 6

6x /6 < -10/6

x  < -5/3

x < -1.67

Hence, the solution of the inequality -1 > 6x + 9 is x < -1.67, therefore -1, -4 and -6 are the solutions of inequality

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The trigonometric function is useful to find the sides of a right-angle triangle. The value of x using the trigonometric function sin will be 7.884.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

Given right angle triangle,

Use sin trigonometric function.

Sin21° = x=22

x = 22 × 0.358

x = 7.884

Hence "The trigonometric function is useful to find the sides of a right-angle triangle. The value of x using the trigonometric function sin will be 7.884".

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The number of tiles need to cover the closet floor is 180 tiles

The length of the side of the tile = 1/3 feet

The area of the square = Side × Side

The area of the tile = (1/3) × (1/3)

= 1/9 square feet

The width of the closet = [tex]3\frac{1}{3}[/tex] feet

Convert the mixed fraction to simple fraction

[tex]3\frac{1}{3}[/tex] feet = 10/3 feet

The length of the closet = 6 feet

Total area of the closet = 10/3 × 6

= 20 square feet

Number of tiles needed = The area of the closet /  The area of the tile

Substitute the values in the equation

= 20 / (1/9)

= 180 tiles

Hence, the number of tiles need to cover the closet floor is 180 tiles

The complete question is

Vanessa wants to cover her closet floor with SRB tiles that are 1/3 foot on each side. The closet is   [tex]3\frac{1}{3}[/tex] feet wide and 6feet deep, How many tiles will Vanessa need to cover the closet floor?

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An equation of the function in standard form for the given table of values is 3x² + 24x + 50 = 0.

First, let us understand the standard form of a quadratic equation:

In Mathematics, the standard form of a quadratic equation is given by;

y = g(x) = ax² + bx + c = 0

To write a quadratic function equation in standard form, we would construct the following system of equations from the data in the given table:

5 = a(-5)² + b(-5) + c  ⇒ 5 = 25a - 5b + c     .......equation 1.

2 = a(-4)² + b(-4) + c  ⇒ 2 = 16a - 4b + c      .......equation 2.

5 = a(-3)² + b(-3) + c  ⇒ 5 = 9a - 3b + c       .......equation 3.

14 = a(-2)² + b(-2) + c  ⇒ 14 = 4a - 2b + c    .......equation 4.

From equation 1 and equation 3, we derive:

25a - 5b + c = 9a - 3b + c

⇒ 25a - 9a = -3b + 5b

⇒ 16a = 2b

⇒ b = 8a

Substituting the value of b into equation 2 and 4, we derive the following equations:

2 = 16a - 4 * 8a + c     ⇒ 2 = - 16a + c

14 = 4a - 2 * 8a + c     ⇒ 14 = -12a  + c

By using the elimination method, the value of a is given by:

2 - 14 = (-16a + 12a) + (b - c)

-12 = - 4a

a = 3

Next, we would determine the value of b as follows:

b = 8a

b = 8 * 3

b = 24

For the value of c, we have:

2 = - 16a + c

c = 16 * (3)+ 2

c = 48 + 2

c = 50.

Substituting the respective values of a, b and c into the standard form of a quadratic equation:

ax² + bx + c = 0

3x² + 24x + 50 = 0

Thus, an equation of the function in standard form for the given table of values is 3x² + 24x + 50 = 0.

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Answer:

Step-by-step explanation:

Ok:

Area's formula is width* length

1. 120 square meters and width of 8 meters. Reversing the formula, divide area by width to get length!

120/8=15 meters

2. Answer: 15 meters

Taking into consideration the upstream and downstream speed, and the equal time taken to travel upstream and downstream distance, the speed of the boat in the still water is found out to be 10mph.

It is given to us that -

The speed of the river current = 2mph

Time taken for the boat to travel 30 miles downstream = Time taken for the boat to travel 20 miles upstream --- (1)

We have to find out the speed of the boat in still water.

Let us say that the speed of the boat in still water is x mph.

We know that -

Speed = Distance/Time

=> Time = Distance/Speed ----- (2)

When travelling upstream, the boat is slower and thus, we subtract speed of the current from the speed of the boat.

When travelling downstream, the boat is faster as it goes with the current and thus, we add the speed of the current with the speed of the boat.

From equation (1), we have

Time to travel 30 miles downstream = Time to travel 20 miles upstream

[tex]= > \frac{30}{x-2} =\frac{20}{x+2} \\= > 30(x+2)=20(x-2)\\= > 30x+60=20x-40\\= > 10x=100\\= > x=10[/tex]

Thus, taking into consideration the upstream and downstream speed, the speed of the boat in the still water is 10mph.

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The solution to the trigonometric equation 5cos(5x) = 4 is given as follows:

x = 7.37º.

The definition of the trigonometric equation is presented as follows:

5cos(5x) = 4

The first step towards solving the trigonometric equation is isolating the trigonometric variable, hence:

cos(5x) = 4/5.

Then we have to isolate the variable x, which is done applying inverse trigonometric functions, as follows:

arccos(cos(5x)) = arccos(4/5)

5x = arccos(4/5)

Using a trigonometric calculator to obtain the arc cosine of four fifths, for the smallest positive integer, we have that:

5x = 36.86º.

Now we only apply the division to isolate the variable x and obtain the solution, as follows:

x = 36.86º/5

x = 7.37º.

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Answer: 1

Step-by-step explanation:

Answer:

The correct answer is 1.

Step-by-step explanation:

The greatest common factor of two non-zero integers, x(7) and y(8), is the greatest positive integer m(1) that divides both x(7) and y(8) without any remainder. Therefore, the greatest common multiple of 7 and 8 is 1.

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From the calculation, the two fractional parts are; 6/14.

We know that a fraction is composed of a numerator and a denominator. A numerator is the number that is found at the top while the denominator is the number that is found below. We are told that we have the 6/7 and we are told to express it as the sum of two equal fractional parts;

Hence let the fractional parts be x. We know that the fractional parts are equal hence;

2x = 6/7

x = 6/7 * 1/2

x = 6/14

To check our working;

6/14 + 6/14 = 12/14 = 6/7

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The equation of the line in slope-intercept form is y = 2x-8.

According to the question,

We have the following information:

Slope of the line = 2

Points through which the line is passing = (3,-2)

We know that the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x') where m is the slope of the line

In this case, we have the followings values:

m = 2

x' = 3 and y' =-2

y-(-2) = 2(x-3)

y+2 = 2x-6

Subtracting 2 from both sides of the equation:

y = 2x-6-2

y = 2x-8

Hence, the equation of the line in slope-intercept form is y = 2x-8.

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Answer:

Step-by-step explanation:

after 9 months, the man will have received $836. It would take 4 years to get $992 with a 6% simple interest annually

For the given equation -2(5x + 8) = 14 + 6x, the statements for the process used to achieve steps 1 - 4 should be completed as follows:

In Mathematics, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In this exercise, you're required to describe the steps that should be taken to rearrange and solve for x. Therefore, the appropriate and required steps that were used to achieve steps 1 - 4 include the following:

Multiplying 5x and 8 by -2, we have the following:

-2(5x + 8) = 14 + 6x

-10x - 16 = 14 + 6x

Subtracting 6x from both sides of the equation, we have the following:

-10x - 16 - 6x = 14 + 6x - 6x

-16x - 16 = 14

Next, we would add sixteen (16) to both sides of the equation as follows:

-16x - 16 + 16 = 14 + 16

-16x = 30

Dividing both sides of the equation by -16, we have the following:

x = -30/16

x = -15/8.

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