Find the area of this circle. Use 3.14 for pie?

If you want to have $70,000 in 15 years, you need start saving money now in a savings account that earns 6.0% annually compounded weekly.

When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.Compounding is effective for both promised and unguaranteed products. All or part of your money could be lost.

Use the compound interest formula and enter the figures you are familiar with. Then find a solution for the unknown number.

A = P(1 +r/n)^(nt)

where A represents the balance of the account, P represents the amount invested, r represents the yearly rate, n represents the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, we have ...

70000 = P( 1 + 0.06/52)^(52*15) = P(2.4583)

P = 70000/2.4583 = 28474.96

You would need to deposit 28474.96 in order to have 70000 in 15 years.

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201.06 square units (rounded to 2 decimal places) is the area of the given circle.

The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).

Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:

r = d/2

= 16/2

= 8

A=πr2

AND HALF THE DIAMETER IS THE RADIUS (r)

r=8

A= πr2 = π (8) squared = 64 * π = 200.96

or,

Now, substituting the values of r and π into the formula for the area of a circle, we get

A = πr²

= (3.14159)(8²)

= (3.14159)(64)

= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.

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8x-12+3x+5=180(sum of straight angles)

8x+3x-12+5=180

11x-19=180

11x=180-19

11x=161

x=161÷11

Step-by-step explanation:

sum of straight angles are 180

Step-by-step explanation:

2 q and 7 dimes kkkkkkkkk

Answer:

q = 2

d = 7

Step-by-step explanation:

System of Equations:

d + q = 9

10d + 25q = 120

Use Substitution:

let d = 9 - q

10(9 - q) + 25q = 120

90 - 10q + 25q = 120

15q = 30

q = 2

d = 7

Answer:

c

Step-by-step explanation:

use that the sum of angles in a triangle is 180°

you know 2 angles so you can find the third

x= 180 -90-48 =42°

Answer:

c. x = 42 degrees

Step-by-step explanation:

A right triangle is 90 degrees

90 - 48 = 42

So, the measure of x is 42 degrees

Answer: [tex]219.94\ cm^2[/tex]

Step-by-step explanation:

Given

The central angle of a sector measures [tex]175^{\circ}[/tex]

The radius of the circle is [tex]r=12\ cm[/tex]

The area of the sector is given by

[tex]\Rightarrow A=\dfrac{\theta }{360^{\circ}}\pi r^2[/tex]

Insert the values

[tex]\Rightarrow A=\dfrac{175^{\circ}}{360^{\circ}}\cdot \pi \times 12^2\\\\\Rightarrow A=219.94\ cm^2[/tex]

The experimental probability of spinning a number less than 3.

7/25.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The total number of spuns.

= 8 + 6 + 9 + 11 + 9 + 7

= 50

Total number of spuns of the spinner less than 3.

= 8 + 6

= 14

The probability of spinning a number less than 3.

= 14/50

= 7/25

Thus,

The probability is 7/25.

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Answer:

[tex]\boxed{22}.[/tex]

Step-by-step explanation:

Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.

If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.

Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.

Answer:

67

Step-by-step explanation:

The interior angles of triangles always equal 180 degrees. That means that angle R is equal to 67.

Therefore, angle U is equal to 67, as corresponding angles are the same.

Hope that this helps!

Answer:

The answer is B.

Step-by-step explanation:

Its B because the lower the altitude the higher the pressure, and in this case the air towards the ground is being moved up, which is letting cold air sink back down.

Answer:

x = 3.1 as a decimal or x = 28/9 as a fraction

Step-by-step explanation:

Given:

The quadratic equation is:

[tex]10m^2-7m+3=0[/tex]

To find:

The solutions for the given equation by using the quadratic formula.

Solution:

If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have,

[tex]10m^2-7m+3=0[/tex]

Here, [tex]a=10,b=-7,c=3[/tex]. Using the quadratic formula, we get

[tex]m=\dfrac{-(-7)\pm \sqrt{(-7)^2-4(10)(3)}}{2(10)}[/tex]

[tex]m=\dfrac{7\pm \sqrt{49-120}}{20}[/tex]

[tex]m=\dfrac{7\pm \sqrt{-71}}{20}[/tex]

[tex]m=\dfrac{7\pm i\sqrt{71}}{20}[/tex]             [tex][\because \sqrt{-a}=i\sqrt{a},a>0][/tex]

Therefore, the solution set of the given equation is [tex]\left\{\dfrac{7- i\sqrt{71}}{20},\dfrac{7+ i\sqrt{71}}{20}\right\}[/tex]. Hence, the correct option is D.

Answer:

19a - 6

Step-by-step explanation:

Answer:

4a + 3 ( 5a - 2 )

= 4a + [ 3 ( 5a - 2 ) ]

= 4a + [ 15a - 6 ]

= 4a + 15a - 6

= 19a -6

Answer:

MATH is not a parallelogram

Step-by-step explanation:

(sqrt means squareroot)

To prove that quadrilateral MATH is a parallelogram, we can use the following formula:

A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.

In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.

To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.

The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.

Substituting the coordinates of points M and A, we get:

d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)

= sqrt((-3 + 5)^2 + (2 + 2)^2)

= sqrt(8^2 + 4^2)

= sqrt(64 + 16)

= sqrt(80)

= 8.944

Substituting the coordinates of points T and H, we get:

d = sqrt((1 - 3)^2 + (-2 - 2)^2)

= sqrt((-2)^2 + (-4)^2)

= sqrt(4 + 16)

= sqrt(20)

= 4.472

Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.

Answer:

1. 2 runners

2. 25 runners

3. 24%

4. 15 runners

5. 60%

6. uh I think it's asking the same thing as 3, so 24%?

A person can rent any of the vehicles shown in the table for a minimum of two to three days before it becomes more expensive for a week.

Algebra state that it is the study of the laws and symbols of mathematics as well as the manipulation of these symbols.

The rent of the small car for a week is $250 and for a day is $100. Then,

The maximum number of days that a car could be rented is,

= 250÷100

= 2.5 days

≅ 3 days

Then, for the medium car is,

= 290÷110

= 2.7 days

≅ 3 days

For the luxury car is,

= 325÷120

= 2.7 days

≅ 3 days

For Small van is,

= 350÷150

= 2.3 days

≅ 2 days

For Large van is,

= 390÷170

= 2.2 days

≅ 2 days

We can conclude from the above calculations that a person can rent a car for 2-3 days before it becomes more expensive for a week.

The complete question is -

For any of the vehicles listed in the table, how many days can you rent the vehicle before it would be less expensive to rent for the week?

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Answer:

n = 7

n = -3

Step-by-step explanation:

4n+6 = n²-15

4n = n² - 21

n² - 4n - 21 = 0

(n-7)(n+3) = 0

n = 7

n = -3

Answer:

A) 5t + 10s = 132.50

B) 3t + 5s = 69.50

We multiply B) by -2

B) -6t -10s = -139.00 then we add A)

A) 5t + 10s = 132.50

-t = -6.50

t-shirt price = 6.50

Source: http://www.1728.org/unknwn2.htm

Step-by-step explanation:

The area of the rectangle is 69.12 square inches.

We know that for a rectangle of length L and width W, the area is given by the formula:

A = L*W

Here we know that the length is 14.4 inches, then:

L = 14.4 in

And the width is one-third of that length, then we can write:

W = (1/3)*L

Replacing the value of L, we will get:

W = (1/3)*14.4 inches

W = 4.8 inches.

Then the area of the rectangle is:

A=  (4.8 in)*(14.4 in) = 69.12 in²

That is the area of the rectangle.

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Answer:

The difference is 2:1.5

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

Y=2000(1.05)^x

Step-by-step explanation:

This is because 2000 is the fixed beginning value and should stay by itself.

While the interest rate of 5% is 1.05 because the amount of money George will have will be going up based on the fixed beginning value.

4π

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = [tex]\frac{1}{2}[/tex] x b x h      -------------(i)

Where;

A = 18[tex]\sqrt{3}[/tex]

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

Substitute these values into equation(i) and solve as follows:

18[tex]\sqrt{3}[/tex] =  [tex]\frac{1}{2}[/tex] x b x 6

18[tex]\sqrt{3}[/tex] =  3b

Divide through by 3

6[tex]\sqrt{3}[/tex] =  b

Therefore, b = XZ = 6[tex]\sqrt{3}[/tex]

Now, assume that the circle is centered at O;

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180°   [sum of angles in a triangle]

=>  XOZ + 30° + 30° = 180°

=>  XOZ + 60° = 180°

=>  XOZ = 180° - 60°

=>  XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

[tex]\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}[/tex]

[tex]\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}[/tex]

[tex]\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}[/tex]

[tex]\frac{1}{12} = \frac{1}{2|OZ|}[/tex]

[tex]\frac{1}{6} = \frac{1}{|OZ|}[/tex]

|OZ| = 6

The radius of the circle is therefore 6.

Now, let's calculate the length of the arc XZ

The length(L) of an arc is given by;

L = θ / 360 x 2 π r          ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

Answer:

1157.09

Step-by-step explanation:

Using the fact that the triangles are similar, we will see that:

x = 5.626

On the image we can see two triangles, such that one is inscribed on the other.

Just because of that, it is obvious that the two triangles are similar.

And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:

3/x = 8/15

The quotient is "left side over the bottom side"

We can solve that equation for x:

3/x = 8/15

3 = (8/15)*x

(15/8)*3 = x

45/8 = x

5.625 = x

That is the value of x.

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Answer: Hypotenuse

Step-by-step explanation:

The Hypotenuse is known as the longest side of a triangle.