At age ​, someone sets up an IRA​ (individual retirement​ account) with an APR of ​%. At the end of each month he deposits ​$ in the account. How much will the IRA contain when he retires at age​ 65? Compare that amount to the total deposits made over the time period.
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Part 1
After retirement the IRA will contain ​$

enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answer:

13.) y=(x-4)^(2)+3

Step-by-step explanation:

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

a. The probability of rolling a number greater than 10 is 1/6.

b. The probability of rolling a number less than 5 is 1/3.

c. The expected number of times a 4, 6, or 9 will be rolled in 200 rolls is 50

a. The probability of rolling a number greater than 10 is equal to the number of faces with numbers greater than 10 (i.e., 11 and 12) divided by the total number of faces. Thus, P(number greater than 10) = 2/12 = 1/6.

b. The probability of rolling a number less than 5 is equal to the number of faces with numbers less than 5 (i.e., 1, 2, 3, and 4) divided by the total number of faces. Thus, P(number less than 5) = 4/12 = 1/3.

c. The probability of rolling a 4, 6, or 9 is equal to the number of faces with those numbers (i.e., 1 each) divided by the total number of faces. Thus, the probability of rolling a 4, 6, or 9 is 3/12 = 1/4.

Therefore, the expected number of times a 4, 6, or 9 will be rolled in 200 rolls is:

(expected number of times) = (probability of rolling a 4, 6, or 9) x (total number of rolls)

= (1/4) x (200)

= 50

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Answer:

Step-by-step explanation:

yes since they are both divisible by their denominators and equal the same thing

Answer:

yes, they are equivalent

Step-by-step explanation:

2/2 = (2/2)x(4/4) = 8/8 = 1

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields such as mathematics, statistics, science, and finance to make predictions and analyze data.

Here,

1. The z-score for a sample mean of $75 is calculated as:

z = (75 - 76) / (6 / √(40)) = -2.36

Using a z-table, the probability of a z-score less than -2.36 is 0.0099 (rounded to 4 decimal places).

2. The z-score for a sample mean of $75 is calculated as:

z1 = (75 - 76) / (6 / √(40))

= -2.36

The z-score for a sample mean of $77 is calculated as:

z2 = (77 - 76) / (6 / √(40))

= 0.79

Using a z-table, the probability of a z-score between -2.36 and 0.79 is 0.8669 (rounded to 4 decimal places).

3. The z-score for a sample mean of $77 is calculated as:

z1 = (77 - 76) / (6 / √(40))

= 0.79

The z-score for a sample mean of $78 is calculated as:

z2 = (78 - 76) / (6 / √(40))

= 1.57

Using a z-table, the probability of a z-score between 0.79 and 1.57 is 0.0823 (rounded to 4 decimal places).

4. The standard error of the mean (SEM) is calculated as:

SEM = standard deviation / sqrt(sample size)

SEM = 6 / √(40) = 0.9487

The z-score for a sampling error of $1.50 is calculated as:

z = 1.50 / 0.9487 = 1.58

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

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The values of the variables in the semicircle shown are:

x = 63 degrees; y = 90 degrees.

A semi-circle is exactly half of a full circle and has a measurement of 180 degrees; the two endpoints of the diameter form the endpoints of the semi-circle. If an angle is enclosed inside a semi-circle, the angle formed measures 90 degrees.

Therefore, it means the value of the variable, y = 90 degrees.

Thus, using the triangle sum theorem, we have:

x = 180 - 90 - 27

x = 63 degrees.

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A. The length of the cord needed to reach corner C is 17.6 m

B. The distance between the electrical outlet and corner N is 14.3 m

The length of the cord needed can be obtained as follow:

Sine θ = opposite / hypotenuse

Sine 27 = 8 / Length of cord

Cross multiply

Length of cord × sine 27 = 8

Divide both sides by sine 27

Length of cord = 8 / sine 27

Length of cord = 17.6 m

First, we shall determine the length OB. Details below:

Tan θ = Opposite / Adjacent

Tan 27 = 8 / Length OB

Cross multiply

Length OB × tan 27 = 8

Divide both sides by tan 27

Length OB = 8 / tan 27

Length OB = 15.7 m

Finally, we shall determine the distance between the electrical outlet and corner N. Details below:

Length BN = Length OB + Length ON

30 = 15.7 + Distance

Collect like terms

Distance = 30 - 15.7

Distance = 14.3 m

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Answer:

2/5 of the cookie

Step-by-step explanation:

12 friends need to split 4 cookies

4 cookies needs to divided by 10 people

[tex]\frac{4cookies}{10 people}[/tex] = [tex]\frac{4}{10}[/tex]

simplify: [tex]\frac{4}{10} = \frac{2}{5}[/tex]

The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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Answer: decrease in the GDP by 2.5%.

Step-by-step explanation:

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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Answer:

Measures of Central Tendancy

Mean: 429

Median: 344

Mode: 134,185,193,217,471,580,799,853

Range: 719

Step-by-step explanation:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

[tex]\mu = \frac{{\sum}x}{N}[/tex]

The formula for the mean of a sample is

[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:

[tex]\frac{3432}{8} = 429[/tex]

The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:

[tex]134, 185, 193, 217, 471, 580, 799, 853[/tex]

Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 217 and 471. The median is the average of these numbers. We have

[tex]{\frac{ 217 + 471 }{2}}[/tex]

Therefore, the median is

[tex]344[/tex]

The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are

[tex]134,185,193,217,471,580,799,853[/tex]

Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.

a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:

"O" = 79

"K" = 75

Next, we use the RSA encryption formula:

C ≡ [tex]M^{e}[/tex] (mod n)

For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)

For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)

Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).

b) To encrypt "HELP", we break it up into two blocks:

Block 1: "HE"

Block 2: "LP"

For block 1, we have:

"H" = 72

"E" = 69

Using the RSA encryption formula, we get:

C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)

C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)

Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).

For block 2, we have:

"L" = 76

"P" = 80

Using the RSA encryption formula, we get:

C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)

C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)

Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).

The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).

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Answer:

p= -3-1/2

p= -7/2

Step-by-step explanation:

(you transpose the fraction /take the liketerms)

( you transpose your fraction will change the sign and become negative then -3-0.5or -3-1/2=-7/2.)then you substitute to the original equation 1/2+p=-3 check your answer .

Answer: To solve the problem, we can use Bayes' theorem. Let D be the event that a device is defective, and let A be the event that the quality assurance check concludes that a device is defective.

We want to find P(A and not D) + P(not A and D), which represents the probability of an incorrect conclusion.

We know that P(D) = 1 - P(not D) = 1 - 0.84 = 0.16, and that P(A | not D) = 0.03 and P(A | D) = 0.97.

Using Bayes' theorem, we can compute:

P(not A | not D) = 1 - P(A | not D) = 1 - 0.03 = 0.97

P(not A | D) = 1 - P(A | D) = 1 - 0.97 = 0.03

Therefore,

P(A and not D) = P(not D) * P(A | not D) = 0.84 * 0.03 = 0.0252

P(not A and D) = P(D) * P(not A | D) = 0.16 * 0.03 = 0.0048

So the probability of an incorrect conclusion is:

P(A and not D) + P(not A and D) = 0.0252 + 0.0048 = 0.03

Therefore, the probability of an incorrect conclusion is 0.03, or 3% (rounded to the nearest tenth of a percent).

Why was this answer deleted prior?

Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.

The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.

Here,

=>  A = L x W,

where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.

Inputting the numbers provided yields:

=>  A = (7/4) x (1/3)

These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.

The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:

=>  A = (7 x 1) / (4 x 3)

When we multiply the numerator by the remainder, we obtain:

=> A = 7/12

The rectangle's size is 7/12 square inches as a result.

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The value of the limit of the expression Limit x tend to π 1-sinx/2(π-x) ² is infinity (∝)

Given that

Limit x tend to π 1-sinx/2(π-x) ²

To solve this expression, we make use of

If limit of x to a+ of f(x) = limit of x to a- = L, then limit of x to a+ of f(x) = L

The interpretation is that we solve the expression by direct substitution

So, we have

Limit = 1 - sin(π)/2(π - π) ²

Evaluate the difference

Limit = 1 - sin(π)/2(0)²

Evaluate the exponent and the bracket

Limit = 1 - sin(π)/0

Divide

Limit = ∝

Hence, the limit of the expression is ∝

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Therefore, the value of x is 9.

A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with three-line segments. The three line segments that connect the three points are called sides of the triangle, and the points themselves are called vertices. The angle formed between any two adjacent sides of a triangle is called an interior angle of the triangle. The sum of the interior angles of a triangle is always 180 degrees.

There are many different types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles. An equilateral triangle is a triangle in which all three sides are equal, an isosceles triangle is a triangle in which two of the sides are equal, and a scalene triangle is a triangle in which none of the sides are equal. An acute triangle is a triangle in which all three interior angles are less than 90 degrees, an obtuse triangle is a triangle in which one of the interior angles is greater than 90 degrees, and a right triangle is a triangle in which one of the interior angles is exactly 90 degrees.

Given by the question.

According to Thel's theorems

[tex]\frac{5}{3} =\frac{15}{x}[/tex]

5x=45

x=9

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Answer:

Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:

tan(1) = 2tan(1/2) / (1 - tan^2(1/2))

To find tan(1/2), we can use the half-angle formula for tangent:

tan(1/2) = sin(1) / (1 + cos(1))

We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:

tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)

Again, we cannot simplify this expression any further without a calculator.

For the second expression, we are asked to find the value of:

tan(arctan(6/4))

By definition, tan(arctan(x)) = x for all x, so we have:

tan(arctan(6/4)) = 6/4 = 3/2

Therefore, the exact value of the expression tan(6/4) is 3/2.

Answer: D. 9.68

Step-by-step explanation:

145.2 oz/ 15 cups = 9.68 oz per cup

Answer:

(a) 22 inches

(b) 770 inches

(c) 26,950 inches

Step-by-step explanation:

(a) To find the perimeter of the drawing, we add up the lengths of all four sides:

Perimeter of drawing = 7 + 4 + 7 + 4 = 22 inches

(b) The length and width of the actual garden are 35 times larger than the dimensions in the drawing. This means that the actual length is 7 x 35 = 245 inches and the actual width is 4 x 35 = 140 inches. To find the perimeter of the actual garden, we add up the lengths of all four sides:

Perimeter of actual garden = 245 + 140 + 245 + 140 = 770 inches

(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden will also be multiplied by 35. This is because each side will increase by a factor of 35, so the total length of all four sides will increase by a factor of 35 as well. Therefore, the new perimeter will be:

New perimeter = 35 x Perimeter of actual garden = 35 x 770 = 26,950 inches

Answer:

The probability that a randomly selected subject tested negative or did not use marijuana is 0.589.

Step-by-step explanation:

Simultaneous equations are a set of equations that are solved together to determine the values of the variables that satisfy both equations.

1) 4x + 5y = 3 ---(1)

y - 3x = -7 ----(2)

Using the substitution method;

y = -7 + 3x ----(3)

Thus

4x + 5(-7 + 3x) = 3

4x -35 +15x = 3

19x - 35 = 3

19x = 3 + 35

x = 2

Then

4(2) + 5y = 3

8 + 5y = 5

y = 13/5

y = 2 3/5

2) 2x - 4y = 24 ----- x 3

  -3x + 2y = -48 ----- x 2

   6x - 12 y = 72 ---- (3)

  -6x + 4y = -96 ---- (4)

Add 3 and 4

         16y = -24

y = -24/16

Substitute y = -24/16 into (1)

2x - 4(-24/16) = 24

2x + 6 = 24

x = 15

3) -x + y = 13 --- 1

  3x - 4y = 46 ---- 2

y = 13 + x ---- 3

Substitute 3 into 2

3x - 4(13 + x) = 46

3x - 52 - 4x = 46

-x - 52 = 46

x = 98

Substitute x = 98 into (1)

-98 + y = 13

y = 13 + 98

y = 111

Let C be x and D be y

x + y = 180

x = 33 + 6y

x - 6y = 33

x = 180 - y

Substitute and obtain;

180 - y - 6y = 33

180 - 7y = 33

y = 33 - 180/-7

y = 21

Then

x + 21 = 180

x = 180 - 21

x = 159

Lastly

Let small = x , medium = y

x + y = 150

4x + 6y = 764

x = 150 - y

4(150 - y) + 6y = 764

600 - 4y + 6y = 764

600 + 2y = 764

2y = 764 - 600

y = 82

Then;

x + 82 = 150

x = 68

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The solutions to the simultaneous equations are:

1) x = 2 and y = -1

2) x = 18 and y = 3

3) y = -7 and x = 6

There are three main methods in solving simultaneous equations and they are:

1) Elimination Method

2) Substitution Method

3) Graphical Method

1) 4x + 5y = 3

y = 3x - 7

Substitute 3x - 7 for y in the first equation to get:

4x + 5(3x - 7) = 3

4x + 15x - 35 = 3

19x - 35 = 3

19x = 35 + 3

19x = 38

x = 38/19

x = 2

Thus:

y = 3(2) - 7

y = -1

2) 2x - 4y = 24

-3x + 2y = -48

Multiply eq 2 by 2 and eq 1 by 1 to get:

2x - 4y = 24    -----(3)

-6x + 4y = -96   -----(4)

Add eq 3 to eq 4 to get:

-4x = -72

x = 18

2(18) - 4y = 24

36 - 4y = 24

36 - 24 = 4y

4y = 12

y = 3

3) -x + y = -13

3x - 4y = 46

From eq 1, x = y + 13

Thus:

3(y + 13) - 4y = 46

3y + 39 - 4y = 46

39 - y = 46

y = 39 - 46

y = -7

x = -7 + 13

x = 6

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The value of the expression 34 - 9 x 2 is 16.

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. These rules help to ensure that mathematical expressions are evaluated correctly and consistently. The order of operations is typically summarized by the acronym PEMDAS, which stands for:

Parentheses: Perform operations inside parentheses first.

Exponents: Evaluate exponents (powers and square roots, etc.) next.

Multiplication and Division: Perform multiplication and division, from left to right.

Addition and Subtraction: Perform addition and subtraction, from left to right.

In the given questions,

In this case, there are no parentheses or exponents, so we move on to multiplication before subtraction.

We perform the multiplication first, following the rule of performing multiplication before addition or subtraction.

9 x 2 = 18

Then, we subtract the result from 34:

34 - 18 = 16

Therefore, the value of the expression 34 - 9 x 2 is 16.

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Answer:

To solve 2^x = 32, we need to find the value of x that satisfies the equation.

We can rewrite 32 as a power of 2 by noting that 2^5 = 32. Therefore, we have:

2^x = 2^5

Since the bases of the powers are equal, we can equate the exponents:

x = 5

So the solution to 2^x = 32 is x = 5.

To rewrite this equation in a logarithmic form, we can use the definition of logarithms:

log(base 2)32 = x

Here, the logarithm with base 2 of 32 is equal to x.

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Evaluating the linear equation in x = 19 we can see that the temperature was 5.76 degrees, so your answer is correct.

Here we have a linear equation that relates the wind temperature with the wind's velocity.

The linear equation is:

y = -0.36*x + 12.6

Where y is the temperature and x is the wind speed. We want to find the temperature when the speed is 19 miles per hour, to get it, just replace x by 19 in the linear equation above, then we will get:

y = -0.36*19 + 12.6

y = -6.84 + 12.6

y = 5.76

So your answer is correct.

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the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.

How to solve and what is angle?

An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.

Any angle coterminal with 8° can be expressed as:

θ = 8° + 360°k

where k is an integer.

Therefore, the expression describing all the angles that are coterminal with 8° is:

θ = 8° + 360°k, where k is an integer.

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.

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By circle , 15 is the length of x .

What is a circle, exactly?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by each line that traverses the circle.

                                Moreover, every angle has rotational symmetry around the center. With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.

AE² = EC . CD

10² = 5 * x

100 = 5 * x

100/5 = x

 20 = x

ED = 20 - 5   = 15

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Answer:

6 weeks and 840 hours

Step-by-step explanation:

There are 168 hours in one week.

24 hrs/day * 7 days = 168 hours

1008 hours ÷ 24 hours(1 day) = 42 days ÷ 7 days in a week = 6 weeks

168 hours/week * 5 weeks = 840 hours