Kevin needs 2/3 of a yard to make a pillow. He has 3 1/3 yards of fabric. How many pillows can he make? A). 2 2/9 B. ) 3 2/3 C. ) 5 D. ) 6

Answer:

5.6 miles

Step-by-step explanation:

the patteren in 0.3    0.6     0.3       0.6

The solution to the system of differential equations x' = y - x + t and y' = y with initial conditions x(0) = 9 and y(0) = 4 is x(t) = 10e^t - t - 1 and y(t) = 9e^t - 5t - 5.To find this solution, we first solve for y in the second equation:y' - y = 0y(t) = Ce^tNext, we substitute this expression for y into the first equation and solve for x:x' = Ce^t - x + tx' + x = Ce^t + tMultiplying both sides by e^t, we get:(e^t x)' = Ce^2t + te^tIntegrating both sides:e^t x(t) = (C/2)e^2t + te^t + DUsing the initial condition x(0) = 9, we get:D = 9Using the expression for y(t) and the initial condition y(0) = 4, we get:C = 5Substituting these values into the equation for x(t), we get:x(t) = 10e^t - t - 1Finally, we substitute the expression for y(t) into the given initial condition y(0) = 4 and solve for the constant C:C = 9 - 5tSubstituting this expression for C into the equation for y(t), we get:y(t) = 9e^t - 5t - 5

For more similar questions on topic Vectors in 2D is a sub-topic in linear algebra that deals with the study of vectors in two-dimensional space. In two-dimensional space, vectors are represented as ordered pairs of real numbers and can be used to describe quantities such as displacement, velocity, and force. The magnitude and direction of a vector can be calculated using trigonometry, and vectors can be added, subtracted, and multiplied by scalars using the rules of vector algebra.

In the context of the given problem, we are asked to find two unit vectors in 2D that make an angle of 45 degrees with a given vector 6i + 5j, where i and j are the unit vectors in the x and y directions, respectively. To solve this problem, we need to use the properties of vectors and trigonometry to find the appropriate unit vectors that satisfy the given conditions. The solution to this problem involves finding the components of the given vector, calculating the angle between this vector and the x-axis, and using this angle to construct the desired unit vectors.

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The solution to the system of differential equations is:
x(t) = 5 e^(t/2) - 4 e^(3t/2)
y(t) = 4

To solve this system of differential equations, we can use Laplace transforms. Taking the Laplace transform of both sides of each equation, we get:

sX(s) - x(0) = Y(s) - X(s) + T Y(s)
sY(s) - y(0) = Y(s)

Substituting in the initial conditions x(0) = 9 and y(0) = 4, we can solve for X(s) and Y(s):

X(s) = (s + 1)/(s^2 - s - T)
Y(s) = 4/s

To find x(t) and y(t), we need to inverse Laplace transform these expressions. We can use partial fractions to simplify the expression for X(s):

X(s) = A/(s - r1) + B/(s - r2)

where r1 and r2 are the roots of the denominator s^2 - s - T, given by:

r1 = (1 - sqrt(1 + 4T))/2
r2 = (1 + sqrt(1 + 4T))/2

Solving for A and B, we get:

A = (r2 + 1)/(r2 - r1)
B = -(r1 + 1)/(r2 - r1)

Substituting these values back into the expression for X(s), we get:

X(s) = (r2 + 1)/(r2 - r1)/(s - r1) - (r1 + 1)/(r2 - r1)/(s - r2)

Taking the inverse Laplace transform of this expression, we get:

x(t) = (r2 + 1)/(r2 - r1) e^(r1 t) - (r1 + 1)/(r2 - r1) e^(r2 t)

Substituting in the values for r1 and r2, we get:

x(t) = 5 e^(t/2) - 4 e^(3t/2)

Similarly, taking the inverse Laplace transform of Y(s) = 4/s, we get:

y(t) = 4

Therefore, the solution to the system of differential equations is:

x(t) = 5 e^(t/2) - 4 e^(3t/2)
y(t) = 4

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The approximate total amount of string needed to keep the tree perpendicular to the ground is 4.02 feet, which is closest to answer choice C, 5.83 ft.

Assuming that Luis attached the ropes at the same height on the tree, the length of the rope needed for each side of the tree would be equal to the distance from the tree to the stake.

To keep the tree perpendicular to the ground, the distance from the tree to the stake should be equal to half of the diameter of the tree's canopy.

However, since the diameter of the canopy is not given, we can estimate it based on the height of the tree.

According to some tree experts, the average height-to-canopy-diameter ratio for a mature tree is about 5:1.

This means that if the tree is 20 feet tall, its canopy diameter is approximately 4 feet.

Using this estimate, we can assume that the canopy diameter of Luis's tree is about 4 feet, or 1.33 yards.

Thus, the distance from the tree to the stake should be approximately 0.67 yards.

Since there are two sides of the tree, Luis would need a total of 2 times 0.67 yards, or approximately 1.34 yards of rope.

Converting yards to feet, we get:

[tex]1.34 yards * 3 feet/yard = 4.02 feet[/tex]

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An equation representing the statement that 282828 is 121212 less than kkk is kkk = 282828 + 121212.

An equation is a mathematical statement showing that two or more mathematical or algebraic expressions share equality or equivalence.

Equations are represented using the equal symbol (=).

Unlike equations, mathematical expressions do not use the equal symbol.

282828 = kkk - 121212

kkk = 282828 + 121212

Thus, one way of representing the statement that that 282828 is 121212 less than kkk is by forming an equation like kkk = 282828 + 121212.

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The measure of center that best represents the data is mean and its values for José and Manuel are 20.1 and 21.8, respectively. Comparing the mean values, José generally scores less goals in a game than Manuel.

To find the measure of center that best represents the data, we will use the mean.

The measure is calculated by adding up all the values and dividing by the total number of values.

The mean number of goals for José is:

= (7+12+17+4+18+25+38+32+37+11)/10

= 20.1

The mean number of goals for Manuel is:

= (17+23+21+31+30+5+26+37+19+9)/10

= 21.8.

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The greatest whole number that rounds to 500 when rounding to the nearest hundred is 550.

When rounding a number to the nearest hundred, you need to look at the digit in the tens place. If that digit is 5 or greater, you round up the hundreds digit; if it is less than 5, you round down the hundreds digit.

For example, let's say we have the number 2,548. The digit in the tens place is 4, which is less than 5, so we round down the hundreds digit (2) to get 2,500.

Now, if we are looking for the greatest whole number that rounds to 500 when rounded to the nearest hundred, we need to find the largest number that has 5 in the tens place and 0 in the ones place. That number is 550. When we round 550 to the nearest hundred, we get 500.

Therefore, the greatest whole number that rounds to 500 when rounded to the nearest hundred is 550.

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The rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

To maximize the area of the pen, we need to create a rectangular shape. We can use all 40 cubes to create a rectangular pen with dimensions 5 x 6 x 2.

To build the pen, we can use 10 cubes for the base layer, then add 15 cubes for the second layer, and finally add 15 cubes for the third layer, creating a total of 40 cubes.

The base layer will be a rectangle with dimensions 5 x 6, and we will use 10 cubes to create it. Then we can stack two more layers of cubes on top of the base layer, each layer will have dimensions 5 x 6 and will use 15 cubes.

To prove that this pen has the largest area that can be made with 40 cubes, we can compare it with other possible shapes. For example, if we try to create a cube-shaped pen, we would only be able to create a cube with side length 3, which would have a volume of 27 and therefore could not use all 40 cubes.

Therefore, the rectangular pen with dimensions 5 x 6 x 2 is the largest pen that can be made using all 40 cubes.

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Area of sector = 161.1 square inches

Activity 1:

The radius of the pizza is half of its diameter, which is 16/2 = 8 inches.

The central angle of the sector is 80%, which is 0.8 times 360 degrees = 288 degrees.

To find the area of the sector, we use the formula:

Area of sector = (central angle / 360) x πr^2

Area of sector = (288 / 360) x π x 8^2

Area of sector = (0.8) x π x 64

Area of sector = 161.1 square inches (rounded to the nearest tenth)

Activity 2:

The unit of measurement for the area of the sector is square inches (in²).

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It is not possible to use n = 10.

It is not possible to use n = 20.

It is possible to use n = 25.

1. The error probabilities for n = 10 are as follows:

- P-value: It is not possible to use n = 10 because there is no value of x which results in a p-value.
- Beta (0.3): B(0.3) > 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too high.

Therefore, it is not possible to use n = 10.

2. The error probabilities for n = 20 are as follows:

- P-value: It is not possible to use n = 20 because it results in a beta error probability (B(0.3)) < 0.1, which means the probability of incorrectly rejecting the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too low.
- Beta (0.3): B(0.3) > 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is too high.

Therefore, it is not possible to use n = 20.

3. The error probabilities for n = 25 are as follows:

- P-value: P(0.3) < 0.1, which means the probability of incorrectly rejecting the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is low enough to proceed with production.
- Beta (0.3): B(0.3) < 0.1, which means the probability of failing to reject the null hypothesis (p = 0.1) when the true probability of a leak is actually 0.3 is low enough to proceed with production.

Therefore, it is possible to use n = 25.

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If he water in Earth’s oceans has a volume of about 3.2x10⁸ cubic miles, it would take 3.52x10²⁰ gallon jugs to hold all the water in Earth's oceans.

To calculate how many gallon jugs it would take to hold all the ocean water on Earth, we need to multiply the volume of the water by the conversion factor from cubic miles to gallons.

Given that the water in Earth's oceans has a volume of about 3.2x10⁸ cubic miles and there are about 1.1x10¹² gallons in 1 cubic mile, we can calculate the total number of gallons using the following equation:

Total gallons = (Volume in cubic miles) x (Gallons per cubic mile)

Substituting the given values, we get:

Total gallons = (3.2x10⁸) x (1.1x10¹²) = 3.52x10²⁰

This number is very large and is written in scientific notation to make it more manageable. Scientific notation is a compact way of writing very large or very small numbers using a power of ten. In this case, the number is expressed as a coefficient (3.52) multiplied by 10 raised to the power of 20 (10²⁰).

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In order for a triangle to be acute, the relationship that c² must have with a² + b² is c² < a² + b².

An acute triangle is a triangle in which all three angles are acute angles, which means they are less than 90 degrees. In other words, an acute triangle is a triangle with three acute angles.

To understand why the relationship between c^2 (the square of the longest side) and a^2 + b^2 (the sum of the squares of the other two sides) is important in determining whether a triangle is acute, we need to delve into the concept of the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b represent the other two sides.

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side.

This can be visualized as follows: If we were to draw a right triangle with the shorter sides represented by segments a and b, and the longest side represented by segment c, the acute triangle would be formed by making the length of segment c shorter than the length determined by the Pythagorean theorem. This ensures that the angle opposite to the longest side remains acute.

On the other hand, if c^2 were equal to a^2 + b^2, we would have a right triangle, not an acute triangle. If c^2 were greater than a^2 + b^2, we would have an obtuse triangle since the angle opposite to the longest side would be greater than 90 degrees.

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Step-by-step explanation:

Los 10 m representan 1/3 del camino, ya que si sumamos 10 + 20 + 30, obtenemos la distancia total del camino, que es 60 m.

Si la casa se encuentra a 25 m del camino, entonces está a una distancia de 5 m del final del camino, ya que 25 + 5 = 30. Por lo tanto, la casa está a 2/3 del camino, es decir, a una fracción de 2/3 de la distancia total del camino.

La casa está representada a 2/3 del camino, lo que corresponde a una distancia de 40 m (2/3 de 60 m). Por lo tanto, la casa está representada a 40 m del comienzo del camino.

Los 20 m representan 1/3 del camino, ya que si sumamos 10 + 20 + 30, obtenemos la distancia total del camino, que es 60 m. Por lo tanto, los 20 m representan la misma fracción que los 10 m, que es 1/3 del camino.

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The red arc or chord in the key of C, or the solution to the provided question based on the circle, is 11.

A chord is a piece of a straight line that connects two points on a circle's circumference. When it crosses the circle at two different locations, it is also occasionally referred to as a secant.

The following formula can be used to determine a chord's length:

chord length = 2*radius*sin(angle/2)

where angle is the central angle that the chord is subtended by, and radius is the radius of the circle. In geometry and trigonometry, chords are frequently used to compute circle properties including area, circumference, and arc length.

Since the circle P ≅ circle C

In circle P the radius of PN =7 and

chord LM = 11 with an angle 104°

And  In circle C  the radius =7 and Circle and chord QR are both making the same angle. P = 104°

So the circle P ≅ circle C

The red arc or chord in C is consequently 11.

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Answer:

x = 73, y = 88, z = 45

Step-by-step explanation:

40+52+y = 180 (Angle Sum Property)

=> y = 180-40-52

=> y = 88

x + (15 + 40) + 52 = 180 (Angle Sum Property)

=>x = 180 - 52 - 55

=> x = 73

40 + 43 + (52+z)  = 180

=> z = 180 -53 - 40 -43

=> z = 45

The mean per capita income in thousands of dollars with 99% confidence interval and sample size of 1417 is equal to CI = (23.7, 24.3).

Construct the 99% confidence interval for the mean per capita income, use the formula,

CI = x ± Z× (σ / √n)

where

x is the sample mean,

σ is the population standard deviation,

n is the sample size,

Z is the z-score corresponding to the desired level of confidence.

Using attached z-score table,

For a 99% confidence interval, the corresponding z-score is 2.58

Substituting the given values, we get,

⇒CI = 24 ± 2.58 × (5.1 / √1417)

Simplifying the expression inside the parentheses, we get,

⇒CI = 24 ± 0.349

⇒CI = (23.7, 24.3)

Rounding to one decimal place, the confidence interval is (23.7, 24.3) thousands of dollars.

Therefore, the 99% confidence interval for the mean per capita income is CI = (23.7, 24.3).

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(a) The value of the constant is 1/24, (b) P(X<=1,Y<=1)  is 5/48 and (c)  P(X + Y <= 1) is also 5/48

(a) The constant C can be found by using the fact that the total probability of the joint density function over the entire space is equal to 1. Therefore, we integrate the joint density function over the region where it is defined and set it equal to 1:

∫∫f(x,y) dA = 1

∫[0,2]∫[0,4] Cx(1+y) dy dx = 1

C∫[0,2]x[(y+(y²)/2)] [0,4] dx = 1

C(24/5) = 1

C = 5/24

(b) To find P(X <= 1, Y <= 1), we integrate the joint density function over the region where X <= 1 and Y <= 1:

P(X<=1,Y<=1) = ∫[0,1]∫[0,1] (5/24) x(1+y) dy dx

= (5/24) ∫[0,1] x(1+(1/2)) dx

= (5/24) [(1/2) + (1/6)]

= 5/48

(c) To find P(X + Y <= 1), we integrate the joint density function over the region where X + Y <= 1:

P(X+Y<=1) = ∫[0,1]∫[0,1-x] (5/24) x(1+y) dy dx

= (5/24) ∫[0,1] x(1+(1-x)/2) dx

= (5/24) [(1/2) - (1/12)]

= 5/48

Therefore, P(X + Y <= 1) = 5/48.

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The inequality which is used to represent normal "temperature-range" for  "human-body", is (d) |t − 98.6| ≤ 1.8.

The "average-temperature" of body is = 98.6° F, and it can vary by 1.8°F.

The inequality |t − 98.6| ≤ 1.8 indicates that the absolute difference between the body temperature and the average temperature is less than or equal to 1.8° F.

This means that the body temperature t can vary within a range of 1.8° F from the average temperature of 98.6° F.

Which means, the temperature cam range from :

⇒ 98.6-1.8 ≤ t ≤ 98.6+1.8,

⇒ 96.8 ≤ t ≤ 100.4;

Therefore, the correct inequality is (d) |t − 98.6| ≤ 1.8.

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The given question is incomplete, the complete question is

The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.

(a) |t − 1.8| ≥ 98.6

(b) |t − 1.8| ≤ 98.6

(c) |t − 98.6| ≥ 1.8

(d) |t − 98.6| ≤ 1.8

Answer: |t − 98.6| ≤ 1.8

Step-by-step explanation: If takes then takes then takes then takes then takes.

The only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.

The range of a function is the set of all possible output values. In this case, we are given that the ranges of two functions, f(x) and g(x), are the same.

The function f(x) = √(mx) has a domain of x ≥ 0, since the square root of a negative number is not a real number. The function g(x) = m√x has a domain of x ≥ 0 for the same reason.

To find the range of these functions, we need to consider the possible values of the input x. For f(x), as x increases, the output √(mx) also increases, and as x approaches infinity, so does the output. For g(x), as x increases, the output m√x also increases, and as x approaches infinity, so does the output.

Therefore, if the ranges of f(x) and g(x) are the same, this means that they both have the same maximum and minimum values, and these values are achieved at the same inputs.

In particular, if we consider the minimum value of the range, this is achieved when x = 0, since both functions are defined only for non-negative inputs. At x = 0, we have f(0) = g(0) = 0, so the minimum value of the range is 0.

To find the maximum value of the range, we need to consider the behavior of the functions as x approaches infinity. As noted above, both functions increase without bound as x increases, so the maximum value of the range is infinity.

Therefore, the only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.

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Mike will need 28 feet of fencing.

To solve the problem, we can use the formula for the area of a rectangle:

A = L × W

where A is the area, L is the length, and W is the width.

We know that the area of the patio is 192 ft^2, so we can write:

192 = L × W

We also know that the length is 4 feet longer than the width, so we can write:

L = W + 4

Substituting L = W + 4 into the equation for the area, we get:

192 = (W + 4) × W

Expanding the right side of the equation, we get:

192 = W^2 + 4W

Rearranging, we get a quadratic equation in standard form:

W^2 + 4W - 192 = 0

We can solve for W by factoring or using the quadratic formula, but in this case, we can recognize that 12 and -16 are two numbers that multiply to -192 and add up to 4. Therefore, we can write:

W^2 + 4W - 192 = (W + 16) × (W - 12) = 0

This gives us two possible values for W: W = -16 or W = 12. Since the width cannot be negative, we reject the solution W = -16 and choose W = 12.

Using the equation L = W + 4, we find that the length is L = 16.

Finally, we can calculate the amount of fencing Mike will need by adding up the lengths of the three sides that need to be fenced. The two lengths are L = 16 feet each, and the width is W = 12 feet. Therefore, Mike will need a total of 16 + 16 + 12 = 44 feet of fencing. However, since one side of the patio is adjacent to the back of his house, he only needs to fence three sides.

Therefore, he will need 44 - 16 = 28 feet of fencing.

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The height of tank which is 65 cm wide and 85 cm long is 40 cm and when it is 3/4 filled the water height is 30cm.

Mika can follow these steps to find the height of the water:

1. Convert the volume from liters to cubic centimeters: 221 L * 1000 cm³/L = 221,000 cm³
2. Calculate the total volume of the tank: V = lwh (where V is the volume, l is the length, w is the width, and h is the height)
3. Solve for the height of the tank: 221,000 cm³ = 65 cm * 85 cm * h
4. Calculate the height of the tank: h = 221,000 cm³ / (65 cm * 85 cm) ≈ 40 cm
5. Since Mika plans to fill the tank 3/4 full, calculate the height of the water: (3/4) * 40 cm = 30 cm

So, the correct steps are:

- Divide the volume by the length and width to find the height
- Calculate the total volume of the tank
- Find the height of the tank
- Calculate the height of the tank
- Calculate the height of the water when the tank is 3/4 full

The height of the water will be 30 cm.

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The fraction of her clothes that is left is 1/8.

To solve this problem, we first need to determine the fractions of clothes Christen sells to Maria and Alexandra. Christen sells 5/8 of her clothes to Maria and 1/4 to Alexandra. To find the total fraction of clothes sold, we can add these two fractions:

(5/8) + (1/4)

To add fractions, we need a common denominator. In this case, the least common denominator is 8. We can convert 1/4 to 2/8:

(5/8) + (2/8) = 7/8

Christen sold 7/8 of her clothes to Maria and Alexandra. To find the fraction of clothes left, we subtract this value from the total, which is 1:

1 - (7/8) = 1/8

So, Christen has 1/8 of her clothes left after selling to Maria and Alexandra.

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Answer:

To make the polynomial 9x^10 + ax^b + 100 a perfect square trinomial, we need to add a constant term to it such that it becomes a square of a binomial.

Let's first write the square of a binomial in general form:

(a + b)^2 = a^2 + 2ab + b^2

If we compare this general form with our polynomial, we can see that the first term, 9x^10, is equal to (3x^5)^2, which means that we can write our polynomial as:

(3x^5)^2 + ax^b + 100 = (3x^5 + c)^2

Expanding the right-hand side of this equation, we get:

(3x^5 + c)^2 = 9x^10 + 6cx^15 + c^2

Comparing the coefficient of x^15 on both sides, we get:

6c = 0

Since c cannot be zero (otherwise we would end up with the original polynomial), this means that we must have:

c = 0

Therefore, we can write our polynomial as:

(3x^5)^2 + ax^b + 100 = (3x^5)^2

Expanding the right-hand side, we get:

(3x^5)^2 = 9x^10

Therefore, we must have:

a = 0

b = 10

So the values of a and b that make the polynomial 9x^10 + ax^b + 100 a perfect square trinomial are a = 0 and b = 10.

Answer:

AB = 15

Step-by-step explanation:

6(6 + x + 6) = 7(7 + 11)

72 + 6x = 126

6x = 126 - 72 = 54

x = 54/6

   = 9.

So AB = 9 + 6 = 15.

Margo is right; Jules made a 45 degree angle.

To determine who is right about the angle made by Jules while taking the first piece of pizza, we need to compare their estimates of 20 degrees and 45 degrees.

Since angles are measured using a protractor or other measuring tools, we rely on accurate measurement techniques to determine their values. If both Jules and Margo used appropriate measuring tools and techniques, we would expect their measurements to be close.

However, a 20-degree angle is significantly smaller than a 45-degree angle. Therefore, based on the provided information, Margo's estimate of a 45-degree angle seems more reasonable and likely to be correct.

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Keegan will have approximately $878.85 in the account after 5 years.

What is Compound interest ?

Compound interest is the interest that is earned not only on the initial amount of money invested (known as the principal), but also on any interest earned on that principal over time. In other words, compound interest is interest on interest.

The compound interest formula is given by:

A = P[tex](1 + r/n)^{nt}[/tex]

where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, Keegan deposited $675, the annual interest rate is 4.8%, the interest is compounded quarterly, and the investment is for 5 years. Therefore, we can plug in these values into the formula to get:

A = 675[tex](1 + 0.048/4)^{20}[/tex]

A = 675[tex](1.012)^{20}[/tex]

A ≈ $878.85

Therefore, Keegan will have approximately $878.85 in the account after 5 years.

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The value of x in the given circle is 18.1 units.

Given is a circle, where two radii are given one chord is given,

We need to find the value of the x which is also the radius,

We know all the radii in a circle are equal,

So, here the radius = 7.9+10.2 = 18.1 units.

Hence the value of x in the given circle is 18.1 units.

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1. The next two term for the sequence using Geometric Progression is 8 and 16

2. The next two terms for the sequence using arithmetic progression is 7 and 11

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

Using Geometric Progression, the common ratio is 2/1 = 2

therefore the next two terms will be

4× 2 = 8 and 8× 2 = 16

Using Arithmetic progression , the common difference will be increasing by 1 per number of term, i.e r+1

for the fourth term ,common difference = 2+1 = 3

fourth term = 4+3 = 7

for the fifth term , common difference = 3+1 = 4

fifth term = 7+4 = 11

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