Write the solutions to the equation x^2=5 using exponents.​

Rhett will pay approximately $4,800 in interest on the 10-year $7,500 Federal Direct Unsubsidized Loan. Rhett will pay approximately $4,800 in total interest on this loan.

When Rhett decides to capitalize the interest on the loan, it means that instead of making interest payments while he is in college, the accrued interest is added to the principal balance. As a result, the interest starts accruing on the new higher principal balance.

The interest rate on the loan is 6.4%. To calculate the total interest paid, we need to determine the total accrued interest over the loan period. The loan has a 10-year term, and Rhett will begin making payments six months after graduation. This means the interest accrues for 10 years and six months.

Using the formula for compound interest, we can calculate the total interest as follows:

Principal = $7,500

Interest Rate = 6.4% = 0.064

Time = 10.5 years

Total Interest = Principal *\((1 + Interest Rate)^Time\) - Principal

Plugging in the values:

Total Interest =\($7,500 * (1 + 0.064)^10.5 - $7,500\)

≈ $4,800

Therefore, Rhett will pay approximately $4,800 in total interest on this loan if he chooses to capitalize the accrued interest before making payments.

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An ordered rooted tree is a tree data structure in which each node has a specific parent-child relationship with its adjacent nodes. Each node in the tree has an address or path that specifies its location in the tree.

Given an ordered rooted tree T with vertex v at address 3.4.5.2.4, we can answer the following questions:

The level of a vertex in a tree is the number of edges on the path from the root to that vertex. In this case, the root is at address 3, and the path from the root to v has four edges: 3->4, 4->5, 5->2, and 2->4. Therefore, v is at level 5.

The parent of a vertex is the node that is immediately above it in the tree. In this case, the parent of v is the node at address 3.4.5.2. Therefore, the address of the parent of v is 3.4.5.2.

The siblings of a vertex are the nodes that have the same parent as the vertex. In this case, we do not have enough information to determine the number of siblings of v. We only know the address of v and its parent, but we do not know the structure of the tree beyond that.

The number of vertices in a tree can be calculated using the formula n = m + 1, where n is the total number of vertices and m is the number of edges. In this case, we know that the path from the root to v has four edges, so there are at least five vertices in the tree (including the root). However, we do not have enough information to determine the exact number of vertices in T, as there may be additional branches and nodes that are not specified.

Based on the address of v, we can determine some of the other addresses that must occur in the tree. For example, the address 3.4.5 must occur in the tree, as this is the parent of v. Additionally, the address 3.4 must occur in the tree, as this is the parent of 3.4.5. However, we cannot determine all of the other addresses that must occur in the tree without additional information about its structure.

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The initial velocity is the speed of the plane before entering the intersection, which is not given in the question. Without the initial velocity, we cannot accurately calculate the time needed to clear the intersection.

(a) To find the distance traveled during the entire trip, we can calculate the distance traveled during each part and then sum them up.

Distance traveled during the first part = Average speed * Time = 6.31 m/s * 18.3 minutes * (60 seconds / 1 minute) = 6867.78 meters

Distance traveled during the second part = Average speed * Time = 4.39 m/s * 30.2 minutes * (60 seconds / 1 minute) = 7955.08 meters

Distance traveled during the third part = Average speed * Time = 16.3 m/s * 8.89 minutes * (60 seconds / 1 minute) = 7257.54 meters

Total distance traveled = Distance of first part + Distance of second part + Distance of third part

= 6867.78 meters + 7955.08 meters + 7257.54 meters

= 22080.4 meters

Therefore, the bicyclist traveled a total distance of 22080.4 meters during the entire trip.

(b) To find the average speed of the bicyclist for the trip, we can divide the total distance traveled by the total time taken.

Total time taken = Time for first part + Time for second part + Time for third part

= 18.3 minutes + 30.2 minutes + 8.89 minutes

= 57.39 minutes

Average speed = Total distance / Total time

= 22080.4 meters / (57.39 minutes * 60 seconds / 1 minute)

≈ 6.42 m/s

Therefore, the average speed of the bicyclist for the trip is approximately 6.42 m/s.

(c) To find the time needed for the plane to clear the intersection, we can use the formula:

Final velocity = Initial velocity + Acceleration * Time

Here, the initial velocity is the speed of the plane before entering the intersection, which is not given in the question. Without the initial velocity, we cannot accurately calculate the time needed to clear the intersection.

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The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:

x=-11/2

Step-by-step explanation:

The amount of time that it will take for the champion to complete a circle will be 48 minutes.

The beginner skier takes 50 minutes to complete a lap, so the champion skier completes each lap 2 minutes faster. This means that the champion skier overtakes the beginner every 24 minutes.

Therefore, the champion skier completes a full circle in 48 minutes, which is equal to 24 minutes for the beginner skier. This means the champion skier completes 2 laps at the same time it takes the beginner skier to complete one lap.

So, 24×2 = 48

In conclusion, it takes the champion skier 48 minutes to complete a full circle.

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Answer:

3.99

Step-by-step explanation:

The total sum of central angle of circle is 360 which mean the area of the circle = (12.36 x 360)/89

A=πr^2

=> (12.36 x 360)/89 = 3.14(r^2)

r^2 = 15.92

r = 3.99

Answer:

\(x=-\frac{16}{23}\)

I hope this helps!

Answer:

The answer is  43.9822972 rad but you could just round and put 43.98

Step-by-step explanation:

The scatter plot indicates that the best graph with a line that fits the data is one with a line passing through approximately 2 comma 5 and 4 comma 4.

Data visualisation that demonstrates the link between various variables is known as a scatter plot. Different data points are positioned between an x- and y-axis to display this data. Each of these data points appears to be "scattered" across the graph, which is how this kind of data visualisation gets its name.

This is because the main trend of the data, which seems to slope downwards, is captured by the line that passes through these places. The other lines don't seem to cover as many points or represent the data trend as effectively.

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Answer:

60 ft

Step-by-step explanation:

a² + b² = c²

20² + 15² = c²

c = √625

c = 25

total distance = 20 ft + 15 ft + 25 ft = 60 ft

The formula for the n-th term is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

For a geometric sequence where the first term is a₁ and the common ratio is r, the formula for the n-th term is:

aₙ = a₁*(r)⁽ⁿ⁻¹⁾

Here we know that the first term is a₁ = 3 and the common ratio is r = 1/2.

Then the formula for the n-th term of the sequence is:

aₙ = 3*(1/2)⁽ⁿ⁻¹⁾

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Answer:

10) 1/2 lao per minute

11) 15 grams per serving

Step-by-step explanation:

10)

laps per minute

The laps are increasing by 1 as the minutes are increasing by 2

11)

The grams are increasing by 15 as the servings are increasing by 1

Answer:

The answer should be 12

Step-by-step explanation

he has 60 in his account already so add 35 and 15 (60+35+15=110) then add 48+24+50 which equals 122. Now subtract 110-122 and you'll get 12. so the answer is 12.

Answer: -1/9 * x.

Step-by-step explanation:

To simplify the expression (5x^2) / (-45x), we can divide the coefficients and subtract the exponents:

(5 / -45) * (x^2 / x)

Simplifying the coefficient:

-1/9 * (x^2 / x)

Now, simplify the variables:

-1/9 * x^(2-1) = -1/9 * x

Therefore, the simplified expression is -1/9 * x.

The squares have same area thus if we suppose that the area of one of them is A the other one has a area of A .

The shaded area is 20/100 × A thus the unshaded area is ( 80/100 × A )+ ( 80/100 × A ) , So the unshaded area is 160/100 × A .

Thus the ratio of the shaded area of the figure to unshaded area of the figure is :

( 20A / 100 ) ÷ ( 160A / 100 ) =

A / 100 s are simplify

20 ÷ 160 =

2 ÷ 16 =

1/8

Answer:

Step-by-step explanation:

1/8

Answer:

772 hamburgers sold on monday

Step-by-step explanation:

add the problem

Answer: 3/2

Step-by-step explanation: y2-y1/ x2- x1

Answer:

C

Step-by-step explanation:

Slope can truly be anything as long as they're equal

Answer:

c.their slopes are equal

Answer:

53/25 x 100 = 212% increase

The probability of exactly 6 Mexican-Americans among 12 jurors is 0.0312 (rounded to four decimal places).

The given problem requires us to find the probability of exactly 6 Mexican-Americans among 12 jurors. To solve the problem, we need to use the binomial probability formula that can be expressed as:P(x) = C(n, x) * p^x * (1-p)^(n-x)Here,x = 6 (number of Mexican-Americans) p = 0.25 (probability of a Mexican-American being chosen as a juror)n = 12 (total number of jurors)C(n,x) is the combination of n things taken x at a time. It can be calculated as follows:C(n,x) = n! / x!(n-x)!Therefore, the required probability is:P(6) = C(12, 6) * (0.25)^6 * (0.75)^6P(6) = 924 * 0.0002441 * 0.1785P(6) ≈ 0.0312Rounding the answer to four decimal places, we get the final probability as 0.0312. Therefore, the probability of exactly 6 Mexican-Americans among 12 jurors is 0.0312 (rounded to four decimal places).

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To find the probability of exactly 6 Mexican-Americans among 12 jurors, we need to use the binomial distribution formula.

The binomial distribution is used when we have a fixed number of independent trials with two possible outcomes and want to find the probability of a specific number of successes. In this case, the two possible outcomes are Mexican-American or not Mexican-American, and the number of independent trials is 12. The formula for the binomial distribution is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)where P(X = k) is the probability of getting k successes, n is the total number of trials, p is the probability of success, and (n choose k) is the number of ways to choose k successes out of n trials. In this case, we want to find the probability of exactly 6 Mexican-Americans, so k = 6.

We are not given the probability of a juror being Mexican-American, so we will assume that it is 0.5 (a coin flip) for simplicity. Plugging in the values, we get:

P(X = 6) = (12 choose 6) * 0.5^6 * (1 - 0.5)^(12 - 6)

= 924 * 0.015625 * 0.015625

= 0.0233 (rounded to four decimal places)

Therefore, the probability of exactly 6 Mexican-Americans among 12 jurors is 0.0233.

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The value of c+d is 0. To explain why, we need to consider the definition of differentiability at a point. If f is differentiable at x=2, it means that the function is smooth and has a well-defined derivative at that point. Right answer is (c).

The derivative of a function measures its rate of change, and it is represented by the slope of the tangent line to the graph of the function at that point.

In this case, since f is differentiable at x=2, it implies that the function is continuous at that point and has a well-defined tangent line. For a function to be differentiable, the left-hand derivative and the right-hand derivative at that point must exist and be equal. In other words, the function should have the same slope from both sides of the point x=2.

The fact that c and d are constants suggests that the function f(x) has a linear form, represented by f(x) = cx + d. Since the function is differentiable at x=2, the slope of the tangent line at that point must be equal to the derivative of the function at x=2.To find the derivative of f(x), we differentiate f(x) with respect to x:f'(x) = cSince the derivative is constant, the slope of the tangent line is the same at all points, including x=2. Therefore, the value of c+d must be 0, as the constant term d does not contribute to the slope of the tangent line at x=2. Thus, the correct answer is 0.

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The data set can be said to be continuous because it represents a range of possible values that can be obtained by players in the English Premier League.

Mohamed Salah is a prolific striker for Liverpool F.C. with an impressive record in the English Premier League (EPL).

The number of assists a player can achieve ranges from 0 to infinity mathematically, and it is not possible to achieve negative assists while it is not feasible for a player to score 1000 goals.

Likewise, the number of goals a player can score ranges from 0 to infinity,

and it is not mathematically feasible to achieve negative goals while it is highly unlikely for a player to score 1000 goals. The data set can be best classified as continuous data because it can take any value within a given range.

Continuous data is data that can take any value within a given range, which means that it is not possible to list all the possible values in a set. Therefore, the data set can be said to be continuous because it represents a range of possible values that can be obtained by players in the English Premier League.

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Length of KL is 31.5 unit.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.

Given in the figure

GJ = 15

GH = 8

KN = 59

KL = x

GHIJ and KLMN are similar

therefore, ratio of the sides will be equal

GJ/GH = KN/KL

15/8 = 59/x

x = 59 × 8/15

x = 472/15

x = 31.4667

Hence,31.5 is length of KL.

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SOLUTION:

The z-score is gotten as;

Inserting, the values we have;

Thus, using a significance level of 0.05;

Thus, the answer is OPTION C

Answer:

Step-by-step explanation:

Given :

x = -6

-7x + 6y = -18 ... i)

Putting the value of x in equation ...i)

=> -7 (-6) + 6y = -18

=> 42 + 6y = -18

=> 6y = -18 -42

=> 6y = - 60

=> y = -60/6

=> y = -10

The value of y = -10 and x = -6

Answer:

x= 4, y=6

Step-by-step explanation:

9x-9y = -18

9x=-18+9y

x=-2+y

-6(-2+y) + 9y = 6

-12-6y+9y=6

3y=18

y=6

9x -9(6)=-18

9x-54=-16

9x=36

x=4

Any system of geometry that is not based on the principles of Euclidean geometry is known as non-Euclidean geometry.

Many geometrical systems that are not based on the parallel postulate or other Euclidean axioms are referred to as non-Euclidean geometry.

The parallel postulate asserts that given a line and a point off the line, there is only one line that can be drawn through the point parallel to the provided line.

Attempts to establish or refute this postulate gave rise to non-Euclidean geometries. Contrarily, non-Euclidean geometries are founded on diverse axioms that allow for various kinds of parallel lines, including multiple parallel lines in hyperbolic geometry and no parallel lines in elliptic geometry.

Non-Euclidean geometry is important to many fields of mathematics and science, including relativity theory and cosmology.

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