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Therefore, a monthly payment of $168.62 must be made to pay off the $3,500 balance on the credit card in two years.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life.

Here,

To calculate the monthly payment required to pay off the $3,500 balance on a credit card that charges 16.5% interest, compounded monthly, in two years, we can use the formula for the present value of an annuity:

[tex]PMT = PV * r / (1 - (1 + r)^{-n})[/tex]

where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

First, we need to convert the annual interest rate of 16.5% to a monthly interest rate:

r = 0.165 / 12

= 0.01375

Next, we need to calculate the total number of payments over two years:

n = 2 * 12

= 24

Now we can plug in the values into the formula:

[tex]PMT = 3500 * 0.01375 / (1 - (1 + 0.01375)^{-24}) = $168.62[/tex]

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The probability that a person rolling a die gets the first 2 on the third roll is 25/216 and the first 2 on the fifth roll is 15625/7776.

The probability that a person rolling a die gets a) the first 2 on the third roll b) the first 2 on the fifth roll are calculated as follows:

(a) The probability of getting a 2 on any roll is 1/6.The probability of not getting a 2 on the first roll is 5/6The probability of not getting a 2 on the second roll is also 5/6The probability of getting a 2 on the third roll is 1/6Therefore, the probability of getting a 2 on the third roll is: 5/6 × 5/6 × 1/6 = 25/216

(b) The probability of getting a 2 on any roll is 1/6.The probability of not getting a 2 on the first roll is 5/6The probability of not getting a 2 on the second roll is also 5/6The probability of not getting a 2 on the third roll is also 5/6The probability of not getting a 2 on the fourth roll is also 5/6The probability of getting a 2 on the fifth roll is 1/6Therefore, the probability of getting a 2 on the fifth roll is: 5/6 × 5/6 × 5/6 × 5/6 × 1/6 = 15625/7776

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Answer:  The area of the smaller circle is [tex]65.6cm^{2}[/tex].

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex], r is the radius.

1. Find out the diameter of the small circle.

[tex]\frac{1}{3}(27)= 9[/tex]

2) Find out the radius, r.

[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]

3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.

[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]

Answer: Substitute x back into one of the equations to solve for y.

Step-by-step explanation:

The value of x that makes the given image to be a rectangle is: x = 2.5

The length of the diagonals of a rectangle are equal and congruent to each other. It is also pertinent to note that the diagonals of a rectangle bisect each other at the center. Thus:

From the given parameters, we see that half of the diagonals have been labelled and as such we have:

8x - 3 = 4x + 7

Rearrange to have like terms on same side and so we have:

8x - 4x = 7 + 3

4x = 10

x = 10/4

x = 2.5

Thus, the value of x from the calculation above of the rectangle is 2.5

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Answer:

Yes, I can find the absolute value of -3 2/3.

The absolute value of a number is the distance of the number from zero on the number line. It is always a positive number.

To find the absolute value of -3 2/3, we need to ignore the negative sign and just look at the magnitude of the number.

So, the absolute value of -3 2/3 is:

|-3 2/3| = 3 2/3

Therefore, the absolute value of -3 2/3 is 3 2/3.

The inequality to determine how much more money he needs to save so he can buy the shoes is x ≥ $45

Let x be the amount of money Jordan still needs to save to buy the shoes.

The total cost of the shoes is $75, and Jordan has already saved $30. Therefore, the amount of money he still needs to save is:

x = $75 - $30

Simplifying the right side:

x = $45

So, the inequality that represents how much more money Jordan needs to save is:

x ≥ $45

This means that Jordan needs to save at least $45 more to be able to buy the shoes.

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There are 11 people in your sample size and 80% of them can read.

To be 87% sure that 7 of the 11 people could read, you would need to interview eight people.

To calculate this, you need to use a binomial probability formula.

This formula will allow you to calculate the number of successes (people who can read) that must be achieved in order to have an 87% certainty that the sample size of 11 people is representative of the population.

The formula you need to use is P(x) = n! / (x! (n - x)!).

You'll want to plug in x = 7, n = 8. This will give you the probability of 8 successes in 8 trials, which is equal to 0.87. Therefore, you will need to interview 8 people in order to be 87% sure that 7 of the 11 people could read.

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The value of the missing angles of the quadrilateral are:

a = 110°

b = 70°

c = 20°

Theorem sum of angles in a triangle states that they sum up to 180 degrees. Thus:

d = 180 - (78 + 32)

d = 70°

Similarly:

e = 180 - (78 + 32 + 18)

e = 20°

Sum of angles on a straight line is 180 degrees. Thus:

a = 180 - 70

a = 110°

We can see that e + b will be equal to 90 degrees because of the definition of right angles. Thus:

b = 90° - 20°

b = 70°

From sum of angles in a triangle as 180° is:

c = 180 - (90 + 70)

c = 20°

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Answer:

We can start by using algebra to solve for the total goal of the canned food drive. Let's let "g" be the total goal in number of cans.

If 600 cans is 80% of their goal, then we can write:

0.8g = 600

To solve for "g", we can divide both sides by 0.8:

g = 600 / 0.8

g = 750

So the total goal of the canned food drive is 750 cans.

To find out how many more cans the students need to collect to reach their goal, we can subtract the number of cans they've already collected from the total goal:

750 - 600 = 150

Therefore, the students need to collect 150 more cans to reach their goal.

The variance of 2X + 3Y is 35.52.

The solution to the problem is as follows:

First, find the mean and variance of X and Y:

E(X) = 3/5

Var(X) = 3/25

E(Y) = 1

Var(Y) = 1/25

Then, use the properties of variance to find the variance of 2X + 3Y:

Var(2X + 3Y)

= 4Var(X) + 9Var(Y) + 12Cov(X,Y)Cov(X,Y)

= E[(2X - 6/5)(3Y - 1)]

= 6E(XY) - 6E(X) - 3E(Y) + 2

= 6 * (integral from 0 to infinity integral from 0 to infinity of xyf(x,y)dxdy) - 6 * 3/5 - 3 * 1 + 2 = 6 * (integral from 0 to infinity 15xye^-3xdydx) - 8

= 54/5

Therefore,

Var(2X + 3Y) = 4(3/25) + 9(1/25) + 12(54/5)

                     = 888/25

                     = 35.52.

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Answer:

x ≥ 2

Step-by-step explanation:

8x + 3 ≥ 19

8x ≥ 19 - 3

8x / 8 ≥ 16 / 8

x ≥ 2

Answer:

Sure, I can solve for x:8x + 3 ≥ 19Subtracting 3 from both sides:8x ≥ 16Dividing both sides by 8:x ≥ 2Therefore, the solution is x ≥ 2.

the perimeter of the door on the scale drawing is 4 centimeters. A scale drawing is a representation of an object that is drawn to a smaller or larger size than the actual object, but the proportions between the dimensions of the object are maintained.

In this case, we are given a rectangular door of a dollhouse with a height of 5 centimeters and a width of 3 centimeters, and we are asked to find the perimeter of the door on a scale drawing that uses the scale 2:8.

The scale 2:8 means that every 2 units on the scale drawing represent 8 units on the actual object. To find the dimensions of the door on the scale drawing, we can divide both the height and the width by 8 and then multiply by 2, since the scale ratio is 2:8. This gives us the following dimensions on the scale drawing:

Height = (5/8) x 2 = 1.25 centimeters

Width = (3/8) x 2 = 0.75 centimeters

Now, we can use these dimensions to find the perimeter of the door on the scale drawing. The perimeter of a rectangle is given by the formula:

Perimeter = 2 x (Length + Width)

In this case, the length and width of the door are the same as the height and width of the door, respectively. So, we can write:

Perimeter = 2 x (Height + Width)

= 2 x (1.25 + 0.75)

= 2 x 2

= 4

Therefore, the perimeter of the door on the scale drawing is 4 centimeters.

In summary, we can find the dimensions of the door on the scale drawing by dividing the actual dimensions by 8 and multiplying by 2, and we can find the perimeter of the door on the scale drawing using the formula for the perimeter of a rectangle.

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Answer:

x > 25.5

Step-by-step explanation:

2.5 < [tex]\frac{1}{3}[/tex] (x - 18 ) ← multiply both sides by 3 to clear the fraction

7.5 < x - 18 ( ad 18 to both sides )

25.5 < x , then

x > 25.5

Multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d.

The impact of multiplying all values in a normally distributed random sample and population by 2 on Cohen's d is an increase in effect size. Cohen's d measures the degree of difference between two sets of scores, calculated by dividing the difference between the two means by the pooled standard deviation. Therefore, when values are multiplied by 2, the means increase, leading to an increase in effect size as measured by Cohen's d.

In addition, multiplying values by 2 also increases the magnitude of the standard deviation, which is a measure of spread. When the standard deviation is larger, it requires a larger mean difference for Cohen's d to register a significant effect. Therefore, by increasing the standard deviation, the effect size measure will increase.

To summarize, multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d. This is because multiplying values by 2 increases both the mean and the standard deviation, which results in a larger mean difference and a larger standard deviation, respectively. Consequently, the effect size measure increases.

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A multiple regression equation that can be used to analyze the data for a two-factorial design with two levels for factor A and three levels for factor B can be written as:

Y = b0 + b1A + b2B + b3AB + e

where Y is the dependent variable, A is the independent variable for factor A, B is the independent variable for factor B, A*B is the interaction between A and B, and e is the error term.

The variables can be defined as follows:

Y: The dependent variable that is being measured in the study.

A: The independent variable representing factor A, which has two levels (A1 and A2).

B: The independent variable representing factor B, which has three levels (B1, B2, and B3).

A*B: The interaction term between factor A and factor B.

e: The error term that captures the variability in the dependent variable that is not explained by the independent variables.

This equation allows us to examine the main effects of both factors (A and B) as well as their interaction (A*B) on the dependent variable Y in a two-factorial design.

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The domain of the function is: Domain = {-8, -6, -4, -2, 1, 2} and  range of the function is :- Range = {-8, -6, -4, -2, 0}.

A function is a rule that maps each element in one set, called the domain, to a unique element in another set, called the range.

It is a relation between two sets where each input in the domain corresponds to a unique output in the range.

Functions are often represented by equations, graphs, or tables, and they are used to model real-world phenomena and solve mathematical problems in various fields such as science, engineering, economics, and more.

The domain of the function is the set of all possible input values, which in this case are the x-coordinates of the given points on the graph. So, the domain is:

Domain = {-8, -6, -4, -2, 1, 2}

The range of the function is the set of all possible output values, which in this case are the y-coordinates of the given points on the graph. So, the range is:

Range = {-8, -6, -4, -2, 0}

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Answer: yes, yes, no

Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.

Answer: answer is 9.9

Step-by-step explanation: becuz 31.2 - 21.3 = 9.9

u have to substract 21.3 from 31.2 . if u subtract 21.3 from 31.2 then it will be 9.9  

but ig u did subtract 31.2 from 21.3....

By using equation in two variable we need to use 2 eggs to make all the cookies with 1.33 cups of butter.

To make six dozen cookies, the recipe calls for two cups of butter and three eggs. We can use proportionality to solve this question: If 2 cups of butter require 3 eggs to make 6 dozen cookies, then 1.33 cups of butter require x eggs to make all of the cookies.

x eggs = (1.33 cups of butter x 3 eggs)/(2 cups of butter). x = 1.99 eggs. Since we cannot use .99 eggs to make cookies, we would need to round up to the nearest whole number of eggs.

Therefore, we need to use 2 eggs to make all the cookies with 1.33 cups of butter.

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Answer: The area of a triangle is 1036.8 square units.

To find the area of a triangle, we can use the formula

Area = (1/2) * base * height

In this case, we are given that the first base is 32 and the second base is twice the first base, or 2*32 = 64. The height is given as 21.6. Therefore, we can plug these values into the formula and solve for the area:

Area = (1/2) * (32 + 64) * 21.6

Area = (1/2) * 96 * 21.6

Area = 1036.8

Therefore, the area of the triangle is 1036.8 square units.

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The standard deviation of the number of claims filed, in this case, is equal to 1.732. This is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed.

The standard deviation of the number of claims filed is equal to the square root of the mean. In this case, the mean is equal to three. Thus, the standard deviation of the number of claims filed is equal to the square root of three, which is equal to 1.732.

To explain further, the Poisson distribution is a discrete probability distribution that is used to calculate the probability of a certain number of events occurring within a given time interval. It is based on the assumption that these events occur independently and at a constant rate. In this case, the rate is equal to the mean, which is equal to three. Thus, the standard deviation is equal to the square root of the mean.

The standard deviation of the number of claims filed is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed. The larger the standard deviation, the greater the amount of variation, and vice versa. In this case, the standard deviation is relatively low, which suggests that the number of claims filed is relatively consistent.

In conclusion, the standard deviation of the number of claims filed, in this case, is equal to 1.732. This is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed.

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A' is complement of A, A∩B is intersection of A and B, A∪B is union of A and B.

In set theory, the complement of a set is the set of all elements in the universal set that are not in the given set. In other words, it is the set of all elements in the universal set that are outside of the given set.

Ω = {2, 3, 4, 5, 6, 7, 8, 9} (whole numbers from 2 to 9)

A = {4, 6, 8} (even numbers from Ω)

B = {2, 3, 5, 7} (prime numbers from Ω)

a. A' (complement of A, i.e. elements in Ω that are not in A)

A' = {2, 3, 5, 7, 9} (odd numbers and 9 are not in A)

b. A∩B (intersection of A and B, i.e. components found in both A and B)

A∩B = {2} (the only even prime number is 2)

c. A∪B (union of A and B, i.e. elements that can be found in A, B, or both)

A∪B = {2, 3, 4, 5, 6, 7, 8} (all the even numbers and prime numbers from Ω).

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The complete question is:

ASAP

Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:

a. A’

b. A∩B

c. A∪B

The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.

This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.

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Overall, the shape of the magnetosphere is determined by the interaction of the solar wind and the Earth's magnetic field.

The shape of Earth's magnetosphere is modified by the solar wind. The Earth's magnetosphere is a protective magnetic shield around the Earth that protects us from the harmful particles and radiation from the Sun. The magnetosphere is not a perfect sphere, but rather a complex shape that is constantly changing due to the interaction of the solar wind and the Earth's magnetic field.The solar wind is a continuous stream of charged particles, mostly protons and electrons, that are ejected from the Sun's outer atmosphere. When these charged particles come into contact with the Earth's magnetic field, they are deflected around the Earth, forming a bow shock in front of the magnetosphere.

The magnetosphere then acts as a barrier, trapping many of the charged particles and preventing them from reaching the Earth's surface. However, some particles are able to penetrate the magnetosphere and reach the upper atmosphere, where they can cause auroras and other phenomena.The shape of the magnetosphere is constantly changing due to the changing conditions in the solar wind.

For example, during periods of high solar activity, the magnetosphere can become compressed and distorted, leading to more auroras and other phenomena. During periods of low solar activity, the magnetosphere can expand and become more symmetrical.

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Step-by-step explanation:

Lets assume this is a right triangle.

If you use pythagorean theorem, lets assume the tower is the longest line on the triangle.

If this is true, lets say that 9^2 (distance from end of slide to base of tower) + x^2 (length of slide) = 23^2 (height of tower)

we get the length of the slide is 21.2 meters.

Answer:

c

Step-by-step explanation:

Answer:

To calculate the time it will take Tom to complete the 1-mile kayak trip, we need to take into account the speed of the current and the speed at which Tom can paddle relative to the current.

Let's first consider the time it would take for Tom to go upstream against the current. In this case, the speed of the current is subtracted from Tom's paddling speed, so his effective speed is:

Effective speed upstream = 4 miles per hour - 3 miles per hour = 1 mile per hour

To travel 1 mile at 1 mile per hour, Tom would take:

Time upstream = Distance / Effective speed upstream = 1 mile / 1 mile per hour = 1 hour

Now let's consider the time it would take for Tom to go downstream with the current. In this case, the speed of the current is added to Tom's paddling speed, so his effective speed is:

Effective speed downstream = 4 miles per hour + 3 miles per hour = 7 miles per hour

To travel 1 mile at 7 miles per hour, Tom would take:

Time downstream = Distance / Effective speed downstream = 1 mile / 7 miles per hour ≈ 0.14 hours or about 8 minutes

Therefore, the total time it would take Tom to complete the 1-mile kayak trip, including going upstream and downstream, would be:

Total time = Time upstream + Time downstream = 1 hour + 0.14 hours ≈ 1.14 hours or about 68 minutes.

The linear correlation coefficient of 0.3 indicates a moderate positive correlation between the two variables.

This suggests that when one variable increases, the other variable tends to increase too. However, there is not a strong linear relationship between the two variables, meaning that the increase in one variable does not guarantee a predictable change in the other variable.


When interpreting the findings of a correlation study, it is important to note the strength of the relationship between the two variables. A linear correlation coefficient of 0.3 indicates a moderate positive correlation, meaning that the two variables increase together but there is not a strong linear relationship between the two variables.

This means that the increase in one variable does not guarantee a predictable change in the other variable. To put it another way, the strength of the correlation means that when one variable increases, it is likely that the other will increase as well, but it is not guaranteed.

Therefore, caution should be used when making predictions based on the results of a correlation study.

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