Find the savings plan balance after

4

years with an APR of

8​%

and monthly payments of

​$150.

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Part 1

The balance is

​$enter your response here.

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

The value of x that makes A parallel to B is 15.

Alternate exterior angles are a pair of angles that lie outside of two parallel lines and are on opposite sides of the transversal. In other words, they are a pair of non-adjacent angles that are formed when a transversal intersects two parallel lines. The angles are congruent, meaning that they have the same measure.

The term "alternate" refers to the fact that they are on opposite sides of the transversal and "exterior" indicates that they are outside of the parallel lines. Alternate exterior angles are important in geometry because they can be used to prove that two lines are parallel. If the alternate exterior angles are congruent, then the lines are parallel.

Since the alternate exterior angles are equal, we can set them equal to each other:

8x + 30 = 10x

Subtracting 8x from both sides, we get:

30 = 2x

Dividing both sides by 2, we get:

15 = x

So the value of x that makes A||B is 15.

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Answer:

It depends on the context of the problem and the interpretation of the ratio represented by the point (7, 8).

If we interpret the point (7, 8) as representing the ratio 7:8, then Adela's claim is incorrect. Adding the same number to both coordinates of the point would change the value of the ratio. For example, adding 1 to both coordinates would give the point (8, 9), which represents the ratio 8:9, which is not equivalent to 7:8.

However, if we interpret the point (7, 8) as representing a different type of ratio, such as the ratio of the distances from the point to two fixed points or the ratio of the areas of two shapes, then it may be possible to find an equivalent ratio by adding the same number to both coordinates of the point. In this case, Adela's claim could be correct.

Without more information about the context and interpretation of the ratio represented by the point (7, 8), it is difficult to determine the correctness of Adela's claim.

Answer:

Put the point a tiny bit more than half way between 14 and 15.

Step-by-step explanation:

If you are allowed to use a calculator, put in sqrt215 and you get out 14.66, that goes a little bit more than halfway between 14 and 15.

If you are not allowed to use a calculator, think of the numbers on the numberline in terms of answers to *perfect square* questions.

So 12 is sqrt 144.

13 is sqrt 169.

14 is sqrt 196.

15 is sqrt 225.

So the 215 in your question is in between 196 and 225.

215 is closer to 225 (than to 196) so put the point closer to sqrt 225. That is, in between 14 and 15 and just a tad bit closer to 15.

The probability of both gumballs not being red is 11/21.

What is the probability?

The probability of the first gumball not being red is:

P(first gumball not red) = P(blue) + P(yellow)

= (6/15) + (5/15)

= 11/15

After removing the first gumball, there are 14 gumballs left in the bag. The probability of the second gumball not being red depends on what color the first gumball was.

Case 1: The first gumball was blue

If the first gumball was blue, there are 5 blue, 4 red, and 5 yellow gumballs left in the bag. The probability of the second gumball not being red is:

P(second gumball not red | first gumball was blue) = P(blue or yellow)

= P(blue) + P(yellow)

= (5/14) + (5/14)

= 5/7

Case 2: The first gumball was yellow

If the first gumball was yellow, there are 6 blue, 4 red, and 4 yellow gumballs left in the bag. The probability of the second gumball not being red is:

P(second gumball not red | first gumball was yellow) = P(blue or yellow)

= P(blue) + P(yellow)

= (6/14) + (4/14)

= 5/7

The probability of both gumballs not being red is the product of the probabilities of each event:

P(both gumballs not red) = P(first gumball not red) * P(second gumball not red | first gumball not red)

P(both gumballs not red) = (11/15) * (5/7)

P(both gumballs not red) = 55/105

P(both gumballs not red) = 11/21

Therefore, the probability of both gumballs not being red is 11/21.

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Step-by-step explanation:

so, it is

sqrt(y + 3) = sqrt(y) + sqrt(3)

first we square both sides :

y + 3 = y + 3 + 2×sqrt(y)×sqrt(3) =

= y + 3 + 2×sqrt(3y) =

= y + 3 + sqrt(4×3y) = y + 3 + sqrt(12y)

0 = sqrt(12y)

we square again :

0² = 12y

0/12 = 0 = y

according the given question the exact value of given expression is [tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]

First, we need to find [tex]$\sin x$[/tex] using the identity[tex]$\cos^2x + \sin^2x = 1$:$\sin^2x = 1 - \cos^2x = 1 - \left(-\frac{4}{5}\right)^2 = \frac{9}{25}$[/tex]

Since  [tex]$\frac{\pi}{2} < x < \pi$[/tex], we know that  [tex]$\frac{\pi}{4} < \frac{x}{2} < \frac{\pi}{2}$[/tex]. Therefore, we can use the

identity [tex]$\tan\frac{x}{2} = \frac{\sin x}{1 + \cos x}$[/tex]:

[tex]$\tan\frac{x}{2} = \frac{\sqrt{\frac{9}{25}}}{1 - \frac{4}{5}} = \frac{\frac{3}{5}}{\frac{1}{5}} = \boxed{3}$[/tex]

[tex]If $\tan x = \frac{40}{9}$ and $\pi < x < \frac{3\pi}{2}$, find $\cos\frac{x}{2}$.[/tex]

First, we need to find [tex]$\sin x$[/tex] using the identity [tex]$\tan^2x + 1 = \sec^2x$[/tex]:

[tex]$\sin x = \frac{\tan x}{\sec x} = \frac{\frac{40}{9}}{-\frac{9}{40}} = -\frac{160}{81}$[/tex]

[tex]Since $\pi < x < \frac{3\pi}{2}$, we know that $\frac{\pi}{2} < \frac{x}{2} < \frac{3\pi}{4}$[/tex]. Therefore, we can use the identity [tex]$\cos\frac{x}{2} = \pm\sqrt{\frac{1 + \cos x}{2}}$[/tex]:

[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1 + \cos x}{2}} = -\sqrt{\frac{1 + \frac{\cos^2x}{\sin^2x}}{2}} = -\sqrt{\frac{\sin^2x + \cos^2x}{2\sin^2x}} = -\sqrt{\frac{1}{2(1 - \sin^2x)}}$[/tex]

Plugging in [tex]$\sin x = -\frac{160}{81}$[/tex] , we get:

[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]

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The skater's total score would be 58 points (7.25 x 8 = 58).

Just dividing the total number of values in a data set by the sum of all of the values yields it. A frequency table of data or raw data can both be used for the calculation.

The following equation can be used to determine each skater's overall score, s, assuming that they each receive evaluations from eight judges and have a mean score of 7.25 points:

s = 7.25 x 8

The total score is determined by multiplying the average score by the quantity of judges in this equation. In this instance, the skater would have earned 58 points overall (7.25 x 8 = 58).

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In a skating competition each skater receives scores from eight judges a skater has a mean (average) of 7.25 points. Write an equation to find the skaters total score?

a. 7.25 × 8

b. 7.25⁸

c. 7.25 - 8

d. 7.25/8

Answer:

C

.........................

Answer: the answer is A

Step-by-step explanation: The process of nuclear fusion is the union of two light atomic nuclei into one heavier one while releasing enormous quantities of energy.

There is a 1/4 or 25% chance that Jamal will end up with tails on the coin and an even number on the die when he rolls the die and tosses the coin.

The probability of rolling an even number on the die is 3/6 or 1/2, since there are three even numbers (2, 4, 6) out of the six possible outcomes. Similarly, the probability of getting tails on the coin is 1/2 since there are two possible outcomes, heads or tails. To find the probability of both events happening simultaneously, we need to multiply the probabilities of each event. Thus, the probability of getting tails on the coin and an even number on the die is:

P(tails and even) = P(tails) × P(even)

= 1/2 × 1/2

= 1/4

Therefore, there is a 1/4 or 25% chance that Jamal will end up with tails on the coin and an even number on the die when he rolls the die and tosses the coin.

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The graph represents a proportional relationship.

What is proportional relationship?

A proportional relationship is a relationship between two variables where their ratio remains constant. This means that as one variable increases or decreases, the other variable changes proportionally in order to maintain a constant ratio. In other words, the two variables are directly proportional to each other. This relationship can be represented by a straight line passing through the origin on a graph. Proportional relationships are commonly used in various fields such as physics, finance, and engineering to analyze and predict outcomes.

Explaining the table, equation and graph to know which represents a proportional relationship :

The relationship between the values in the given table is not proportional. If it was a proportional relationship, then the ratio of y to x would be constant. However, in this case, the ratios are not equal. For example, the ratio of y to x for the first row is 3.6/3 = 1.2, but the ratio of y to x for the second row is 6/5 = 1.2, and the ratio of y to x for the third row is 7.2/8 = 0.9. Therefore, the ratios are not equal and the relationship is not proportional.

The equation y=2x+5 does not represent a proportional relationship. In a proportional relationship, there is a constant ratio between the two variables. However, in this equation, the ratio between y and x is not constant, but rather it increases as x increases.

The graph represents a proportional relationship as the ratio between y and x is  constant.

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If her hοuse actually 56 feet wide, then scale οf her drawing is scale = 56 feet / (drawing width)

The slοpe is a mathematical cοncept that refers tο the steepness οf a line. It is cοmmοnly denοted by the letter "m" and can be calculated using the fοrmula:      

slοpe (m) = (change in y) / (change in x)

Withοut having the actual measurements οf the drawing, we cannοt determine the scale.

Tο find the scale οf a drawing, yοu need tο knοw the actual measurements οf the οbject being drawn as well as the cοrrespοnding measurements in the drawing. Fοr example, if yοu knοw that the actual width οf Rοse's hοuse is 56 feet and the width οf the hοuse in the drawing is 8 inches, yοu can determine the scale by using the fοllοwing fοrmula:

scale = actual width/drawing width

Using this fοrmula with the given infοrmatiοn, we get:

scale = 56 feet / (drawing width)

Therefοre, we dο nοt have the drawing width, we cannοt calculate the scale.

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For the given function  f(x) = ⁿ√p(x), The Domain depends on the value of n and The Domain is all real numbers if n is ODD.

What is the definition of a function?

In mathematics, a function is a relation between a set of inputs (also known as the domain) and a set of possible outputs (also known as the range) with the property that each input is associated with exactly one output.

In other words, a function takes an input value, performs a specific operation or set of operations on it, and produces an output value. It can be represented by a rule, formula, or graph that relates each input to its corresponding output.

Now,

The domain of the function f(x) = ⁿ√p(x) depends on the value of n.

If n is odd, then the function is defined for all real numbers, and the domain is all real numbers.

If n is even, then the function is defined only for non-negative real numbers, and the domain is all non-negative real numbers.

Therefore, the statement "The Domain is all real numbers" is not always true for the function f(x) = ⁿ√p(x). The correct statements are:

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By using chi-squared test, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

What is chi-squared test?

To perform a chi-squared test for independence between breed and milk yield, we need to set up the hypotheses:

Null hypothesis: There is no association between breed and milk yield.

Alternative hypothesis: There is an association between breed and milk yield.

We will use a significance level of 0.05.

To calculate the expected counts for each cell, we will use the formula: (row total x column total) / grand total.

The observed counts and expected counts are:

The grand total is 100.

The degrees of freedom for the test are (number of rows - 1) x (number of columns - 1) = (2 - 1) x (3 - 1) = 2.

Using a chi-squared distribution table or calculator, we find the critical value for a chi-squared test with 2 degrees of freedom and a 0.05 significance level to be 5.99.

To calculate the test statistic, we use the formula:

chi-squared = [tex]sum((observed\ count - expected\ count)^2 / expected\ count)[/tex]

The calculated value of chi-squared is:

[tex]chi-squared = ((32-25.76)^2 / 25.76) + ((20-19.04)^2 / 19.04) + ((16-13.20)^2 / 13.20) + ((10-16.24)^2 / 16.24) + ((18-18.96)^2 / 18.96) + ((4-4.80)^2 / 4.80) = 10.92[/tex]

The degrees of freedom for the test are 2, and the critical value is 5.99.

Since the calculated value of chi-squared (10.92) is greater than the critical value (5.99), we reject the null hypothesis.

Therefore, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

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Answer:1 and 2

Step-by-step explanation:

so, they asked 50 students and then that was later broke down to smaller groups.

10,15,25

so, for every 10 students will be one. 1 vote= 10 students.

also, the dinosaur had the greatest number of votes so that explains answer 2.

The slope for the given point through which it passes through the graph is [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = infinity .

What about slope?

The slope of a line is a measure of its steepness. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points. In other words, it is the rate at which the line rises or falls as we move along it in the horizontal direction.

Define graph:

In mathematics, a graph is a visual representation of a set of data or mathematical relationships between variables. Graphs can be used to display and analyze data in a variety of formats, including line graphs, bar graphs, scatter plots, and pie charts.

According to the given information:

As, we know that the slope =  [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

⇒ In which the point given are (-1,8) and (-1,-4)

By putting the value of the given point we have that

⇒ [tex]\frac{-4-(8)}{-1-(-1)}[/tex] = infinity.

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We will use sine function, and length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

To solve for the opposite side of the right triangle, we would use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

In this problem, we are given that one angle of the right triangle is 60 degrees and the hypotenuse is 25 feet. Let's label the opposite side as x and the adjacent side as y. Then we can use the sine function:

[tex]$\sin 60^\circ = \frac{x}{25}$[/tex]

Simplifying the left side, we have:

[tex]$\frac{\sqrt{3}}{2} = \frac{x}{25}$[/tex]

Multiplying both sides by 25, we get:

[tex]$x = \frac{25\sqrt{3}}{2}$[/tex]

Therefore, the length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

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The credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

First, let's calculate the monthly interest rate by dividing the APR by 12:

11.99% / 12 = 0.99917%

Next, let's calculate the interest paid on the monthly balance for each of the 11 months before the final payment:

Month 1:

Interest = $7,568.19 x 0.99917% = $75.59

Month 2:

Balance = $7,568.19 - $350 - $75.59 = $7,142.60

Interest = $7,142.60 x 0.99917% = $71.38

Month 3:

Balance = $7,142.60 - $350 - $71.38 = $6,721.82

Interest = $6,721.82 x 0.99917% = $67.11

Month 4-11: (follow the same process as above)

Interest for Month 4: $63.82

Interest for Month 5: $60.51

Interest for Month 6: $57.17

Interest for Month 7: $53.80

Interest for Month 8: $50.41

Interest for Month 9: $47.00

Interest for Month 10: $43.56

Interest for Month 11: $40.11

Now, at the end of month 11, the cardholder has a balance of:

$7,568.19 - ($350 x 11) - $75.59 - $71.38 - $67.11 - $63.82 - $60.51 - $57.17 - $53.80 - $50.41 - $47.00 - $43.56 - $40.11 = $1,225.74

Finally, the cardholder pays off the remaining balance of $1,225.74 at the end of month 12. The interest charged for this month would be:

Interest = $1,225.74 x 0.99917% = $12.25

So the total interest paid by the cardholder over the 12 months is:

$75.59 + $71.38 + $67.11 + $63.82 + $60.51 + $57.17 + $53.80 + $50.41 + $47.00 + $43.56 + $40.11 + $12.25 = $720.27

Therefore, the credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.

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Answer:

4/8 in lowest terms is 1/2.

Step-by-step explanation:

Answer: 1/2

4/8 is equivalent to 1/2

For the first equation, we can complete the square to find its vertex form. Here's how we do it:

0 = x^2 - 18x + 1

0 = (x - 9)^2 - 80

So we have (x - 9)^2 = 80. This is in the form (x - p)^2 = q, where p = 9 and q = 80.

For the second equation, we can complete the square in a similar way:

x^2 + 26x + 167.5 = 0

x^2 + 26x = -167.5

x^2 + 26x + (26/2)^2 = -167.5 + (26/2)^2

(x + 13)^2 = 9.25

So we have (x + 13)^2 = 9.25. This is in the form (x - p)^2 = q, where p = -13 and q = 9.25.

I hope that helps!

Answer:

1x

Step-by-step explanation:

Firstly lets expand the brackets for the equation

(x - 7 )2 = 36

If we multiply what's in the brackets by 2 we get this:

2x - 14 = 36

Add 14 to both sides:

2x = 50

Divide both sides by 2:

x = 25

Answer = 1x (Only possible solution

Answer:

The two solutions to the given equation are x = 13 and x = 1.

Step-by-step explanation:

To solve the given equation (x - 7)² = 36, begin by square rooting both sides:

[tex]\implies \sqrt{(x-7)^2}=\sqrt{36}[/tex]

[tex]\implies x-7=\pm6[/tex]

Now add 7 to both sides of the equation:

[tex]\implies x-7+7=\pm6+7[/tex]

[tex]\implies x=7\pm6[/tex]

Therefore, the two solutions are:

[tex]\implies x=7+6=13[/tex]

[tex]\implies x=7-6=1[/tex]

The differentiation of the variable y is equal to  [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]  for the differential equation.

Given equation: [tex](x^{2} +y^{2} )^{2} = 2xy^{2}[/tex]

differentiate with respect to x

2 [tex](x^{2} + y^{2})[/tex] [ [tex]2x+2y.\frac{dy}{dx}[/tex] ] =[ (1).[tex]y^{2}[/tex] + [tex]x (2y) + \frac{dy}{dx}[/tex] ]

4 [tex](x^{2} + y^{2})[/tex] [ [tex]x+y \frac{dy}{dx}[/tex] ] = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]

4( [tex]x^{3} + x^{2} y \frac{dy}{dx} + xy^{2} + y^{3} \frac{dy}{dx}[/tex] ) = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]

[tex]4x^{3} +4 x^{2} y \frac{dy}{dx} +4 xy^{2} +4 y^{3} \frac{dy}{dx}[/tex] = [tex]y^{2}[/tex] +  [tex]2xy \frac{dy}{dx}[/tex]

[tex]4x^{2}y \frac{dy}{dx}[/tex] + [tex]4y^{3}[/tex] [tex]\frac{dy}{dx}[/tex] - [tex]2xy\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]

[tex](4x^{2}y + 4y^{3} - 2xy )[/tex]  [tex]\frac{dy}{dx}[/tex] =  [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]

[tex]\frac{dy}{dx}[/tex]  = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex] / [tex](4x^{2}y + 4y^{3} - 2xy )[/tex]

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]

Hence solved. The differentiation for the given differential equation is done using the technique of implicit differentiation. The differentiation of the variable y is equal to  [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]  for the differential equation.

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The total distance that the water tanker has covered in March of 2022 is given as follows:

1860 kilometers.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for this problem are given as follows:

Hence the total distance is then obtained as follows:

d = v x t

d = 60 x 31

d = 1860 kilometers.

The complete question is:

"Assuming that the water tanker travels an average of 60 kilometers a day, calculate the total distance that the water tanker has covered in March 2022​".

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Answer: sorry I can't see it.

Step-by-step explanation:

The graph is increasing from 0 minutes to 40 minutes, decreasing from 40 minutes to 80 minutes, and constant from 80 minutes to 200 minutes.

The rate of global warming is increasing. Every year, average global temperatures continue to rise, leading to more extreme weather events and disruptions to the environment. This has been caused by human activities, such as burning fossil fuels, which release carbon dioxide and other greenhouse gases into the atmosphere. These gases trap heat, leading to a rise in temperatures.

The domain of the relation is the set of all time values, ranging from 0 minutes to 200 minutes. The range of the relation is the set of all depth values, ranging from 0 feet to 8 feet.

The graph represents a function because for every value of time, there is exactly one corresponding value of depth.

The graph shows the depth of water in a horse trough over a certain amount of time. The graph starts at 0 feet and increases to a maximum of 8 feet over the first 40 minutes. After 40 minutes, the depth of the water starts to decrease until it reaches a minimum of 2 feet at 80 minutes. After 80 minutes, the depth of the water remains constant at 2 feet until the end of the graph at 200 minutes.

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Felicia swims 0.43 miles, walks 0.0057 miles and runs 0.57 miles. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," are said to adequately describe all real numbers. The mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.

We are given that she swims 15 laps in a pool where each lap is 50 yards.

By using arithmetic operations, we get

Total yards = 15 * 50 = 750 yard

We know that 1 mile = 1760 yards

So,

750 yards = 0.43 miles

She walks 30 feet.

We know that 1 mile = 5280 feet

So,

30 feet = 0.0057 miles

She runs 5 laps around an indoor track that is 600 feet long.

So, total feet she ran = 5 * 600 = 3000 feet

We know that 1 mile = 5280 feet

So,

3000 feet = 0.57 miles

Hence, she swims 0.43 miles, walks 0.0057 miles and runs 0.57 miles.

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There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Each classroom has 6 rows of 5 desks.

So the total number of desks in one classroom.

= 6 rows x 5 desks per row

= 30 desks

To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.

= 30 desks per classroom x 45 classrooms

= 1,350 desks

Therefore,

There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.

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All the true statements, if each interior angle measure of a regular polygon is (2x + 20)° include the following:

A. If x = 60, then the regular polygon is a nonagon.

C. If x = 77, then the regular polygon is a 60-gon.

D. If x = 65, then the regular polygon is a dodecagon.

D. If x = 44, then the regular polygon is a pentagon.

In Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:

Interior angle = [180 × (n - 2)]/n

Where:

n represents the number of sides of a regular polygon.

When x = 60, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(60) + 20)° = [180 × (n - 2)]/n

140 = [180 × (n - 2)]/n

140n = 180n - 360

360 = 40n

n = 9 sides.

When x = 77, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(77) + 20)° = [180 × (n - 2)]/n

174 = [180 × (n - 2)]/n

174n = 180n - 360

360 = 6n

n = 60 sides.

When x = 65, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(65) + 20)° = [180 × (n - 2)]/n

150 = [180 × (n - 2)]/n

150n = 180n - 360

360 = 30n

n = 12 sides.

When x = 41, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(41) + 20)° = [180 × (n - 2)]/n

102 = [180 × (n - 2)]/n

102n = 180n - 360

360 = 78n

n = 4.6 sides.

When x = 44, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(44) + 20)° = [180 × (n - 2)]/n

108 = [180 × (n - 2)]/n

108n = 180n - 360

360 = 72n

n = 5 sides.

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Answer:

Step-by-step explanation:

Your sister can use the formula for calculating the present value of an annuity to determine how much she can withdraw each year.

The formula for the present value of an annuity is:

PV = Payment x (1 - (1 + r)^-n) / r

Where:

- PV is the present value of the annuity

- Payment is the amount of each withdrawal

- r is the annual interest rate

- n is the number of periods (in this case, 25 years)

We can rearrange this formula to solve for Payment:

Payment = PV x r / (1 - (1 + r)^-n)

We know that your sister has R375 000 to start with, and she wants to end up with zero in 25 years. So, her present value (PV) is R375 000, and we can assume her future value (FV) is zero.

Using the future value formula, we can calculate the interest rate she needs to earn in order to end up with zero in 25 years:

FV = PV x (1 + r)^n

0 = 375000 x (1 + r)^25

(1 + r)^25 = 1

1 + r = (1)^1/25

r = 0

This means that your sister needs to withdraw all of her money over the 25 years in order to end up with zero at the end.

Her withdrawal each year would be:

Payment = PV x r / (1 - (1 + r)^-n)

Payment = 375000 x 0.08 / (1 - (1 + 0.08)^-25)

Payment = R34,028.82 per year

Your sister can withdraw R34,028.82 at the beginning of each year for the next 25 years, and she will end up with zero at the end, assuming she earns an 8% return on her invested funds.

The type of transformation represented in the figure is the translation transformation i.e. (c) none of these

Given the triangles ABC and A'B'C'

The transformation between the triangles is translation

The translation transformation is a type of transformation that moves an object without changing its size, shape, or orientation.

This transformation involves sliding an object in a particular direction by a certain distance, either horizontally or vertically.

In this case, the direction is horizontally and vertically

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