Each year a certain amount of money is deposited in an account which pays an annual interest rate of so that at the end of each year the balance in the account is multiplied by a growth factor of . $500 is deposited at the start of the first year, an additional $200 is deposited at the start of the next year, and $600 at the start of the following year. Write an expression for the value of the account at the end of three years in terms of the growth factor . What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%?

Answer:

Step-by-step explanation:

Answer:

B, C, and D.

Step-by-step explanation:

1. Finding the midpoint of a portion

2. Drawing an opposite line portion from an offered indicate a given fragment

3. Drawing an opposite line portion through a given point on a given section

4. Drawing a line through a given guide parallel toward a given line

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Answer:

x>−42

Step-by-step explanation:

Multiply both sides by 7.

x>−6×7

 Simplify times 6×7  to 42.

x>−42

Answer:

h(t)=-36.25cos(0.2618t)+34.25

Step-by-step explanation:

We can start by drawing a sketch of what the whaterwheel's height over time looks like. (See attached picture.)

We can see on the graph that at t=0, the bucket will be located at its lowest point. So in this case we can make use of a cosine function. Cosine functions look like this:

\(y=Acos(\omega t + \phi)+b\)

where:

A=amplitude

\(\omega\) = angular speed

\(\phi\)=phase shift

b= vertical shift.

So let's find each of the necessary data:

The amplitude is the distance between the highest point of the trajectory and the middle point of the sine wave, so:

\(A=\frac{highest-lowest}{2}\)

\(A=\frac{70.5ft-(-2ft)}{2}\)

A=36.25 ft

since the trajectory starts at its lowest point when t=0 we will make the amplitude a negative amplitude, so:

A=-36.25ft

Next, we can find the angular speed:

\(\omega = \frac{2\pi}{T}\)

Where T is the period (the time it takes the wheel to make one whole turn) so:

\(\omega=\frac{2\pi}{24}\)

\(\omega=0.2618 rad/s\)

the phase shift in this case is zero since the graph starts at the lowest point.

the vertical shift is the distance between the x-axis and the middle point of the graph. So we find the midpoint between the lowest and the highest point of the graph:

\(b=\frac{highest+lowest}{2}\)

\(b=\frac{70.5ft-2ft}{2}\)

b=34.25ft

so we can now input all this data into the formula to get:

\(h(t)=-36.25cos(0.2618 t)+34.25\)

Answer:

(x,y)--(-X, "): A' is at (5, -1)

Step-by-step explanat

Answer:

(x,y)→(−x,−y); A' is at (5, −1)

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

180-75=105

Answer:

5 and then 2:5

Step-by-step explanation:

For every 2 triangles, there are 5 total shapes, therefore the simplified of triangles to total shapes is 2:5

The correct answer is d) To avoid a large number of classes with very small frequencies.

Unequal class intervals are sometimes used in a frequency distribution to avoid a large number of classes with very small frequencies. This can occur when the data range is very large or when there is a lot of variability in the data.

For example, if we have a dataset with values ranging from 0 to 1000, using equal class intervals of size 100 would result in 10 classes. However, if the data is skewed and most of the values fall in the lower range, many of the classes may have very small frequencies. Using unequal class intervals can help group the data in a way that results in more meaningful class frequencies.

Additionally, unequal class intervals can be used to better represent the distribution of the data. For example, if there is a cluster of values around a certain range, using a smaller class interval around that range can provide more detail and information about the data distribution.

Therefore, the correct answer is d) To avoid a large number of classes with very small frequencies.

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Answer:

im passing this concept trust me the anser is airplane B

Step-by-step explanation:

No, the sample mean does not always have to correspond to one of the observations in the sample. The sample mean is calculated by summing up all the observations in the sample and dividing it by the total number of observations. It represents the average value of the sample.

In some cases, the sample mean may coincide with one of the observations if that particular observation holds a significant weight in determining the overall average. However, in most cases, the sample mean will be a value that falls between the individual observations.

For example, consider a sample with the observations: 5, 7, 9, 11, and 13. The sum of these observations is 45, and there are a total of 5 observations. The sample mean in this case is 45/5 = 9. However, none of the observations in the sample is exactly equal to 9.

Therefore, while the sample mean represents the average value of the sample, it does not necessarily correspond to one of the specific observations in the sample. It is a calculated value that provides a summary measure of the central tendency of the sample data.

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Answer:

1. Equation: x/-9=-16

solution: x=144

2. Equation:15*x=-75

solution: x=-5

3.Equation:0.75n=36

solution: n=48

Step-by-step explanation:

Answer:

5.46π cm³

Step-by-step explanation:

Volume of sphere= 4/3πr³

= 4/3×π×(1.6)³ cm³

=5.46π cm³

hope this helped you!

Answer:

Step-by-step explanation:

H = ∠XAP    {alternate interior angles are congruent}

C =∠YBP      {Alternate interior angles are congruent}

∠APB = H + C

          = ∠XAP + ∠YBP

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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The value of the given sine function is √3/2, so the correct option is 2nd.

Given that an function Sin (-5π/3) we need to evaluate the expression,

To evaluate the trigonometric function sine of the angle (-5π/3), we can use the periodicity of the sine function.

Since the sine function has a period of 2, the sine of any given angle is equal to the sine of that angle plus or minus any multiple of 2.

To find an equal angle inside the main range (between -π and π), we can add 2 to the angle (-5/3).

Once adding 2:

(-5π/3) + 2π = (-5π/3) + (6π/3) = π/3

Now we can evaluate the sine of π/3, which is a commonly known angle. The sine of π/3 is √3/2.

Therefore, sin(-5π/3) = sin(π/3) = √3/2.

Hence the correct option is √3/2

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Answer: x = 6

y= 6x2/13 + 5/13

Step-by-step explanation: to solve for and y: Isolate the variable by dividing each side by factors that don't contain the variable

Heidi will have approximately 360 kilometers remaining on her trip when her tank is empty.

This is calculated by dividing the total kilometers to travel, 550, by the miles per gallon, 55. This results in a total of 10 gallons of fuel needed to complete the trip. Subtracting the 6 gallons Heidi has in her tank from the 10 gallons needed leaves 4 gallons that need to be acquired.

Multiply the 4 gallons by the miles per gallon to find the distance travelled in miles, which equals 220 miles. To convert to kilometers, divide 220 miles by 0.62, which is approximately equal to 360 kilometers.

To sum up, Heidi will have 360 kilometers remaining on her trip when her tank is empty. She needs to purchase 4 gallons of gas to complete the trip, and will travel a total of 220 miles. To convert this to kilometers, divide 220 miles by 0.62. This results in an approximate total of 360 kilometers.

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The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Therefore , the solution of the given problem of triangle comes out to be DE = 15, EF = 20, and m∠D = 35, so the solution is A.

A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.

Here,

We must demonstrate that the respective sides and angles of two triangles are proportional in order to establish their similarity.

We are aware of the lengths of two of the sides and one of the angles in the triangular ABC. The third side's length can be determined using the Law of Cosines:

=> BC² = AB² + AC² - 2ABACcos(35°)

=> 9² + 12² - 2912*cos(35°) = BC²

=> BC ≈ 8.455

The edges of triangle ABC are therefore AB = 9, AC = 12, and BC 8.455.

=> A. DE=15, EF=20, and m=35

The angle measurement is 35 degrees, which corresponds to the angle in the triangular ABC. If the ends are proportionate, we can verify this:

=> DE/AB = 15/9 = 1.67

=> EF/AC = 20/12 ≈ 1.67

This collection of measurements meets the requirements for the triangles to be similar because the ratios are equal.

=> DE = 15, EF = 20, and m∠D = 35, so the solution is A.

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Answer: 40 students

Step-by-step explanation: All we need to do is do 16/40 to get 0.4 or 40%. So 100% = 40.

Using Algebraic expression , Tebogo will pay R52 200 after a year if Tebogo pays R4 350 a month for a house that she is ranting.

A combination of variables and constants is an algebraic expression.

A mathematical expression known as an algebraic expression can include exponents, parenthesis, variables, integers, and arithmetic operators (such as addition, subtraction, multiplication, and division).

Tebogo's payment after a year will be determined by multiplying the monthly payment by the 12 months that make up a year.

Amount Tebogo will pay in a year = 12 x R4 350 = R5 2200

Therefore, Tebogo will pay R52 200 after a year if Tebogo pays R4 350 a month for a house that she is ranting.

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To say that two variables are negatively correlatted means that when one variable increases, the other variable decreases.

Negative correlation refers to a relationship between two variables where they tend to move in opposite directions. When one variable increases, the other variable tends to decrease, and vice versa. This negative relationship indicates an inverse association between the two variables.

Option A, "When one variable increases, the other decreases," accurately describes negative correlation. As one variable increases, the other variable decreases, reflecting the negative relationship between them.

Negative correlation does not imply that both variables change at the same rate (Option D). In negative correlation, the relationship is characterized by the opposite direction of change, not necessarily the same magnitude or rate of change.

Option B, "When variable increases, the other also," suggests a positive correlation, where both variables move in the same direction. This is not the case in negative correlation.

Option C, "When one variable decreases, the other also decreases," is a misinterpretation of negative correlation. In negative correlation, when one variable decreases, the other variable tends to increase, not decrease.

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Answer:

OOOOOOOOHHH SHUTE BROTHER SORRY WISHED I COULD HELP but im blonde so sowwy

To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:

New x-coordinate = -2 * old x-coordinate

New y-coordinate = -2 * old y-coordinate

Let's apply these formulas to each point in triangle ABC:

Point A: (-3, 4)

New x-coordinate of A = -2 * (-3) = 6

New y-coordinate of A = -2 * 4 = -8

New coordinates of A: (6, -8)

Point B: (1, 1)

New x-coordinate of B = -2 * 1 = -2

New y-coordinate of B = -2 * 1 = -2

New coordinates of B: (-2, -2)

Point C: (5, -2)

New x-coordinate of C = -2 * 5 = -10

New y-coordinate of C = -2 * (-2) = 4

New coordinates of C: (-10, 4)

Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:

A: (6, -8)

B: (-2, -2)

C: (-10, 4)

Answer:

r= -35

Step-by-step explanation:

First, move the -8 over to the other side by multiplying by -8

r=5×(-8)

r= -35

The numerical value of the substitution effect on the consumption of good x is $36, and the numerical value of the income effect on the consumption of good x is -$54.

To find the numerical values of the substitution effect and the income effect on the consumption of good x, we need to analyze the impact of the price change from $4 to $9 on the consumer's utility and consumption choices.

The substitution effect measures the change in consumption of good x due to the change in its relative price while keeping utility constant. In this case, since the utility function is U(x,y) = 2xy, we can set up the equation U(x,y) = U(x', y') where x' and y' represent the new consumption bundle after the price change. Solving for x' in terms of y', we can find the numerical value of the substitution effect, which is $36.

The income effect measures the change in consumption of good x due to the change in purchasing power caused by the change in price. In this case, since the consumer's income is $144, we can calculate the initial budget constraint equation as 4x + y = 144. After the price change, the new budget constraint equation becomes 9x' + y' = 144. By comparing the solutions for x in the initial and new budget constraint equations, we can find the numerical value of the income effect, which is -$54.

Therefore, the numerical value of the substitution effect is $36, indicating an increase in the consumption of good x due to the relative price change. The numerical value of the income effect is -$54, indicating a decrease in the consumption of good x due to the change in purchasing power caused by the price change.

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The area of the rectangle is equal to 216ft^2.

We have given that,

A flower bed is in the shape of a rectangle.

It measures 7 yards long and 3 yards wide. David wants to use a mulch to cover the flower bed.

The mulch is sold by the square foot.

A yard is equal to 3 feet.

7 yards = 7(3) = 24 feet

3 yards = 3(3) = 9 feet

What is the formula for the area of the rectangle?

Area of the rectangle=  Lw

Area of the rectangle= 24(9)

Area of the rectangle= 216 ft^2

Therefore the area of the rectangle is equal to 216ft^2.

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