Select the correct answer from each drop-down menu.

The total area of the three triangles is
square units.
The area of the figure is
square units.

Sarah earns $6,810 this month.

1. First, let's calculate Sarah's base earnings for the month. She earns $540 per week, so her base earnings for four weeks would be $540 * 4 = $2,160.

2. Next, we need to determine Sarah's commission on sales over $5,750. Her sales for the month are $22,500, and we need to subtract $5,750 from this amount to find the sales that qualify for commission. $22,500 - $5,750 = $16,750.

3. Sarah's commission rate on sales over $5,750 is 6%, so we can calculate her commission earnings by multiplying the sales amount by the commission rate. 6% of $16,750 is (6/100) * $16,750 = $1,005.

4. Finally, we can find Sarah's total earnings for the month by adding her base earnings to her commission earnings. $2,160 (base earnings) + $1,005 (commission earnings) = $3,165.

Therefore, She earns $6,810 this month.

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Step-by-step explanation:

3x × 8x- 3x×16

24x -48x

-24x

Answer:

65000=15×N+5000

65000-5000=15×N

60000=15×N

60000/15=N

N=4000

While this analysis provides a basic understanding of the stock's movement, it should not be regarded as a definitive forecast.

At 9 a.m., the price of stock A stood at $12.67. From that point onwards, the price of the stock has been experiencing a consistent increase of $0.06. This means that for every hour that passes, the price of stock A rises by $0.06.

If we were to track the price of stock A throughout the day, we would observe a gradual ascent in its value. By 10 a.m., the price would reach $12.73, then $12.79 by 11 a.m., and so on.

This pattern continues throughout the day, with the price increasing by $0.06 for each subsequent hour.

If we assume a linear growth pattern, we can calculate the price at any given time after 9 a.m. For instance, after one hour, at 10 a.m., the price would be $12.67 + $0.06 = $12.73. Similarly, after two hours, at 11 a.m., the price would be $12.67 + ($0.06 × 2) = $12.79.

This trend continues, with the price increasing by $0.06 for each hour elapsed. Therefore, at 12 p.m., three hours after the initial price, the price of Stock A would be $12.67 + ($0.06 × 3) = $12.8

It's important to note that this projection assumes a constant rate of increase. However, the actual stock market is subject to various factors that can influence price fluctuations, such as market demand, economic news, and company performance.

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Answer:

  197 ft

Step-by-step explanation:

You want to know the height of a tower if the angle of elevation to its top is 23° and the angle of depression to its base is 20° from a spot 250 ft away horizontally.

The tangent ratio is ...

  Tan = Opposite/Adjacent

In this geometry, the height above the horizontal line of sight is the side of the right triangle that is opposite the angle of elevation. The distance below the line of sight is opposite the angle of depression. The adjacent side is the 250 ft distance between the viewpoint and the tower.

  tower height = Adjacent×Tan(23°) +Adjacent×Tan(20°)

  tower height = (250 ft)(tan(23°) +tan(20°)) ≈ 197 ft

The tower is about 197 feet tall.

<95141404393>

The height of the tower is approximately 95.64 feet.

To find the height of the tower, we can use trigonometry and the concept of similar triangles. Let's denote the height of the tower as h.

From the window, the person observes the tower's top at an angle of elevation of 23 degrees. This forms a right triangle with the height of the tower as the opposite side and the distance from the window to the tower as the adjacent side. Using the tangent function, we have tan(23°) = h/250.

Similarly, the person observes the bottom of the tower at an angle of depression of 20 degrees. This forms another right triangle with the height of the tower as the adjacent side and the distance from the window to the tower as the opposite side. Using the tangent function, we have tan(20°) = h/250.

Solving these two equations simultaneously, we can find the value of h. By rearranging the equations, we have h = 250 * tan(23°) and h = 250 * tan(20°). Evaluating these expressions using a calculator, we find that h is approximately 95.64 feet.

Therefore, the height of the tower is approximately 95.64 feet.

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Oakwood Plowing Company needs to find an investment that offers at least 10.28% annual interest rate to pay for the plows in 200 days.

To calculate the rate of interest required to pay off the plows in 200 days, we need to use the formula for simple interest, which is:

I = P * r * t

Where,

I = Interest

P = Principal or amount borrowed

r = Rate of interest

t = Time

In this case, the principal is $19,800, the time is 200 days, and the total amount to be repaid is $20,493. We can rearrange the formula to solve for the interest rate:

r = (I / P * t)

We know that the interest (I) is the difference between the amount to be repaid and the principal amount, which is $20,493 - $19,800 = $693. So, plugging in the values in the formula, we have:

r = (693 / (19,800 * (200/365)))

Simplifying this formula, we get:

r = 0.1028 or 10.28%

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R s an equivalence relation on the set of integers Z using the properties of reflexivity, symmetry, and transitivity.

To show that the relation R defined on the set of integers Z is an equivalence relation, we need to demonstrate that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer a, a + a = 2a, which is always even. Therefore, aRa holds true for all integers a, showing that R is reflexive.

Symmetry: If aRb holds, then a + b is even. However, the sum of two integers is unaffected by their order. So if a + b is even, b + a will also be even. Hence, if aRb, then bRa, establishing symmetry.

Transitivity: Suppose aRb and bRc, meaning a + b and b + c are both even. In this case, we can express a + c as (a + b) + (b + c) - 2b. Since the sum of two even numbers is even, and 2b is also even, it follows that a + c is even. Therefore, if aRb and bRc, then aRc, demonstrating transitivity.

In conclusion, the relation R satisfies the properties of reflexivity, symmetry, and transitivity, proving that it is an equivalence relation on the set of integers Z.

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The correct statement about rectangles is:

1. All rectangles are parallelograms.

2. Parallelograms have exactly 1 pair of parallel sides.

3. So, all rectangles have exactly 1 pair of parallel sides.

A rectangle is a type of parallelogram that has additional properties. By definition, a rectangle is a quadrilateral with four right angles. This means that opposite sides of a rectangle are parallel. Since all four sides of a rectangle are right angles, it follows that a rectangle has exactly 1 pair of parallel sides.

Option 1 states that only some rectangles are parallelograms, which is incorrect. All rectangles are parallelograms because they have opposite sides that are parallel.

Option 2 states that parallelograms have 2 pairs of parallel sides, which is also incorrect. Parallelograms have exactly 2 pairs of parallel sides, not 4. A rectangle is a special type of parallelogram that has additional properties such as all angles being right angles.

Option 3 states that only some rectangles have 2 pairs of parallel sides, which is incorrect. All rectangles have exactly 1 pair of parallel sides, not 2. Having 2 pairs of parallel sides would make a shape a parallelogram, not a rectangle.

Therefore, the correct statement is that all rectangles are parallelograms and have exactly 1 pair of parallel sides. 1,2,3 are correct.

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The average Height for a two-year-old is 32.67 inches.

A scatter plot is a graph that depicts the connection between two variables. The independent variable is generally plotted on the x-axis, whereas the dependent variable is plotted on the y-axis. The independent variable is used to forecast the dependent variable, and this relationship is reflected in a line on the scatter plot.What is a linear equation?

Linear equations depict straight lines on a graph. They are frequently expressed in the following manner: y = mx + b. The y value is the dependent variable, while the x value is the independent variable. The m value is the slope of the line, or the rate at which the y value changes in relation to the x value. The b value is the y-intercept, or the point where the line intersects the y-axis. Linear equations are frequently used in algebra, geometry, and science to describe the connection between two variables.Let's take a closer look at the given problem and how it can be resolved.The scatter plot demonstrates the average heights of children up to age 5. We must utilize the linear equation y = mx + b to predict the average height for a two-year-old. If we can establish the slope and y-intercept of the line, we can calculate any value on the line.Let's begin with the y-intercept. If we look at the graph, we can see that the line passes through the y-axis at around 28.

Therefore, b = 28.We can now calculate the slope. Let's examine two points on the line to accomplish this. For example, we could utilize the points (2, 33) and (5, 40).m = (y2 - y1) / (x2 - x1)m = (40 - 33) / (5 - 2)m = 7/3Therefore, the equation for the line is:y = (7/3)x + 28Now that we have the equation for the line, we can forecast the average height for a two-year-old.x = 2y = (7/3)(2) + 28y = 32.67

Therefore, we can predict that the average height for a two-year-old is 32.67 inches.

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Answer:

Step-by-step explanation:

360 = 1/3x + (x-20) + (x-10) + 40

360 = 1/3x + x - 20 + x - 10 + 40

360 + 20 + 10 - 40 = 1/3x + 2x

350 = 1/3x + 2x

350 = 7/3x

x = [tex]\frac{-(350)}{-7/3}[/tex]

x = [tex]-\frac{(150)}{(-1)}[/tex]

x = 150

-------------------------------

360 = 1/3 × 150 + 150 - 20 + 150 - 10 + 40

360 = 50 + 150 - 20 + 140 + 40

360 = 200 - 20 + 180

360 = 180 + 180

360 = 360

same value the answer is good

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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The domain of the function f(x) = (-x + 3)^2 is x ≤ 3, indicating that the function is defined for all real numbers less than or equal to 3. No Option is correct.

To determine the domain of the given function f(x) = (-x + 3)^2, we need to identify the values of x for which the function is defined.

In this case, the function is defined for all real numbers, except for any values of x that would result in an undefined operation or create a complex number.

The function involves squaring the expression (-x + 3), which means the expression inside the square root must be non-negative to avoid complex numbers. Thus, (-x + 3) must be greater than or equal to 0.

Solving the inequality (-x + 3) ≥ 0, we can find the range of x values that satisfy this condition.

Adding x to both sides of the inequality, we have 3 ≥ x.

This inequality implies that x must be less than or equal to 3. No Option is correct.

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The best assessment of the linearity of the relationship between the day of the month and account balance would be "Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month."The correct answer is option C.

When assessing linearity, it is important to examine both the scatterplot and the residual plot. The scatterplot is used to visualize the relationship between the variables, while the residual plot helps us assess the appropriateness of a linear model by examining the pattern of the residuals (the differences between observed and predicted values).

If the scatterplot appears reasonably linear, it suggests that there is a linear relationship between the variables. In this case, since the scatterplot appears linear, it supports the use of a linear model to predict the account balance based on the day of the month.

Furthermore, the residual plot is used to check for any patterns or systematic deviations from the line of best fit. If the residual plot exhibits no obvious pattern and the residuals appear randomly distributed around zero, it indicates that the linear model captures the relationship adequately.

Therefore, if the residual plot shows no obvious pattern, it provides further evidence in favor of using the line of best fit to predict the account balance based on the day of the month.

In conclusion, when the scatterplot appears linear and the residual plot shows no obvious pattern, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.

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Answer:

person above

Step-by-step explanation:

the obvious

The linear equation for the attendance in terms of the price, p. (A = mp+b) is A = -64.29p + 1900.06

(x1, y1) = (14, 1000)

(x2, y2) = (7, 1450)

find the slope m

m = y2 - y1 / x2 - x1

= (1450 - 1000) / (7 - 14)

= 450/-7

m = -64.29

using one of the points

A = mp + b

1000 = -64.29(14) + b

1000 = -900.06 + b

1000 + 900.06 = b

1900.06 = b

A = -64.29p + 1900.06

Hence, A = -64.29p + 1900.06 is the linear equation which represents the attendance in terms of the price, p.

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Answer:

There are 14 blue marbles in the bag.

Step-by-step explanation:

Let's call the number of green marbles "x". Then we know that the number of red marbles is 112 more than x, or x+112. We can use the ratio to find the number of blue marbles.

First, we need to find the total number of parts in the ratio. That's 12+5+2=19.

Next, we can use the ratio to set up an equation. The number of blue marbles is 2/19 of the total number of marbles. We can write this as:

2/19 (x + x + 112 + blue) = blue

Simplifying this equation, we get:

2x + 224 = 17blue

Now we can solve for blue:

blue = (2x + 224)/17

We know that blue is a whole number, so we need to find a value of x that makes the numerator of this fraction divisible by 17. After some trial and error, we find that x=3 works:

blue = (2(3) + 224)/17 = 14

Therefore, there are 14 blue marbles in the bag.

The new loan amount under the assumption of exact interest is $1,846.53.Given that Jennifer Rick borrowed $1,800 at 712% interest on September 14 and planned to repay the loan on January 27.

To calculate the loan for Jennifer under the assumption of exact interest, follow the steps provided below:Step 1: Find the number of days from September 14 to January 27. There are 135 days in between these dates.Step 2: Find the exact interest to be paid by using the following formula:

Exact Interest = (Principal × Rate × Time) / (365 or 366)Exact Interest = (1,800 × 7.12% × 135) / 365 = $46.53Step 3: Find the new loan amount by adding the exact interest to the original amount.

New Loan Amount = Principal + Exact Interest = 1,800 + 46.53 = $1,846.53.Therefore, the new loan amount under the assumption of exact interest is $1,846.53.

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The period of the given trigonometric graph is identified as: ²/₃π

The period of a trigonometric function is defined as the time it takes to complete one complete cycle. For y = sinx and y = cosx , you can measure the duration between consecutive maxima or minima, or other repeated points in the figure that have the same function values ​​and properties.

Now, looking at the given trigonometric graph, it is very clear that the amplitude is 1 while the period is ²/₃π

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A

to find inverse, substitute x for y and y for x. then solve for y

Answer:23

Step-by-step explanation:

The measure of the top angle is 180 - 95 = 85 degrees

All angles of the inside of a triangle should equal 180 degrees

180 - 85 - 72 = 23 degrees

The half-life of the radioactive substance is approximately 18.81 years. This means that it takes around 18.81 years for half of the substance to decay.

To calculate the half-life of a radioactive substance, we need to determine the time it takes for half of the substance to decay.

In this case, we know that the substance decays at a rate of 3.6% per year.

Let's assume we start with a certain amount of the substance.

After one year, 3.6% of the substance will decay, leaving us with 96.4% of the original amount.

If we continue this process, we can calculate the remaining amount of the substance after each year:

Year 1: 96.4% remains

Year 2: 96.4% of 96.4% remains = 96.4% [tex]\times[/tex] 96.4%

Year 3: 96.4% of 96.4% of 96.4% remains = 96.4% [tex]\times[/tex] 96.4% [tex]\times[/tex] 96.4%

...

Year n: [tex](96.4)^n[/tex]% remains

To find the half-life, we need to solve the equation [tex](96.4)^n[/tex]%

Let's solve this equation:

[tex](96.4)^n[/tex] = 50%

Taking the logarithm of both sides:

[tex]log((96.4)^n) = log(50)[/tex]

n [tex]\times[/tex] log(96.4%) = log(50%)

n = log(50%) / log(96.4%)

Using a calculator, we can evaluate the right-hand side of the equation:

n ≈ -0.301 / -0.016

Simplifying the division, we get:

n ≈ 18.81.

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Answer:

45

43

Step-by-step explanation:

88-45

43

88-43

45

the measurements of the angels are 43 and 45

From the two column proof below, we have seen AE ≅ CE and BE ≅ DE because of the Parallelogram side theorem

The two column proof to show that AE ≅ CE and BE ≅ DE is as follows;

Statement 1: ABCD is a parallelogram

Reason 1: Given

Statement 2: <ABE and <CDE are alternate interior angles.

Reason 2: Definition of alternate Interior angles

Statement 3: <ABE and <DCE are alternate interior angles.

Reason 3: Definition of alternate Interior angles

Statement 4; AE ≅ CE and BE ≅ DE

Reason 4: Parallelogram side theorem

Thus, that is the two column proof showing us the congruent sides of the parallelogram.

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Answer:

49,321

Step-by-step explanation:

there's no explanation just add them

Answer:

x < 4

Step-by-step explanation:

The inequality:

[tex]x2.5 < 10[/tex]

Divide each side by 2.5 to isolate x (make x alone):

[tex]\frac{x2.5}{2.5} < \frac{10}{2.5} \\x < 4[/tex]

The pairs of congruent angles are;

A. IRF and MRN

C. QRT and QRU

D. CRU and IRM

Two angles are said to be congruent when they are of equal measurement and can be placed on each other without any gaps or overlaps. The congruent angles symbol is ≅.

Angles IRF and MRN are congruent because they are vertically opposite angles. Angles QRT and QRU are congruent because they are alternate interior angles. Angles CRU and IRM are not congruent because they are not related by any congruence property.

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The z-scores for the given X values are approximately:

X = 45: z ≈ 0.4167

X = 52: z = 1

X = 41: z ≈ 0.0833

X = 30: z ≈ -0.8333

X = 25: z ≈ -1.25

X = 38: z ≈ -0.1667

To find the z-score for each X value given a population with a mean (μ) of 40 and a standard deviation (σ) of 12, we can use the formula:

z = (X - μ) / σ

where X is the given value, μ is the population mean, and σ is the population standard deviation.

Let's calculate the z-scores for each X value:

X = 45:

z = (45 - 40) / 12 = 5 / 12 ≈ 0.4167

X = 52:

z = (52 - 40) / 12 = 12 / 12 = 1

X = 41:

z = (41 - 40) / 12 = 1 / 12 ≈ 0.0833

X = 30:

z = (30 - 40) / 12 = -10 / 12 ≈ -0.8333

X = 25:

z = (25 - 40) / 12 = -15 / 12 ≈ -1.25

X = 38:

z = (38 - 40) / 12 = -2 / 12 ≈ -0.1667

Therefore, the z-scores for the given X values are approximately:

X = 45: z ≈ 0.4167

X = 52: z = 1

X = 41: z ≈ 0.0833

X = 30: z ≈ -0.8333

X = 25: z ≈ -1.25

X = 38: z ≈ -0.1667

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The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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Answer:

A

Step-by-step explanation:

According to the graph attached to this answer, the amplitude is 3 and the period is 8π/8, or just π. This means that A is the correct answer.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Each expression should be matched with its simplified form as follows;

P(x) · Q(x)  ⇒  [tex]\frac{12}{(3x - 1)(-3x+2)}[/tex]

P(x) ÷ Q(x)  ⇒  [tex]\frac{-3x+2}{3(3x - 1)}[/tex]

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the corresponding composite function of P(x) and Q(x) under the given mathematical operations (multiplication and division) in simplified form as follows;

P(x) · Q(x) = [tex]\frac{2}{3x - 1} \cdot \frac{6}{-3x+2}[/tex]

P(x) · Q(x) = [tex]\frac{2}{3x - 1} \times \frac{6}{-3x+2}[/tex]

P(x) · Q(x) = [tex]\frac{12}{(3x - 1)(-3x+2)}[/tex]

P(x) ÷ Q(x) = [tex]\frac{2}{3x - 1} \div \frac{6}{-3x+2}[/tex]

P(x) ÷ Q(x) = [tex]\frac{2}{3x - 1} \times \frac{-3x+2}{6}[/tex]

P(x) ÷ Q(x) = [tex]\frac{2(-3x+2)}{6(3x - 1)}[/tex]

P(x) ÷ Q(x) = [tex]\frac{-3x+2}{3(3x - 1)}[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.