A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.

Which graphical representation would be best for his data?

Stem-and-leaf plot
Histogram
Circle graph
Box plot

Answer: (-15, 20)

Step-by-step explanation:

we can see that the equation is the standard form of a circle:

(X-h)

^2 + (y-k)r^2

Where (h,k) is the center of the circle and r is the radius

H= -15

K= 20

R^2= 100

The exterior angle at K in triangle HJK is 139°, whereas the exterior angle at J is 53°. Shortest side is JK.

We know that the sum of exterior angles of a triangle is 360°. So,

Exterior angle at K + exterior angle at J + exterior angle at H = 360°

139 + 53 + exterior angle at H = 360

exterior angle at H + 192 = 360

exterior angle at H = 360 - 192

exterior angle at H = 168°

Now, we will calculate the interior angles of triangle HJK. We know that exterior and interior angles are supplementary and makes a sum of 180 degree.

Interior angle K + exterior angle K = 180

Interior angle K + 139 = 180

Interior angle K = 180 - 139 = 41°

Interior angle H + exterior angle H = 180

Interior angle H + 168 = 180

Interior angle H = 180 - 168 = 12°

Interior angle J + exterior angle J = 180

Interior angle J + 53 = 180

Interior angle J = 180 - 53 = 127°

A triangle's shortest side is always opposite the smallest angle. So, in this question the smallest angle is ∠H and the side opposite to it is KJ, hence KJ is the shortest side.

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The fuel efficiency of the vehicle with the greatest weight which is around 2375kg on this scatter-plot showing vehicle weights & fuel efficiency is 16 mpg.

The relationships between two variables in a data set are represented by graphs or scatter plots.  It displays data points on a Cartesian system or a two-dimensional plane. The dependent variable is represented or plotted on the Y-axis, while the independent variable or attribute is plotted or represented on the X-axis. The scatter plot's objective is to show what happens to one variable when another variable is modified. A theory that the two variables are connected is tested using the scatter plot.

The scatter plot shows the vehicle weights & fuel efficiency.

Data represented on X-axis(independent variable) : weights of vehicle

Data represented on Y-axis(dependent variable) : fuel efficiency.

Lowest weight of vehicle=1125 kg(approx)

Greatest weight of the vehicle=2375 kg(approx)

Lowest fuel efficiencies of surveyed vehicles=16 mpg.

Greatest fuel efficiency of surveyed vehicles=30 mpg.

∴The fuel efficiency of the heaviest vehicle=16 mpg.

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The total surface area of a gift box is  42.06 square feet

We know that the formula for the surface area of rectangular prism is:

A = 2(lw + wh + lh)

where l is the length

w is the width

and h is the height

The box shaped like a rectangular prism is 3.2 feet long and 2.1 feet wide and 2.7 feet high.

⇒ l = 3.2 ft,

w = 2.1 ft

and h = 2.7 ft

Using above formula the total surface area of the box would be,

A = 2(lw + wh + lh)

A = 2 × [(3.2 × 2.1) + (2.1 × 2.7) + (3.2 × 2.7)]

A = 2 × 21.03

A = 42.06 square feet

Therefore, the required area is  42.06 square feet

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The remainder of the f(x) = 3x³ + 6x² - 3x + 2 and divisor x + 3 applying synthetic division is equal to -16.

Use synthetic division and the remainder theorem to find the remainder of f(x) when divided by x- c,

Set up the synthetic division table with c on the left side, and the coefficients of f(x) on the top row.

Bring down the first coefficient of f(x) into the first box below the horizontal line.

Multiply c by the number in the first box and write the result in the second box.

Add the number in the second box to the coefficient in the second column, and write the result in the third box.

Repeat steps 3 and 4 until you reach the last box. The number in the last box is the remainder.

Check if the remainder is zero. If it is zero, then x -c is a factor of f(x),

and g(x) = (x- c) is a factor of f(x).

Dividend is equal to,

f(x) = 3x³ + 6x² - 3x + 2

Divisor is equal to,

g(x) = x + 3

Synthetic division is attached in the figure.

Expressed in remainder theorem

3x² -3x + 6 + ( -16 / x + 3 )

Therefore, the remainder of the synthetic division for the given dividend and divisor is equal to -16.

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The factor that does not influence the consumer when deciding to buy a product is Time period. The correct option is C

An identifiable length of time such as a day, week, month, or year is referred to as a time period. Given that it can affect consumer behavior market conditions and the efficacy of various plans and tactic time is a crucial factor in many facets of business and marketing.

Therefore, Note that time is not a factor that influences customer behavior when determining whether to purchase a product in the context of the initial query. The factor that does not influence the consumer when deciding to buy a product is Time period

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The values of the exponential function are calculated below and as x increases, the exponential function increases.

In the table of function given, we can calculate the value of f(x) as it relates to x.

The given exponential function is ;

f(x) = 2ˣ

Substituting the values;

f(-4) = 2⁻⁴ = 1/2⁴ = 1/16

f(-3) = 2⁻³ = 1/2³ = 1/8

f(-2) = 2⁻² = 1/2² = 1/4

f(-1) = 2⁻¹ = 1/2

f(0) = 2⁻⁰ = 1/2⁰ = 1

As the value of x increases, the exponential function increases.

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Answer:

An equivalent equation would be 2x = 4.

Step-by-step explanation:

Expanding the brackets and simplifying, we get:

8x + 4 - 3x + 6 = 20

Combining like terms, we get:

5x + 10 = 20

Subtracting 10 from both sides, we get:

5x = 10

Dividing both sides by 5, we get:

x = 2

So an equivalent equation would be 2x = 4.

Answer:

The equivalent equation to 4(2x+1)-3(x-2)=20 is 5x+11=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

The problem shows a 90° angle split by a ray, we know that both angles are equal to 90° because the whole is equal to the sum of its parts therefore adding 6b+7 and 7b-8 gives us 90° which is simplified as

13b°-1°= 90°

add 1  to both sides

13b°-1° + 1° = 90° +1°

13b° = 91°

divide by 13

13b°/13 = 91°/13

b= 7°

The side length of the juice box is given as follows:

5 cm³.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

The total volume of the box in this problem is given as follows:

55 + 40 + 30 = 125 cm³.

Hence the side length of the juice box is given as follows:

a³ = 125

a³ = 5³

a = 5 cm.

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Answer:

y=-0.5x+3

Step-by-step explanation:

The equation of a line is

y=mx+b, with m being the slope, and b being the y-intercept

The slope is -0.5, and the y intercept is 3

so:

y=-0.5x+3

Answer:

y= -1/2x+3

Expiation:

you can find the equation between two points by using the slope formula and the slope intercept form which is y=mx+b.

The total distance that Dr. Price travels during her observations is 2567.1 meters, and the distance between Location D and the point halfway between Locations B and C is 1,317.125 meters.

First, we can look at the distances between each location. The table tells us that the difference between Location A and Location B is 203.15 meters. The difference between Location B and Location C is 1686.55 meters, and the difference between Location C and Location D is 474.25 meters.

To calculate the total distance that Dr. Price travels, we need to add up the distances for each part of her journey. First, she travels from Location A to Location B, a distance of 203.15 meters. Then she returns to Location A, so she travels the same distance back, for a total of 406.3 meters. Next, she descends from Location A to Location C, a distance of 1686.55 meters. Finally, she descends further to Location D, a distance of 474.25 meters. Adding up these distances, we get a total distance of 2567.1 meters.

For the second part of the question, we need to find the distance between Location D and the point halfway between Locations B and C. To do this, we first need to find the depth at the midpoint between Locations B and C. We can do this by taking the average of the depths for Locations B and C, which gives us -1,941.875 meters.

Next, we can calculate the distance between Location D and the midpoint between B and C. This is simply the difference in depth between Location D (-3,259 meters) and the midpoint (-1,941.875 meters), which gives us a distance of 1,317.125 meters.

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Complete Question:

Dr. Price uses a table to organize the types of sea life and the positions relative to sea level of each location. Complete each sentence. The difference between Location A and Location B is meters. The difference between Location B and Location C is meters. The difference between Location C and Location D is meters. After observing Location B, Dr. Price returns to Location A before descending to Location C. What is the total distance she travels? Dr. Price descends to Location D to observe shrimp. She then ascends and stops to observe sea life that is halfway between Location B and Location C. What is the total distance between Location D and where Dr. Price stopped to observe?

Location                         Sea Life               Depth Relative to Sea Level (m)

A                                             Eels                                 -895.9

B                                              Eels                                 -1,098 3/20

C                                           Shrimp                            -2,784.75

D                                          Shrimp                                -3,259

Answer: $31,920.

Step-by-step explanation:

The banker's rule is a method used by lenders to determine the maximum amount of money that a borrower can afford to repay. According to this rule, the maximum amount of money that Lee can afford to borrow is determined by multiplying his annual income by a factor of 0.28.

Using this rule, the amount that Lee can afford to borrow can be calculated as:

Maximum affordable monthly payment = 0.28 x monthly income

Maximum affordable monthly payment = 0.28 x (24700/12)

Maximum affordable monthly payment = 0.28 x 2058.33

Maximum affordable monthly payment = 576.66

Therefore, Lee can afford to make monthly payments of up to $576.66. To calculate the total amount he can borrow, we need to determine the total cost of the loan, including principal and interest.

Assuming a 5-year loan with an interest rate of 4%, the total cost of the loan can be calculated using an online loan calculator or spreadsheet software.

Plugging in the numbers, the total amount that Lee can borrow is approximately $31,920.

It's important to note that this calculation is based on the banker's rule and assumes that Lee has no other debt obligations. Actual loan approval and loan amounts may vary depending on other factors such as credit score, debt-to-income ratio, and other lender-specific requirements.

Step-by-step explanation:

h o g   =   6 ( x^2 + x - 2)   + 1

             = 6x^2 + 6x -12 + 1

             = 6x^2 + 6x -11              put in -7 for 'x'

                  6 (-7^2) + 6 (-7) - 11

               = 241

* * * edited * * *

Corresponding to the data, we can deduce that the stairs can be broken into a series of blockish prisms.

The stairs can be broken into a series of blockish prisms. The confines of each blockish prism would be the same range and height as the stairs, but the length of each blockish prism would be the depth of one step.

To determine the quantum of concrete demanded to form the stairs, you would need to calculate the total volume of all the blockish prisms that make up the stairs. This can be done by multiplying the length, range, and height of each blockish prism and also adding the volumes of all the blockish prisms together.

The formula for calculating the volume of a blockish prism is V = l x w x h, where V is the volume, l is the length, w is the range, and h is the height. So, for illustration, if each stair is 3 bases wide,1.5 bases high, and 1 bottom deep, and there are 10 stairs, also the total volume of concrete demanded would be

V = (3 x 1.5 x 1) x 10 = 45 cubic feet of concrete.

Note that this calculation assumes that there is no space between the stairs or the rectangular prisms making up the stairs. If there is any space between the stairs or the rectangular prisms, this would need to be accounted for in the calculation.

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The expression that is equivalent by the Distributive Property is A 3x+12

this is the only answer that actually uses the distributive property.

The Distributive Property is a mathematical rule that applies to operations such as multiplication and addition or subtraction. It states that when you multiply a number by a sum or difference of two or more numbers, you can distribute the multiplication over each of the individual terms in the sum or difference.

3 can be multiplied by both x and 4 to get 3x+12 (which is using the distributive property)

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To proof that ΔLMQ ≅ ΔNPQ; we use the given statement "∠L is congruent to ∠N"

To complete the proof that ΔLMQ is congruent to ΔNPQ, we have to follow the following steps.

Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.

There are several ways to show that two triangles are congruent, including:

We will apply ASA method to proof that ΔLMQ ≅ ΔNPQ;

∠L is congruent to ∠N

Length LM is congruent to length NP

Looking at the options, only one was stated. (∠L is congruent to ∠N).

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Answer:

15 boxes of eggs × 6 eggs/box =

90 total eggs

3 boxes of eggs × 6 eggs/box = 18 eggs

The ratio of the number of eggs in 3 boxes to the total number of eggs is 18/90 = 1/5.

The possible side lengths of rectangle B are 12 cm and 7 cm, or 9 cm and 5.25 cm, etc.

The side length of rectangle B is calculated as follows;

Side length of rectangle A = 6 cm and 3.5 cm

If the two rectangles are proportional, the possible side lengths of rectangle B is calculated as follows;

Length of B = 2 x 6 cm = 12 cm

Width of B = 2  x 3.5 cm = 7 cm

or

Length of B = 1.5 x 6 cm = 9 cm

Width of B =1.5  x 3.5 cm = 5.25 cm

Thus, the side lengths of rectangle B will be increasing or decreasing at equal proportion.

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They will need an additional 18/11 days to finish the job.

There are two sides to it—a left side and a right side—and an equals sign (=) divides them. The members of the equation are the expressions on either side of the equals sign.

From straightforward arithmetic equations like 2 + 2 = 4 to more intricate equations in algebra and calculus, equations can be used to represent a broad variety of mathematical connections.

By determining the values of the variables that make the equation true, equations are frequently employed to solve issues. This is usually accomplished by manipulating the equation with algebraic operations like addition, subtraction, multiplication, and division on both sides of the equation.

In a variety of disciplines, including physics, chemistry, and engineering, equations can also be used to simulate real-world occurrences. For instance, the equation [tex]d=1/2gt^2[/tex] can be used to represent the motion of an object falling, where d is the distance fallen, g is the acceleration caused by gravity, and t is the amount of time that has passed.

Assume that there are D total papers that need to be translated. Then, we can claim that Ann's daily translation rate is D/10 and that she can translate D documents in 10 days. Ben's daily translation pace is D/12 since he can translate D documents in 12 days.

While Ben is still waiting to start working, Ann begins translating the documents at her daily rate. The total amount of work that Ann has finished is (x/10)D after she has worked for x days. Now that Ben has joined them, they can finish the remaining (1 - x/10)D work jointly at a rate of (D/10 + D/12) papers per day. To find x, we can construct the following equation:

(x/10)D + [(1 - x/10)D]/[(D/10 + D/12)] = D

When we simplify the equation, we obtain:

x/10 + (12 - x)/15 = 1

When both sides are multiplied by the least common multiple of 10 and 15, or 30, we obtain:

3x + 2(12 - x) = 30

Solving for x, we get:

x = 6

So, before Ben starts working, Ann finishes (6/10)D = (3/5)D of the work, and the two of them together finish the remaining (2/5)D of the job at a combined rate of (D/10 + D/12) = (11/60)D per day. Therefore, the total number of days required to accomplish the work is:

(2/5)D / (11/60)D = 24/11 days

Ben and Ann will need to work an extra 24/11 - 6 = 18/11 days to finish the work because Ann has already put in 6 days of effort. As a result, they will need an additional 18/11 days to finish the job.

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A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C. preconditions. These elements help provide a clear understanding of how a system should interact with its users and the expected outcomes.

A document can be defined as a form of information that might be useful to a user or set of users1. It can be either digital or nondigital1. Different methods are used to store digital and non-digital documents

There are different types of documents such as job descriptions2, and project descriptions. and technical descriptions5.

A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C.

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Answer: To expand the expression, we can use the distributive property of multiplication:

(x+3)(x-3)(3x+2)

= (x^2 - 9)(3x+2) // using (a+b)(a-b) = a^2 - b^2

= 3x(x^2) + 2(x^2) - 9(3x) - 18 // using FOIL

= 3x^3 + 2x^2 - 27x - 18

This is the expanded form of the expression.

To simplify further, we can factor out the greatest common factor of the terms:

= 3(x^3 - 9x) + 2(x^2 - 9)

= 3x(x^2 - 9) + 2(x^2 - 9)

= (3x+2)(x^2 - 9)

= (3x+2)(x-3)(x+3)

So, the simplified expression is (3x+2)(x-3)(x+3).

The y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

When the line touches the y-axis, it forms a y-intercept.

Find the y when x = 0 to find these.

When the line touches the x-axis, the position for the y-intercept will look like (0,y).

So, have the given quadratic function:

y = x² + 2x − 8

Now, plot the given quadratic function on the graph:

(Refer to the graph attached below)

As we can see that the y-intercept is -4.

Therefore, the y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

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If a line with slope 4 has one point of intersection with the quadratic function y = x² + 2x − 8, what is the y-intercept of the line?

a. -4

b. 10

c.-10

d. 4

e. -8

First, let's calculate the monthly interest rate (i), which is the APR divided by 12 months:

i = APR / 12 months

i = 5.3% / 12

i = 0.00442 or 0.442%

Next, let's calculate the number of months (n) for the mortgage, which is 15 years multiplied by 12 months:

n = 15 years x 12 months/year

n = 180 months

Now, let's calculate the monthly payment (PMT) using the following formula:

PMT = P * i / [tex](1 - (1 + i)^(-n)[/tex])

where P is the principal amount, i is the monthly interest rate, and n is the number of months.

PMT = $325,000 * 0.00442 / (1 - [tex](1 + 0.00442)^(-180)[/tex]

PMT = $2,613.67 (rounded to the nearest cent)

Now, let's create the amortization table for the first two months:

Month | Payment | Interest | Principal | Remaining Balance

1 | $2,613.67 | $1,431.25 | $1,182.42 | $323,817.58

2 | $2,613.67 | $1,428.60 | $1,185.07 | $322,632.51

For each month, the Payment column shows the fixed monthly payment, the Interest column shows the calculated interest based on the remaining balance multiplied by the monthly interest rate, the Principal column shows the portion of the payment that goes towards reducing the principal, and the Remaining Balance column shows the remaining balance after subtracting the principal payment from the previous remaining balance.

The amortization table will continue in this manner for the remaining months until the mortgage is paid off.

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The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

To complete the two-month amortization table, we need to calculate the monthly payment, as well as the principal and interest amounts for each payment.

The formula for calculating a fixed-rate mortgage payment is:

[tex]Payment = P * r * (1 + r)^n / [(1 + r)^n - 1][/tex]

Where:

P = Principal amount borrowed

r = Monthly interest rate

n = Total number of payments

First, let's calculate the monthly interest rate.

Since the APR is an annual rate, we need to divide it by 12 to get the monthly rate:

Monthly interest rate = 5.3% / 12 = 0.0044167

Next, we need to calculate the total number of payments.

Since this is a 15-year mortgage, and we're completing a two-month amortization table, the total number of payments is:

Total number of payments = 15 years * 12 months per year = 180

Number of payments for two months = 2

Now we can plug these values into the formula to calculate the monthly payment:

Payment = [tex]$325,000 * 0.0044167 * (1 + 0.0044167)^180 / [(1 + 0.0044167)^180 - 1][/tex]

= $2,549.67

So the monthly payment is $2,549.67

Now we can use this value to complete the two-month amortization table:

Payment Interest Principal Balance

Month 1 $1,426.25 $1,123.42 $323,876.58

Month 2 $1,420.47 $1,129.20 $322,747.38

To calculate the interest and principal amounts for each payment, we use the following formulas:

Interest = Balance * Monthly interest rate

Principal = Payment - Interest

Balance = Balance - Principal

We start with the initial balance of $325,000 and apply the formulas for each payment.

The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

And so on, for each subsequent payment.

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The greatest distance, in feet, a person could be from the parking lot light and be detected is 4 ft. So, correct option is B.

The equation (x + 10)^2 + (y−8)^2=16 describes a circle with center (-10,8) and radius 4. The distance from the center of a circle to any point on its circumference is equal to the radius. Therefore, the greatest distance a person could be from the parking lot light and still be detected is equal to the radius of the circle, which is 4 feet.

This means that any point on the circumference of the circle with a distance of 4 feet or less from the center (-10,8) would be within the range of the motion detector.

Option (a) 2 feet is too small and would fall inside the circle, meaning the person would not be detected. Option (c) 9 feet and option (d) 256 feet are too large and fall outside the circle, meaning the person would also not be detected.

Therefore, the correct answer is option (b) 4 feet.

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Therefore, using simple exponential smoothing with a = 0.75, the forecast for water pump sales for February through May are:- February: 26.5 units,  March: 37.63 units, April: 72.66 units.

To use simple exponential smoothing with a = 0.75, we first need to calculate the forecast for January:
F1 = 25 (given)
Next, we calculate the forecast for February using the formula:
F2 = a * Y1 + (1 - a) * F1
F2 = 0.75 * 28 + 0.25 * 25
F2 = 26.5 (rounded to one decimal place)
We repeat this process for each month, using the previous month's forecast and the actual sales data for the current month. The results are as follows:
Month      Actual Sales    Forecast
-------------------------------------
January           28          25
February          72          26.5
March             98          37.63
April            126          72.66
- May: 101.17 units
Hi, I'd be happy to help you with your question. To use simple exponential smoothing with a smoothing constant α = 0.75 to forecast the water pump sales for February through May, given that the forecast for January was 25 units, follow these steps:
Step 1: Start with the given forecast for January, which is 25 units.
Step 2: Calculate the forecast for February using the formula:
Forecast_February = α * (Actual_January) + (1 - α) * Forecast_January
Step 3: Calculate the forecast for March using the formula:
Forecast_March = α * (Actual_February) + (1 - α) * Forecast_February
Step 4: Calculate the forecast for April using the formula:
Forecast_April = α * (Actual_March) + (1 - α) * Forecast_March
Step 5: Calculate the forecast for May using the formula:
Forecast_May = α * (Actual_April) + (1 - α) * Forecast_April
Please note that you have provided sales data for air-conditioning sales, but the question is about water pump sales. If you meant to ask about air-conditioning sales, you can use the given sales data to calculate the forecasts for February through May. If you need help with water pump sales, please provide the correct sales data for January through April, and I will gladly help you with the calculations.

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Answer:

There are 2 answers:

Step-by-step explanation:

110 = c²

√110 = √c²

±10.5 = c

Solve for c:

[tex]110=c^2[/tex]

Take the square root of 110

[tex]10.48\thickapprox10.5[/tex]

[tex]\longrightarrow \boxed{\bold{c=10.5}}[/tex]

[tex]\text{so} \ \boxed{110=\bold{10.5^2}}[/tex]

Answer: C Q

Step-by-step explanation:

You need to Use Q And C In algebra if thats what your going for. Hopefully this help's.