Using unit multipliers:
27 cubic feet per minute is equivalent to approximately 57.074 liters per hour.
To convert 27 cubic feet per minute to liters per hour, we can use unit multipliers and conversion factors.
Start with the given value: 27 cubic feet per minute.
Use the conversion factor for volume: 1 cubic foot = 28.3168466 liters. This conversion factor allows us to convert cubic feet to liters.
Set up the first unit multiplier to cancel out the cubic feet:
Multiply by (27 cubic feet / 1) to cancel out the cubic feet unit.
Use the conversion factor for time: 1 minute = 60 minutes. This conversion factor allows us to convert minutes to hours.
Set up the second unit multiplier to convert minutes to hours:
Multiply by (60 minutes / 1 hour) to convert minutes to hours.
Combine the unit multipliers and the conversion factors:
Multiply (27 cubic feet / 1) by (1 cubic foot / 28.3168466 liters) by (60 minutes / 1 hour).
Simplify the expression by canceling out the appropriate units:
The cubic feet units cancel out, and the minutes units cancel out.
Perform the calculation:
(27 / 1) x (1 / 28.3168466) x (60 / 1) = 27 x 60 / 28.3168466 = 57.074 liters per hour.
Therefore, 27 cubic feet per minute is equivalent to approximately 57.074 liters per hour.
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On September 14, Jennifer Rick went to Park Bank to borrow $1,800 at 712% interest. Jennifer plans to repay the loan on January 27. Steven Linden met Jennifer Rick at Park Bank and suggested she consider the loan on exact interest. Calculate the loan for Jennifer under this assumption.
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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Please, help me find the answer
The probability values for the questions posed are :
11/20probability of Public speaking given that student is majoring in Business Administration1/3A.)
Number of students Taking a public speaking class majoring in business administration.
10 + 45 = 55P(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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A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 23 degrees and that the angle of depression to the bottom of the tower is 20 degrees. How tall is the tower?
In feet
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.
TangentThe 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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Sarah Jones earns $540 per week selling life insurance for Farmer’s Insurance plus 6% of sales over $5,750. Sarah’s sales this month (four weeks) are $22,500. How much does Sarah earn this month?
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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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the functions given below.
Match each expression with its simplified form.
arrowRight
arrowRight
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]
What is a function?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.
Solve for x.
x2.5<10
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]
360 = 1/3x + (x-20) + (x-10) + 40
Answer:
x = 150Step-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
-------------------------------
Check
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
a radioactive substance used in nuclear weapons decays at the rate of 3.6% per year. Calculate the half life of the radioactive substance
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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A clock manufacturer’s fixed costs per month are $5000. The unit cost for each clock is $15. Find the number of clocks made during a month in which the total cost was $65,000. Use the formula T = UN + F, where T is the total cost, U is the cost per unit, N is the number of units made, and F is the fixed costs.
Answer:
65000=15×N+5000
65000-5000=15×N
60000=15×N
60000/15=N
N=4000
the scatter plot shows the average heights of children up to age 5.
what is the equation for the trend line (remember you’re looking for the closest answer)
y= ?x+?
using the linear equation above predict the average height for a two year old
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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A local movie theater found that if the price of admission was $14, the attendance was about 1000 customers per day. When the price of admission was dropped to $7,
attendance increased to about 1450 per day. Write a linear equation for the attendance in terms of the price, p. (A mp+b)
The linear equation for the attendance in terms of the price, p. (A = mp+b) is A = -64.29p + 1900.06
How to write linear equation?(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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find the inverse of each function
A
to find inverse, substitute x for y and y for x. then solve for y
Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE CE and BE DE
B
A
M
D
Correct! Assemble the next
statement.
Angles Segments Triangles Statements Reasons
ABCD is a parallelogram
ZABE and ZCDE
are alt. interior angles
ZBCE and ZDAE
are alt. interior angles
Statements
✓1. ABCD is a parallelogram
ZCBE and ZADE
are alt. interior angles
Reasons
1. given
ZBAE and ZDCE
are alt. interior angles
plssss help
From the two column proof below, we have seen AE ≅ CE and BE ≅ DE because of the Parallelogram side theorem
How to solve two column proof problems?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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The price of stock A at 9 a.m. was 12.67. Since then, the price had been increasing at the rate of $
0.06
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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Jolly Goods Limited specialized in hand-made christmas ornaments. these ornaments go through three processes: cutting, assembling and finishing. two days ago, the company received an unexpected order for 2,000 ornaments. both the cutting and assembling depatments have the capacity to fulfill the order and would have to work at 100% capacity to complete it. due to the amount of detailed work required to produce each ornament, the finishing department does not have enough time to meet the deadline. the company as a whole is working at 85% of capacity. as a result, the company is concerned that it will be unable to accept the order.
Jolly Goods Limited may not be able to accept the order for 2,000 ornaments due to the limited capacity of the finishing department. While the cutting and assembling departments have the capacity to fulfill the order by working at 100% capacity, the finishing department cannot complete the required work within the given deadline. The company as a whole is operating at 85% of capacity, which suggests that the finishing department is already working close to its maximum capacity.
Jolly Goods Limited specializes in hand-made Christmas ornaments and has three processes: cutting, assembling, and finishing. The company received an unexpected order for 2,000 ornaments. To determine if the order can be accepted, we need to assess the capacity of each department and their ability to meet the demand.The cutting and assembling departments have the capacity to fulfill the order since they can work at 100% capacity. This means that they have the resources and time required to complete the cutting and assembling processes for 2,000 ornaments.However, the finishing department does not have enough time to meet the deadline. The detailed work involved in the finishing process takes longer than the available time. As a result, the finishing department is operating at a limited capacity and cannot handle the additional workload of the unexpected order.The overall capacity of the company is operating at 85%. This indicates that the company's resources are already allocated to other orders and projects. Working at 100% capacity in the cutting and assembling departments means that there is limited room to accommodate the additional workload in the finishing department.Therefore, based on the limited capacity of the finishing department and the company as a whole, Jolly Goods Limited may not be able to accept the order for 2,000 ornaments.For more such questions on Jolly Goods Limited, click on:
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help i needa graduate
The period of the given trigonometric graph is identified as: ²/₃π
How to find the period of the trigonometric graph?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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I need help , any of u guys have the answer?
Please help!!
The function f(x)=-3cos(2x+pi/4) has…
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!!!
On Tuesday, you have two orders. You may send each order to a separate factory OR both to the same factory. If they are both sent to be fulfilled by a single factory, you must use the total of the two orders to find that factory's cost per unit for production on this day. Remember that the goal is to end the day with the lowest cost per unit to produce the company's products. Order B is 7,000 units, and Order C is 30,000 units. First consider giving the orders to separate factories. Use the values and the following formula to calculate the average weighted cost per unit. Second, consider sending both orders to a single factory that had the lowest cost per unit to produce 37,000 units.
Answer:
49,321
Step-by-step explanation:
there's no explanation just add them
please help me to solve this question
The binary and quinary numbers of P = (10A010)₂ and Q = (1B3)₅, indicates;
5. (a) A = 1
(b) B = 2
(c) P - Q = 100₂
What are binary numbers?Binary numbers are numbers represented using only the digits of 0 and 1.
5. The binary number is P = (10A010)₂
The quinary number is Q = (1B3)₅
(a) The value of A if P = 42₍₁₀₎ is therefore;
42/2 = 21 R 0
21/2 = 10 R 1
10/2 = 5 R 0
5/2 = 2 R 1
2/2 = 1 R 0
1/2 = 0 R 1
42₍₁₀₎ = 101010₂ = (10A010)₂
A = 1
(b) P + Q = 80₍₁₀₎
P = 42₍₁₀₎, therefore;
Q = 80₍₁₀₎ - 42₍₁₀₎ = 38₍₁₀₎
Convert 38₍₁₀₎ to base 5, we get;
38/5 = 7 R 3
7/5 = 1 R 2
1/5 = 0 R 1
42₍₁₀₎ = 123₅ = (1B3)₅
B = 2
(c) P - Q = 42₍₁₀₎ - 38₍₁₀₎ = 4₍₁₀₎
The value of the decimal 4₍₁₀₎ to base 2 can be found as follows;
4/2 = 2 R 0
2/2 = 1 R 0
1/2 = 0 R 1
4₍₁₀₎ = 100₂
P - Q = 100₂
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Oakwood Plowing Company purchased two new plows for the upcoming winter. In 200 days, Oakwood must make a single payment of $20,493 to pay for the plows. As of today, Oakwood has $19,800. Assume the Oakwood puts the money in a bank today, what rate of interest will it need to pay off the plows in 200 days?
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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3x+(8x-16) simplest form
Step-by-step explanation:
3x × 8x- 3x×16
24x -48x
-24x
struggling pls show how you work out
Answer:
[tex]sin^{-1}[/tex] (0.5) = 30°
Step-by-step explanation:
taking the sine if an angle gives a value
doing the reverse ( the inverse ), that is the inverse sine [tex]sin^{-1}[/tex] of the value obtained by sine gives the angle, that is
sin30° = 0.5 , then
[tex]sin^{-1}[/tex] (0.5) = 30°
Find the Measurement of angle 2. URGENT!
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
An angle measures 88 degrees more than the measures of its complementary angle. What is the measure of each angle?
Answer:
45
43
Step-by-step explanation:
88-45
43
88-43
45
the measurements of the angels are 43 and 45
23 This shows a pattern.
ooo oooooo
Which function can be used to determine the number of circles in the nth figure in
the pattern?
A an = 3 + 20-1
B an = 3 + 2n
C an = 3(2)n-1
D an = 3(2)"n
From the question the correct sequence can be obtained as an = 3(2)^n. Option D
What is a sequence?A sequence is a specific type of ordered list where each element is associated with a unique position or index. The elements in a mathematical sequence are typically numbers or mathematical objects that follow a specific pattern or rule. Each element in the sequence is identified by its position, often denoted by a subscript or index.
Testing the sequence;
3(2)^0 = 3
3(2)^1 = 6
3(2)^2 = 12
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The residual plot shows the residuals for the day of the month and the amount in Kali’s checking account. Which statement best assesses the linearity of the relationship between the day of the month and account balance if the scatterplot appears to be reasonably linear?
A) Because the residual plot has an 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.
B) Because the residual plot has an obvious pattern, and the scatterplot appears linear, it is not appropriate to use the line of best fit to predict the account balance based on the day of the month.
C) 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.
D) Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is not appropriate to use the line of best fit to predict the account balance based on the day of the month.
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
Question 8 of 10
Origami is the Japanese art of paper folding. The diagram below represents
an unfolded paper kabuto, a samurai warrior's helmet. From the kabuto below,
which of the following are pairs of congruent angles?
Check all that apply.
W
OA. ZIRF and MRN
B. ZONT and
MTN
C. ZQRT and ZQRU
OD. CRU and ZIRM
The pairs of congruent angles are;
A. IRF and MRN
C. QRT and QRU
D. CRU and IRM
How to explain the anglesTwo 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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(-x+3)
2
What is the domain of the function =
= In
O x<2
O x>2
O x <3
Ox>3
?
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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For a population with a mean of f = 40 and o = 12, find the z-score for each of the following
X values.
X = 45: z =
X = 52: z =
X = 41: z =
X = 30: z =
X = 25: z =
X = 38: z =
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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