The original height of the candle was approximately 26 inches. Rounded to the nearest inch, it will be 27 inches.
Formula for the surface area of a cylinder:
S = 2πrh + 2πr^2
where S is the surface area, r is the radius, and h is the height.
The radius is 2 inches and that the surface area after burning half the candle is 176 square inches. Substitute this values in the equation for surface area:
176 = 2π(2)(h/2) + 2π(2)^2
Simplifying:
176 = 2πh + 8π
168 = 2πh
h = 168/(2π)
h ≈ 26.75
So the original height of the candle was approximately 26 inches. Rounded to the nearest inch, the original height is 27 inches.
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(4, 6) on a coordinate plane
Answer:
(4,6) on the coordinate plane is the 1st quadrant. You start at the origin, go 4 to the right and 6 up.
Hope this helped !!
PLEASE HELP WILL MARK BRANLIEST!!!
The child can make 120 different bracelets using one of each charm. To solve this problem, we need to use a combinatorial approach.
The number of different bracelets that the child can make depends on the number of charms that can be used for each bracelet & the order in which they are arranged. Since each charm can be used only once, we have to choose five charms out of the total of five available charms, which can be done in 5C5 ways.
We can think of this problem as a permutation problem. There are five distinct charms, and we need to choose five of them to make a bracelet. The order in which we choose the charms matters, as each order gives us a different bracelet. Therefore, we need to use the formula for permutations.
The formula for permutations is given by:
nPr = n! / (n-r)!
where n is the total number of objects, and r is the number of objects we want to choose.
For this problem, n = 5 (since there are five distinct charms), and r = 5 (since we want to choose all five charms).
Plugging these values into the formula, we get:
5P5 = 5! / (5-5)! = 5! / 0! = 5 x 4 x 3 x 2 x 1 / 1 = 120
Therefore, the child can make 120 different bracelets.
Alternatively, we can also think of this problem as a multiplication principle problem. There are five distinct charms, & we need to choose one charm out of five for the first position, one charm out of four for the second position, one charm out of three for the third position, one charm out of two for the fourth position, & one charm out of one for the fifth position.
Using the multiplication principle, we can multiply these numbers together to get the total number of different bracelets:
5 x 4 x 3 x 2 x 1 = 120
Therefore, the child can make 120 different bracelets using one of each charm.
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Anyone who knows how to do this please help answer!! Fill in the correct numbers in both sides of the chart and answer the bottom questions.
WILL MARK BRAINLIEST!!!
a) Here is the chart showing the number of bacteria after 0 to 4 hours:
| Time (hours) | Number of bacteria |
|--------------|--------------------|
| 0 | 50 |
| 1 | 150 |
| 2 | 450 |
| 3 | 1,350 |
| 4 | 4,050 |
b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:
Number of bacteria = Initial number of bacteria x Growth factor^nIn this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:
Number of bacteria = 50 x 3^nc) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:
Number of bacteria = 50 x 3^12= 26572050
Therefore, there are approximately 2.7 billion bacteria present after 12 hours.Sylvia Baxterâs Cape Cod home has an assessed value of $64,000 and her land has an assessed value of $4,800. If the rate of assessment in her municipality is 35 percent, what is the market value of her property?
a
$196,571. 43
b
$44,720. 00
c
$68,800. 00
d
$113,520. 00
The market value of Sylvia Baxter's property are $68,800.00. The correct answer is (c)
To find the market value of Sylvia Baxter's property, we need to divide the assessed value by the assessment rate and then multiply by 100.
Assessed value of the home = $64,000
Assessed value of the land = $4,800
Assessment rate = 35% = 0.35 (as given in the problem)
So, the total assessed value of the property = $64,000 + $4,800 = $68,800
Now, to find the market value, we need to divide the assessed value by the assessment rate and multiply by 100:
Market value = (Assessed value / Assessment rate) x 100
Market value = ($68,800 / 0.35) x 100 = $196,571.43 (rounded to the nearest cent)
Therefore, the market value of her property is $68,800.00.
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A famer planted 154 tomato plants. 46 of the plants died. He replanted the plants in rows, with each row containing 9 plants. Which equation can be used to find p the number of rows the farmer planted
The equation we can use to find the number of rows the farmer planted is 108 = 9p.
To find the remaining number of plants, we subtract 46 from 154:
154 - 46 = 108 tomato plants
Now, the farmer replants the remaining plants in rows with 9 plants in each row. To find the number of rows (p), we can use the following equation:
108 = 9p
This equation represents the total number of remaining tomato plants (108) being divided into rows with 9 plants each, resulting in the number of rows (p).
Simplifying this equation will give us the value of p, which is:
p = 12
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Henry's candy jar has the following pleces of candy in it:
3 Snickers
1 Reese's
1 Twix
2 Milky Ways
2 Skittles Packs
Henry will randomly choose one piece of candy,
He will then put it back and randomly choose another piece
of candy. What is the probability that he will
choose a Milky Way and then a Snickers?
The probability of Henry choosing a Milky Way and then a Snickers is 2/27.
1. First, let's find the total number of candy pieces in Henry's candy jar:
3 Snickers + 1 Reese's + 1 Twix + 2 Milky Ways + 2 Skittles Packs = 9 pieces of candy.
2. Next, we'll calculate the probability of choosing a Milky Way on the first pick:
There are 2 Milky Ways and 9 total pieces of candy, so the probability is 2/9.
3. Since Henry puts the candy back, there are still 9 pieces of candy for the second pick. Now, we'll calculate the probability of choosing a Snickers on the second pick:
There are 3 Snickers and 9 total pieces of candy, so the probability is 3/9 (or 1/3).
4. Finally, we'll multiply the probabilities of each individual event to find the probability of both events occurring together (choosing a Milky Way and then a Snickers):
(2/9) * (1/3) = 2/27
So, the probability of Henry choosing a Milky Way and then a Snickers is 2/27.
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Question 10 Multiple Choice Worth 4 points)
(Diversifying Portfolios MC)
Name of Stock Symbol High Low Close
Stock A
105.19 103.25 103.38
Stock B
145.18 143.28 144.05
A
B
Last year, an investor purchased 115 shares of stock A at $90 per share and 30 shares of stock B at $145 per share. What is the difference in overall loss or gain between selling
at the current day's high price or low price?
The difference in overall gain is $208.10.
The difference in overall loss is $208.10.
The difference in overall gain is $280.10.
P
The difference in overall loss is $280.10.
The difference in overall gain is $280.10. OPtion C
How to solveWe have to first find the gains for Stock A and Stock B at high and low prices:
Stock A:
High price gain: 115 * ($105.19 - $90) = $1,747.85
Low price gain: 115 * ($103.25 - $90) = $1,523.75
Stock B:
High price gain: 30 * ($145.18 - $145) = $5.40
Low price gain: 30 * ($143.28 - $145) = -$51.60
Calculate total gains:
High price total gain: $1,747.85 + $5.40 = $1,753.25
Low price total gain: $1,523.75 + (-$51.60) = $1,472.15
Difference in overall gain: $1,753.25 - $1,472.15 = $280.10
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To meet the company’s sales goals, the sales director for the pet food company decided to provide training for some of the sales representatives in the Midwest and Northeast regions. After conducting a one-month training program, the sales director analyzed the effectiveness of the program by conducting a statistical study.
Question 1
The purpose of the sales director’s study is to determine whether attending the training program caused an increase in sales for representatives from the two regions. So the sales director collected sales data from both groups (those receiving training and those receiving no training) for three months after the one-month program and compared the number of orders secured by those who attended the training program with the number of orders secured by those who didn’t attend.
Part A
Question
Select the correct answer from each drop-down menu.
The sales director conducted _______ because a treatment _____ applied to the sales representatives. This is the best statistical study for this situation because the sales director is trying to establish _______.
1. ) An experiment
An observational
A survey
2. ) was
was not
3. ) causality
correlation
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The edge of a cube-shaped box is 1 yard long. Three students each made an observation about the box. • Janae said that the area of each face of the box is 9 square feet. • Archie said that the perimeter of each face of the box is 3 feet. • Gail said that the volume of the box is 1 cubic yard. Whose observations about the box are correct?
Gail's observations about the box is correct. According to the question the edge of a cube-shaped box is 1 yard.
Now convert the edge length to feet as : 1 yard = 3 feet.
On checking the observations:
1. According to Janae the area of each face is 9 square feet. Calculating the surface area of one face of the cube is given by:
Area = (edge length)² = (3 feet)² = 9 square feet.
Now, Total surface area = 6*9square feet= 54 square feet.
Hence Observations of Janae is not correct.
2. According to Archie perimeter of each face of the box is 3 feet. Calculating the perimeter of each face of the cube is given by:
Perimeter= 4 × (edge length)=4×1 yard= 4×3feet=12 feet
Hence Archie observation is not correct also.
3. According to Gail the volume of the box is 1 cubic yard.
The volume of a cube is given by:
volume= (edge length)³ = (1 yard)³ = 1 cubic yard.
Therefore Gail's observation is correct.
From all the above observations it can be concluded that only Gail's observation is correct.
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A cylinder has a height of 4 in and a base circumference of 12. What is the approximate volume of the cylinder? Round to the nearest whole number.
Answer: 48 inches
Step-by-step explanation:
The measurements for a television are 120 cm
wide, 68 cm high, and 14 cm deep. What is the
total surface area of the television?
The total surface area of the television is 21,584 square centimeters.
To find the total surface area of the television, we need to calculate the area of all six sides and add them up.
The front and back sides have the same dimensions and area, so we can find the area of one and multiply it by two. The same goes for the left and right sides.
The area of the front/back sides is:
120 cm x 68 cm = 8160 sq cm
Multiplying by 2 gives us the total area of both front/back sides:
2 x 8160 sq cm = 16,320 sq cm
The area of the left/right sides is:
68 cm x 14 cm = 952 sq cm
Multiplying by 2 gives us the total area of both left/right sides:
2 x 952 sq cm = 1904 sq cm
The area of the top and bottom sides is:
120 cm x 14 cm = 1680 sq cm
Multiplying by 2 gives us the total area of both top/bottom sides:
2 x 1680 sq cm = 3360 sq cm
Adding up all six sides, we get:
16,320 sq cm + 1904 sq cm + 3360 sq cm = 21,584 sq cm
Therefore, the total surface area of the television is 21,584 square centimeters.
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Find the value of x
Hellpppp
Answer:
r = 14.60
Step-by-step explanation:
r²= 9²+(23/2)²
= 9²+11.5²
= 81+132.25
r² = 213.25
r = √213.25
= 14.60 to 2d.p
An administrator of a large middle school is installing some vending machines in the school. She wants to know what type of machine would be most popular.
Conducting a survey among the students would be the best way to determine the most popular type of vending machine.
In order to accurately determine the most popular type of vending machine, it is important to gather data from the intended audience - the students. By conducting a survey, the administrator can gather information on the types of snacks and drinks that the students prefer, as well as their pricing preferences.
This will allow the administrator to make an informed decision on which type of vending machine will be most popular and profitable for the school.
Additionally, by involving the students in the decision-making process, they may feel more invested in the vending machines and be more likely to use them, ultimately leading to a successful vending program.
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The end of a car tunnel has the shape
of a semi-circle on top of a rectangle.
The tunnel is exactly 4 km long.
a) Calculate the volume of air in the
tunnel with no cars in it.
b) The air in a car tunnel must be
exchanged frequently. If the exhaust
system pumps the air out at a rate of
10 m3
per second, how long does it
take to replace the stale air with fresh
air in the entire tunnel? Give your
answer in hours and minutes.
Answer:
a) 149,270 m³
b) 4 hours 9 minutes
Step-by-step explanation:
You want to know the volume of air in a 4 km tunnel 8 m high and 5 m wide with a semicircular cross section at the top. And you want to know the replacement time for that air if it is exchanged at 10 m³ per second.
AreaThe area of the semicircular top of the tunnel is ...
A = π/8d²
A = π/8·(5 m)² = 25π/8 m²
The area of the rectangular bottom of the tunnel is ...
A = LW
A = (5 m)(8 -2.5 m) = 27.5 m²
So the total cross sectional area of the tunnels is ...
(25π/8 +27.5) m² ≈ 37.317477 m²
a) VolumeThe volume of the tunnel is ...
V = Bh
V = (37.317477 m²)(4000 m) ≈ 149269.9 m³
The volume of the air in the tunnel is about 149269.9 m³.
b) Exchange timeAt 10 m³ per second, the air will be replaced after ...
(149269.9 m³)/(10 m³/s) = 14926.99 s ≈ 4 hours 9 minutes
The given pump takes 4 hours 9 minutes to replace the air in the entire tunnel.
__
Additional comment
This tunnel would not meet any standard of safety.
A typical building is supposed to have about 5 air exchanges per hour. That's about 21 times the rate given here. Some tunnel structures need to have the air exchanged once per minute. (Here, that would mean the wind in the tunnel is 149 mph.)
The breathing requirements of the tunnel occupants need to be considered, as well as removal of air pollutants.
There are 3600 seconds in 1 hour.
<95141404393>
What is the actual perimeter of the kitchen? (ft^2)
Explain
The actual perimeter of the kitchen is 8 inch
How to find the perimeterTo find the perimeter, we have to get the length of all of the sides of the kitchen
The kitchen is a rectangle
perimeter of rectangle = 2(l + b)
= 2 (2 1/4 + 1 3/4)
2(9/4 + 7/4)
2 * 4
= 8
The perimeter of the kitchen is 4 inch
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1. If RZ = 2x + 5 and TW = 5x - 20, find the value of 'x'. (just write the number no
text) *
The value of the x is 8.33 under the given condition that RZ is given as 2x + 5 and TW is given as 5x - 20.
From the given question and illustrative diagram we can clearly see that
RZ = 2x + 5
TW = 5x - 20
Now, we have to find the value of 'x' if RZ = 2x + 5 and TW = 5x - 20.
Then, from the given rectangle figure, we can say that RZ is equal to TW.
Hence equating both the equation we can evaluate that the value of x and the equation can be expressed in the forms of
RZ = TW
2x + 5 = 5x - 20
20 + 5 = 5x - 2x
25 = 3x
x = 25/3
x = 8.33
Then, the value of the x is 8.33.
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As a volunteer at the animal shelter, uma weighed all the puppies. she made a list of the weights as she weighed them. the puppies weights were 3 3/4 lb, 4 1/4 lb, 3 1/2 lb, 3 3/4 lb, 3 1/4 lb, 3 3/4 lb, 3 1/2 lb, 4 1/4 lb, and 3 3/4 lb. draw a line plot of the puppies weights. use the line plot to write and answer a question about the data
Using this line plot, we can answer questions such as:
What is the most common weight for the puppies?
The most common weight is 3 3/4 lb, which occurs 3 times.
What is the range of weights for the puppies?
The range of weights is from 3 1/4 lb to 4 1/4 lb.
How many puppies weigh less than 4 lb?
Four puppies weigh less than 4 lb.
How many puppies weigh exactly 3 1/2 lb?
Two puppies weigh exactly 3 1/2 lb.
What is the frequency?
The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.
The line plot of the puppies' weights is in the attached image.
Each "*" represents a puppy's weight.
The horizontal axis represents the weight values, and the vertical axis represents the frequency of each weight.
Hence, Using this line plot, we can answer questions such as:
What is the most common weight for the puppies?
The most common weight is 3 3/4 lb, which occurs 3 times.
What is the range of weights for the puppies?
The range of weights is from 3 1/4 lb to 4 1/4 lb.
How many puppies weigh less than 4 lb?
Four puppies weigh less than 4 lb.
How many puppies weigh exactly 3 1/2 lb?
Two puppies weigh exactly 3 1/2 lb.
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Given n with chord AB, which point lies on the perpendicular bisector of AB?
The Midpoint of AB ((x1 + x2)/2, (y1 + y2)/2) lies on the perpendicular bisector of AB.
Which point lies on the perpendicular bisector of AB?Assuming that chord AB is a straight line segment, the point that lies on the perpendicular bisector of AB is the midpoint of AB. This is because the perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to it.
Therefore, to find the point that lies on the perpendicular bisector of chord AB, we need to find the midpoint of AB. This can be done by finding the average of the x-coordinates and the average of the y-coordinates of points A and B, respectively.
Let (x1, y1) and (x2, y2) be the coordinates of points A and B, respectively. Then the midpoint of AB is:
((x1 + x2)/2, (y1 + y2)/2)
This point lies on the perpendicular bisector of AB.
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PLS HELP ️️ “The area of the circle is 7 square units.”
“Drag the black point to create a sector with an area of 2 square units.”
In order to create a sector with an area of 2 square units, we need to draw a central angle of approximately 24.4 degrees and a radius of approximately 1.49 units.
How to create the sectorIn order to create a sector with an area of 2 square units, we need to find the radius of the circle and then calculate the central angle that corresponds to an area of 2 square units.
Let's start by using the formula for the area of a circle, which is:
A = πr²
We know that the area of the circle is 7 square units, so we can write:
7 = πr²
Solving for r, we get:
r = √(7/π)
r ≈ 1.49
Now, we can use the formula for the area of a sector, which is:
A = (θ/360)πr²
where θ is the central angle in degrees.
To find the central angle that corresponds to an area of 2 square units, we can write:
2 = (θ/360)π(1.49)²
Solving for θ, we get:
θ ≈ 24.4 degrees
So, to create a sector with an area of 2 square units, we need to draw a central angle of approximately 24.4 degrees and a radius of approximately 1.49 units.
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PLEASE HELP!!!!!!!! The graph shows two lines, A and B. A coordinate plane is shown. Two lines are graphed. Line A has the equation y equals x minus 1. Line B has equation y equals negative 3 x plus 7. Based on the graph, which statement is correct about the solution to the system of equations for lines A and B? (4 points) Question 4 options: 1) (1, 2) is the solution to both lines A and B. 2) (−1, 0) is the solution to line A but not to line B. 3) (3, −2) is the solution to line A but not to line B. 4) (2, 1) is the solution to both lines A and B.
The correct statement regarding the solution to the system of equations is given as follows:
4) (2, 1) is the solution to both lines A and B.
How to solve the system of equations?The system of equations in the context of this problem is defined as follows:
y = x - 1.y = -3x + 7.Replacing the second equation into the first, the value of x is obtained as follows:
-3x + 7 = x - 1
4x = 8
x = 2.
Hence the value of y is given as follows:
y = 2 - 1
y = 1.
Meaning that point (2,1) is a solution to both lines.
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The coach of the soccer team is asked to select 5 students to represent the team in the Homecoming Parade. The coach decides to randomly select 5 students out of the 38 members of the team.
a. What is the population for this problem?
b. What is the sample for this problem?
c. Suggest a method for selecting the random sample of 5 students
The population is 38, and the sample is 5 students.
find out the population, sample, and method for selection?. The population for this problem is the entire soccer team, which consists of 38 members.
b. The sample for this problem is the group of 5 students who are selected by the coach to represent the team in the Homecoming Parade.
c. One method for selecting a random sample of 5 students from the team is to use a random number generator to choose 5 numbers between 1 and 38, representing the 38 team members. The coach can then select the students who correspond to the chosen numbers. Another method is to write the names of all 38 team members on identical slips of paper, place the slips in a container, mix them up, and then randomly select 5 slips to determine the students who will participate in the parade. It is important to ensure that the selection method is truly random to avoid any bias or non-representativeness in the sample.
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A company makes cones out of solid foam. Each cone has a height of inches, and its base has a radius of inches. How much foam is needed to make cones?
The total foam needed to make n cones is (n/3)πr^2h cubic inches.
What is the total volume of foam required to manufacture a certain number of cones with a given height and base radius?The volume of a cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base, h is the height, and π is the mathematical constant pi.
In this case, the height of each cone is given as h inches, and the radius of the base is given as r inches. So, the volume of each cone can be calculated as:
V = (1/3)πr^2h
Now, let's assume that the company wants to make n cones. Then, the total amount of foam needed to make these cones would be:
Total foam needed = n × V
Substituting the expression for V, we get:
Total foam needed = n × (1/3)πr^2h
Therefore, the total foam needed to make n cones is (n/3)πr^2h cubic inches.
Note that the given values of h and r are necessary to compute the total foam required.
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15. sheila has an eye-height of 5.4 feet and is standing 33 feet from a building. the angle of elevation from her line of
sight to the top of the building is 71 degree how tall is the building? round to the nearest tenth.
The height of the building is approximately 102.3 feet, rounded to the nearest tenth.
Step 1: Draw a right triangle with Sheila's eye-height as the base, the building's height as the vertical side, and the distance between Sheila and the building as the horizontal side.
Step 2: We are given the angle of elevation (71 degrees) and the horizontal distance (33 feet). To find the vertical distance, we can use the tangent function in trigonometry. The formula is:
tan(angle) = (opposite side) / (adjacent side)
Step 3: Plug in the given values into the formula:
tan(71) = (vertical distance) / 33
Step 4: Solve for the vertical distance:
vertical distance = 33 * tan(71) ≈ 96.9 feet
Step 5: Add Sheila's eye-height to the vertical distance to find the total height of the building:
total height = eye-height + vertical distance
total height = 5.4 + 96.9 ≈ 102.3 feet
The height of the building is approximately 102.3 feet, rounded to the nearest tenth.
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Greta sells advertising space for her school yearbook. Last year, a quarter-page ad cost $110. This year, Greta's teacher asks her to mark down the price by 15% to attract more sponsors. Greta wants to know the price after the markdown.
The price of the advertisement that originally costs $110 after a 15% markdown is $ 83.5.
Original price = $110
Markdown percent = 15%
Reduce in price = 15% of 110
To calculate this, we divide the percent by 100 and multiply it by the number given. Like in the above case, we divide 15 by 100 to get 0.15 and multiply it by 110.
= 0.15 * 110 = 16.5
Price after markdown = original price - reduction in price
= 110 - 16.5
= $ 83.5
Thus, the price for a quarter-page ad of the school yearbook which used to be $110 has come down to $83.5 after a 15 % markdown to attract more sponsors.
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HELP ME PLEASE ANYBODY I NEED IT URGENTLY
I also have to show my work
Thank you.
20 pt if someone can answer this!!!
Pls help.
The median value is____
Answer:
The median value is 45.
Step-by-step explanation:
"The median is the middle number in a sorted, ascending or descending list of numbers"
The middle number here is 45
50
Step-by-step explanation:
I put the explanation on the attachment. please see it.
Write the equation for shifting the parent function of the absolute value function 3 units down.
The vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point. The parent function of the absolute value function is f(x) = |x|.
To shift this function 3 units down, we need to subtract 3 from the function's output (y) at every point on the graph. This can be expressed as:
f(x) = |x| - 3
The absolute value function is symmetric around the y-axis, which means that any shifts to the left or right do not affect the shape of the graph, only its position on the coordinate plane.
However, a vertical shift up or down will change the location of the vertex, the point where the graph changes direction. In this case, the vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point.
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Luna and ger friend maka sandwiches with 1/3 of a baguette. They sahre the baguette equally
Luna and her friend Maka decided to make sandwiches using 1/3 of a baguette. To ensure fairness, they agreed to divide the baguette equally between them. They carefully measured the baguette and cut it into two equal parts, ensuring each of them received an equal portion.
Luna and Maka then began assembling their sandwiches. They spread their preferred fillings on their respective portions of the baguette, adding layers of vegetables, meats, and condiments to create delicious sandwiches.
After completing their sandwich preparation, Luna and Maka sat down together to enjoy their culinary creations. They appreciated the taste and quality of their sandwiches, delighted by the shared experience and the equal distribution of the baguette.
As they savored each bite, Luna and Maka cherished their friendship and the simple joy of sharing a meal together. They found contentment in the realization that even the smallest things, like a shared baguette, could strengthen their bond and create lasting memories.
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1. assume that abc company uses a margin of 40% on all items it purchases for resale, so that the firm sells $ x worth of merchandise. the company also incurred selling expenses which it budgeted at 15% of the volume of sales. the company also budgets fixed expenses at $ 600.a. write the equation relating total cost and sales volumeb. what will total cost and net profit before taxes on sales of $ 80,000c. what is the breakeven level of sales volume
a. The equation is Total Cost = 0.75x + $600
b. Total cost is $60,600 and net profit is $19,400.
c. The breakeven level of sales volume is $2,400.
a. The equation relating total cost and sales volume can be expressed as:
Total Cost = Cost of Goods Sold + Selling Expenses + Fixed Expenses
where Cost of Goods Sold = 60% (100% - 40%) of the sales volume
Selling Expenses = 15% of the sales volume
Fixed Expenses = $600.
Therefore, the equation can be written as:
Total Cost = 0.6x + 0.15x + $600
= 0.75x + $600
b. For sales of $80,000, we can substitute x = $80,000 into the equation:
Total Cost = 0.75x + $600
= 0.75($80,000) + $600
= $60,000 + $600
= $60,600
To calculate net profit before taxes, we need to subtract the total cost from the sales volume:
Net Profit before Taxes = Sales - Total Cost
= $80,000 - $60,600
= $19,400
c. To find the breakeven level of sales volume, we need to set the net profit before taxes to zero and solve for x:
Net Profit before Taxes = Sales - Total Cost
0 = x - (0.6x + 0.15x + $600)
0 = 0.25x - $600
0.25x = $600
x = $2,400
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What is the equation, in slope-intercept form, of the line that passes through
(0, 5) and has a slope of -1? (6 points)
Oy=-x-5
Oy=x+5
Oy=-x+5
Oy=x-5
Answer:
C) y = - x + 5---------------------------
The given point (0, 5) represents the y-intercept and we have a slope of -1.
It translates as:
m = - 1, b = 5 in the slope-intercept equation of y = mx + bBy substituting we get equation:
y = - x + 5This is option C.