Answer:
Total cost= $5,425
Step-by-step explanation:
Giving the following information:
Month Machine _Hours Amount
January 200 $2,800
February 350 3,000
March 450 4,000
April 500 5,000
May 600 5,200
June 580 5,800
First, we need to calculate the fixed and variable costs. To do it, we will use the high-low method:
Variable cost per unit= (Highest activity cost - Lowest activity cost)/ (Highest activity units - Lowest activity units)
Variable cost per unit= (5,800 - 2,800) / (600 - 200)
Variable cost per unit= $7.5 per hour
Fixed costs= Highest activity cost - (Variable cost per unit * HAU)
Fixed costs= 5,800 - (7.5*600)
Fixed costs= $1,300
Fixed costs= LAC - (Variable cost per unit* LAU)
Fixed costs= 2,800 - (7.5*200)
Fixed costs= $1,300
Now, we can determine the total cost for 550 hours:
Total cost= 1,300 + 7.5*550
Total cost= $5,425
3) Use the situation to choose the correct answer.
A radioactive substance loses its mass at a rate of 12% every second. At the beginning
of an experiment, the substance has a mass of 6 centigrams.
After 5 seconds, how much mass is left of the radioactive substance? Round your
answer to the nearest hundredth centigram.
5.28 cg
03.17 cg
O 3.60 cg
O 0.72 cg
Answer: 3.60 cg
Step-by-step explanation:
just did the assignment
You are painting a room that is 16 feet long, 10 feet wide, and 8 feet high. On the walls of the room, there are two windows that are each 2 feet wide and 5 feet tall, and a door that is 4 feet wide and 7 feet tall. A gallon of paint covers 350 square feet. How many gallons of paint do you need to cover the 4 walls with one coat of paint, not including the windows and the door
You will need approximately 1.33 gallons of paint to cover the four walls with one coat, not including the windows and the door.
Given that,
Room dimensions:
Length: 16 feet
Width: 10 feet
Height: 8 feet
Features on the walls:
Two windows:
Width: 2 feet
Height: 5 feet
One door:
Width: 4 feet
Height: 7 feet
Paint coverage:
1 gallon of paint covers 350 square feet
Calculate the area of the walls first:
Subtract the area of the windows and door area from the total wall area.
The total wall area is the sum of the areas of all four walls.
The area of each wall is calculated by multiplying the height of the room by its length.
So, the area of each wall = 8 feet (height) x16 feet (length)
The area of each wall = 128 square feet.
Calculate the area of the windows and the door.
The area of each window is calculated by multiplying its width by its height.
So, the area of each window = 2 feet (width) x 5 feet (height)
The area of each window = 10 square feet.
The area of the door is calculated by multiplying its width by its height. So,
The area of the door = 4 feet (width) x 7 feet (height)
The area of the door = 28 square feet.
Now, subtract the total area of the windows and the door from the total wall area.
Total wall area = 4 walls x 128 square feet
Total wall area = 512 square feet
The total area of the windows = 2 windows x 10 square feet
The total area of the windows = 20 square feet
The total area of the door = 1 door x 28 square feet
The total area of the door = 28 square feet
Area to be painted = Total wall area - Total area of the windows - Total area of the door
Area to be painted = 512 square feet - 20 square feet - 28 square feet
Area to be painted = 464 square feet.
Now, we can determine the number of gallons of paint needed.
Since 1 gallon of paint covers 350 square feet,
Divide the area to be painted by 350.
The number of gallons of paint needed = Area to be painted / Coverage per gallon
The number of gallons of paint needed = 464 square feet / 350 square feet/gallon
The number of gallons of paint needed ≈ 1.33 gallons.
Hence, you will need approximately 1.33 gallons of paint to cover the four walls with one coat, not including the windows and the door.
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Please help!!!!
If f(1) = 2 and f(n+1) = f(n)^2 – 3 then find the value of f(3).
Answer:
The value of f(3) is -2.
Step-by-step explanation:
This is a recursive function. So
[tex]f(1) = 2[/tex]
Now, we find f(2) in function of f(1). So
[tex]f(1+1) = f(1)^2 - 3[/tex]
[tex]f(2) = f(1)^2 - 3 = 2^2 - 3 = 1[/tex]
Now, with f(2), we can find the value of f(3).
[tex]f(2+1) = f(2)^2 - 3[/tex]
[tex]f(3) = f(2)^2 - 3 = 1^2 - 3 = -2[/tex]
The value of f(3) is -2.
I need this help me please
Answer:
I think its B
Step-by-step explanation:
Bob was thinking of two numbers. He said the larger of his numbers was 8 more than the smaller number. He chose to represent the smaller number with an x. Which of the following is an expression that can be used to represent the larger number in terms of x?
Answer:
x+8
Step-by-step explanation:
What operation should be done first to solve 6x + 5 = 35?
Answer:
Subtract 5
Step-by-step explanation:
Pemdas is done backwards in algebra
Translate the following, "Three times a number is at least that number plus 1 ""
Answer:
3x ≥ x+1
Step-by-step explanation:
Let the number be x.
ATQ,
Three times of a number = 3x
At least means ≥
So,
3x ≥ x+1
So, the required inequality is 3x ≥ x+1.
The functions f(x) and m(x) are graphed below. If m(x) = f(x) + k, what is the value of k
Answer:
k = m(x) - f(x)
Step-by-step explanation:
m(x) = f(x) +k
m(x) - f(x) = k
Here is a rectangle
7 cm
3 cm
Nor drawn
accurately
A square has the same perimeter as the rectangle.
What is the side length of this square?
Answer:
a square and rectangle have the same perimeter. the length of the rectangle is 4 cm less than twice the side of the square, and the width of the rectangle is 6 cm less than the side of the square.
Step-by-step explanation:
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The required side length of the square is 5 cm.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
Length of rectangle = 7 cm,
Width of rectangle = 3 cm.
The perimeter of rectangle = 2(length + width)
= 2(7 + 3)
= 2 x 10
= 20
Also, given that the perimeter of the rectangle is equal to the perimeter of a square,
Let side of square is a then perimeter = 4a
⇒ 4a = 20
⇒ a = 5
The side length of the square is 5 cm.
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find the x- and y- intercepts of the following: 10x-4y=-20
Answer:
y-intercept=5
x-intercept=-2
Step-by-step explanation:
To find the y intercept, plug in 0 for x. So you get 10(0)-4y=-20. Simplify, and clear out the negatives on both sides because they cancel each other out. 4y=20 would be your final equation. y=5.
To find the x intercept, you plug in 0 for y this time. The equation is 10x-4(0)=-20. Simplify to get, 10x=-20. You cannot remove the negative because there isn't a negative sign on the 10x. -20/10 is -2.
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write the equation of the line that is parallel to y=4x-1 and passes through the point (4.9)
9514 1404 393
Answer:
y = 4x -7
Step-by-step explanation:
Rearranging the slope-intercept for equation, we can find the intercept:
y = mx +b
y -mx = b . . . . . subtract mx
We know the slope of the parallel line is the same as that of the given line (m=4), so we only need to find 'b'.
b = 9 -4(4) = -7
The desired equation is ...
y = mx +b
y = 4x -7
In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What are the lower and upper limits of a box-and-whiskers display of this data
Answer:
[tex]L =52[/tex] --- Lower Limit
[tex]U =82[/tex] --- Upper Limit
Step-by-step explanation:
Given
[tex]N = 10[/tex]
[tex]Data: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66[/tex]
Required
Determine the lower and upper limits of box and whisker display
First, arrange the data in ascending order
The sorted data is:
[tex]Data: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77[/tex]
The lower limit (L) is calculated using:
[tex]L = Q_1 - 1.5 * (Q_3-Q_1)[/tex]
The upper limit (U) is calculated using:
[tex]U =Q_3 + 1.5 * (Q_3-Q_1)[/tex]
Q1 is calculated using:
[tex]Q_1 = \frac{1}{4}(N+1)[/tex]
[tex]Q_1 = \frac{1}{4}(10+1) = 2.75 = 3rd\ data[/tex]
[tex]Q_1 = 67[/tex]
Q3 is calculated using:
[tex]Q_3 = \frac{3}{4}(N+1)[/tex]
[tex]Q_3 = \frac{3}{4}(10+1) = 8.25= 8th\ data[/tex]
[tex]Q_3 = 77[/tex]
So:
[tex]L = Q_1 - 1.5 * (Q_3-Q_1)[/tex]
[tex]L =67 - 1.5*(77-67)[/tex]
[tex]L =67 - 1.5*10[/tex]
[tex]L =67 - 15[/tex]
[tex]L =52[/tex]
[tex]U =Q_3 + 1.5 * (Q_3-Q_1)[/tex]
[tex]U =67 + 1.5*(77-67)[/tex]
[tex]U =67 + 1.5*10[/tex]
[tex]U =67 + 15[/tex]
[tex]U =82[/tex]
The price of lunch in the school cafeteria was 2.50$ last year this year the price is 2.70$. What is the percent increase
Answer:
8 percent
Step-by-step explanation:
There is an 8 percent increase, because if you do 20 cents divided by 250 cents, you get 0.08, which is 8 percent. Also to double check, you can do 250 * 1.08. By the way, that is some rip off lunch.
The price of technology stock has risen $9.87 today yesterday's price is $9.74 find the percentage increase round your answer to the nearest 10th of a percent percentage.
Step-by-step explanation:
To find the percent increase, divide the increase by the original price.
P1 = price yesterday
P2 = price today
To find percent increase
[tex] \frac{(p2 - p1)}{p1} [/tex]
Or to answer the question,
P1 = 9.74
P2 = 9.87
[tex] \frac{(9.87 - 9.74)}{9.74} = 0.013347[/tex]
Or 1.33%
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 72.6 Mbps. The complete list of 50 data speeds has a mean of x=18.55 Mbps and a standard deviation of s=19.69 Mbps. a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the carrier's highest data speed to a z score. d. If we consider data speeds that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?
Answer:
a. 54.05 Mpbs.
b. 2.745... standard deviations.
c. The z-score is 2.745....
d. The carrier's highest data speed is significantly high.
Step-by-step explanation:
a. The difference between the highest measured data speed and the mean is 72.6 - 18.55 = 54.05 Mbps.
b. The amount of standard deviations of 54.05 Mbps is equal to this value divided by the standard deviations, so we yield [tex]\frac{54.05}{19.69} = 2.745...[/tex] standard deviations.
c. The z-score is equal to the difference between the mean and a data point in standard deviations, so the z-score is 2.745....
d. 2.745... is not between -2 and 2, so the carrier's highest data speed is not insignificant - so it's significantly high.
A college admits a freshman class of 330 students at the beginning of each academic year and graduates 145 students twice a year. What will be the net change in student population after 5 years?
Answer:
200 studentsStep-by-step explanation:
Change in one year:
330 - 2(145) = 330 - 290 = 40Change after 5 years:
40*5 = 200 studentsWrite 0.000 97 in standard form
Answer:
[tex]9.7 \times 10 {}^{ - 4} [/tex]
The standard form of given number [tex]9.7[/tex]×[tex]10^{-4}[/tex]
What is standard form?Standard form is a way of writing down in easy form of very large or very small numbers.
Let E is the standard form of given number
E=0.00097
E= [tex]\frac{97}{100000}[/tex]
E=97×[tex]10^{-5}[/tex]
E=[tex]9.7[/tex]×[tex]10^{-4}[/tex]
The standard form of given number [tex]9.7[/tex]×[tex]10^{-4}[/tex]
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The graph below shows a linear representation of a jogger’s heartbeat in beats per minute, as his speed is increased (in feet per second). What is the slope of the line?
Answer:
The slope is 3.75 OR 3 3/4.
Step-by-step explanation:
So the formula for slope I am using NOW, is based on the variables I named my dimensions. WARNING: NOT SLOPE FORMULA YOU MIGHT BE USING
y = 95 - 80
x = 10 - 6
Slope Formula: y/x
Substituted Slope Formula: (95 - 80)/(10 - 6)
Simplified Substituted Slope Formula: 15/4 OR 3.75
Hope this helps!!
The slope of the given linear equation is 3.75.
Given that, the graph given shows a linear representation of a jogger’s heartbeat in beats per minute, as his speed is increased (in feet per second).
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
From the given graph we have the coordinates (6, 80) and (10, 95).
The slope of an equation = (y2-y1)/(x2-x1)
=(95-80)/(10-6)
=15/4
=3.75
Therefore, the slope of the given linear equation is 3.75.
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A student has to buy graph paper and printer paper. The graph paper, x, costs $2, while the printer paper, y, costs $3. She wants to buy at least 8 packs of paper but wants to spend at most $23.
Enter a system of inequalities for the given situation and select the graph of the system. Then determine if the point (3, 6) is a solution to the system.
The system of inequalities is _______ and ______
The point (3, 6)____ a solution because it _______lie in the region shared by the two inequalities, and it ______ satisfies both inequalities.
Answer:
8+3+23
Step-by-step explanation:
i need help with this
Answer:
just put any number for the answer if im reading it right they should all answer 0
Step-by-step explanation:
hope i helped ;)
A cylinder has a base diameter of 6 centimeters and a height of 15 centimeters. What is its volume in cubic centimeters, to the nearest tenths place?
Please help
Step-by-step explanation:
V
≈
424.12
cm³
d
Diameter
cm
h
Height
cm
Find the value of x. 5+x=7
Choose Yes or No to tell if the fraction
will make each equation true.
3
+ a
=
23
24
Choose.. v
+=
Choose.. v
13
18
Choose.. v
-=+
Choose.. v
15
Answer:
yes
yes
no
yes
Step-by-step explanation:
LOOK AT PIC, ASAP, ROGHT ANSWER GETS BRAINLIEST !
Answer:
Step-by-step explanation:
The teacher has 7/8 pounds of clay given.
gives out 1/16 per station
7/8= 0.875 pound
7/8 / 1/16 pound= 14 maximum stations
14 stations divided by 2 classes = 7 in each room
6/5 of ______ is 30
Please help
It is 36.
180/5 = 36
5/5 = 1
When we put that together, we can see that our complete answer is:
36/1
The complete and simplified answer to the question what is 6/5 of 30 is:
36.
A TV Screen is measured according to the diagonal of the screen. If a 65-inch TV has a height f 33 inches, what is it's width?
Answer:
The width of the TV screen is 56 inches.
Step-by-step explanation:
We can find the width of the TV screen by using Pitagoras:
[tex] D^{2} = H^{2} + W^{2} [/tex]
Where:
D: is the diagonal = 65 in
H: is the height = 33 in
W: is the width =?
Then, the width is:
[tex] W = \sqrt{D^{2} - H^{2}} = \sqrt{(65 in)^{2} - (33 in)^{2}} = 56 in [/tex]
Therefore, the width of the TV screen is 56 inches.
I hope it helps you!
Answer:
56in
Step-by-step explanation:
Which of the following is the smallest element in the set of natural numbers?
-1
O 1
There is no smallest element; the set is infinite.
0
Answer:
your answer would be 0 mark as brainliest
Find the total surface and each pyramid. Round to the sea
SHOW YOUR WORK!
Answer:
328 square inches
PLZ MARK AS BRAINLIEST
Step-by-step explanation:
Lateral Area of Pyramid:
L = 1/2Pl
l = 15.9
P = 2(8.2) + 2(8.2) = 32.8
L = 1/2(32.8)(15.9) = 260.76
Surface Area:
SA = B + L
B = (8.2)(8.2) = 67.24
L = 1/2(32.8)(15.9) = 260.76
SA = 67.24 + 260.76 = 328
write the fraction 4/10 as a product of a whole number and a unit fraction
Answer:
Step-by-step explanation:
Answer:
4 x 1/10
Step-by-step explanation:
All you have to do is to add 1/10 + 1/10 + 1/10 + 1/10.
Add the numerators 1+1+1+1=4 and keep your denominator.
So just add 1/10 4 times, thas why the answer is 4 x 1/10.
Subtract. Write your answer as a fraction in simplest form. 1/9−(−4/9)=?
Answer:
1/3
Step-by-step explanation:
i hope its right ...
