Answers
Option A is correct: the cross-section of a sphere must be a circle.
When a sphere is cut by a plane, the resulting cross-section will always be a circle, regardless of the orientation or angle of the cut. This is because all cross-sections of a sphere have the same shape and size as a great circle, which is a circle that passes through the center of the sphere and divides it into two equal halves.
Option B is not correct because an ellipse is not a possible cross-section of a sphere.
Option C is not correct because the cross-section of a sphere can only be a circle, not an ellipse.
Option D is not correct because a line is not a possible cross-section of a sphere. A line can only be a cross-section of a cylinder or a cone, but not a sphere.
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Related Questions
Factoring polynomials
Solve the following by factoring:
2x² + 16x + 14 = 0
Answers
Answer:
x = -1, -7
Step-by-step explanation:
(2x + 14) (x + 1) = 0
2x + 14 = 0, 2x = -14, x = -7.
x + 1 = 0, x = -1.
The equation E = mgh gives the gravitational potential energy of an object, where g is the
acceleration due to gravity, m is the mass of the object, and h is the height of the object.
Solve for h in terms of E, m, and g.
Answers
Step-by-step explanation:
Starting with the equation E = mgh, we can solve for h in terms of E, m, and g as follows:
E = mgh
Divide both sides by mg:
E/mg = h
Therefore, h = E/mg.
So the solution for h in terms of E, m, and g is h = E/mg.
Find dx/dt when x = e^6t
Answers
The derivative of the exponent and e^6t
Determine how long it will take for a principal amount of $1,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded.
guys pls help
Answers
Step-by-step explanation:
Continuous compounding formula e^(rt)
2 = e^(.13 * t) '2' is 'double r = .13 which is 13% in decimal
LN both sides
ln(2) = .13 t
ln (2) / .13 = t = 5.33 yrs
tly cloudy
The value of a certain investment over time is given in the table below. Answer the
questions below to determine what kind of function would best fit the data, linear or
exponential.
Number of
Years Since
Investment
Made, x
Value of
Investment
(s), f(x)
1
27,171.30
22,507.26 18,718.31
3
values change
function is approximately
function would best fit the data because as x increases, the y
The
of this
Q Search
15,412.40
GM
Answers
An exponential function would best fit the data because as x increases, the y values change multiplicatively. The rate of change of the function is of approximately 0.8275.
How to identify an exponential function?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant, which is the rate of change of the exponential function.
The rate of change for this problem is approximated as follows:
22507.26/27171.30 = 0.828.18712.31/22507.26 = 0.831.15412.4/18712.31 = 0.824.Hence the rate can be rounded to 0.8275.
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Write an exponential function
Answers
The exponential function for the data in the table is given as follows:
[tex]y = 0.0625(2)^x[/tex]
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.When the input x increases by one, the output y is doubled, hence the parameter b has the value given as follows:
b = 2.
The parameter a is the value of y when x = 0. When x = 1, the output is double when x = 0, as b = 2, hence:
2a = 0.125
a = 0.0625.
Thus the function is:
[tex]y = 0.0625(2)^x[/tex]
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Snow-House sells a $1,501 snow thrower on the installment plan. The installment agreement includes a 20% down payment and 12 monthly payments of $170 each. What is the finance charge?
Answers
Answer:
$839.20
Step-by-step explanation:
To find the finance charge, we need to first calculate the total amount financed, which is the price of the snow thrower minus the down payment.
The down payment is 20% of $1,501, which is:
0.20 x $1,501 = $300.20
So the total amount financed is:
$1,501 - $300.20 = $1,200.80
The total amount of the 12 monthly payments is:
12 x $170 = $2,040
The finance charge is the difference between the total amount of the payments and the amount financed:
$2,040 - $1,200.80 = $839.20
Therefore, the finance charge is $839.20.
Find the x intercepts of the parabola with vertex (-1,2) and y intercept (0,3).
Answers
The x intercepts of the parabola are -1 + i√(2) and -1 - i√(2)
How to find the x intercepts of the parabolaUsing the equation:
y = a(x - h)²+ k
where (h, k) is the vertex of the parabola
y = a(x + 1)²+ 2
solving for a at the y intercept
y = a(x + 1)²+ 2
3 = a(0 + 1)²+ 2
a = 1
To find the x intercepts we need to set y = 0 and solve for x:
0 = (x + 1)²+ 2
x + 1 = ±√(-2)
x + 1 = ±i√(2)
x = -1 ± i√(2)
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Find the area of the shaded region. Round your answer to the nearest hundredth. A circle and two triangles drawn inside it. The two circles are congruent and share a common side. This common side is the diameter of circle. The third vertex of both triangles lie on the circle. The lengths of sides apart from diameter are labeled 3 meters and 4 meters. The region inside circle and outside triangles is shaded. The area is about __square meters.
Answers
Answer: 7.635 square meters
Step-by-step explanation:
Both triangles have the diameter as one of their sides and they both have a vertex on the circumference of the circle. Thus, the two triangles are right triangles, and the hypotenuse of the triangles is the diameter.
Use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
Square root both sides to isolate c (hypotenuse/diameter): [tex]c=\sqrt{a^2+b^2}[/tex]
Plug in the values of a and b to calculate c: [tex]c=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]
The diameter of the circle is 5 meters, so the radius of the circle is 2.5 meters.
Plug in the radius into the equation for the area of a circle: Area = [tex]\pi r^2=\pi *2.5^2=6.25\pi[/tex] square meters.
The equation for the area of a triangle is [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle and h is the height of the triangle.
Since we have two congruent triangles, the total area of the two triangles combined is simply b*h.
Plug in the values of b and h to get b*h = 3*4 = 12 square meters.
Subtract the total area of the two triangles combined from the area of the circle to get the area of the shaded region: [tex]6.25\pi - 12=7.635[/tex] square meters.
15. Find the sum of the first six terms of the geometric sequence for which a2 = 0.7 and a3 = 0.49.
16. Rewrite using radicals.
17. Rewrite using rational exponents.
Answers
Find the sum of the first six terms of the geometric sequence for which a2 = 0.7 and a3 = 0.49.
Let the common ratio of the geometric sequence be r. Then we have:
a2 = ar = 0.7
a3 = ar^2 = 0.49
Dividing the second equation by the first, we get:
r = a3/a2 = 0.49/0.7 = 7/10
So the first six terms of the sequence are:
a1 = a2/r = 0.7/(7/10) = 1
a2 = 0.7
a3 = 0.49
a4 = ar^2 = 0.343
a5 = ar^3 = 0.2401
a6 = ar^4 = 0.16807
The sum of the first six terms is:
S6 = a1 + a2 + a3 + a4 + a5 + a6
S6 = 1 + 0.7 + 0.49 + 0.343 + 0.2401 + 0.16807
S6 = 2.94017
Therefore, the sum of the first six terms of the geometric sequence is approximately 2.94017.
Rewrite using radicals.
The expression (x^3/4)^2 can be rewritten as:
(x^3/4)^2 = x^3/4 * x^3/4
(x^3/4)^2 = (x^3)^2 / 4^2
(x^3/4)^2 = x^6 / 16
So (x^3/4)^2 is equivalent to (x^6/16) using radicals.
Rewrite using rational exponents.
The expression √(a^3b^2) can be rewritten using rational exponents as:
√(a^3b^2) = (a^3b^2)^(1/2)
√(a^3b^2) = a^(3/2)b^(1)
So √(a^3b^2) is equivalent to a^(3/2)b^(1) using rational exponents.
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 13 millimeters long, and the height of the equilateral triangle is 11.3 millimeters. The pyramid's slant height is 17 millimeters. What is its surface area?
Answers
The surface area of the Triangular pyramid is approximately 331.3 square millimeters.
The surface area of a triangular pyramid, we need to calculate the area of its base and the area of each triangular face, then add them together. The formula for the surface area of a triangular pyramid is:
SA = (1/2)P*l + B
where SA is the surface area, P is the perimeter of the base, l is the slant height of each triangular face, and B is the area of the base.
In this case, the base of the triangular pyramid is an equilateral triangle with legs of 13 millimeters and a height of 11.3 millimeters. To find the area of the base, we can use the formula for the area of an equilateral triangle:
B = (sqrt(3)/4)*a^2
where a is the length of a side of the equilateral triangle.
Substituting a = 13 into the formula, we get:
B = (sqrt(3)/4)*13^2
B = (sqrt(3)/4)*169
B = 43.7 square millimeters (rounded to one decimal place)
Next, we can find the perimeter of the base:
P = 3a
P = 3*13
P = 39 millimeters
Now we can use the formula for the surface area of a triangular pyramid:
SA = (1/2)P*l + B
Substituting P = 39, l = 17, and B = 43.7, we get:
SA = (1/2)*39*17 + 43.7
SA = 331.3 square millimeters (rounded to one decimal place)
Therefore, the surface area of the triangular pyramid is approximately 331.3 square millimeters.
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What is the solution to 4|x – 6| ≤ 16?
Answers
Answer:
Step-by-step explanation:
4 | x - 6 | ≤ 16
| x - 6 | ≤ 4
-4 ≤ x - 6 ≤ 4
-4 + 6 ≤ x ≤ 4 + 6
2 ≤ x ≤ 10
Complete both transformations below.
Then enter the final coordinates of the figure.
A(-3,-2)
C(-4,-4)
B(0-4)
1) <6,4>
2) Dilate K = 4
A" ([?], [])
B" ([],[])
C" ([],[_])
Enter
Answers
The final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)
To translate the figure by <6,4>:
Add 6 to the x-coordinate of each point to get the new x-coordinate
Add 4 to the y-coordinate of each point to get the new y-coordinate
New coordinates:
A'(-3+6,-2+4) = (3,2)
C'(-4+6,-4+4) = (2,0)
B'(0+6,-4+4) = (6,0)
To dilate the figure K=4:
The coordinates x and y are multiplied by 4.
New coordinates:
A"(-34,-24) = (-12,-8)
C"(-44,-44) = (-16,-16)
B"(04,-44) = (0,-16)
Hence, the final coordinates of the transformed figure are A"(-12,-8), B"(0,-16) and C"(-16,-16)
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Could you help answer this step by step please?
Answers
The linear function giving the volume of the balloon after t seconds is given as follows:
V(t) = 4 + 0.5t.
The time that it takes to fill the balloon is given as follows:
24 seconds.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The slope and the intercept for this problem are given as follows:
m = 0.5 -> volume increases by 0.5 ft³/s.b = 4 -> initial volume of the balloon.Hence the linear function giving the volume of the balloon after t seconds is given as follows:
V(t) = 4 + 0.5t.
The total capacity is of 16 ft³, hence the time needed to fill the balloon is obtained as follows:
16 = 4 + 0.5t
0.5t = 12
t = 12/0.5
t = 24 seconds.
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48+24x3-x+10x4-5x2 in standard form
Answers
The Standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.
To write an expression in standard form, we need to arrange the terms in descending order of degree and combine like terms.
The given expression is:
48 + 24x3 - x + 10x4 - 5x2
First, we arrange the terms in descending order of degree:
10x4 + 24x3 - 5x2 - x + 48
Next, we combine the like terms:
10x4 + 24x3 - 5x2 - x + 48 = 10x^4 + 24x^3 - 5x^2 - x + 48
Therefore, the standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.
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The ages of Ben, Graham and Pam are in the ratio 3:7:8.
Pam is 25 years older than Ben. How old is Graham?
Answers
Answer:
35
Step-by-step explanation:
2
S17
3
Check
5
7
(about 89%) of the
(a) According to Chebyshev's theorem, at least
lifetimes lie between] hours and hours. (Round your answer to the
nearest whole number.)
(b) According to Chebyshev's theorem, at least (Choose one) of the
lifetimes lie between 746 hours and 1110 hours.
BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries. To investigate its new line of Ultra batteries, BIG
randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 928 hours, with a standard deviation of 91 hours. Suppose that this mean and
standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries.
Search
X
10
3
11
12
13
Save For Later
Submit As
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Answers
a) According to Chebyshev's Theorem, at least 89% of the lifetimes are between 655 hours and 1201 hours.
b) According to Chebyshev's theorem, at least 75% of the lifetimes lie between 746 hours and 1110 hours.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100\left(1 - \frac{1}{k^{2}}\right)[/tex].The lifetimes within 2 standard deviations of the mean are given as follows:
928 - 2 x 91 = 746 hours.928 + 2 x 91 = 1110 hours.The lifetimes within 3 standard deviations of the mean are given as follows:
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During a three-way tug-of-war competition, each of the three ropes is tied to a center knot. One man pulls his rope North with a force of 301 N. Another man pulls his rope at 10.0° South of East with a force of 280 N. If the third man pulls on his rope Southwest with a force of 313 N, what is the net force on the knot?
Responses
62.7 N
62.7 N
72.7 N
72.7 N
52.7 N
52.7 N
42.7 N
Answers
The net force on the knot is 42.7 N. Therefore, option D is the correct answer.
The force of 301 N to the North can be broken into components of 301 N in the x-direction and 0 N in the y-direction.
The force of 280 N at 10.0° South of East can be broken into components of 250.5 N in the x-direction and -247.8 N in the y-direction.
The force of 313 N to the Southwest can be broken into components of -208.1 N in the x-direction and -278.9 N in the y-direction.
The net force is then the sum of the components in both the x- and y-directions.
The net force in the x-direction is 301 N + 250.5 N - 208.1 N = 343.4 N and the net force in the y-direction is 0 N - 247.8 N - 278.9 N = -526.7 N.
The net force is then the hypotenuse of a right triangle with the x- and y-components as the legs.
The net force is thus equal to √(343.4 N² + (-526.7 N)²) = 42.7 N.
Therefore, option D is the correct answer.
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Are any of these numbers a solution to the
equation x2 = 2?
• 1
2
3
7
5
순
Answers
The number 1 is a solution to the equation 2x = 2.
We have the Equation
2x = 2
Now, dividing both side by 2 we get
2x/2 = 2/2
x = 1
So, the number 1 is a solution to the equation 2x = 2.
When x is 1, the left side of the equation becomes 2(1) = 2, which is equal to the right side of the equation.
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A retirement account has a balance of $300,000. You want to receive monthly payments(withdrawals) from the account for a total of 25 years. The retirement account earns 4% interest. How much will you be able to receive each month?
Answers
The monthly payments you can withdraw from the retirement account is $1,583.4.
What is the amount received each month?The monthly payments you can withdraw from the retirement account, is calculated as;
PV = Px [(1 - (1 + r)⁻ⁿ) / r]
where;
PV is the present value of the annuity P is the monthly payment you want to receiver is the interest rate per period n is the total number of periodsThe total number of periods = 25 years x 12 months/year = 300 months
PV = P x [(1 - (1 + r)⁻ⁿ) / r]
$300,000 = P x [(1 - (1 + 0.04/12)⁻³⁰⁰) / (0.04/12)]
$300,000 = P x 189.47
P = $300,000 / 189.47
P= $1,583.4
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If a rectangular container is 25cm by 37cm by 21cm how much does it overflow
Answers
If a rectangular container is 25cm by 37cm by 21cm, then it will overflow after reaching the volume of 19425 cm³.
To know the volume after which the container will overflow, first we have to calculate the volume it can contain.
As, Volume of cuboid= length × breadth × height
So, Volume of rectangular container = 25 × 37 × 21 cm³
Volume = 19425 cm³
So, volume of rectangular container whose dimensions are 25cm by 37cm by 21cm is 19425 cm³ and it will overflow after reaching this volume.
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10. A plane is flying from Winnipeg to Calgary against a strong headwind of 50 km/hr. The plane
1/2 takes hour longer for this flight than it would take in calm air. If the distance from Winnipeg to
Calgary is 1200 km, what is the speed of the plane in calm air, to the nearest kilometer per hour?
Answers
The speed of the plane in calm air is 372 km/h
Given that a plane is travelling from Winnipeg to Calgary against a 50 km/hr headwind.
This flight takes half an hour longer than it would in calm air.
The distance between Winnipeg and Calgary is 1200 km.
Since we know that,
Speed may be defined as the distance travelled by an item in relation to the time it takes to travel that distance.
In other words, it measures how rapidly an item travels but does not provide direction. The term "velocity" refers to the combination of direction and speed.
The speed is defined by the rate of distance.
We must determine the plane's speed in calm air.
xy=1200
(x-50)(y+1/2) =1200
x² - 50 x-12000=0
By using quadratic formula.
x=372 as x>0
Hence, 372 km/h is the speed of the plane in calm air
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Which measurement is the same for Charles and Jermod?
median
Orange
Olower quartile
Oupper quartile
These dot plots show how many minutes Charles and Jermod spent on homework per day
for three weeks.
15 20 25 30
40 45 50 55 60
Charles's Homework (minutes per day)
15 20 25 30 35 40 45 50 55 60
Jermod's Homework (minutes per day)
Which measurement is the same for Charles and Jermod?
Answers
The median is the measurement that is the same for Charles and Jermod.
In a dot plot, the median represents the middle value when the data points are arranged in ascending or descending order.
From the given dot plots, we can see that both Charles and Jermod have their median values at 35 minutes per day.
Therefore, the median is the measurement that is the same for Charles and Jermod.
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A second function, g, is defined by
g
(
x
)
=
–
3
x
+
2.
Select the correct phrase in each drop-down menu to complete the sentence.A second function, g, is defined by
g
(
x
)
=
–
3
x
+
2.
Select the correct phrase in each drop-down menu to complete the sentence.
Answers
The figure shows a graph of the function fx in the coordinate plane. f2 is greater than g2.
As the graph of function f(x) is a parabola, so that the equation of function f(x) is:
f(x) = [tex]ax^2+bx+c[/tex]
As it can be seen in thee figure, the graph of function f(x) cross points (0;8) ;(-2; 0) and (4;0)
=> f(0) = 8; f(-2) = 0; f(4) = 0
We have:
f(x=0) = a x 0 + b x 0 + c = 8 => c = 8
We have:
+) 4a -2b + 8 = 0 => 2 x (4a -2b + 8) = 8a - 4b + 16 = 0 (1)
+) 16a + 4b + 8 = 0 (2)
We take (2) minus (1)
=> (16a + 4b + 8) - (8a - 4b + 16) = 0
=> 8a - 8 = 0 => a = 1
Replace a = 1 into (1)
=> 8 x 1 - 4b + 16 = 0 => b = 6
f (2) = 2^2 + 6 x 2 + 8 = 24
g (2) = 3 -2 + 2 = 3
Thus, f(2) is greater than g(2).
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Write a exponential function
Answers
Answer:
2f2y3ui2ke9i22881o228j11 GJ
Answer:
[tex]y = 0.0625(2) {}^{x} [/tex]
Step by step
[tex]y = a(b^{x} )[/tex]
X = 1 y = 0.125
[tex]0.125 = ab^{1} \\ a = \frac{0.125}{b} [/tex]
X = 4 y = 1
[tex]1 = a( {b}^{4} ) \\ ab^{4} = 1 \\ replace \: a = \frac{0.125}{b} \: in \: ab^{4} = 1 \\ \frac{0.125}{b} \times b^{4} = 1 \\ {b}^{3} = \frac{1}{0.125} \\ b = \sqrt[3]{ \frac{1}{0.125} } \\ b = 2[/tex]
[tex]replace \: b = 2 \: in \: a = \frac{0.125}{b} \\ a = \frac{0.125}{2} \\ a = 0.0625[/tex]
[tex]therefore \: \\ y = 0.0625( {2})^{x} [/tex]
Number 5 Please help with it.
Answers
this photo is not clear.Am sorry
HOMEWORK HELP PLEASE!!!!
Answers
The y-intercept of the graph of 3x + y = 6 is (0,
A graph of 3x + y = 6 is shown in the image below.
A graph of x + y = 4 is shown on the same grid in the image below.
A solution to the simultaneous equations is (1, 3).
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear equation or function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Based on the information provided about the equation, the y-intercept can be calculated as follows:
3x + y = 6
y = -3x + 6
f(0) = -3(0) + 6
f(0) = 0 + 6
f(0) = 6.
Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph, which is given by the ordered pair (1, 3).
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Write an expression to represent:
5 times the sum of x and 3
Answers
Answer:
5(x + 3)
Step-by-step explanation:
the sum of x and 3 is x + 3, then multiply by 5 to obtain
5(x + 3)
help! Find the base angles of the figure below.
A) 130°
B) 65°
C) 25°
D) 50°
Answers
Answer:
C
Step-by-step explanation:
x=base angle
2x+130=180
2x=50
x=25
base angle = 25
Prepare a contribution margin income statement.
Naomi's Quilt Shoppe sells homemade Amish quilts. Naomi buys the quilts from local
Amish artisans for $290 each, and her shop sells them for $490 each. She also pays a
sales commission of 8% of sales revenue to her sales staff. Naomi leases her country-
style shop for $1,300 per month and pays $1,800 per month in payroll costs in addition
to the sales commissions. Naomi sold 95 quilts in February,
Answers
The operating charges, including parcel expenditure and payroll costs( including sales commissions, amounted to$ 7,242. thus, the net profit before levies for the month of February was$ 11,758.
Donation periphery income statement for Naomi's Quilt Shoppe for the month of February Deals profit 95 bedspreads vended
x$ 490 per spread = $ 46,550 Cost of goods vended 95 bedspreads vended x$ 290 cost per spread = $ 27,550
Gross profit Deals profit- cost of goods
vended = $ 46,550-$ 27,550 = $ 19,000
Operating charges Lease expenditure = $ 1,300
Payroll charges( including deals commissions)$ 1,800 8 of$ 46,550 = $ 5,942
Total operating charges$ 1,300$ 5,942 = $ 7,242.
Net profit before levies Gross profit- operating charges = $ 19,000-$ 7,242 = $ 11,758 .
Naomi's Quilt Shoppe's donation periphery income statement shows that the shop earned$ 19,000 in gross profit from dealing 95 Amish bedspreads, after paying the cost of goods vended.
The operating charges, including parcel expenditure and payroll costs( including deals commissions), amounted to$ 7,242. thus, the net profit before levies for the month of February was$ 11,758.
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