If the current selling price, variable costs, and fixed costs are the same as last year, the expected net income in the current year is $162,105.
Net income can be computes as follows:
Net income = total revenue - total cost
Total cost consists of two costs, fixed cost and total variable cost.
Total cost = fixed cost + total variable cost
Fixed cost does not depend on the produced quantity, while total variable cost is a function of produced quantity.
Let q = produced quantity, then:
Total variable cost = variable cost per unit x q.
Let's assume that the sold quantity = produced quantity. Hence,
Total revenue = selling price x q
Information from last year:
Total revenue = $475,000
475,000 = selling price x q
Here, q = the product quantity sold last year.
Let r = the product quantity sold in the current year. Since the selling price is the same, we have:
500,000 = selling price x r
Comparing with last year, we have:
selling price = 475,000/q = 500,000/r
Hence,
r = (500,000/475,000) q
r = (20/19) q
Hence, the quantity sold this year is 20/19 higher than last year.
Total variable cost this year = variable cost per unit x r.
Substitute r = (20/19) q:
Total variable cost this year = variable cost per unit x (20/19) q
Total variable cost this year = (20/19) x variable cost per unit x q
Total variable cost this year = (20/19) x Total variable cost last year
Total variable cost this year = (20/19) x 150,000 = 157,895
Therefore,
Net income this year = total revenue - fixed cost - total variable cost
= 500,000 - 180,000 - 157,895
= 162,105
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line u - Line v, what is the value of x?
The value of x in the given figure is 6.
What are alternate angles?Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
Given that, two lines are parallel, line U ║ line V, we need to find the value of x,
Using the concept of alternate interior angles between parallel lines,
Alternate angles between the parallel, line are equal,
Therefore,
16x-6 = 90
16x = 96
x = 6
Hence, the value of x in the given figure is 6.
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please help me!!:)
MULTIPLE CHOICE QUESTION
A car was purchased in 2010 for $20,000.
The car is depreciating by 15% each year.
What is the "a" value?
Answer:
20,000
Step-by-step explanation:
I'm assuming your class is using this model of the exponential decay function:
f(x) = a(1 - r)^x
In this case, the equation would be:
f(x) = 20,000(1 - .15)^x
or, when 1 - r is calculated:
f(x) = 20,000(.85)^x
The "a" value is basically the starting value, because on a graph, the starting value would be where x = 0. Anything to the 0th power is 1, and anything multiplied by 1 is the same thing, making "a" the same as the starting value, or the y-intercept.
Therefore, a = 20,000.
Hope this helps!
If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x).
The statement "If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x)." is incorrect.
The origin of the coordinate plane is the point (0, 0), and it is the center of rotation for many geometric transformations.
When a point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, x). This is because rotation by 90 degrees counterclockwise causes the x-coordinate to become the negative of the original y-coordinate and the y-coordinate to become the original x-coordinate.
To see this, imagine the point (x, y) on the coordinate plane and draw a line segment connecting the point to the origin. The length of this line segment is given by the Pythagorean theorem as the square root of x² + y². After rotating the point 90 degrees about the origin, the line segment will be perpendicular to the original line segment and have a length equal to y and -x.
In summary, rotating a point (x, y) at 90 degrees about the origin results in the point (-y, x) due to the change in the direction and length of the line segment connecting the point to the origin.
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The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: "The poll has a margin of error of plus or minus three percentage points at a 95% confidence level." You can safely conclude that
A. 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.
B. the percent of the population who jog is certainly between 15% and 21%.
C. 95% of the population jog between 15% and 21% of the time.
D. we can be 95% confident that the sample proportion is captured by the confidence interval.
E. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.
The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.
The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.
Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.
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Which of the following gives the correct range for the piecewise graph?
51y
-5 -4 -3
0-2≤x≤5
O-2≤y≤5
O-4≤x≤3
O-4 sys3
4
3
2
1
-2 -1 0
-2
-3
A
-5
1
2
3
4
X
5
The range of the given piecewise function is -
-4 ≤ x ≤ 3.
What is Piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function.
Given is the piecewise function as shown in the image.
Range is the set of values that exist for a specific value in the domain of the function. So, we can write the range as the set of {y} values for the function. From the graph, we can write the range as -
-4 ≤ x ≤ 3
Therefore, the range of the given piecewise function is -
-4 ≤ x ≤ 3.
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Again no rush need an answer in about 5 hours or so I’d say!
The amount of square feet that will be needed is given as follows:
122 ft².
How to obtain the amount of square feet needed?The amount of square feet needed is given by the total area of the figure, which is composed as follows:
Rectangle of dimensions 6 ft and 15 ft.Trapezoid of bases 6 ft and 10 ft, along with height 4 ft.The area of the rectangle is given by the multiplication of the dimensions, hence:
Ar = 6 x 15 = 90 ft².
The area of the trapezoid is given by half the multiplication of the sum of the bases and the height, hence:
At = 0.5 x 4 x (6 + 10) = 32 ft².
Hence the total area is given as follows:
A = Ar + At
A = 122 ft².
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what is -0.28125 to 6 decimal places
Answer:
[tex]-0.281250[/tex]
Step-by-step explanation:
The given number has [tex]5[/tex] after the decimal point, so add a trailing zero.
For a project in her Geometry class, Ai Mi uses a mirror on the ground to measure the height of her school building. She walks a distance of 7.95 meters from the building, then places a mirror flat on the ground, marked with an X at the center. She then walks 2.3 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the school clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
The height of the school is approximately 5.96 meters.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.
The mirror and the triangles formed by the mirror, the top of the school, and the ground are similar. This means that the corresponding sides of the triangles are proportional.
Let x be the distance from the mirror to the top of the school. Then:
[tex]\dfrac{x} {7.95} = \dfrac{(x + h) }{ 2.3}[/tex]
We can simplify this equation by cross-multiplying and solving for x:
2.3x = 7.95(x + h)
2.3x = 7.95x + 7.95h
5.65x = 7.95h
[tex]x = \dfrac{7.95h} { 5.65}[/tex]
Now we can use the measurement of the distance from Ai Mi's eyes to the ground to find h. Let d be the distance from the mirror to Ai Mi's eyes. Then:
d = 1.15 meters
The triangles formed by Ai Mi's eye, the mirror, and the ground are similar, so:
[tex]\dfrac{h} { d} =\dfrac{ x} { (d + 2.3)}[/tex]
We can substitute the value of x from earlier:
[tex]\dfrac{h} { 1.15} = \dfrac{(\dfrac{7.95h} { 5.65)}} { 3.45}[/tex]
Simplifying:
[tex]h = \dfrac{(1.15 \times 7.95\times 3.45)}{ 5.65}[/tex]
h = 5.96 meters
Therefore, the height of the school is approximately 5.96 meters. Rounded to the nearest hundredth of a meter, the answer is 5.96 meters.
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Solve for x in the following circle: D X 140⁰E 160
10 degrees is the measure of angle x from the circle
Theorems in circle geometryIn order to determine the value of x from the given circle, we will use the theorem ' angle at the centre of the circle is twice the angle at the circumference.
Mathematically;
360 - 140 = 2arcED
220 = 2arcED
arcED = 220/2
arcED = 110 degrees
Hence the measure of angle x from the given figure is 110 degrees
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What percent of 96 is 73
Answer: 70.08
Step-by-step explanation:
0.96*73=
WHAT IF? The total cost of the vans for Location A is $228,500. The total cost for Location B is $153,000. What is the cost of
each type of van? Location A buys 7 large and 2 small vans, location B buys 2 large and 3 small vans
The cost of each large van is 22,323.53 and each small van is 36,117.65.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the cost of a large van and y be the cost of a small van.
The total cost of the vans for Location A is $228,500.
Location A buys 7 large and 2 small vans.
So we have a linear equation,
7x + 2y = 228,500
The total cost for Location B is $153,000.
Location B buys 2 large and 3 small vans.
So we have a linear equation,
2x + 3y = 153,000
Multiplying the first equation with 3 and the second equation with 2,
21x + 6y = 685,500
4x + 6y = 306,000
Subtracting,
17x = 379,500
x = 22,323.53
Substituting in one of the equation,
y = 36,117.65
Hence the cost of each large and small van are 22,323.53 and 36,117.65 respectively.
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The question is in the picture.
Answer:
x = 9 , y = 5
Step-by-step explanation:
Consider the figure to be a parallelogram.
• the diagonals bisect each other
then
2x - 4 = x + 5 ( subtract x from both sides )
x - 4 = 5 ( add 4 to both sides )
x = 9
and
9y - 13 = 5y + 7 ( subtract 5y from both sides )
4y - 13 = 7 ( add 13 to both sides )
4y = 20 ( divide both sides by 4 )
y = 5
how many cubic feet to liters?
One cubic foot is equal to approximately 28.3168 liters. So to convert cubic feet to liters, you can multiply the number of cubic feet by 28.3168.
Unit conversion is the process of converting a value expressed in one unit of measurement to an equivalent value expressed in another unit of measurement. For instance, to convert 10 feet to meters, you would use the conversion factor 1 foot = 0.3048 meters.
For example, if you have a volume of 5 cubic feet, you can convert it to liters as follows:
5 cubic feet * 28.3168 liters/cubic foot = 141.584 liters
Therefore, 5 cubic feet is equivalent to 141.584 liters (approximately).
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3. Xavier has $43 in his savings account and plans to save $15 each week. Write an algebraic expression to represent how much Xavier will have in his savings account after w weeks.
An algebraic expression representing the amount Xavier will have in his savings account after w weeks is 43 + 15w.
What is algebraic expression?Algebraic expressions consist of numbers, variables, and the mathematical operations, especially addition, subtraction, division, and multiplication.
An algebraic expression does not have the equation symbol (=) unlike an equation because it is not a complete mathematical statement.
The amount Xavier already has in his savings account = $43
The planned weekly savings = $15
The period of savings = w
Algebraic Expression:43 + 15w
Thus, using an algebraic expression, after w weeks, Xavier will have 43 + 15w in his savings account.
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A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the proportion who are satisfied with the firm's performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the proportion of all customers who are satisfied. The marketing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error and confidence interval? True Statements False Statements The margin of error will be about 2 times larger. The margin of error will be about 4 times larger The margin of error will be about the same size. The margin of error will be about half as farge. The margin of error will be about one-fourth as large. The confidence interval will be wider. The confidence interval will be narrower.
Is the relation a function?
{(-6, 1), (2, 3), (3, 4), (4, 5)}
Answer:
The one you provided in your text: Yes, each input has exactly one output.
The second one: No. 3 has two outputs.
The third one: No, two outputs for each x>-4.
The fourth one: Yes, unique y for each x.
elevation of 30 feeet below sea level
The elevation of the diver after the dive can be found to be 42 feet below sea level or - 42 feet.
How to find the elevation ?If the diver's elevation is -30 feet relative to sea level, and she dives down 12 feet, we can find her new elevation by adding the change in depth to her initial elevation:
New elevation = Initial elevation + Change in depth
New elevation = - 30 feet + ( - 12 feet )
New elevation = - 42 feet
Therefore, the diver's new elevation after the dive is -42 feet relative to sea level.
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The full question is :
A divers elevation is -30 feet below sea level. She dives down 12 feet. What is her elevation after the dive?
What are the coordinates of the point (−9, −5) after being reflected across the y-axis on a coordinate plane?
To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).
Answe
To reflect a point across the y-axis, you multiply the x-coordinate of the original point by -1 while keeping the y-coordinate the same. So, reflecting the point (-9, -5) across the y-axis results in the point (9, -5).
Step-by-step explanation:
help please I don’t know
Answer:
the value of x is 12 as per my calculation it goes in equation
Quadratic functions q and w are graphed on the same coordinate grid.
The vertex of the graph of q is 18 units below the vertex of the graph of w.
Which pair of functions could have been used to create the graphs of q and w?
)= 18x2 and w(x) = x²
dx)= x2 + 18 and w(x)=x²
dx)=18x2 and w(x) = x²
Oqx)=x²-18 and w(x) = x²
Fe
Answer: The correct pair of functions that could have been used to create the graphs of q and w is:
q(x) = x² - 18 and w(x) = x²
The vertex of the graph of q is (0, -18) and the vertex of the graph of w is (0, 0). Since the vertex of the graph of q is 18 units below the vertex of the graph of w, this is the pair of functions that would produce the given information.
Step-by-step explanation:
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
The following table contains the appropriate values for A, B, and C:
White 13 52 91 130 Black 9 36 63 90
What does "proportional relationship" mean?Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality". We'll now look at an instance of a proportionate relationship in real life: The amount of money we will have to spend while filling up our automobile with gas is inversely proportional to the number of gallons we put in the tank. In other words, the amount of gas we use will determine how much we pay.The definition of a proportionate relationship is as follows:
y = kx.
where k is the proportionality constant.
The following are the input and output variables for this issue:
Number of black keys to enter.
Number of white keys is the output.
The constant k is then obtained using the formula:
91 = 63k
k = 91/63
k = 13/9.
Hence the equation is:
y = 13x/9.
Hence the values are given as follows:
A: when x = 9, y = 13.
B: when x = 36, y = 13 x 36/9 = 52.
C: when x = 90, y = 13 x 90/9 = 130.
Hence the first table is correct.
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(3x^3+7x-1) +4x^3-9x^2-11x+1) urgent need
STANDARD FORM
The standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3x³+7x-1+4x³-9x²-11x+1 we need to make it in a standard form,
To arrange this expression in a standard form, we will just have to perform operations in like terms and then arrange them in decreasing order of the power of the variables,
Therefore,
3x³+7x-1+4x³-9x²-11x+1
Adding the like terms
= 4x³+3x³+7x-11x-9x²+1-1
= 7x³-9x²-4x
Hence, the standard form, of the expression 3x³+7x-1+4x³-9x²-11x+1 is 7x³-9x²-4x
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A university has 36,180 students. In a random sample of 210 students, 14 speak three or more languages. Predict the number of students at the university who speak three or more languages.
The expected number of students at the university who speak three or more languages is __________.
Answer:
2,412
Step-by-step explanation:
[tex]\displaystyle E(X)=np=(36180)\biggr(\frac{14}{210}\biggr)=2412[/tex]
Therefore, we can expect 2,412 students at the university to speak 3 or more languages.
i need help on this can question can anybody explain how to solve it and please solve in the simplest form
The slope of the segment [tex]\overline{DC}[/tex] of the line DA is equivalent to the slope of the segment [tex]\overline{BA}[/tex], which is 2/5. Therefore;
Slope of [tex]\overline{DC}[/tex] = [tex]\frac{2}{5}[/tex]
What is the slope of a graph of a linear function?The slope, m, of a graph with points (x₁, y₁), and (x₂, y₂) can be found using the formula;
[tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]
The colinear points are; D, C, B, and A
The slope of the each section of a straight line graph are equivalent, therefore;
The slope of the line DA using the segment [tex]\overline{BA}[/tex] is the same as the slope of the line DA found using the segment of the line [tex]\overline{DC}[/tex].
The slope of a line is the ratio of the rise to the run of the line
Slope = Rise/Run
The rise of a segment of a line is the vertical elevation of the line segment, while the run of the segment of a segment of the line is the horizontal distance between the boundaries of the segment of the line.
The rise of the line between points A and B is 2 unit while the run of the segment [tex]\overline{BA}[/tex] is 5 units.
The slope of [tex]\overline{BA}[/tex] = (2 units)/(5 units) = 2/5
The slope of [tex]\overline{DC}[/tex] = The slope of BA = 2/5
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(3c)° 42° 111°
Find the value of C in the figure
9 is the value of C.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The three given angles are (3c)° 42° 111°
We need to find the value of C.
The figure might be a triangle because there are three angles.
From angle sum property , the sum of three angles of triangle is 180 degrees.
3c+42+111=180
3c+153=180
Substitute 153 from both sides
3c=27
Divide both sides by 3
c=9
Hence, the value of c is 9.
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how much is a 1 gallon to litre?
The gallon is a unit of volume that represents the capacity of a liquid in both conventional and US imperial systems of measurement. 1 gallon is defined as 4.54609 liters.
Gallon:
The gallon is a common unit of volume in both English and US customary units. There are three types of gallons in use today: Imperial Gallon, US Gallon, and US Dry Gallon. There are 4 quarts in a gallon, for a total of 8 pints, and each system has a different volume.
Current use of the imperial gallon as of 2021 is still used as the standard unit of petrol in four British overseas territories. It is also the standard unit of measure for six countries: Antigua and Barbuda, Grenada and Saint Lucia.
Liter:
A liter is a metric unit of volume. A liter costs 1/1000 of a cubic meter. The liter was used as the base unit of the basic French metric system. 1 liter is the volume of a cube, i.e. 10 cm x 10 cm x 10 cm, so 1 liter = 1000 cm3 and 1 liter = 0. 2641720524 gallons.
This unit of volume can be used in the International System of Units even though it is not an SI unit. Current use of liters . The liters are primarily used for pourable items (these items can be solid or liquid). These items are measured by the size or capacity of the container. It is also used to measure non-liquid volumes such as backpacks, car trunks, etc.
Formula for Converting Gallons to liters
The formula for converting 1 gallon of water in liters is :
Liter = Gallon x 3.785411784
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3.
Consider this system of equations: y = - +4
3x - 4y = 12
Solve the system by graphing.
Click the line tool and select two points to create the line.
Select the point where the lines intersect and label the point. You will need to use decimal notation instead of fraction notatic
in your label.
Answer:
(4,0)
Step-by-step explanation:
I will assume the fiorst equation is missing an "x," so I'll assume it was meant to be: y = -x + 4
See the attached graph. The lines cross at (4,0).
Joselyn ran 2 miles north, 10 miles east, 4 miles north, 4 miles east and 2 mile north. How far is joselyn from where she started? Leave the answer in simplified radical form.
The distance of 2√65 miles Joselyn is from where she started.
What is the distance between two points?The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
Her initial position is the origin (0, 0), and she ran 2 miles north to reach (0, 2). Then, she ran 10 miles east to reach (10, 2). After that, she ran 4 miles north to reach (10, 6). Then, she ran 4 miles east to reach (14, 6). Finally, she ran 2 miles north to reach (14, 8).
To find the magnitude of Joselyn's displacement, we can use the Pythagorean theorem.
We can consider the displacement from the starting point to Joselyn's final position as the hypotenuse of a right triangle, and the north-south and east-west displacements as the two shorter sides.
Thus, the displacement (d) can be calculated as:
d = √((14 - 0)² + (8 - 0)²)
d = √(14² + 8²)
d = √(196 + 64)
d = √(260)
d = 2√65
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A vine called the mile-a-minute weed is known for growing at a very fast rate. It can grow up to 0.5 ft per day. How fast in inches per hour can the mile-a-minute weed grow up to? Show your work using the correct conversion factors.
please show your work step by step by step.
the mile-a-minute weed can grow up to 0.25 inches per hour.
What is fraction?A fraction is a mathematical expression that represents a part of a whole. It is written as a ratio of two numbers, the numerator and the denominator, separated by a horizontal line. The numerator represents the part of the whole that is being considered, while the denominator represents the whole.
Given by the question.
To convert 0.5 ft per day to inches per hour, we can use the following conversion factors:
1 ft = 12 inches (since there are 12 inches in a foot)
1 day = 24 hours (since there are 24 hours in a day)
So, to convert 0.5 ft per day to inches per hour, we can use the following steps: Convert feet to inches:
0.5 ft x 12 inches/ft = 6 inches
Convert days to hours:
1 day = 24 hours, so:
6 inches/24 hours = 0.25 inches per hour
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What is "a" in the equation
a/2.1 = 4.34
Answer:
a = 9.114
Step-by-step explanation:
[tex]\frac{a}{2.1}[/tex] = 4.34 ( multiply both sides by 2.1 to clear the fraction
a = 2.1 × 4.34 = 9.114