The contribution margin ratio for Lee+Company is 47%. This means that 47% of the sales revenue is available to cover the fixed costs
The contribution margin ratio is calculated by subtracting the variable costs from the sales revenue and dividing the result by the sales revenue. In this case, the sales revenue is $525,000 and the variable costs are 53% of the sales.
To calculate the contribution margin ratio, we can subtract 53% of the sales revenue from the total sales revenue:
$525,000 - (0.53 * $525,000) = $246,750.
Then, we divide the contribution margin ($246,750) by the sales revenue ($525,000) and multiply by 100 to express it as a percentage:
(246,750 / 525,000) * 100 = 47%.
Therefore, the contribution margin ratio for Lee+Company is 47%. This means that 47% of the sales revenue is available to cover the fixed costs and contribute to the operating income of $19,000.
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y = 1/2 x + 1
-2x + 4y = 4
need an answer please
y = -x - 3
y + x = 2
There are infinitely many solutions and thus infinitely many values for x and y in the first system of equations. There are no solution for the second system of equations.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
The first system of equations are,
y = 1/2 x + 1
-2x + 4y = 4
Multiplying throughout the first equation by 4, we get
4y = 2x + 4
and the second equation is 4y = 2x + 4
Both the equations are same and so the lines coincide.
They have infinitely many solutions.
The second system of equations are,
y = -x - 3
y + x = 2 ⇒ y = -x + 2
Both are in the form of y = mx +c, which is the equation of the line in slope intercept form.
Here m is the slope.
Given lines have the coefficient of x same, and so slopes are same.
So the lines are parallel.
Two parallel lines does not have a solution.
Hence the first system of equations have infinitely many solutions and second system of equations does not have any solution.
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A store sells two shades of purple paint. The tables show the number of gallons of blue paint and the number of gallons of red paint used to make each shade of purple paint.
Shade A
Number of Gallons of Blue Paint
8
12
16
24
Number of Gallons of Red Paint for shade A
12
18
24
36
Shade B
Number of Gallons of Blue Paint
5
7
9
12
Number of Gallons of Red Paint
10
14
18
24
Based on the tables, which statements are true? Choose all that apply.
A. The ratio of the number of gallons of red paint to the number of gallons of blue paint in
shade B is 2:1.
B. Shade B should be redder than shade A because shade B has 2 gallons of red paint for every 1 gallon of blue paint. Shade A has 13 gallons of red paint for every 1 gallon of blue paint.
C. Shade A should be bluer than shade B because shade A has 1 gallon of blue paint for every 2 gallons of red paint. Shade B has 1 gallon of blue paint for every 1/2 gallons of red paint.
D. Shade A should be bluer than shade B because shade A has gallons of blue paint for every 1 gallon of red paint. Shade B has gallon of blue paint for every 1 gallon of red paint.
E. If the store owner adds 1 gallon of blue paint to 20 gallons of shade A, she creates 21 gallons
of shade B.
Answer:
A. False
B. False
C. False
D. False
E. False
Explanation:
A. The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 2:1, but this statement only holds true for the first set of values provided.
B. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.
C. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.
D. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.
E. The statement is not true since there's no information about how the shade A is made.
Step-by-step explanation:
A can of tomato sauce contains 8 oz of sauce a case contains 12 cans chef Hugo orders some cases of tomato sauce and gets a total of 480 oz of sauce use 12(8)x=480 to find out how many cases of tomato sauce chef Hugo orders x.
The problem states that a can of tomato sauce contains 8 oz of sauce and a case contains 12 cans. We are trying to find out how many cases of tomato sauce Chef Hugo orders and we know that he gets a total of 480 oz of sauce.
What in mathematics is a linear equation?
According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We can use the formula 12(8)x = 480 to find out the number of cases of tomato sauce that Chef Hugo orders.
Here's the calculation:
12(8)x = 480
96x = 480
x = 5
Therefore, Chef Hugo orders 5 cases of tomato sauce.
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Which of the following does not represent a function? Explain why you chose the answer. I will mark you brainliest!!!
Table B and C
In Table B, the X coordinate of -3 has two different answers which is impossible in a function because it only has one output or one answer which is y.
In Table C, the X coordinate of 0 also has two different outputs or two different answers, and with a function, there is only one y coordinate for each X coordinate.
Power of a power quotient rule
The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents.
What is power?The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents. A power series is an infinite series in mathematics in which a represents the coefficient of the nth term and c is a constant. Power series may be found in mathematical analysis as Taylor series of indefinitely differentiable functions. The power of a number indicates how many times the number may be multiplied. Exponents and Indices are other names for powers. For example, 8^2 might be labeled "8 to the power 2" or "8 to the second power", or simply "8 squared".
Here,
The quotient rule essentially asserts that as long as the base is the same, we may divide two powers by subtracting the exponents. This is a shortcut for simplifying exponents.
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find the maximum value of y= -8x^2 + 80x -196
Answer:
(5,4)
Step-by-step explanation:
first, if you have a calculator you can put the equation into y = and just find the maximum point there
to find the x value of the maximum point you do -B/2A
-80/2(8) = 5 so the x value would be 5
then to find y just plug in 5 for x and you should get 4
Answer:
Maximum value of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]
is
[tex]\boxed{f(x) = 4}[/tex]
Step-by-step explanation:
The maximum or minimum value of a function f(x) occurs when the first derivative equals zero
The first derivative of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]
[tex]f'(x) = \dfrac{d}{dx}\left(-8x^2+80x-196\right)[/tex]
[tex]=-\dfrac{d}{dx}\left(8x^2\right)+\dfrac{d}{dx}\left(80x\right)-\dfrac{d}{dx}\left(196\right)[/tex]
[tex]\dfrac{d}{dx}\left(8x^2\right) = 16x\\\\=- \dfrac{d}{dx}\left(8x^2\right) = -16x\\\\\\\dfrac{d}{dx}\left(80x\right)=80\\\\\dfrac{d}{dx}\left(196\right)=0[/tex]
[tex]\dfrac{d}{dx}\left(-8x^2+80x-196\right) \\\\\\ =-16x + 80 + 0\\\\= -16x + 80\\\\[/tex]
Set this expression equal to 0 and solve for x to find the x value which maximizes or minimizes the function
[tex]-16x + 80 = 0\\\\\implies -16x = -80\\\\x = -80/-16\\\\x = 5\\\\[/tex]
Plug this value of x into the original function to get the maximum or minimum value.
[tex]f(5) = -8(5^2) + 80(5) - 196\\\\= -8 (25) +400 -196\\\\= -200 + 400 - 196\\\\= 4\\\\[/tex]
So the maximum value of [tex]\boxed{f(x) = 4}[/tex] ANS
and occurs at [tex]x = 5[/tex]
(Strictly speaking to find if this is a maximum or minimum, we have to find the second derivative and see if it is negative or positive. If negative, it is a maximum, if positive it is a minimum
But since the question does not ask for this, I am skipping it. In case you are interested, the second derivative of f(x) is the derivative of f'(x) which will work out to -16 so it is a maximum)
Why is it called a secant?
A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.
what is circle ?In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.
given
The Latin verb secare, which means to cut, is where the word secant originates.
A secant crosses a circle at precisely two points in the case of a circle. A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.
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the sum of the angle measures of a quadrilateral is 360 find the measure of the missing angle (please help)
How to learn table 1 to 20?
Therefore , the solution of the given problem of tables comes out to be to recall multiplication tables without just repeating the numbers is by using skip counting.
Explain a table.A mathematical list is a list of numbers that represents the results of a calculation with several inputs. organized in rows and columns, data consists of numbers and descriptions. It is simple to recall the table and the 10 pattern. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the numerals in numerical order. Value mapping are used to illustrate the connections between various data elements.
Here,
One of the most effective techniques to recall multiplication tables without just repeating the numbers is by using skip counting.
When counting by skips, you always start with the integer you're counting by and keep adding it.
For instance, if you skip count by 2, you would get 2, 4, 6, 8, 10, etcetera.
Therefore , the solution of the given problem of tables comes out to be to recall multiplication tables without just repeating the numbers is by using skip counting.
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The town of springfield, usa has a population of 990099009900 people. The population is growing at a rate of 2. 3\%2. 3%2, point, 3, percent each year. Which expression gives the town's population 555 years from now?.
The expression that gives the town's population 555 years from now can be calculated using the following formula:
Population (t) = Population (0)×[tex](1+growth rate)^{t}[/tex]
Where t is the time period, in this case 555 years, Population (0) is the initial population, and Growth Rate is the rate of growth, in this case 2.3%.
Plugging in the values, the expression giving the town's population 555 years from now is:
990099009900 × [tex](1+0.023)^{555}[/tex]
This expression gives a population of 236793241036.6 people, which is the estimated population of the town of Springfield, USA 555 years from now.
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Use the slider to change the scale factor.
8
6
4
2
0
2
Scale: 1
4
6
8
Consider the original rectangle and the rectangle that
has been reduced by 0.5.
What is the perimeter of the original figure?
What is the perimeter of the scale figure?
On solving the provided question, we can say that - There exist 333 integers smaller than 1000 that are evenly divisibility test by 3 if you divide 1000 by 3, which results in 333 with a residual of 1.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
here,
1000/3
remainder = 1
divisor = 333
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On solving the provided question, we can say that in the rectangle L = 6 units and B = 2 units, Perimeter, P = 2(L+B) => P = 2(6+2) => P = 16 units
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
in the rectangle
L = 6 units
B = 2 units
Perimeter, P = 2(L+B)
P = 2(6+2)
P = 16 units
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There is a line whose slope is eight and whose Y intercept is five what is it equation in slope intercept form
Answer:
y=8x+5
Step-by-step explanation:
y=mx+b is slope intercept form
m stands for Slope = 8
b is y intercept = +5
plug it in and you get y=8x+5
Which of the following is the correct solution for the equation 5t 3 3t 5?A. -1B. -2C. 1D. 2
The solution for the equation 5t - 3 = 3t - 5 is when value of t is equal to -1.
Therefore the answer is A. -1.
To find the solution, you can start by isolating the variable t on one side of the equation by adding 3 to both sides and subtracting 3t from both sides:
5t - 3 + 3 = 3t - 5 + 3
5t = 3t - 2
Then subtract 3t from both sides:
5t - 3t = 3t -2 - 3t
2t = -2
Finally, divide both sides by 2 to solve for t:
t = -2/2
t = -1
So, the value of t that satisfies the equation 5t - 3 = 3t - 5 is -1.
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Solve the equation 3x + 4y = 7 for y.
y equals the quantity negative 3 times x plus 7 end quantity over 4
y equals the quantity 3 times x plus 7 end quantity over 4
y equals negative 3 over 4 times x plus 7
y equals negative 3 times x plus 7 over 4
y equals the quantity negative 3 times x plus 7 end quantity over 4.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given a linear equation in two variables.
3x+ 4y = 7
We have to find an expression to calculate y from the equation.
Subtracting both sides of the equation with 3x, we get,
3x + 4y - 3x = 7 - 3x
4y = 7 - 3x
Dividing throughout by 4,
4y/4 = (7 - 3x)/4
y = (7 - 3x) / 4
Hence the value of y is the quantity negative 3 times x plus 7 end quantity over 4.
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How do you find the ratio of a circle formula?
The ratio of a circle can be found through the formula A = πr2, where A is the area of the circle and r is the radius of the circle.
To find the ratio of a circle, you must first calculate the area of the circle. To calculate the area, multiply the value of π (3.14159) by the square of the radius (r2). For example, if the radius of the circle is 4, the area of the circle would be 3.14159 x 42, which is equal to 50.2653. The ratio of a given circle can then be found by dividing the area of the circle (50.2653) by the square of the radius (42), which gives 1.273.
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Jon and Becky measured the circle-shaped part of a sun they drew on the sidewalk. The diameter of the circle is 66 centimeters. What is the approximate area of the circle? (Use 3.14 for .) A. 854.865 cm2 B. 3,419.46 cm2 C. 207.24 cm2 D. 13,677.84 cm2
The correct option for the area of the circle is B. 3,419.46 cm².
What is area of a circleThe area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr².
Area of circle = πr²
π = 3.14
radius = diameter/2
radius of the circle = 66 cm/2
radius of the circle = 33 cm
Area of the circle = 3.14 × (33 cm)²
Area of the circle = 3.14 × 1089 cm²
Area of the circle = 3419.46 cm²
Therefore, the area of the circle measured by Jon and Becky is equal to 3,419.46 cm².
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Help please and thank you
Answer:
A.
Step-by-step explanation:
looking at the scatter plot, we can sort of determine a line of best fit, so if we imagine a linear line passing through the middle of the plots, the slope of the line would be positive :)
In ∆ABC, if m ABC, if m∠A is seven
more than four times
m∠B and m∠C is eleven C is eleven
more than m more than m∠B, find B, find the
The measure of the angle ∠B of the triangle ABC will be 27°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In ∆ABC, if m∠A is seven more than four times m∠B and m∠C is eleven more than m∠B. Then the equations are given as,
∠A = 4∠B + 7 ...1
∠C = ∠B + 11 ...2
∠A + ∠B + ∠C = 180° ...3
From equations 1, 2, and 3, then we have
4∠B + 7° + ∠B + ∠B + 11° = 180°
6∠B = 162°
∠B = 27°
The measure of the angle ∠B of the triangle ABC will be 27°.
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please help i dont know what im doing
Answer:
87-5x Gespil=13+8x
Step-by-step explanation:
dubble started with 87, so we but 87 as the y-intercept. Every month he LOSES elentires, therefore minus. The months are represented by x, because we don’t know how many have passed. Same thing for Gespil except it increases for her.
if possible could i maybe get brainilest???? if i cant then its okay.
Tom would like to take out a secured loan to help pay for a vacation this summer. he has offered his car as collateral. his car is worth $3,500. his bank can offer loans for 80% of collateral value. the vacation he has planned will cost $4,750. approximately how much additional collateral will tom need to offer in order to borrow enough to go on his vacation as planned? a. $1,000.00 b. $1,362.50 c. $2,437.50 d. $2,800.00 please select the best answer from the choices provided a b c d
Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.
What is unitary method?This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
According to our question-
automobile is priced at $3,500.
Tom needs more collateral, so P
=P + 3500 Total Collateral Value
His bank is able to lend up to 80% of the value of the collateral.
=> loan = (80/100)(P + 3500)
=> loan = 0.8P + 2800
Loan amount needed: 4,750.
0.8P + 2800 = 4,750.
=> 0.8P = 1950
=> P = 2,437.5
Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.
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The mobile company charges $180 for an hour of service. How many dollars are customers charged every minute?
Answer: $3
Step-by-step explanation:
Since the company charges $180 for an hour of service, we can say that it charges $180 for 60 minutes of service.
Let the cost of service per minute be C
The equation would be
60C = 180
Simplify, and you'll get
C = 3
And there's your answer.
What is the value of 7’3•7’2
Answer:
When adding the fractions 2/7 and 3/7 you'll get 5/
Step-by-step explanation:
pls mark as brainliest
Randi and Leah are studying together for an exam. Let X represent the number of hours Randi spends studying
nightly, and let y represent the number of hours Leah spends studying nightly. The mean of X is 4.5 hours with a
standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours. Assuming
these are independent random variables, which answer choice correctly calculates and interprets the standard
deviation of the sum, S = X + Y?
subscript u s=0.7; Randi and Leah can expect the total number of hours spent studying to vary by approximately 0.7 hours from the mean.
subscript s = 1.7; Randi and Leah can expect the total number of hours spent studying to vary by approximately 1.7 hours
from the mean.
subscript s=2.1; Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.
subscript = 2.9; Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.9 hours
from the mean.
Answer:
2.1
Step-by-step explanation:
σ total ^ 2 = σ randi ^2 + σ leah ^2 = 1.1^2 + 1.8^2 = 4.45
σ total = √4.45 = 2.1
Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.
The correct option is C.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Given:
Randi and Leah are studying together for an exam.
Let X represent the number of hours Randi spends studying nightly, and let y represent the number of hours Leah spends studying nightly.
The mean of X is 4.5 hours with a standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours.
Assuming these are independent random variables,
S = X + Y
σ² = σ²(Randi)² + σ²(Leah)
= (1.1)² + (1.8)²
=√(4.45)
σ = 2.1
Therefore, the sum is 2.1.
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What is the value of R in the equation 2 2r 8 3r 16 4 points a 0 b2 C 10 D 32?
The equation 2 2r 8 3r 16 is a linear equation in two variables (r and 3r).
To solve for r, we can use the method of elimination. First, we subtract the second equation from the first equation:
2 2r 8 3r 16
-2 2r 8 3r 16
------------------------
0 0 0
Since the equation is now equal to 0, this means that r is equal to 0. We can confirm this by substituting 0 in for r in both equations:
2 2(0) 8 3(0) 16
2(0) 8(0) 16
0 0 16
Since 0 = 16 is not true, this confirms that r = 0.
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1/3 of a gallon equally with 3 friend elect the equation that how how to calculate the fraction
The fraction that can be equally distribute the equation is 1/9.
The term fraction is defined as the representation of the part of whole thing and it has two parts that is namely numerator and denominator.
Here we have given that is 1/3 gallon of water in a 3 gallon container.
Here we have the amount of water is 1/3 gallon and the container capacity is 3.
Now, we have to equally distribute it across the given contained for that one we have to divide it by the total amount of the container then we get,
=> (1/3)/3
When we rewrite the fraction, the we get the expression as,
=> 1/3 x 1/3
When we multiply this one, then we get,
=> 1/9
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find vertical and horizontal asymptotes
A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.
A slant asymptote exists of the form y = mx + b where m ≠ 0.
What is the difference between vertical and horizontal asymptotes?Vertical lines go up and down and are in the form of x = a, where a stands for the common x-coordinate of all locations, whereas horizontal lines go left to right and take the shape of y = b, where b stands for the y-intercept.
A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's domain, the graph can never cross it. There may be multiple vertical asymptotes for a given function. All common factors are cancelled in the denominator, D(x).
A horizontal asymptote exists of the form y = k where x→∞ or x→ -∞ if the value of the one/both of the limits lim ₓ→∞ f(x) and lim ₓ→ -∞ f(x).
A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.
A slant asymptote exists of the form y = mx + b where m ≠ 0.
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Complete the table of values and answer these questions. Which function has the greater rate of change between 0 and 1? Which function has the greater rate of change between 1 and 2? Which function has the greater rate of change between 0 and 2?
The table is completed using the function f(x) = 3ˣ and g(x) = 3x as shown below
x f(x) g(x)
0 1 0
1 3 3
2 9 6
f(x) has a greater rate of change between 1 and 2
f(x) has a greater rate of change between 0 and 2
How to find the function that has the greater rate of changeThe table is completed by substituting the values of x into the functions of f(x) and g(x)
The rate of change between 1 and 2
f(x)
= change in y / change in x
= (9 - 3) / (2 - 1)
= 6
g(x)
= change in y / change in x
= (6 - 3) / (2 - 1)
= 3
The rate of change between 0 and 2
f(x)
= change in y / change in x
= (9 - 1) / (2 - 0)
= 4
g(x)
= change in y / change in x
= (6 - 0) / (2 - 0)
= 3
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What is the formula to calculate pixel?
By dividing the width and height by the dpi, one may get the pixel size. Additionally, a digital camera will have pixel dimensions, which are the sum of its resolution's horizontal and vertical pixel counts (e.g., 2,048 by 3,072), this is the formula to calculate pixel.
What is pixel made of?The smallest component of a visual display or digital image is a pixel, also known as a picture element. A grid of pixels is used to create computer screens. Red, blue, and green illumination components make up each pixel, which may produce millions of distinct colors by combining them in various ways and at various intensities.
For instance, a computer with a display resolution of 1280 x 768 will create up to 98,3040 pixels on a display screen. The number of pixels per inch of the monitor screen affects image quality; more pixels per inch produce better images.
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Ms. Wells is going to order 4 large cheese pizzas for a class pizza party at the end of the school year. She expects she'll spend at least $40 on the pizzas. Let x represent how much ms. Wells expects each pizza to cost. Which inequality describes the problem?.
The correct inequality that describes the problem is 4x ≥ 40. Thus, the correct answer is A.
The answer is A because Ms. Wells is ordering 4 large cheese pizzas, and she expects to spend at least $40 on the pizzas. The inequality 4x ≥ 40 represents the total cost of the pizzas, which is 4 times the cost of each pizza (4x) and should be greater than or equal to $40. This inequality tells us that the total cost of the pizzas is at least $40, which is what Ms. Wells expects.
Option B, 4x > 40x, is incorrect because it doesn't make sense mathematically. The right side of the inequality is 40x, which is not related to the problem, and it also doesn't make sense that each pizza will cost 40 dollars.
Option C, 4x ≤ 40, is incorrect because it represents the total cost of the pizzas as less than or equal to $40, which doesn't match with Ms. Wells' expectation that she expects to spend at least $40 on the pizzas.
This question should be provided with answer choices, which are:
A. 4x ≥ 40B. 4x > 40xC. 4x ≤ 40The correct answer is A.
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A cylinder has base radius x cm and height 2x cm. A cone has base radius x cm and height h cm. The volume of the cylinder and the volume of the cone are equal. Find h in terms of x. Give your answer in its simplest form.
The value of h in terms of x when the volume of cylinder is equal to that of cone is h = 6x²
What is volume of cylinder and cone?Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.
The volume of a cone is linked to the volume of a cylinder. A cone is one third of the volume of a cylinder. The volume of a cone is ¹/₃ × π × r² × l. To calculate the volume we multiply these values together.
The volume of cylinder = πr²h
and volume of cone = 1/3 πr²h
since the volume of the cone and cylinder are equal
πr²h = 1/3 πr²h
r in cylinder = x cm and h is 2x
r in cone = x cm
therefore πx²×2x = 1/3πxh
divide both side by πx
π2x³/πx = h/3
2x² = h/3
therefore h = 3×2x²
h = 6x²
therefore the value of h in terms of x is h = 6x²
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