The volume of a cylinder is given by the formula V = pier2, where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius (x + 8) and height (2x + 3). Which expression represents the volume of the can?
Answers
Answer:
The volume of the cylinder is defined by the expression .
\(V=\pi (x+8)^2 (2x+3) or V=\pi (2x^3 + 35x^2 + 176x +192)\)
The volume of the cylinder where the radius is r = ( x + 8 ) and height is h = ( 2x + 3 ) is given by the expression V = π ( 2x³ + 35x² + 176x + 192 ) units³
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the volume of the cylinder be V
Now , the radius of the cylinder is r = ( x + 8 ) units
The height of the cylinder is h = ( 2x + 3 ) units
And , Volume of Cylinder = πr²h
On simplifying , we get
The volume of cylinder V = π ( x + 8 )² ( 2x + 3 ) units³
The volume of cylinder V = π ( x² + 16x + 64 ) ( 2x + 3 )
The volume of cylinder V = π ( 2x³ + 35x² + 176x + 192 ) units³
Hence , the volume of cylinder is V = π ( 2x³ + 35x² + 176x + 192 ) units³
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Related Questions
The triangles are similar. Find the area of the smaller one.
Answers
Answer:
B: 24cm squared
Step-by-step explanation:
For 12 to convert to 3, you divide by 4. So 96 divided by 4 is 24!
Darnell has 3 1/2 pies. He gives each of his five friends 3/8 of a pie. How much pie does Darnell have left?
Answers
Answer:
1 5/8
Step-by-step explanation:
3 1/2 = 3 4/8
3 (from 3/8) x 5 = 15/8
3 4/8 - 15/8 = 1 5/8
there are n invitation cards with the names of n different people and n envelopes with their names. we put the cards at random into the envelopes, one card per envelope. what is the chance that not a single invitation landed in the correct envelope?
Answers
The probability that not a single invitation landed in the correct envelope is P(n) = D(n) / n! , where D(n) is the number of derangements of n objects.
The number of derangements of n objects is denoted by D(n).
The first few values of D(n) are given below: D(1) = 0 (trivially)D(2)
= 1 (the two objects must switch places)D(3)
= 2 (out of the six possible permutations, only two are derangements)D(4)
= 9 (out of the 24 possible permutations, nine are derangements)D(5)
= 44 (out of the 120 possible permutations, 44 are derangements)
The formula for the number of derangements is D(n) = n! × (1/0! - 1/1! + 1/2! - 1/3! + ··· + (-1)^n / n!), where n! is the factorial of n, 0! = 1 by definition, and (-1)^n is (-1) raised to the power of n.
Hence, we can find the probability that not a single invitation landed in the correct envelope as P(n) = D(n) / n!.
Thus, the probability that not a single invitation landed in the correct envelope is P(n) = D(n) / n! , where D(n) is the number of derangements of n objects.
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intermediate accounting
how to get these numbers Or what are the steps(multiply or divide) to get these numbers=10.25776 or the cumulative pv factor 2.5% for 12 periods And 13.69955 or the cumulative pv factor 2.5% for 13th to 37th period?
Answers
The method to get the future cash flow using the cumulative present value factor is explained.
To calculate the numbers you mentioned, you need to use the cumulative present value factor (PV factor) formula. The PV factor represents the present value of a future cash flow discounted at a given interest rate.
To calculate the cumulative PV factor at 2.5% for 12 periods (10.25776),
you need to multiply the PV factor for each period. The formula for the PV factor is 1 / (1 + interest rate) ^ number of periods.
For example, to calculate the PV factor for each period, you would use the following formula: 1 / (1 + 0.025) ^ period number.
Then, multiply these PV factors for each period to get the cumulative PV factor for 12 periods.
To calculate the cumulative PV factor at 2.5% for the 13th to 37th period (13.69955), you would follow the same steps as above.
However, instead of multiplying the PV factors for all 37 periods, you would subtract the cumulative PV factor for 12 periods from the cumulative PV factor for 37 periods.
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Dose this tablet represent a function? Why or why not? {(2,1), (2,4), (3,4), (4,2), (5,5)}
Answers
Answer:
This mapping isn't a function.
Step-by-step explanation:
A mapping specifies a relation between two sets of items (input and output). For example, a mapping of the form \(\lbrace (x_{0},\, y_{0}),\, (x_{1},\, y_{1})\rbrace\) would map the input \(x_{0}\) to output \(y_{0}\) and map the input \(x_{1}\) to output \(y_{1}\).
A function is a mapping where each input is associated with exactly one output.
Note that both \((2,\, 1)\) and \((2,\, 4)\) are in the mapping given in this question. The input \(2\) is mapped to more than one outputs. Thus, this mapping isn't a function.
SOLVE BOTH
if f(x)=2x+8, find f(5)
if f(x)=3x+4, find f(8)
Answers
Answer:
Step-by-step explanation:
simple! plug in the 5 for x, f(5)=2(5)+8
f(5)=10+8
f(5)=18
f(8)=3(8)+4
f(8)=28
Find the area of the shaded region. webassign plot
A = 22 / 7 (7)². A = 22 * 7 =154. The area of the triangle is equal to 154 cm². Area of the shaded region = Area of the large geometrical shape – area of the small geometrical
Answers
The area of the shaded region is 42cm².
Here we have the side of the square as 7 + 7 = 14cm
We know that the area of the square formula is a² and the area of the quadrant is πr²/4.
We can now subtract the area of the square from the area of the 4 quadrants, and we get
Area of shaded region = Area of the square – Area of 4 quadrants.
= (7)² - 4× π(7)²/4
We can now solve the above steps, we get
Area of shaded region = 14×14 - 22/7 ×7×7 = 196-154 = 42cm².
The location is the degree of a place's size on a floor. The area of a plane vicinity or aircraft region refers to the place of a shape or planar lamina, even as floor area refers back to the location of an open surface or the boundary of a 3-dimensional object. The place may be understood as the amount of fabric with a given thickness that could be vital to fashion a model of the form or the amount of paint necessary to cover the floor with an unmarried coat. it's far the two-dimensional analog of the period of a curve (a one-dimensional concept) or the extent of a solid (a three-dimensional concept).
There are several well-known formulations for the areas of easy shapes including triangles, rectangles, and circles. using these formulas, the location of any polygon may be observed by means of dividing the polygon into triangles. For shapes with curved boundaries, calculus is typically required to compute the location. certainly, the trouble of figuring out the location of aircraft figures changed into a prime motivation for the ancient improvement of calculus.
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What is the slope-intercept form of the line represented in the table shown?
X Y
-2 14
-1 12
0 10
1 8
2 6
3 4
Step 1: Find the y-intercept:
Step 2: Choose any two points from the table to find the slope:
Step 3: Use the newly-found slope to write the slope-intercept equation. The form
for that is y = mx + b.
Step 4: Check your work. Choose an ordered pair from the table and substitute
into the newly-found equation
Answers
Answer: The slope-intercept form is y = -2x + 10
Step-by-step explanation:
Step 1: The y-intercept is the point where x=0, so that is (0,10)
Step 2: Use the points (-2,14) and (-1,12) to find the slope
Slope (m) = ΔY/ΔX = -2/1 = -2
Step 3: The slope-intercept form is:
y = mx+b
y = (step 2 value) x + (step 1 value)
y = -2x+10
Please remember to vote this as Brainliest if I earned it!
I have no idea what I’m doing
Answers
Answer:
15.2 cm, 130 m
Step-by-step explanation:
1. The sine of angle Z is XY/17.4; (opposite/hypotenuse);
sin(61) = XY/17.4; multiply both sides by 17.4 to find XY
17.4sin(61) = 15.2 cm
2.
This triangle is made by the anchor of the balloon to the ground, the balloon, and the area on the ground directly below the balloon.
The hypotenuse of the triangle is the 170 m string.
The angle of inclination is 50 degrees.
The height of the triangle will be opposite of the angle of inclination.
Therefore,
sin(50) = height/170 (opposite/hypotenuse)
170sin(50) = 130.2 meters
write the equation of the line perpendicular to y=3x-1 that passes through the point (3,-4)
explanation or step by step pls
thanku
Answers
Answer:
\(y=-\frac{1}{3}x - 3\)
Step-by-step explanation:
Hi there!
We want to write an equation of the line that is perpendicular to y=3x-1 and passes through (3, -4)
Perpendicular lines have slopes that multiply to get the value of negative one.
Let's first figure out the slope of y=3x-1
The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
3 is in the place of where m is, so 3 is the slope of y=3x-1
Now let's find the slope of the line perpendicular to it.
We can use a formula like this:
\(m_1 * m_2= -1\)
If 3 is \(m_1\), then:
\(3*m_2=-1\)
Divide both sides by 3
\(m_2=-\frac{1}{3}\)
So the slope of the perpendicular line is -1/3
We can write this equation in slope-intercept form. So far, we know that the equation of the line is:
y=\(-\frac{1}{3}x + b\)
So let's find b
Remember that we are given that the line passes through the point (3, -4). That means that point is a solution to the equation that we're trying to find. Therefore, the values of that point should create a true statement when plugged into the equation.
So we can substitute 3 as x and -4 as y to help solve for b.
-4=\(-\frac{1}{3}(3)+b\)
Multiply
-4=\(-\frac{3}{3}\) + b
Simplify
-4 = -1 + b
Add 1 to both sides to isolate b
-3 = b
Substitute -3 as b in the equation
\(y=-\frac{1}{3}x - 3\)
Hope this helps!
$14,000 is deposited into a savings account with an annual interest rate of 4% compounded continuously. How much will be in the account after 3 years? Round to the nearest cent. $15,784.96 $15,820.00 $43,714.05 $46,481.64 if you could could you please explain thank you.
Answers
Formula for compound interest = P(1+Interest Rate)^n
=> 14000(1.04)^3
=$15,748.096
$14,000 is deposited into a savings account with an annual interest rate of 4% compounded continuously then $15,784 is the amount after 3 years.
What is Probability?
It is a branch of mathematics that deals with the occurrence of a random event.
Given that $14,000 is deposited into a savings account with an annual interest rate of 4% compounded continuously.
We need to find the amount in the account after 3 years.
\(A=Pe^r^t\)
where A is the amount of money after t years,
P is the principal amount
r is the annual interest rate
P = $14,000, r = 0.04 and t=3
\(A = 14000e^(^0^.^0^4^3)\)
A = 15,784
Hence, $14,000 is deposited into a savings account with an annual interest rate of 4% compounded continuously then $15,784 is the amount after 3 years.
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Assume you want to calculate the means of the 4 numeric variables in iris but you do not know the function name. How do you proceed? 2.3.2. Which function(s) does R provide for calculating the mean? Which arguments does/do itthey accept? 2.3.3. Does RStudio also offer ways to help? 2.3.4. Which ways of code completion does RStudio offer? And how do they differ? 2.3.5. Use the read.table command and auto completion to read mylris.csv into a new variable. 2.3.6. Activate all R diagnostics related to syntactic errors.
Answers
The above code will read the data in mylris.csv into a new variable named my_data and store it in the R environment. To activate all R diagnostics related to syntactic errors, use the following command below:options(show.error.messages = TRUE)
To calculate the means of the 4 numeric variables in iris, follow the steps below: First, you will need to load the iris dataset. You can do this by using the command below. data(iris)To find the mean of the numeric variables, you can use the function mean() which is available in R.
It calculates the arithmetic mean of a vector of values. To find the mean of the numeric variables in iris, you can use the following code below.mean
(iris$Sepal.Length)mean(iris$Sepal.Width)mean(iris$Petal.Length)mean(iris$Petal.Width)
The above code will display the means of the four numeric variables in iris.R provides multiple functions for calculating the mean. The most commonly used ones are mean(), colMeans(), and rowMeans().The mean() function takes a vector as an argument and calculates the arithmetic mean of the values in the vector.
The col Means() and rowMeans() functions take a matrix or a data frame as an argument and calculate the means of the columns or rows, respectively. RStudio provides multiple ways to help with coding. Code completion is one such feature. Code completion is a feature that allows you to autocomplete code while you are typing. RStudio offers multiple ways of code completion.
The most commonly used ones are Basic Completion, Contextual Completion, and Shorthand Completion.
To use the read.table command to read mylris.csv into a new variable, use the following code below:
my_data <- read.table("mylris.csv", header = TRUE, sep = ",")
The above code will read the data in mylris.csv into a new variable named my_data and store it in the R environment. To activate all R diagnostics related to syntactic errors, use the following command below:options(show.error.messages = TRUE)
The above command will enable R to display all error messages related to syntactic errors.
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Three tennis balls are stored in a cylindrical container with a height of 8.2 inches and a radius of 1.32 inches. The circumference of a tennis ball is 8 inches. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.
Answers
The amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)
The volume of a tennis ball:
The circumference of the tennis ball is 8 inches.
The tennis ball is the form of sphere whose circumference is given by formula \(2\pi r\) , where r is the radius.
Thus, if r is the radius then according to condition,
\(2\pi r\) = 8 or
r = 8/2\(\pi\) inches.
Now, the volume of the sphere of radius r is \(\frac{4}{3}\pi r^3\) hence, find the volume of the given tennis ball by substituting r = 8/2\(\pi\) inches in \(\frac{4}{3}\pi r^3\) and simplify:
Volume = \(\frac{4}{3} \pi\) × \((\frac{8}{2\pi } )^3\)
Volume = 8.65 \(inches^3\)
Hence the required volume of the tennis ball is 8.65 \(inches^3\)
The volume of three tennis balls is (3 × 8.65) \(inches^3\) = 25.96 \(inches^3\)
Find the volume of the cylinder:
The volume of the cylinder with radius r units and height h units is given by \(\pi r^2h\) Hence the volume of the given cylinder with radius 1.32 inches , 8.2 height inches is:
\(\pi (1.32)^2\) × 8.2
= 3.14 × \((1.32)^2\) × 8.2
= 44.86 \(inches^3\)
Hence the volume of the cylinder is 44.86 \(inches^3\)
Find the amount of space within the cylinder not taken up by the tennis balls.
The required volume can be obtained by subtracting the volume three tennis balls from the volume of the cylinder as follows:
Volume of cylinder - volume of three tennis balls = (44.86 - 25.96) = 18.9 \(inches^3\)
Hence, the amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\).
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GEOMETRY: The formula for the perimeter of a rectangle is P=21 + 2w, where l is the length and w is the width. A rectangle has a perimeter of 24 inches. Find its
dimensions if its length is 3 inches greater than its width.
a. 6 in. by 9 in.
b. 4 in. by 7 in.
c. 5 in. by 7 in.
d. 4.5in. by 7.5 in.
Answers
Answer:
d) 4.5in * 7.5 in
Step-by-step explanation:
24 = 2L + 2W
L = W+ 3
then:
24 = 2(W+3) + 2W
24 = (2*W + 2*3) + 2W
24 = 2W + 6 + 2W
24 = 4W + 6
24 - 6 = 4W
18 = 4W
W = 18/4
W = 4.5
L = W+3
L = 4.5 + 3
L = 7.5
Check:
24 = 2(L+W)
25 = 2(7.5 + 4.5)
24 = 2*12
What is the union of the two intervals (2,3] and [3,4], written as a single interval?
Answers
The union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].
What is an interval?
⇒ An interval is an expression that involves a subset of numbers on the actual line. These intervals contain all the actual numbers between the two numbers in the interval.
There are three types of intervals, these are:
Open intervals: are the numbers of the set between two numbers. These are denoted by a parenthesis (a,b), where a and b are any two numbers, and on the actual line, they are identified by an unfilled circle.Closed intervals: are the sets formed by two numbers and those between them. This interval is denoted by square brackets [a,b], and on the actual line, it is identified by two filled circles for each number in the interval.Semi-open interval: these intervals can be opened on the right and closed on the left (a,b] or opened on the left and closed on the right [a,b).⇒ The intervals can be joined if in the math problem the result is between one end of the real line and the other end of the real line. There are two intervals with the sign of union in the middle of them.
The representation of the union of these intervals is given as follows:(2,3]∪[3,4] , the union is denoted by ∪
Now as in every interval the three is part, we can express this union of this set as one in the following way:
⇒ (2,4]
Hence, the union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].
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Which of the following is equivalent to:
−−(2+5)−(3−7)?
Answers
Answer:
You haven't provided expressions, so I can work out the problem for you. When we divide fractions, remember always "keep, switch, flip!" That's what we're gonna do here. We keep the 2/5, switch the sign to multiplication, and flip the 7/8 to 8/7. Therefore, we have 2/5*8/7. That gives us 16/35. Hope this helps!
Step-by-step explanation:
135.85 rounded to the nearest tenth
Answers
Hope my answer helped u :)
Question:
Sara is making hot cocoa. The table represents the number of teaspoons of sugar Sara uses for the number of servings.
1. Graph the table of values.
2. By looking at the graph, how can you tell that the amount of cocoa is proportional to the number of servings?
Answers
Answer:
theres no graph sorry, maybe if u upload it i can help
Step-by-step explanation:
which sequence of transformations creates the function g(x) = .....
Answers
Step-by-step explanation:
f(x)= square root of x
g(x)= - square root of -1/2x+3
Find the expression tree for the formula ((((¬(¬p))∧(¬q))∧r)∨(((¬(¬q))∧(¬r))∧s)↔(s→p) Evaluate the expression tree if proposition p is T, proposition q is T, proposition r is F, and proposition s is F 6. Find the expression tree for the formula ((¬(p∧q))∨(¬(q∧r)))∧((¬(p↔(¬(¬s))))∨((r∧s)∨(¬q)))
Answers
To evaluate the expression tree with p = T, q = T, r = F, and s = F, we can traverse the tree and substitute the corresponding truth values into the logical operators.
Starting from the bottom of the tree, we substitute the truth values:
¬p = ¬T = F
¬q = ¬T = F
¬r = ¬F = T
¬s = ¬F = T
s → p = F → T = T
Moving up the tree, we continue evaluating the logical operators:
(¬(¬p))∧(¬q) = F∧F = F
((¬(¬q))∧(¬r))∧s = F∧T∧F = F
((((¬(¬p))∧(¬q))∧r)∨(((¬(¬q))∧(¬r))∧s) = F∨F = F
((((¬(¬p))∧(¬q))∧r)∨(((¬(¬q))∧(¬r))∧s) ↔ (s→p) = F ↔ T = F
Therefore, the evaluated result of the expression tree is F.
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Using technology, what is the slope of the least-
squares regression line and what is its interpretation?
o the slope is 1.98, which means for each additional
inch in height, the child's weight will increase by 1.98
pounds.
the slope is 1.98, which means for each additional
inch in height, the child's weight is predicted to
increase by 1.98 pounds.
o the slope is 0.50, which means for each additional
pound in weight, the child's height will increase by
0.5 inches.
o the slope is 0.50, which means for each additional
pound in weight, the child's height is predicted to
increase by 0.5 inches.
Answers
The slope is 0.50, which means for each additional pound in weight, the child's height is predicted to increase by 0.5 inches.
Option (D) is the correct interpretation.
What is a regression line?
A regression line is a straight line that is used to model the relationship between two continuous variables. In statistical analysis, a regression line is often used to predict the value of one variable based on the value of another variable.
X Y XY X² Y²
-----------------------------------------------
8 22 176 64 484
12 23 276 144 529
18 26 468 324 676
24 30 720 576 900
30 32 960 900 1024
32 33 1056 1024 1089
35 35 1225 1225 1225
37 36 1332 1369 1296
40 38 1520 1600 1444
-----------------------------------------------
n 9
----------------------------
sum(XY) 7733.00
sum(X) 236.00
sum(Y) 275.00
sum(X²) 7226.00
sum(Y²) 8667.00
b 0.5030
a 17.3658
--------------------------------
y = a + bx
y = 17.37 + 0.50x
Hence, the slope is 0.50, which means for each additional pound in weight, the child's height is predicted to increase by 0.5 inches. is the correct interpretation.
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ASAPP PLSPLS! The line segment reflects across the x-axis. What are the new coordinates for the endpoints? How does the transformation affect the length of the line segment?
Responses
A (4, 8) and (4, 1); The transformed segment is shorter.
B (−4, −8) and (−4, −1); The length of the segment does not change.
C (4, −8) and (−4, 1); The transformed segment is longer.
D (−4, −8) and (4, 1); The length of the segment does not change.
Answers
Answer:
I guess it's no C the transformed segment is longer as this process have ruka and you should follow it
i will give you brainliest!
Answers
Answer:
160
Step-by-step explanation:
Give me brainliest PLz
I need it
need help asap with these would be greatly appreciated
Answers
Answer:
1.) 5,0,-3, -6,-3,0,5 (use the points for the graph and connect them together)
2.a) (0,9) He is starting at the heighest point of the ramp, its the height of where he starts walking.
b.) (10,4) The point where they both are at the same height, at the same time.
c.) (18,0) This is when he reaches to ground level or to 0 feet after a certain amount of time, 18 seconds.
Find the error in the work below. Then show the correct calculation. 8/12x6= 8x1/12x6= 8x1/72= 8/72= 1/9
Answers
The error in the calculation above is that the order of operations was not followed correctly. Multiplication should be performed before division. the correct answer is \(4\) , not \(1/9\) .
What is the multiplication and division?The error in the calculation above is in the first step. When performing multiplication and division in the same step, you should always perform the multiplication before the division. This is known as the order of operations.
The correct calculation would be:
\(8/12 \times6 = (8/12) \times 6\) (perform the multiplication first)
\(= (2/3) \times 6\) (simplify the fraction)
\(= 12/3\)
\(= 4\)
The error in the calculation above is that the order of operations was not followed correctly. Multiplication should be performed before division.
The correct calculation is as follows:
\(8/12 \times 6 = (8/12) x\times6\) // Multiplication first
\(= (2/3) \times 6 /\) / Simplify 8/12 to 2/3
= \(12/3\) // Multiply 2/3 by 6
= \(4\) // Simplify 12/3 to 4
Therefore, the correct answer is \(4\) , not \(1/9\) .
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An investment portfolio is shown below.
Investment Amount Invested ROR
Stock A $1,800 1.5%
Stock B $4,600 3.7%
Stock C $580 11.2%
Stock D $1,122 −2.8%
Using technology, calculate the weighted dollar amount of Stock C.
$27.00
$64.96
$170.20
$184.00
Answers
The required weight of the dollar amount of Stock C is $64.96.
The Correct option is (B).
What is simplification?In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Given:
Investment Amount Invested ROR
Stock A $1,800 1.5%
Stock B $4,600 3.7%
Stock C $580 11.2%
Stock D $1,122 −2.8%
According to the question,
Weight of dollar amount of Stock C
= 580 × 11.2%
= 580 x 0.112
= $64.96
Hence, the required weight is $64.96.
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In a coin game, you toss a coin three times. If all three coin tosses are heads or all three tosses are tails, you win $15. Otherwise, you lose $3. What is the expected profit for one round of the coin game?
Round your answer to the nearest cent.
Enter an expected loss as a negative number.
Answers
Rounding to the nearest cent, the expected profit for one round of the coin game is approximately -$0.38.
To calculate the expected profit for one round of the coin game, we need to consider the probabilities of winning and losing, as well as the corresponding amounts won or lost.
There are 2 possibilities for winning: either getting all three heads or all three tails. Each of these outcomes has a probability of (1/2) * (1/2) * (1/2) = 1/8.
The amount won in each winning case is $15. Therefore, the expected profit from winning is:
(1/8) * $15 = $1.875
The probability of losing is 1 - probability of winning. In this case, it is 1 - (1/8 + 1/8) = 6/8 = 3/4.
The amount lost in each losing case is $3. Therefore, the expected loss from losing is:
(3/4) * (-$3) = -$2.25
Finally, we can calculate the expected profit by subtracting the expected loss from the expected profit from winning:
$1.875 - $2.25 = -$0.375
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1) During second period, Jakhari completed a grammar worksheet. Of the 44
questions, Jakhari got 75% right. How many questions did Jakhari get right
known
Answers
Answer:
33
Step-by-step explanation:
75% is 3/4. 3/4 of 44 is 33.
Write the equation of the line that passes through (-4,1) and is perpendicular to the line y=2x+3
Answers
Answer: y = -(1/2)x - 1
Step-by-step explanation:
y=2x+3
This is written in the format of y = mx + b, where m is the slope and b the y-intercept. The slope of this reference line is 2. Perpendicular lines will have a slope that is the negative inverse of the slope of the reference line. That means out new line will have a slope of -(1/2):
y = -(1/2)x + b
We can find b by entering the x and y for the given point (-4,1) and solve for b:
y = -(1/2)x + b
1 = -(1/2)(-4) + b
1 = 2 + b
b = -1
y = -(1/2)x - 1
This equation is perpendicular to y=2x+3 and goes through point (-4,1). See attachment.
The cost to make each T-shirt is $10. You estimate that you will
sell 50 shirts. If you want to make a profit of at least $250, what
price will you charge for these T-shirts? Show your solution in two
different ways.
Answers
The price per T-shirt should be at least $15 to achieve a profit of $250.
To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.
Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.
Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.
Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.
Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.
By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.
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