Approximately, the unit cost of the plastic cups is $0.25
Here, we want to get the unit rate of the plastic cups
By unit rate, we mean the price of 1
From the question, the total 72 costs $17.99
The cost of one is thus;
[tex]\frac{17.99}{72}\text{ = 0.25}[/tex]1. The number of miles a car can travel on a gallon of gasoline is related to its fuel
efficiency. Fuel efficiency depends on many factors including the speed of the car.
Driving at very slow or very fast speeds uses more gas than driving at a moderate
speed, which means fuel efficiency can often be modeled by a quadratic function.
For a certain model of car the fuel efficiency is maximized at 32 miles per gallon
with a speed of 55 mph. At 65 mph the car can get 31 miles per gallon.
The quadratic equation that models the fuel efficiency of the car is given by:
y = -0.01(x - 55)² + 32.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which the parameters of the equation are described as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficientFor a certain model of car the fuel efficiency is maximized at 32 miles per gallon with a speed of 55 mph, hence the vertex is given by:
(h,k) = (55,32).
Hence the rule is:
y = a(x - 55)² + 32
When x = 65, y = 31, hence we can find the leading coefficient a as follows:
31 = a(65 - 55)² + 32
100a = -1
a = -0.01.
Hence the equation is given by:
y = -0.01(x - 55)² + 32.
What is the missing information?The problem is incomplete, hence we suppose that it asks for the quadratic model of the car's fuel efficiency.
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an exponential function f has a 3-unit growth factor of 1.55. what is the 1-unit growth factor for f ? what is the 2-unit growth factor for f ? what is the 1 2 -unit growth factor for f ?
Given that 3 unit factor growth is 1.65
Then 1 unit growth factor = (1.65)^1/3 = 1.181
2 unit growth factor of F = 1.396
And 1/2 unit growth factor = (1.65)^0.5/3 = (1.65)^0.53/3 = (1.65)^1/6
= 1.0875
or 1/2 unit growth of factor f = 1.0875
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f(x) = 4x³ + 6x² – 3x − 4
g(x) = 4x - 3
Find (f - g)(x).
Solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1
What are algebraic equations?Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of variables, coefficients and constants. Algebraic equations can be of many types, such as monomial algebraic equations, binomial algebraic equations, quadratic algebraic equations, polynomial equations.
Given in the question that the value of f(x) is equal to 4x³+6x²-3x-4
and the value of g(x) is equal to 4x-3.
Subtracting g(x) from f(x) we get,
(f-g)(x)= 4x³+6x²-3x-4-4x+3
4x³+6x²-7x-1
Therefore, solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1.
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Question 1 1 pts If g and h are both positive numbers, which statement is true about the x-intercepts of the function f(x) = (x - g)(x - h). the function has no x-intercepts both x-intercepts are negative one x-intercept is negative and one x-intercept is positive both x-intercepts are positive
for the function
f(x) = (x -g)(x - h)
To get the x-intercept, we can equate the function to zero
f(x) = (x -g)(x - h) = 0
so (x - g) = 0
which gives x = g
And (x - h) = 0
which gives x = h
Since we have been told that g and h are positive, then it follows that both intercepts are positive
for a between-subjects experiment, any factor that increases the variance within treatments also increases the likelihood of finding a significant difference between treatments.
The answer is FALSE. The likelihood of discovering a substantial difference between treatments does not increase with any factor that makes treatments more variable.
In experiments, you create situations where several treatments (such a are used in order to investigate the impact of an independent variation.
Every participant in a between-subjects or between-groups design only experiences one condition, and group differences between participants in various conditions are compared. In contrast, no participant in a within-subjects design is exposed to every condition.
As a result, the likelihood of discovering a substantial difference between treatments is not increased by factors that enhance variation within treatments.
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If the water level rises 12 centimeters every 7 minutes and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.
The rate of change of the given relation is 1.7142 the value of y is 36 centimeters.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
As per the given question,
The water level rises 12 centimeters every 7 minutes.
0 minutes → 0 cm
7 minutes → 12 cm
14 minutes → 24 cm
21 minutes → 36 cm.
Since, (21,y) best match with the above condition.
So, 21 minutes is the time taken while 36 cm is the level of water.
Slope or rate of change = 12/7 cm/minutes.
And, 36/21 = 12/7 (proved)
Hence "The rate of change of the given relation is 1.7142 the value of y is 36 centimeters".
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Johnny drew a scale drawing of an apartment. The scale he used was 8 inches : 3 feet. In the drawing, the broom closet is 16 inches long. What is the length of the actual closet?
The actual closet has a length of 6 feet
How to determine the length of the actual closet?The scale of the drawing is given as
Scale = 8 inches : 3 feet.
Also, we have the length of the closet to be
Length = 16 inches
So, we have
16 inches : Actual length = 8 inches : 3 feet.
Multiply the ratio by 2
So, we have
16 inches : Actual length = 16 inches : 6 feet.
By comparison, we have
Actual length = 6 feet
Hence, the length of the actual closet is 6 feet
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v/8 - 3.1 = -15.9 solve for v
[tex]\frac{v}{8} -3.1=-15.9[/tex]
Simplify equation:
[tex]\frac{1}{8}v+-3.1=-15.9[/tex]
[tex]\frac{1}{8} v-3.1=-15.9[/tex]
Add 3.1 to both sides:
[tex]\frac{1}{8} v-3.1+3.1=-15.9+3.1\\[/tex]
[tex]\frac{1}{8} v=-12.8[/tex]
Multiply both sides by 8:
[tex]8\times(\frac{1}{8} v)=(8)\times(-12.8)\\-102.4[/tex]
[tex]\fbox{v=-102.4}[/tex]
1. Compare two spheres. The first has a diameter of 4 inches.
The second sphere has a diameter of 428 inches.
Determine the ratio of the volume of the large sphere to the volume
of the small sphere.
Ratio =
The ratio of the volume of the large sphere to the volume
of the small sphere is 1226 .
How to find the volume of 3d objects?V = 4/3 r³ is the equation to calculate a sphere's volume. The volume of a sphere is calculated using the following formula: 4/3rds of Pi and the cube of the sphere's radius. A sphere is a geometrical object that is a three-dimensional equivalent of a two-dimensional circle . A sphere is a collection of points in three-dimensional space that are all located at the same r distance from a particular point. The radius of the sphere is equal to r, and the provided point is its center. In the works of the ancient Greek mathematicians, spheres are first mentioned.
In several branches of mathematics, the sphere serves as a basic building block. Also found in nature and industry are spheres and nearly-spherical shapes.
Volume sphere = 4/3πr³
Volume of sphere 1
D = 4 inches
r = 2 inches
So,
Volume = 4/3π(2)³
= 33.51 inches³
Volume of sphere 2
D = 428 inches
r = 214 inches
So,
Volume = 4/3π(214)³
= 4.11 ×[tex]10^{7}[/tex] inches³
Ratio
= sphere 2: sphere 1
= 4.11 ×[tex]10^{7}[/tex] : 33.51
= 1226
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The point (-2, K) lies on the circle x^2 +y^2= 20. Find the values of k. Show all the steps
I will plug in the POINTS including k in the equation each point in its place either x or y.
[tex]( - 2)^{2} +( {k})^{2} = 20 \\ 4 + {k}^{2} = 20 \\ k^{2} + 4 - 20 = 0 \\ {k}^{2} - 16 = 0 \\ (k + 4)(k - 4) = 0 \\ \\ k + 4 = 0 \\ \\ or \\ \\ k - 4 = 0 \\ \\ k = 4 \\ or \\ k = - 4[/tex]
ATTACHED IS THE SOLUTION
Lance the alien is 5 feet tall. His shadow is 8 feet long. At the same time of day, a tre shadow is 24 feet long. What is the height of the tree?
Answer:
15 ft
Step-by-step explanation:
5:8
?:24
8x3=24 SO 5x3=15
Members of our lacrosse team raised 1672.50 to go to a tournament they rented a bus for 1068.50 and budgeted $37.75 per player for meals write and solve an equation which can be used to determine x
The equation is 1068.50 + 37.75 x = 1672.50 and the value of x is 16.
Members of our lacrosse team raised 1672.50 to go to a tournament.
Amount raised by lacrosse team = 1672.50
Let the number of players in lacrosse team = x
They rented a bus for 1068.50 and budgeted $37.75 per player for meals. So, mathematically this can be represented as
1068.50 + 37.75 x
Total amount paid by lacrosse team = 1068.50 + 37.75 x
As amount raised by lacrosse team and the amount paid by lacrosse team are equal so we can write
1068.50 + 37.75 x = 1672.50
37.75 x = 1672.50 - 1068.50
37.75 x = 604
x = 16
Thus, we can conclude that the value of x is 16 and the equation is 1068.50 + 37.75 x = 1672.50.
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At its peak, an online shopping site was selling 420 items per second. How many items would it sell in 30 minutes
The online shopping site would sell 756000 items in 30 minutes
Given
The online site would sell 420 items in a second
To find number of items it would sell in 30 minutes first of all convert minutes into seconds and continue to solve the problem.
To convert minutes into seconds just multiply minutes with 60.
because one minute is equal to 60 seconds.
Therefore 30 minutes = 30 x 60 seconds
30 minutes = 1800 seconds
Say the number of items sold by sire in 30 minutes be x.
now according to the condition in equation
420 x 1800 = x
x= 756000
Hence the site will sell 756000 items in 30 minutes.
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HW Score: 83.33%, 15 of 18 points
Points: 0 of 1
An automobile purchased for $34,000 is worth $2200 after 6 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?
The value 3 years after it was purchased is $
Carmin Wimberley
< Question 13, 1.3.29
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The car' s worth after the end of third year will be $18100.
What is depreciation?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline. Depreciation, or a decline in asset value, can be brought on by a variety of other variables, such as bad market conditions, etc. Depreciation is the estimated decrease in value of fixed assets over the course of a fiscal year. Large lump sum purchases are made for tangible things like real estate, machinery, vehicles, and so forth.
Given Data
An automobile purchased for $34,000 is worth $2200 after 6 years.
Annual depreciation = [tex]\frac{34000-2200}{6}[/tex]
Annual depreciation = [tex]\frac{31800}{6}[/tex]
Annual depreciation = 5300
In 3 years depreciation would be
= 5300(3)
= 15900
Thus the value after the end of third year will be:
34000 - 15900
18100
The car' s worth after the end of third year will be $18100.
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Moores law predicts that the number of transistors that can be fit on a microchip will increase 40% every year. If microchips from a given year could hold about 922,200 transistors, how many transistors could fit on a microchip 19 years later?
If necessary, round your answer to the nearest whole number.
[tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.
Moore's law predicts that the number of transistors that can be fit on a microchip will increase 40% every year.
So the expected increment every year [tex]40\%[/tex].
Microchips from a given year could hold about [tex]922,200[/tex] transistors.
We have to find ow many transistors could fit on a microchip [tex]19[/tex] years later.
From the question total years are [tex]19[/tex].
Since the number of transistors is increased every year so number of transistors of previous year added. So we can see that the number of transistors that can be fit on a microchip is increased compound. We can find the total number of transistors by multiplying number of transistors with the rate assembled by one. So we can use the formula
So the number of transistors could fit on a microchip 19 years later.
Number of transistor = Microchips from a given year could hold about transistors(1 + increment rate)^total years
Number of transistor [tex]=922,200(1+\frac{40}{100})^{19}[/tex]
Number of transistor [tex]=922,200(1+\frac{2}{5})^{19}[/tex]
Number of transistor [tex]=922,200(\frac{5+2}{5})^{19}[/tex]
Number of transistor [tex]=922,200(\frac{7}{5})^{19}[/tex]
After evaluating the expression using the calculator we get
Number of transistor [tex]=551134751.094269[/tex]
Number of transistor [tex]=5.51134751094269\times10^8[/tex]
Hence, [tex]5.51134751094269\times10^8[/tex] transistors could fit on a microchip [tex]19[/tex] years later.
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The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H . A wall of uniform height that is 16 feet long is constructed using 280 bricks. What is the height, in feet, of the wall?
The height of the wall in feet is 2.5 feet.
According to the question,
We have the following information:
The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H .
A wall of uniform height that is 16 feet long is constructed using 280 bricks.
So, we have:
B = 280 and H = 16
Putting these values in the given expression:
B = 7LH
280 = 7*L*16
L = 280/(7*16)
L = 280/112
L = 2.5 feet
Hence, the height of the wall in feet is 2.5 feet.
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joey and chloe and their daughter zoe all have the same birthday. joey is 11 year older than chloe, and zoe is exactly 11 year old today. today is the first of the 99 birthdays on which chloe's age will be an integral multiple of zoe's age. what will be the sum of the two digits of joey's age the next time his age is a multiple of zoe's age?
The sum of the two digits of Joey's age the next time his age is a multiple of Zoe's age is of 11, and this measure was found using a system of equations.
What is the system of equations?The variables for the system of equations in this problem are given as follows:
Variable x: Joey's age.Variable y: Chloe's age.Variable z: Zoe's age.Joey is one year older than Chloe, hence:
x = y + 1.
Zoe is exactly one year old, hence:
z = 1.
The difference between the ages of Chloe's and Zoe's have 9 factors. Numbers with nine factors have the following format:
x² x y² , with different x and y.
These numbers have to be different of 1, due to Zoe's age, hence the smallest number is given as follows:
2² x 3² = 4 x 9 = 36.
Since the difference is of 36 years old, so the ages are as follows:
Zoe: 1 year old. Chloe: 37 years old.Joey: 38 years old.The next time this will happen is in 36 years, hence Joey's age will be of:
36 + 38 = 74 years old.
The sum of the digits will be of:
7 + 4 = 11.
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If line m is parallel to line n then determine the value of x.
If line m is parallel to line n then determine the value of x= 65°
2x+50° = 180°
2x = 180° - 50°
2x = 130°
x = 130°÷2
x = 65°
What are parallel to line?Parallel lines are lines that do not cross or meet at any point in the plane. They are always parallel and equidistant from each other. Parallel lines are non-intersecting lines. We can also say that parallel lines meet at infinity.
Properties of Parallel Lines
They are always straight equidistant from each other. These are coplanar lines. They never cross, no matter how much you try to stretch them in any direction. If there is a transversal that intersects two parallel nets at two different points, it forms angles at each point.To learn more about parallel to line, refer;
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The value of x is 25. It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.
What is parallel?Parallel lines are coplanar straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.
Parallels, paralleling, and paralleled are all word forms. a countable noun A parallel is something that is similar to something else but exists or occurs in a different place or at a different time.
Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that intersect at a right angle (90 degrees).
Two different interior angles.
- (2x - 10)°
- (65 - x)°
Because lines m and n are parallel and because of the alternate angles theorem.
We can see that.
2x - 10 = 65 - x
2x + x = 65 + 10
3x = 75
x = 75/3
x = 25
Hence, the value of x is 25.
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Do number 3 please thank you.
Answer:
Answer down below!
Step-by-step explanation:
Let's rewrite the sentence and then pinpoint the exact points!
Your conclusion will be bolded!
"If you are living in California, then you live in the state that has the tallest mountain in the lower 48 states."
The conclusion is the last part of the statement that clearly states the decision based on the components of the test (or hypothesis)
Jim wants to plan a meal with 150 grams of carbohydrates and 1400 calories. If green beans have 7 grams of carbohydrates and 30 calories per half cup serving and if french fried shrimp have 9 grams of carbohydrates and 190 calories per three-ounce serving, how many servings of green beans and shrimp should he use?
There are 16 half-cup servings of beans and 4, three-ounce servings of shrimp.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represents number of half-cup servings of beans
Let y represents number of 3 ounce servings of shrimp
We have a system of equations, one for carbs and one for calories;
7x + 9y = 150
30x + 190y = 1400
Now,
30(7x + 9y) = 30(150)
-7(30x + 190y) = -7(1400 )
210x + 270y = 4440
-210x - 1330y = -8680
-1060y = -4240
y = 4
Then substitute we get;
7x + 9y = 150
7x + 9(4) = 150
7x + 36 = 150
7x = 112
x = 16
Hence; X = 16 and Y= 4
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Leah can run 720 yards in 4.5 minutes. How many yards can she run in 2 minutes at the same rate?
A. 350
B. 320
C. 160
D. 110
Leah can run 320 yards in 2 minutes at the same rate as she can run 720 yards in 4.5 minutes. The correct option is B. 320.
To find out how many yards Leah can run in 2 minutes at the same rate, we can use the concept of proportionality.
Let's set up a proportion based on the information given:
720 yards / 4.5 minutes = x yards / 2 minutes
To find the value of x, we can cross-multiply:
4.5 minutes × x yards = 720 yards × 2 minutes
Now, divide both sides by 4.5 to solve for x:
x yards = (720 yards × 2 minutes) / 4.5 minutes
x yards = 320 yards
So, Leah can run 320 yards in 2 minutes at the same rate.
The correct answer is B. 320.
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Find all real numbers r for which there exists exactly one real number a such that when (x+a)(x2 +rx+1)
is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero.
All real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero are given as r = -1
A real number is a quantity of a continuous number that can express a distance along a line in mathematics.
Hence the workings for the above result are indicated as follows:
Expanding the brackets, we see that we want the following three inequalities to be true.
a ≥ 0 (constant term) (1)
ar + 1 ≥ 0 (coefficient of x) (2)
a + r ≥ 0 (coefficient of x²) (3)
If r ≥ 0, then any a ≥ 0 meets the requirement of (1), (2), and (3).
It remains to address r < 0. In this case, note that (3) immediately suggests (1)
Hence, we only need to look at (2) and (3). Given that r < 0, inequalities (2) and (3) are equivalent to the following.
a ≤ − 1/r (4)
a ≥ − r (5)
Therefore, we seek all values of r < 0 such that there is exactly one real number satisfying the expression −r ≤ a ≤ −1/r (6)
Thus −r = −1/r ,
This implies r = ±1.
Given that r < 0 we have r = −1.
This implies that the only corresponding value of a is a = 1.
It only remains to follow that (x + 1)(x² − x + 1) = x³ + 1, which has no negative coefficients.
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Full Question:
Find all real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero.
Solve 5(x + 2) = 26 - 3x
x = ...
Halp me with this 1 question Brainliest to correct answer
Answer:
A is correct.
[tex]g = \frac{p}{6} - 15[/tex]
Step-by-step explanation:
[tex]p = 6g + 90[/tex]
[tex]6g = p - 90[/tex]
[tex]g = \frac{p}{6} - 15[/tex]
So A is correct.
This table shows the ratio of the number of adults to the number of students on a class field trip. A 2-column table has 4 rows. Column 1 is labeled Number of adults with entries 1, 2, 4, 6. Column 2 is labeled Number of students with entries 7, x, 28, y. Which values are missing from this table? x = y =
Answer:
x = 14 and y = 42
Step-by-step explanation:
From the two entries that have both the numbers od adults*A) and students(S) we find a ratio of S/A to be 7 for both cases. We'll make the assumption that is the same ratio in the two cases involving x and y.
To find x and y, multiply the number of adults by 7 to find the number of students,
x = 14 and y = 42
A S Ratio S/A = 7
1 7 7
2 x 14
4 28 28
6 y 42
Pleaseee help will give brainliest to best and most detailed answer!
f(x) = x3 + 5x2 –32x – 7 is divided by x – 4
I really need help on this, and please show me every step!
Answer:
[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]
Step-by-step explanation:
Long Division Method of dividing polynomials
Divide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.Given:
[tex]\textsf{Dividend: \quad $x^3+5x^2-32x-7$}[/tex]
[tex]\textsf{Divisor: \quad $x-4$}[/tex]
[tex]\large \begin{array}{r}x^2+9x+4\phantom{)}\\x-4{\overline{\smash{\big)}\,x^3+5x^2-32x-7\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-4x^2)\phantom{-b))))))..)}}\\9x^2-32x-7\phantom{)}\\-~\phantom{(}\underline{(9x^2-36x)\phantom{)))..}}\\4x-7\phantom{)}\\-~\phantom{()}\underline{(4x-16)\phantom{}}\\9\phantom{)}\\\end{array}[/tex]
Therefore:
[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]
Definitions
Dividend: The polynomial which has to be divided.
Divisor: The expression by which the divisor is divided.
Quotient: The result of the division.
Remainder: The part left over.
ear Equations Question 1 of 5 Find the solution to the following system using substitution or elimination: y = 3x + 2 y = -2x - 8 O A. (-3, -8 OB. (1,-6) C. (-2,-4) OD. (-3. - 31
Handmade socks, knitted using pure cashmere wool, are very expensive to buy. Rowena buys cashmere wool in 20g balls. Each ball of cashmere wool costs her £1.42 . She pays her sister £8 to knit each pair of socks. 135g of cashmere wool is used to knit each pair of socks. Rowena sells 40 pairs of cashmere socks at £18.95 per pair. What is her percentage profit? Give your answer correct to 2 significant figures.
The percentage profit for the so is that were made is 40.32%.
How to calculate the profit?From the information, Rowena buys cashmere wool in 20g balls. Each ball of cashmere wool costs her £1.42 and she pays her sister £8 to knit each pair of socks. The cost will be:
= (£1.42 × (20 + 135) + (40 × £8)
= £220.1 + £320
= £540.1
The selling price will be:
= £18.95 × 40
= £758
Therefore, the percentage profit will be:
= Profit / Cost price × 100
= (758 - 540.1) / 540.1 × 100
= 217.9 / 540.1 × 100
= 40.32%
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Translate "the sum of m and 2.33 multiplied by s is 77.77" into an algebraic equation.
Although part of your question is missing, you might be referring to this complete question "Translate the sum of m and 2.33 multiplied by s is 77.77 into an algebraic equation. Do not solve the equation."
Translated equation is m + 2.33s = 77.77
An algebraic equation is the equality of two expressions formulated by applying a set of variables such as addition, subtraction, multiplication, division, raise to power, etc. The phrase " the sum of a and b" into an algebraic expression is determined as a+b. It deals with symbols and these symbols deal with each other through variants.
Hence, the equation translated is a linear equation of algebraic equations. m+ 2.33s = 77.77
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WILL GIVE BRAINLY Given f(x)=3x-1 and (f∘g)(x)=x^2, find g(x)
[tex]\begin{cases} f(x)=3x-1\\\\ (f\circ g)(x) = x^2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (f\circ g)(x)\implies f( ~~ g(x) ~~ )~~ = ~~3( ~~ g(x) ~~ ) - 1\implies \stackrel{(f\circ g)(x)}{x^2}~~ = ~~3g(x)-1 \\\\\\ x^2+1=3g(x)\implies \cfrac{x^2+1}{3}=g(x)[/tex]