Answer:
£ 268.2
Step-by-step explanation:
495(1/3)+124(0.5)+(495(2/3)-124)(0.2)=165+62+41.2
=268.2
Answer: £268.20
Step-by-step explanation:
1/3 of 495 is 165.
124 x .50 = 62.
165 + 124 = 289
495 - 289 = 206
206 x .20 = 41.20
165 + 62 + 41.20 = 268.20
Sally can paint 90 ft2 of wall per hour. Write a linear function that describes how many square feet of wall she can paint over time. Then make a graph to show how many square feet she can paint over the first 4 hours.
Answer:
Hello...
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.Together in 1 hour they can paint: - 1/4 + 1/6 = 5/12th of the house.
Hello...Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.Together in 1 hour they can paint: - 1/4 + 1/6 = 5/12th of the house.Total Hours for painting the house together will be 12/5 = 2.4 Hours.
hope it helps
The linear function that describes how many square feet of wall she can paint over time is y = 90x.
What are linear equations?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given the area painted by Sally in one hour = 90 square feet
so from the given data, we can find that the area painted by Sally is directly proportional to the time,
let she paint for x hours and the area she painted be y,
the equation for the condition is y = 90x,
where x is in hours and y is in square feet,
Table for the area she painted in first 4 hours
x(hours) 1 2 3 4
y ( sq. feet) 90 180 270 360
The graph for the first four hours is attached.
Hence the equation is y = 90x.
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Find the slope from the table.
Answer:
m=0
Step-by-step explanation:
the slope is calculated using two points on the line and the formula
m = (y2 - y1) ÷ (x2 - x1)
where
x1 and y1 are the coordinates of point 1
x2 and y2 are the coordinates of point 2
for example, you can take
point 1 = (x1;y1) = (-2;3)
point 2 = (x2;y2) = (-1;3)
then your slope is
m = (3 - 3) ÷ (-1 - (-2)) = 0
notice that x1 is always at the left of x2 on the x axis
and it makes sense that your slope is 0 because for each x your y is the same
If x-3 is a factor of x4−3x3+kx+3, what is the value of k?
k = -1
ExplanationIf x-3 is a factor of x4−3x3+kx+3, what is the value of k?
1. The remainder theorem tells us that you get the same thing when you
substitute 3 into a polynomial as you get when you divide the polynomial
by x-3 and take only the remainder.
2. The factor theorem thell us that since x-3 is a factor of the polynomial
then if we divided the polynomial by x-3, the remainder would be 0.
Putting these two facts together we can see that if we substituted 3 into
the polynomial, we will get the same result as the remainder would be if we
divided the polynomial by x-3. And furthermore due to 2, that remainder must
be 0. So all we have to do is substitute 3 for x in the polynomial and set
it equal to 0.
So substituting 3 for x in x^4-3x^3+kx+3 gives
3^4-3(3)^3+k(3)+3
81-3(27)+3k+3
81-81+3k+3
3k+3
Setting 3k+3 = 0
3k = -3
k = -1
Now let's check to see if we are right. If we are then the polynomial
x4-3x3^+kx+3 becomes x4-3x3^-x+3. We will divide that
synthetically by x-3 to see if we get a 0 remainder. First we must
insert a +0x2^ term, and write it as x4^--3x3^+0x2^-x+3
3 | 1 -3 0 -1 3
| 3 0 0 -3
1 0 0 -1 0
Sure enough, we do get 0 for a remainder.
So k = -1 is correct.
Find the equation for the line through the point (7/5,1/12) that is perpendicular to the line 3x-4y=7. You may leave your answer in the point-slope form if you wish. If you use slope-intercept form, all fractions must be combined and reduced wherever possible.
The equation of the line is (y - 1/12) = -4/3(x - 7/5).
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.
Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be depicted by
tan θ = Δy/Δx
So, the slope of a line is tan.
The given equation of a line is:
3x-4y=7
-4y = -3x + 7
y = 3/4 x - 7/4
The slope of the line is 3/4.
The slope of the line perpendicular to the given line is - 1/m = - 4/3
The point-slope of a line is y - y₁ = m(x - x₁).
The given point is (7/5,1/12)
The equation of the line is
(y - 1/12) = -4/3(x - 7/5)
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Wagner enterprise sells two products large tractors and small tractors. A large tractor sells for $62,000 per unit with variable costs of $28,520 per unit. Small tractors sell for $34,000 per unit variable costs of $16,320 per unit. Total fixed costs for the company are $1,560,000. Wagner enterprises typically sells two large tractors for every three small tractors
Assuming the sales mix remains constant, how many large and small tractors are sold (in units) at Wagners break even point?
Large Tractors Sold at Break Even Point= 26 units
Small Tractors Sold at Break Even Point= 39 units
What is Break-Even Point?Break-even point is where sales are equivalent to the sum of all costs incurred by the company. It is a significant concept in accounting as it gives the managers vital information on how many units must be sold to make business operations profitable.
From the question, it was stated that Wagner Enterprises sells for every three small tractors, two large tractors. Therefore, the sales mix will be:
Large Tractor = 2/5Small Tractor = 3/5The contribution margin per unit will be computed first, after which we multiply the sales mix by the computed margin per unit to get the Weighted Average Contribution Margin (WACM). This is shown below:
For Large Tractor:
Selling Price per Unit = $62,000
Variable Cost per Unit = $28,520
Contribution Margin per Unit = ($62,000 - $28,520) = #33,480
Multiply by sales-mix of 2/5 = 2/5 times $33,480 = 13,392 (WACM)
For Small Tractor:
Selling Price per Unit = $34,000
Variable Cost per Unit = $16,320
Contribution Margin per Unit = ($34,000 - $16,320) = #17,680
Multiply by sales-mix of 3/5 = 3/5 times $17,680 = 10,608 (WACM)
The Total Weighted Average Contribution Margin per unit is therefore:
$13,392 + $10608, equaling $24,000.
Now we can find the Break-even Point in Unit.
Formula for Break-even Point in Unit = Total Fixed Cost (TFC) divided by Weighted Average Contribution Margin in unit
Total Fixed Costs = $1,560,000
WACM in unit = $24,000
Break-Even Point = \(\frac{1,560,000}{24,000}\) = 65 units
From the calculations, the total units that must be sold to break-even are equivalent to 65 units. Given the above sales mix, the 65 units will be shared thus:
Large Tractor: 2/5 x 65units = 26 units Small Tractor: 3/5 x 65units = 39 unitsTherefore, 26 units of Large Tractors and 39 units of Small Tractors were sold at Wagner's Enterprise break-even point.
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What is the side length of a square with an area of 95
Answer:
23.75
Step-by-step explanation:
95/4
23.75
Answer:
A≈9.75
Step-by-step explanation:
The side length can be found by getting the square root of 95.
Since all sides are the same on a square, this means that 9.75² gives us 95, which it does.
Hope this helps!
-MoCKEry
I NEED YOUR HELP!! I'LL. GIVE YOU BRAINLIEST
Answer: ∠16 and ∠11
Step-by-step explanation:
All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.
The correct corresponding angles are ∠16 and ∠11.
What is 35% of 76.6?
Answer:
26.6
Step-by-step explanation:
Solution for What is 35 percent of 76:
35 percent *76 =
( 35:100)*76 =
( 35*76):100 =
2660:100 = 26.6
Now we have: 35 percent of 76.6 = 26.6
Therefore, 35% of 76.6 is 26.6
(hope this helps can i plz have brainlist :D hehe)
Add the following fractions. Write the sum in simplest form. (the choices are written as mixed numbers): 3/4 + 4/5
Answer:31/20
Step-by-step explanation:
The mean age of 5 people in a room is 39 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room?
Answer:
6.6
Step-by-step explanation:
40/6=6.6
Which any quality represents the statement the sum of -3 and a number is at least 5
Answer: -3 + n >= 5
Step-by-step explanation: I got it wrong on the test but got the correct answer from test review on K12
Primitive function for:
1. f(x)=4e2x+e−x, sådan att F(0)=2
The primitive function for \(f(x) = 4e^{2x} + e^{-x}\) is given by it's indefinite integral.
To calculate it, recall:
\(\frac{d}{dx}e^{ax}=ae^{ax}\)
\(\int c f(x)dx = c\int f(x)dx\)
Let's begin
\(\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\\)
\(F(x) = 2e^{2x}-e^{-x} +c\)
To find the costant, we just need to use the fact that \(F(0)=2\)
\(F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3\)
Therefore,
\(\boxed{F(x) = 2e^{2x} - e^{-x} -3 }\)
Transform the table below given that g(x) = 2 f(6x).+ 8. Enter your answers as reduced fractions if necessary. Make sure your answers line up vertically with the corresponding x and f(x) values. As a hint, you can consider y f(x) to be the base graph of g(x).
The function g(x) = 2f(6x) + 8 is a function transformation of the function f(x)
How to transform the table?The function g(x) is given as:
g(x) = 2f(6x) + 8
The table is not given.
So, I will provide a general explanation
Using the following values of x:
x = 0, 1, 2, 3......
We have:
g(0) = 2f(6 *0) + 8
g(0) = 2f(0) + 8
g(1) = 2f(6 *1) + 8
g(1) = 2f(6) + 8
g(2) = 2f(6 *2) + 8
g(2) = 2f(12) + 8
g(3) = 2f(6 *3) + 8
g(3) = 2f(18) + 8
Next, we assume the following values
f(0) = 4, f(6) = 5; f(12) = 6 and f(18) = 7
The values become:
g(0) = 2f(0) + 8 = 2 * 4 + 8 = 16
g(1) = 2f(6) + 8 = 2 * 5 + 8 = 18
g(2) = 2f(12) + 8 = 2 * 6 + 8 = 20
g(3) = 2f(18) + 8 = 2 * 7 + 8 = 22
So, the table of values would be:
x g(x)
0 16
1 18
2 20
3 22
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if it is given that "x" is 23.5 - proof that it is a point of intersection at y= 1/2(x) - 25 if y is equal to 11. been trying but not working out.
When substituting y = 11 into the equation y = 1/2(x) - 25, we find that x = 72, confirming that (23.5, 11) is a valid point of intersection.
Given that x is 23.5, it is required to prove that it is an intersection point for the equation y = 1/2(x) - 25 when y is equal to 11.
The equation is given as y = 1/2(x) - 25
When y = 11, we can substitute the value of y in the equation to obtain 11 = 1/2(x) - 25
This can be simplified as 11 + 25 = 1/2(x)36 = 1/2(x)
On solving, x = 72Thus, when y is equal to 11 and x is equal to 72, the given point of intersection is valid.
Therefore, it can be concluded that x = 23.5 is a point of intersection for the equation y = 1/2(x) - 25 when y is equal to 11.
In summary, when given an equation with two variables, we can find the point of intersection by setting one of the variables to a given value and solving for the other variable. In this case, when y is equal to 11, we can solve for x and obtain the point of intersection as (72,11).
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CAN SOMEONE PLEASE HELP ME IT IS DUE TODAY
Answer:
63 mill
Step-by-step explanation:
Consider parallelogram QRST below. Use the information given in the figure to find m
The missing values are
<UTQ = 41 degree
x= 1
<UQT = 47 degree
We have a parallelogram QRST.
We know that the opposite sides of the parallelogram is equal and parallel then
QR || ST
QT || SR
Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)
<UTQ = 41
Similarly, <UQT = <SRQ = 47
Now, RU = UT
2x + 1= 3
2x = 2
x= 1
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Felipe is working to find the quotient of 6 and
3
4
6 ÷
3
4
=
6
3
4
= (6) (
4
3
)
= (
6
1
) (
4
3
)
Felipe’s answer will be
The quotient of 6 and 3/4 will be 8 and can be obtained by 24/3 = 8.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
The quotient of 6 and 3/4 is the result of the division of 6 and 3/4.
Therefore, 6 ÷ (3/4)
We know that fraction in the denominator will be inverse in multiplication
⇒ 6 × (4/3)
⇒ (6/1) × (4/3)
Multiply numerator to numerator and denominator to the denominator.
⇒ (6×4) / (1 × 3)
⇒ 24 / 3
⇒ 8
Hence "The quotient of 6 and 3/4 will be 8 and can be obtained by 24/3 = 8".
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The arrangement of the given question is not correct the correct arrangement is given below in the image;
which one is bigger? 3/8 or 2/8
Answer:
3/8 because 3 is bigger than 2.
3 of anything is bigger than 2 of the same thing.
Use the given right triangle to find cos A, sin A, and tan A. Please help asap
The trigonometric ratios are
SinA = 0.8738, CosA =35/72 and TanA = 1.7977What are trigonometric ratios?Trigonometric ratios are the ratio of the sides of a right-angled triangle.
Given the triangle ΔABC to find sinA, we use the trigonometic ratio
SinA = opposite/adjacent = CB/AB
Now, we find CB by pythagoras' theorem.
AB² = CB² + AC²
CB = √(AB² - AC²)
So, substituting these into the equation, we have
SinA = CB/AB
= √(AB² - AC²)/AB
= √[(AB² - AC²)/AB²]
= √[1 - (AC/AB²]
Given that
AB = 12 ft = 12 × 12 in = 144 in and AC = 70 inSo, substituting these into the equation, we haveCB = √(144² - 70²)
SinA = √(AB² - AC²)/AB
SinA = √(144² - 70²)/144
SinA = √(20736 - 4900)/144
SinA = √15836/144
SinA = 125.84 in/144 in
SinA = 0.8738
To evaluate CosB, we use the trigonometric ratio
CosB = adjacent/hypotenuse
= AC/AB
Given that
AB = 12 ft = 12 × 12 in = 144 in and AC = 70 inCosA = AC/AB
= 70 in/144 in
= 35/72
To evaluate TanA use the trigonometric ratio
CosA = opposite/adjacent
= CB/AC
Given that
AB = 12 ft = 12 × 12 in = 144 in and AC = 70 inCosA = CB/AC
= √(AB² - AC²)/AC
= √(144² - 70²)/70 in
= √(20736 - 4900)/70 in
= √15836/70
= 125.84 in/70 in
= 1.7977
So,
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Luis and Roberto are donating some of their baseball cards to the library. Luis started with 50
cards and gave away X number of them. Roberto started with 80 cards and gave away 3 times as
many as Luis had given away.
If they both now have the same number of baseball cards, how many baseball cards did Roberto
give away?
Answer:
X=15
Step-by-step explanation:
50−x=80−3x
Step 1: Simplify both sides of the equation.
50−x=80−3x
50+−x=80+−3x
−x+50=−3x+80
Step 2: Add 3x to both sides.
−x+50+3x=−3x+80+3x
2x+50=80
Step 3: Subtract 50 from both sides.
2x+50−50=80−50
2x=30
Step 4: Divide both sides by 2.
2x \2 = 30 \2
Answer:
x=15
Simplify (4^-2)^5 I have no clue what the answer is
Answer:
1/ 4^10
(ONE on top of a fraction. Four to the tenth power on the bottom of the fraction)
Step-by-step explanation:
When you have a power to a power the short cut (exponent rule) says to multiply the powers.
(4^-2)^5
Keep the same base, the 4
times -2 × 5, you get -10
so far after one step, you have
4^-10
Now usually, you would not leave an exponent negative. So to "fix" the negative exponent, you change it to positive by "pushing it" across the fraction bar.
4^-10
becomes:
1/ 4^10
This is a ONE on top of a fraction and FOUR to the tenth power on the bottom of the fraction.
The answer is:
1/4¹⁰
Work/explanation:
For this problem, I'm going to use the following exponent law:
\(\boxed{\!\!\boxed{\quad\sf{(x^m)^n=x^{mn}}\quad}\!\!}\)
So if we have "a power to a power", we multiply the powers.
And now that we're familiar with this property let's apply it.
\(\sf{(4^{-2})^5=4^{-2\times5}=4^{-10}}\)
Here the next exponent law comes into play.
______________________
\(\boxed{\!\!\boxed{\quad\sf{x^{-m}\:\:=\:\:\dfrac{1}{x^m}\quad}}\!\!}\)
So if we have a number raised to a negative power, we flop it over.
Let's apply the law to our problem now.
Our problem is:
\(\sf{4^{-10}\)
According to the law above, we should do the following:
\(\sf{4^{-10}=\dfrac{1}{4^{10}}}\)
It's better to leave the answer as it is.
Hence, the answer is 1/4¹⁰
What is the cost of a pair of shoes if they retail for $18.50, have a tax of 6%, and you have a coupon for 20% off after taxes
Answer:
$15.69
Step-by-step explanation:
multiply the retail price by 1.06 to get the price after taxes.
find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer
Simplify the expression 2(-2x+4-5-3)
Answer:2 (-2x + 4 - 5 - 3)
2(-2x -4)
-4x - 8
-268=-6(-6-6k)+2k
k= ???
Answer:
k = - 8
Step-by-step explanation:
- 268 = - 6(- 6 - 6k) + 2k ← distribute parenthesis by - 6
- 268 = 36 + 36 k + 2k ( subtract 36 from both sides )
- 304 = 38k ( divide both sides by 38 )
- 8 = k
Find domain of the function
F(x)=7x+4
Answer:
all real numbers or infinity
Step-by-step explanation:
this function is linear and linear functions always have an infinite domain and range
Express 0.00212 in scientific notation.
Answer:
2.12×10-³
Step-by-step explanation:
how?
count all the zeros that u have in this problem u have 3 zeros
help me solve this queston
TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.
And the correct graph is D.
To represent the given problem as a system of equations, we can use the following information:
John is 70 years younger than Sharon: j = s - 70
Sharon is 4 times as old as John: s = 4j
Let's plot the graph for this system of equations:
First, let's solve equation (2) for s:
s = 4j
Now substitute this value of s in equation (1):
j = s - 70
j = 4j - 70
3j = 70
j = 70/3
Substitute the value of j back into equation (2) to find s:
s = 4j
s = 4(70/3)
s = 280/3
The solution to the system of equations is j = 70/3 and s = 280/3
In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.
Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.
And the correct graph is D.
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suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000. a random sample of 400 house-holds has been chosen. in this sample, letxbe the number of households thatearn over 80,000, and letybe the number of households that earn over 450,000.use either the normal or the poisson approximation, whichever is appropriate ineither case, to nd the simplest estimates you can for the probabilitiesp(x48)andp(y2)
The probability of P(X = 48) and P(Y =2) is 0.1056 and 0.2642 respectively.
Suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000.
a random sample of 400 house-holds has been chosen
N = 400
P = 25%
n*p = 400*0.25 = 100
n(1-p) = 400 * 0.75 = 300
100 and 300 are greater than 5 so we use the normal distribution here to estimate further.
mean = n*p = 100
sd = √(np(1 - p))
sd = √(100(1 - 0.25))
sd = √(100 x 0.75)
sd = √75
sd = 8.66
p(X≥48)
= p(X≥47.5)
P(z < (47.5 - 40)/6)
P(z < 1.25)
= 0.8944
1 - 0.8944
= 0.1056
FOR Y
N = 400 p = 0.25% = 0.0025
400 * 0.0025 = 1
1 is less than 5 so we use poisson distribution.
using the excel function,
1 - BINOMDIST(1, 400, 0.0025, TRUE)
= 1 - 0.735759074
= 0.2642
Therefore, the probability of P(X = 48) is 0.1056 and P(Y =2) is 0.2642
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Use the Fundamental Counting Principle to find the total number of possible outcomes.you didn't show me the steps
Therefore , the solution of the given problem of unitary comes out to be 105 different meal combos that could be made.
What is an unitary method?By combining the information obtained using this variable technique with all supplementary data from two individuals who used a specific tactic, the job can be completed. This mean that, if indeed the desired outcome materialises, either the stated person will be recognized or, in actuality, the colour by both huge processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.
Here,
b. The following formula can be used to determine the total interest charged over the loan's term:
=> total interest = (monthly payment X n) - P .
There have been a total of:
=> 120 = ten years times one year.
The entire interest paid is thus:
=> ($3,943.80) (total monthly installments * n) - P
=> (131.19 * 120) - 9900 (rounded to the nearest dollar)
So, rounded to the closest dollar, Reh will pay about $3,944 in interest for the duration of his loan.
=> 7 entree choices, 5 drink options, and 3 dessert options are available.
We must add the number of drink options, entree options, and dessert options together to get the total number of potential meal combinations:
=> 5 x 7 x 3 = 105
There are 105 different meal combos that could be made.
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Work out the area of the triangle. 10m 26m 24m The diagram is not drawn to scale.
Answer:
120m^2
Step-by-step explanation:
this is a pythagorean triple, which means that the three numbers form a right triangle. I recommend memorizing the most popular ones
So the area of this would just be 10m*24m/2 or 120m^2