If A alone can do a piece of work in 6 days and B alone in 8 days, then A and B undertook to do it for $3200 and complete the work in 3 days with the help of C, then C would be paid 400 dollars.
Therefore the answer is $400.
This is a work and time problem that can be solved using the concept of rate of work. Let's call the amount to be paid to C as "x".
A can do 1 piece of work in 6 days. Therefore, his rate of work is 1/6.
B can do 1 piece of work in 8 days. Therefore, his rate of work is 1/8.
Amount of work A and B can do in 3 days is
= 3×(1/6) + 3×(1/8)
= 3×(1/6)×(4/4) + 3×(1/8)×(3/3)
= 12/24 + 9/24
= 21/24
= 7/8
So amount of work C doing is
= 1 - 7/8
= 1/8
As C do 1/8 amount of work, the amount C would receive is
= 3200 × (1/8)
= 400
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Write down the mathematical name of the shape made by each net.
a)
b)
How do I do the picture
Answer:
1. Cube
2. Square-based pyramid
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
a) Cube
b Pyramid
what is the equation of the line containing the points (3,1) (9,3) and (27,9)
The equation of the line containing the points (3,1) (9,3) and (27,9) is y = 1 / 3x
How to find equation of a line?The equation of a line can be found as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
using (3,1) (9,3)
m = 3 - 1 / 9 - 3 = 2 / 6 = 1 / 3
using (3, 1)
1 = 1 / 3(3) + b
1 = 1 + b
b = 0
Therefore,
y = 1 / 3x
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PLS HELP IN SUPER STUCK PLEASE HELP
A man spends 1/4 of his salary on food and 1/8 on transportation. His salary is Rs. 50,000
i) Find his total expenses as a fraction of the salary
ii) Find the amount of salary he spent
iii) Find the remaining balance of the salary
total expenses= 1/4 + 1/8
the denominators should be equal to add the values.
1/4×2(divide both the numerator and denominator by two)
=2/8
=2/8+1/8
3/8//
3/8(fraction of the salary he spent)
3/8 of the salary
3/8×50,000
R.s 6250
balance = 50,000-6,250
= R.s 43,750//
pls help solve this……
Answer:
(a) x = -7, 1
Step-by-step explanation:
In most cases, it is useful to follow the directions. This can be solved easily by completing the square.
Completing the squareThe square is completed by adding the square of the x-term coefficient to both sides.
x² +6x +9 = 7 +9 . . . . . add 9
(x +3)² = 16 . . . . . . . . simplify . . . . write the left side as a square
The square is now complete. We finish the solution by taking the square root.
x +3 = ±√16 = ±4 . . . . take the square root
x = -3 ±4 . . . . . . . . . subtract 3
x = -7, 1
A parachute speed free fall reaches 45 meters per second what is this speed in feet per second at this speed how many feet will the parachutist fall during 5 seconds of free fall in your computations assume that 1 meter is equal to 3.3 feet. Don’t round your answers
The speed is:
S = 742.5ft
The distance that the parachutist falls in 5 seconds is:
D = 742.5ft
How to get the speed in feet per second?
We know that the speed in free fall is:
S = 45 m/s.
We know that:
1 m = 3.3ft
Then we can rewrite the speed as:
S = 45 m/s = 45 *(3.28ft)/s = 148.5 ft/s
Then, the distance that the parachutist falls during 5 seconds is:
D = S*5s = (148.5 ft/s)*5s = 742.5ft
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A newspaper reports the following changes in temperature of the city over 4 days.
3.24 degrees celsius, -3/8 degrees celsius! -0.15 degrees celsius, 7/9 degrees celsius
. write an expression to show the daily average change in the temperature of the city.
write the steps to solve the expression round your answer to the nearest hundreth
(you will get 50 points if you answer my question correct)
The average change in the temperature of the city is 0.87°C.
The average quantity is the sum of all quantities divided by the number of quantities.
In the question, we are informed that a newspaper reports the changes in the temperature of the city over 4 days to be 3.24°C, - 3/8 °C, - 0.15 °C, and 7/9 °C.
We are asked to write an expression to show the daily average change in the temperature of the city.
As we know, the average quantity is the sum of all quantities divided by the number of quantities.
Thus, average = {(3.24 - 3/8 -0.15 +7/9)/4} °C,
or, average = {{324/100 - 3/8 - 15/100 + 7/9}/4} °C,
or, average = [{(23328 - 2700 - 1080 + 5600)/7200}/4] °C,
or, average = 25148/28800 °C,
or, average = 6287/7200 °C = 0.8732 °C ≈ 0.87 °C.
Thus, the average change in the temperature of the city is 0.87°C.
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Which answer best describes the complex zeros of the polynomial function? f(x)=x3+x2+10x+10
"The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location."
Polynomial functions are equations such as quadratic and cubic equations that take only the non-negative integer power of a variable or a positive integer exponent. For example, 2x + 5 is a polynomial with an exponent equal to 1.
A polynomial function is an expression that is a combination of variables of different degrees, non-zero coefficients, positive exponents (of variables), and constants. For example, f (b) = 4b2 – 6 is a polynomial of'b'and has a degree of 2.
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Which expression is not equivalent to 8+(n-4) (8-4+n) 12+n n+4 (8+n)-4
The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.
Given :
Expression - 8 + (n - 4)
To simplify the given expression following steps can be used:
Step 1 - Rewrite the given expression.
= (n - 4) + 8
Step 2 - Now, remove the parenthesis in the given expression.
= n - 4 + 8
Step 3 - Now, write 8 as the addition of 4 and 4.
= n - 4 + 4 + 4
Step 4 - Subtract 4 by 4.
= n + 4
Therefore, the correct answer is (12+n).
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9. The half-life of aspirin in your bloodstream is 12 hours. Use exponential model to
estimate how long for the 500 mg dosage to decay to 70% in your bloodstream.
after 6.2 hours the dose will decay to 70% in your bloodstream.
How long you must wait for the dosage to decay to 70% in your bloodstream?We know that the half-life is 12 hours. Then the exponential relation for an initial dosage of A is:
[tex]D(t) = A*e^{-t*ln(2)/12h}[/tex]
If the dosage needs to decay to a 70% of the initial dosage, then we must have:
[tex]e^{-t*ln(2)/12h} = 0.7[/tex]
Now we need to solve that for t:
If we apply the natural logarithm in both sides, we get:
[tex]ln(e^{-t*ln(2)/12h}) = ln(0.7)\\\\-t*ln(2)/12h = ln(0.7)\\\\t = -ln(0.7)*12h/ln(2) = 6.2h[/tex]
So after 6.2 hours the dose will decay to 70% in your bloodstream.
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Geometry question confused on how to solve this answer
The acute angles of a right triangle are complementary, so [tex]\boxed{m\angle F=34^{\circ}}[/tex].
Using right-angle trigonometry, we know that
[tex]\cos 56^{\circ}=\frac{26}{DF}\\\\DF=\frac{26}{\cos 56^{\circ}}\\\\\boxed{DF \approx 46.5}[/tex]
[tex]\tan 56^{\circ}=\frac{FE}{26}\\\\FE=26 \tan 56^{\circ}\\\\\boxed{FE \approx 38.5}[/tex]
Examine the first two steps for solving this equation. 3x - 6(5x 3) = 9x 6 1. distribute: 3x - 30x - 18 = 9x 6 2. combine like terms: -27x - 18 = 9x 6 what could be the coefficient of x once the variable term is isolated on one side of the equation? check all that apply. –36 –27 –24 24 27 36
Answer:
-36 and 36
Step-by-step explanation:
moving the 9x to the left it changes to -9x and that plus -27x is -36x
-27-9 = -36
moving -27x to the right it changes to 27x so that plus 9x is 36x
27+9 = 36
Answer:
A. -36
F. 36
Step-by-step explanation:
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x Overbar, while the standard deviation is s. What is the 90% confidence interval for the population mean
The mean of the sample is x-bar is determined to be 59.2 and population standard deviation, σ, is known to be 3.8. The 90% confidence interval about μ if the sample size, n, is 45 be 58.27< μ<60.13
A simple random sample of size n is drawn from a population whose population standard deviation, σ, is known to be 3.8. The sample mean, x-bar, is determined to be 59.2.
Hence,
n=45
σ=3.8
x-bar=59.2
The z value for the 90% confidence interval is z=1.645.
Then, μ=(x-bar)±(z×σ/[tex]\sqrt{n}[/tex])
μ=59.2±(1.645×3.8/[tex]\sqrt{45}[/tex])
μ=59.2±0.9318
59.2-0.9318<μ<59.2+0.9318
58.27< μ<60.13
Therefore, The 90% confidence interval about μ if the sample size, n, is 45 be 58.27< μ<60.13
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Given that 20=20+18+16+...+x, how many terms are on the right side of the equation
20 terms on the right side of the given equation [tex]20=20+18+16+...+x[/tex].
How we find the sum of n terms?The first n terms of the arithmetic sequence are added together to form the sum of the first n terms of AP.
Therefore, we can only evaluate the sum of n terms in a sequence if we are aware of the type of sequence it is. Usually, when calculating the sum of an n-number of terms, we take into account arithmetic progression. The common distinction between each following term and each preceding term remains unchanged throughout this progression. Natural numbers are an illustration of Arithmetic Progression, where the common difference is 1. We must therefore be familiar with the formula in order to calculate the sum of natural numbers.
We can use formula for sum of n terms-
[tex]S = \frac{n}{2}(2a + (n-1)d)[/tex]
where, S- sum of n terms
n- number of terms
a- first term
d- difference between two consecutive terms
Here, S= 20 , a = 20, d= -2
we have to find n,
[tex]S = 20 = \frac{n}{2}(2(20) + (n-1)(-2)) \\20 = \frac{n}{2}(40-(2n-2))\\40 = n(40-2n+2)\\40 = 42n-2n^2\\2n^2 -42n +40 = 0[/tex]
solving this quadratic equation-
[tex]2n^2 -42n +40 = 0\\2n^2 -40n-2n+40=0\\2n(n-20)-2(n-20) = 0\\(2n-2)(n-20)=0[/tex]
when,
[tex]2n-2 = 0\\n=1[/tex]
When,
[tex]n-20=0\\ n=20[/tex]
as we can see that there are more than 1 terms present in the series so answer will be 20 terms.
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A local farmer built a rectangular pen for her chickens using 12 meters of fence. She used part of one side of her barn as one length of the rectangular pen. She maximized the area using 12 meters of fence. She then build a rectangular pen for her pigs using 16 meters of fence. She used part of one side of her barn as one length of the rectangular pen. The length of her pen was 2 meters more than the length of the chicken pen. The width of her pen was 1 meter more than the width of the chicken pen. How much larger is the pig pen than the chicken pen
The pig pen is 14 sq. meters larger than the chicken pen built by the former.
What are the perimeter and area of a rectangle?Consider a rectangle with length 'L' and width 'W'.
So, its perimeter = 2(L + W) units and area = L × W sq. units.
Calculating the dimensions of the rectangular pen for chicken:It is given that a farmer built a rectangular pen for chickens.
The chicken pen's perimeter is 12 meters, and she used only one side of the barn as one length of the rectangular pen.
So,
L + 2W = 12
⇒ L = 12 - 2W
Then its area is calculated as below:
Area = L × W
= (12 - 2W) W
= 12W - 2W²
Consider A' = 0 for finding the larger area.
So, differentiating the area w.r.t W,
dA/dW = 12 - 4W
0 = 12 - 4W
⇒ 4W = 12
∴W = 3 meters
Then,
L = 12 - 2W = 12 - 2(3) = 6 meters
So, the area of the chicken pen = 6m × 3m = 18 m²
Calculating the dimensions of the rectangular pen for the pig:It is given that,
The length of the pig pen was 2 meters more than the length of the chicken pen. I.e., L' = L + 2
The width of the pig pen was 1 meter more than the width of the chicken pen. I.e., W' = W + 1
On substituting L and W values to find the dimensions of the pig pen,
L' = 6 + 2 = 8m
W' = 3 + 1 = 4m
Then,
Area = L' × W'
= 8m × 4m
= 32 m²
Finding how much larger is the pig pen than the chicken pen:
Area of the pig pen - Area of the chicken pen
⇒ 32 m² - 18 m² = 14 m²
Therefore, the pig pen is 14 m² larger than the chicken pen.
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Please help me with this polynomial based questions
Answer:
Hello,
Step-by-step explanation:
All is in the following picture:
Which number(s) satisfy a ∩ c? 16, 81 1, 16, 81 1, 4, 9, 16, 25, 36, 49, 81, 100 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer:
Step-by-step explanation:
B: 1, 16, 81
WHY?
Set A is perfect squares from A to 100:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
Set A = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Set C is perfect fourths
1^4 = 1
2^4 = 16
3^4 = 81
4^4 = 254 (This is greater than 100)
Set C = 1, 16, 81
Hope this helps :)
WILL MAKE BRAINLIEST!! Angles a and b are vertical angles. If m
Answer: 127
Step-by-step explanation:
angle b is 127 as well because they're vertical angles and vertical angles are equal to each other.
Mrs. fresneda sells homemade soap at the farmers' market for $4.00 per bar. write an expression for how much mrs. fresneda earns selling bars of soap. then, evaluate the expression to determine how much money she will earn if she sells 26 bars of soap.
The expression which shows the earning of Mrs. Fresneda is 4x and the money that she will earn by selling 26 bars of soap is $144.
Given that price of soap is $4.00 per bar.
We have to find the expression which shows the earning of Mrs. Fresneda after selling soap bars and the money that she will earn by selling 26 bars of soap.
let the number of soap bars be x.
We know that the revenue is the product of price and quantity.
Money that Mrs.Fresneda earns is 4*x
=4x
Expression is 4x which shows that money that Mrs. Freneda will earn by selling soap bars.
We have to just put x=26 in the expression to calculate the money after selling 26 bars of soap.
Money=4*26
=$144
Hence the expression is 4x and the money that Mrs.Freneda will earnby selling 26 bars of soap is $144.
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5.
Factorise each of the following.
(a)-15ab-6ab²
(b) 6x(2y-5)-3(5-2y)
PLEASE HELP AND EXPLAIN
See below for the interpretation of the graph
How to interpret the graph?From the graph, the initial values of x and y are 0
As x increases, y decreases.
This means that the first statement is
Initially, as x increases, y decreases.Slope is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
Using the graph values at the interval x =0 to x = 3, we have:
[tex]m = \frac{-3 - 0}{3 - 0}[/tex]
m = -1
This means that the second statement is
The slope of the graph is equal to -1 for all x between x = 0 and x = 3From the graph, y = -3, when x = 3
As x increases at this point, y increases.
This means that the third statement is
Starting at x = 3, the function value y increases as x increasesUsing the graph values at the interval x = 3 to x = 5, we have:
[tex]m = \frac{3 + 3}{5 - 3}[/tex]
m = 3
This means that the fourth statement is
The slope of the graph is equal to 3 for x between x = 3 and x = 5All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0
So, the last two statements are
For x between x = 0 and x = 4, the function value y is less than 0For x between x = 4 and x = 8, the function value y is greater than 0Read more about functions at:
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HELP HELP HELP HELP
HELP HELP HELP
!!!!!!Please please please help!!!!!!!!Drag each equation to the correct location on the table. Not all equations will be used.
Determine which equations represent lines that are parallel or perpendicular to the linear equation provided on the graph
v =
y = -2z + 1 y = − 2 + 4
2 + 3y = ½z+8 y = 2z+ 2 y = −2+5
-8
-6 -4 2
Parallel Line
4
2
-2-
4
4
2
6 B
Perpendicular Line
The equation of that is parallel to the graph is y = 1 / 2 x + 3 and the equation perpendicular to the graph is y = -2x + 1
How to know equation that a parallel and perpendicular?Equation that are parallel have the same slope.
Equation that are perpendicular gives negative 1 when multiplied .
Therefore, using slope intercept equation,
y = mx + b
where
m = slopeb = y-interceptHence, the equation of the graph can be calculated as follows:
(0, 6)(2, 7)
m = 7 - 6 / 2 - 0 = 1 / 2
Therefore,
y = 1 / 2 x + 6
Therefore, the equation that are parallel to the graph are as follows:
y = 1 / 2 x + 3The equation that are perpendicular to the graph is as follows;
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Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?
The table that describes the behavior of the graph of f(x) = 2x3 – 26x – 24 is known to be table B.
What is the function about?To be able to tell the function one need to use a graphing tool and see the attached figure to better tell and know the problem.
The Relation of graph to the x-axis are shown below
Interval (-∞,-3)- below (the function is said to be negative) - x axisInterval (-3,-1) - above (the function is said to be positive) - x axisInterval (-1,4)- below (the function is said to be negative)- x axisInterval (4,∞) - above (the function is said to be positive) - x axisNote also that in the image attached, the vertical line is the y-axis and the horizontal line is the x- axis.
Hence, the table that describes the behavior of the graph of f(x) = 2x3 – 26x– 24 is known to be table B.
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Answer:
B
Step-by-step explanation:
find the y intercept of the line on the graph
A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Find the width of the freezer.
Step-by-step explanation:
volume = length • width • height
by making width subject
V=LWH
W=V/LH
W= 54/8×3
W=54/24
W=9/4
W=2.25
how do I solve for x? (the picture has the problem)
Answer:
x = 21.013155617496
Step-by-step explanation:
we have a right triangle then ,
[tex]\cos \left( 36\right) =\frac{17}{x}[/tex]
Then
[tex]x=\frac{17}{\cos \left( 36\right) } = 21.013155617496[/tex]
Then
x ≈ 21
Step-by-step explanation:
imagine this right-angled triangle is the sine and cosine scenario in a circle. just turn it in your mind or on the paper until it looks like this.
the point with the 36° angle is the center of this circle.
x is the radius of the circle, that is under 36° connecting the center of the circle with the arc of the circle.
17 is the cosine of the angle multiplied by the radius (as the standard cosine function is normed for the standard circle with radius 1).
and the other leg is the sine of the angle multiplied by the radius (this is FYI, we don't need that for the solution here).
so,
17 = cos(36) × x
x = 17/cos(36) = 21.01315562...
Drag each equation and coordinate to the correct location on the table. Not all equations or coordinates will be used.
In the table below, quadratic equations are given in standard form. Rewrite each equation in the form that reveals the maximum or
minimum value, and then identify the coordinate point of that extreme value.
Completing the squares, we have that:
For the parabola of standard form y = x² - 6x + 17, we have that the equivalent form is (x - 3)² + 8 and the extreme value is (3,8).For the parabola of standard form y = x² + 8x + 21, we have that the equivalent form is (x + 4)² + 5 and the extreme value is (-4,5).For the parabola of standard form y = x² - 16x + 60, we have that the equivalent form is (x - 8)² - 4 and the extreme value is (8,-4).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For the parabola of standard form y = x² - 6x + 17, we have that it can be written as follows, completing the squares:
y = x² - 6x + 17 = (x - 3)² + 8, hence the extreme value is (3,8).
For the parabola of standard form y = x² + 8x + 21, we have that it can be written as follows, completing the squares:
y = x² + 8x + 21 = (x + 4)² + 5, hence the extreme value is (-4,5).
For the parabola of standard form y = x² - 16x + 60, we have that it can be written as follows, completing the squares:
y = x² - 16x + 60 = (x - 8)² - 4, hence the extreme value is (8,-4).
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A snail crawls at the rate of 1cm in 3 minutes.how long will it take to cover 1m distance? answer asap
Answer:
Step-by-step explanation:
velocity = distance divided by time
velocity of the snail = 1cm / 3min
v of snail = 0.333 cm per minute
to calculate the time of 1 meter displacement, we use the formula t = d/V
time = distance divided by velocity
time = 1meter / 0.333cm/min
time = 100cm / 0.333cm/min
time = 300 minutes
hope it helped!
Use the distributive property to write an
addition sentence equivalent to:
8(5+2)
Answer:
8(5) + 8(2)
Step-by-step explanation:
8 (5 + 2) is 8 (7) or 56
If I distribute the 8 through the problem, I will get the same answer
8(5) + 8(2)
40 + 16
56