Answers
The numerical values of x and y are 16 and 63 respectively, where line m and n are parallel to each other.
What are the numerical values of x and y?From the diagram;
Angle (8x - 2)° as a vertical angle of (2y)° forms a same side exterior angle with ( 4x - 10 )°.
Note that, same side exterior angle are supplementary.
Hence;
(8x - 2)° + ( 4x - 10 )° = 180°
Solve for x
8x - 2 + 4x - 10 = 180
Collect like terms
8x + 4x - 10 - 2 = 180
12x - 12 = 180
12x = 180 + 12
12x = 192
x = 192/12
x = 16
Therefore, the numerical value of x is 16.
Next, angle (8x - 2)° forms a vertical angle with angle (2y)°.
Note that, vertical angles are equal.
Hence
(8x - 2)° = (2y)°
Plug in x = 16 and solve for y.
8x - 2 = 2y
8( 16 ) - 2 = 2y
128 - 2 = 2y
126 = 2y
2y = 126
y = 126/2
y = 63
Therefore, the numerical value of y is 63.
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Related Questions
What is the wavelength change of a radio signal changes if the emitting source is moving away at 3,000 km/s. The lab (rest) wavelength of this radio signal is 1 meter
Answers
The change in wavelength of the radio signal is 100m
What is Wavelength ChangeThe change in wavelength of the radio can be calculated using the velocity of the given radio signal.
[tex]c = v \lambda\\[/tex]
c = speed of lightv = velocity y = wavelengthLet's substitute the values and solve.
But then, we have to convert the velocity from km to m
[tex]1km = 1000m\\3000km = x\\x = 3000000m[/tex]
Let's proceed to solve this.
[tex]c = \lambda v\\3.0*10^8 = \lambda * 3.0^6\\\lambda = \frac{3.0*10^8}{3.0*10^6} \\\lambda = 1.0*10^2m\\\lambda = 100m[/tex]
The wavelength of the radio signal is 100m.
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Joel wants to find the best model for a bivariate data set that he is working with. He used a calculator to create a linear model, a quadratic model, and an exponential model. The coefficient of determination for the linear model was 0.45. The coefficient of determination for the quadratic model was 0.38, and the coefficient of determination for the exponential model was 0.51. Which model should he use to represent the data set? Justify your response in at least 2 sentences.
Answers
Answer:
exponential
Step-by-step explanation:
just took the test
Write the equation of the line that passes through the points (-2,-8)(−2,−8) and (9,8)(9,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answers
The equation of a line is y + 8 = 16/11 (x + 2).
Here we have to find the equation of a line which are passing through points (-2, -8) and (9, 8).
Slope of a line = [tex]\frac{y_{2} - y_{1} }{x_{2}- x_{1} }[/tex]
([tex]x_{1} , y_{1}[/tex]) = (-2, -8)
([tex]x_{2} , y_{2}[/tex]) = ( 9, 8)
The slope(m) = [tex]\frac{8-(-8)}{9-(-2)}[/tex]
= 16/ 11
The equation of a straight line is:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
The point ([tex]x_{1} , y_{1}[/tex]) = ( -2, -8)
y - (-8) = 16/11( x -(-2))
y + 8 = 16/11(x + 2)
Therefore the equation of a line is y + 8= 16/11( x +2).
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On a test that has a normal distribution, a score of 41 falls three standard deviation below the mean, and a score of 73folle one standard deviation above the moon. Determine the mean of the test.
Answers
On a test that has a normal distribution, a score of 41 falls three standard deviation below the mean, and a score of 73
folle one standard deviation above the moon. Determine the mean of the test.
we know that
3=(mean-41)standard deviation -------> first equation
1=(73-mean)/standard deviation ------> second equation
solve the system of equations
Isolate deviation standard
sd=(mean-41)/3
sd=73-mean
73-mean=(mean-41)/3
219-3mean=mean-41
3mean+mean=219+41
4 mean=178
mean=44.5Answer:
Step-by-step explanation:
let's denote the mean of the test by u. We know that a score of 41 falls three standard deviations below the mean, and a score of 73 falls one standard deviation above the mean.
From the first statement, we have:
41 = u-3o
where o is the standard deviation.
From the second statement, we have:
73 = u + o
Now we can use these two equations to solve for u. We can start by solving for o and the first equation:
41 = u -3o
41 - u = -3o
o = (u - 41) /3
We can substitute this expression for o into the second equation:
73 = u + o
73 = u + (u - 41 ) / 3
219 = 3u + u - 41
260 = 4u
u = 65
Therefore, the mean of the test is 65.
A pet hotel charges $25 per night to keep a dog. When the dog arrives, there is a mandatory $15 examination fee.
Part A: Write a function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days.
Part B: How much would a 6-night stay cost?
Part C: Does a 3-night stay cost half as much as a 6-day stay since it is half the time? Explain in detail!
Answers
Part A
The function rule for total cost
f(x) = 15+25n
Part B
The cost of 6 night stay = $165
Part C
The 3 night stay cost is not half as much as a 6 day stay
The mandatory examination fee = $15
The cost per night to keep a dog = $25
Consider the number of nights as n
Part A
The function rule for total cost
f(x) = 15 + 25n
Part B
The number of nights = 6 nights
The total cost = 15 + 25n
Substitute the value of n
= 15 + 25×6
= 15 + 150
= $165
Part C
The cost of 3 nights = 15 + 25×3
= 15 + 75
= $90
The cost of 6 nights = $165
The 3 night stay cost is not half as much as a 6 day stay
Hence,
Part A
The function rule for total cost
f(x) = 15+25n
Part B
The cost of 6 night stay = $165
Part C
The 3 night stay cost is not half as much as a 6 day stay
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help me pleasee!!
thank you
Answers
The equation in slope intercept form of the line that passes through the points (-6, -2) and (-9, -1) is y = -1/3x -10/3
How to determine the equation of the line?The points are given as
(-6, -2) and (-9, -1)
Calculate the slope of the points using the following slope formula
m= (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-6, -2) and (-9, -1)
Slope = m
So, we have
m = (-1 + 2)/(-9 + 6)
Evaluate the expression
m = -1/3
The equation of the line is then calculated using the line equation formula
y = m(x - x₁) + y₁
Where
(x₁, y₁) = (-6, -2)
So, we have
y = -1/3(x + 4) - 2
Expand
y = -1/3x - 4/3 - 2
Evaluate
y = -1/3x -10/3
Hence, the equation of the line is y = -1/3x -10/3
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Two questions! Please help! Multiple choice.
Answers
Answer:
8) a. Use center G and the same radius
9) b. WX ≅ JK
Step-by-step explanation:
8) You want to know the next step in constructing a perpendicular bisector.
9) You want to know how WX relates to JK.
8)A perpendicular bisector of GH is the set of points equidistant from G and H. The arc shown is a set of points at some distance from H. We want to find two points on that arc that are the same distance from G, so the next step is ...
a) Using G as a center, draw an arc with the same radius as the first arc
9)All of the points on the arc are the same distance from W as J is from K. Point X is a point on the arc, so WX will have the same length as JK.
b) WX is congruent to JK
Score on last try: 0 of 10 pts. See Details for more. > Next question Get a similar question You can retry this question below 2 Write the following in inequality notation: 3 Inequality notation solution: No solution Question Help: M Message instructor Submit Question
Answers
Given the following:
[tex]\text{ (}\frac{2}{3},\infty)[/tex]Since both ends are in parenthesis ( ), therefore, it means that it is not equal to.
Writing this will be:
[tex]\text{ (}\frac{2}{3},\infty)\text{ = }\frac{2}{3}\text{ }<\text{ x }<\text{ }\infty[/tex]The table shows the proportional relationship between the number of uniform shirts for a soccer team and the cost.
Number of Uniform Shirts Cost (in dollars)
8 140
15 262.50
22 385
Determine the constant of proportionality.
56
7
122.50
17.50
Answers
The constant of proportionality of the given relationship is: d. 17.50.
How to Determine the Constant of Proportionality?To determine the constant of proportionality of a proportional relationship, k, any pair of values from the given table can be used and calculated as:
k = y/x.
From the given table able that represents a proportional relationship, we can use a pair of values, (8, 140):
Constant of Proportionality, k = 140/8
Constant of Proportionality, k = 17.50
Or, we can also decide to use (22, 385):
Constant of Proportionality, k = 385/22
Constant of Proportionality, k = 17.50
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selecting from milligram, gram, kilogram, and tonne, determine the best unit of measure to express a butterfly weight
Answers
Solution
For this case we can conclude that the best answer for this case is:
gram
Since a butterfly can weight about 0.04-1 grams
PLEASE HELP
Solve for m.
-6m = −9(2m - 4)
m =
Answers
Answer: m=3
That's the correct answer
Answer:
m = 3
Step-by-step explanation:
-6m = -18m +36
12m = 36
m = 3
If Jason eats 3/6 of a birthday cake and Mike eats 2/6 of the same cake, how much of the birthday cake was eaten?
a.5/6
b.5/12
If a pizza is divided into 8 equal slices and Lily eats 3/8 of the pizza, how much of the pizza is left?
a.3/6
b.5/8
There are 10 t-shirts. 7/10 of the tee-shirts are blue. The rest are green. How many t-shirts are green?
a.7
b.3
Answers
1. The quantity of the birthday cake eaten by Jason and Mike is a. 5/6 or 83.3%.
2. The quantity of the pizza left after Lily has eaten 3/8 is b. 5/8.
3. The number of green t-shirts is b. 3.
How are the numbers determined?The various numbers are determined using the mathematical operations of subtraction, addition, multiplication, and division.
These basic mathematical operations result in the difference, sum, product, and quotient, respectively.
a) Birthday Cake:The quantity of the birthday cake = 1 or 6/6
The amount consumed by Jason = 3/6
The amount consumed by Mike = 2/6
The total quantity consumed by Jason and Mike = 5/6 (3/6 + 2/6)
b) Pizza:The quantity of the pizza = 1 or 8/8
The amount consumed by Lily = 3/8
The amount left unconsumed = 5/8 (1 - 3/8)
c) T-shirts:The total number of t-shirts = 10
The fractional size of blue t-shirts = 7/10
Since the rest are green, the fractional size of the green t-shirts = 3/10 (1 - 7/10)
3/10 of 10 = 3
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Question 2
I measure the length of a building 10 times, using a tape measure. Use the following observations to
determine the 50% Error of this sample.
26.583m
26.454m
26.858m
26.808m
26.819m
26.573m
26.466m
26.826m
26.872m
26.319m
O 0.1295
0.2024
0.3329
10 pts
0.1365
Answers
The table below shows primary school enrollment for a certain country. Here, x represents the number of years after 1820, and y represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.
See uploaded table in screenshots below
Answers
Linear slope formula,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex] (Equation-1)
We can table-1,
(x , y) = (0 , 0.1)
(x , y) = (5 , 0.1)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (0 , 0.1)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (5 , 0.1)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(0.1) - (0.1)]/5-0
k = 0/5
k = 0
y = kx + b
y = (0)x + b
y = 0+b
y = b
After (x , y) = (0 , 0.1)
Substituting point,
0.1 = b
b = 0.1
Hence,
The slope and intercept to two decimal places are k = 0 ; y = b
We can table-2,
(x , y) = (55 , 3.0)
(x , y) = (60 , 4.5)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (55 , 3.0)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (60 , 4.5)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(4.5) - (3.0)]/60-55
k = 1.5/5
k = 0.3
y = kx + b
y = (0.3)x + b
y = 0.3x + b
After (x , y) = (55 , 3.0)
Substituting point,
3.0 = (0.3)(55) + b
3.0 = 16.5 + b
b = -13.5
Hence,
The slope and intercept to two decimal places are k = 0.3 ; y = 0.3x + b
We can table-3,
(x , y) = (110 , 16.6)
(x , y) = (115 , 17.5)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (110 , 16.6)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (115 , 17.5)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(17.5) - (16.6)]/115-110
k = 0.9/5
k = 0.18
y = kx + b
y = (0.18)x + b
y = 0.18x + b
After (x , y) = (110 , 16.6)
Substituting point,
16.6 = (0.18)(110) + b
16.6 = 19.8 + b
b = -3.2
Hence,
The slope and intercept to two decimal places are k = 0.18 ; y = 0.18x + b
We can table-4,
(x , y) = (160, 63.2)
(x , y) = (165 , 75.0)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (160, 63.2)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (165 , 75.0)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [(75.0-63.2)]/165-160
k = 11.8/5
k = 2.36
y = kx + b
y = (2.36)x + b
y = 2.36x + b
After (x , y) = (160, 63.2)
Substituting point,
63.2 = (2.36)(160) + b
63.2 = 377.6 + b
b = -314.4
Hence,
The slope and intercept to two decimal places are k = 2.36 ; y = 2.36x + b
We can table-5,
(x , y) = (185, 100.0)
(x , y) = (190 , 100.0)
So,
We can write,
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (185, 100.0)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (190 , 100.0)
We can substitute equation-1,
k = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
k = [((100-100)]/190-185
k = 0/5
k = 0
y = kx + b
y = (0)x + b
y = b
After (x , y) = (185, 100.0)
Substituting point,
100 = (0)(185) + b
100 = 0 + b
b = 100
Hence,
The slope and intercept to two decimal places are k = 0 ; y = b
Therefore,
The slope and intercept to two decimal places are k = 0 ; y = b The slope and intercept to two decimal places are k = 0.3 ; y = 0.3x+bThe slope and intercept to two decimal places are k = 0.18 ; y = 0.18x+bThe slope and intercept to two decimal places are k = 2.36 ; y = 2.36x+bThe slope and intercept to two decimal places are k = 0 ; y = bTo learn more about information visit Slope :
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Find the greatest common factor of the following monomials50a^5b^2 6a^3b^4 12a^4b^4
Answers
From the question;
We are to find the greatest common factor of the following monomials
[tex]\begin{gathered} 50a^5b^2 \\ 6a^{3^{}}b^4 \\ 12a^4b^4 \end{gathered}[/tex]solution
By prime factorisation
[tex]\begin{gathered} 50a^5b^2\text{ = 2 }\times5\times5\times a\times a\times a\times a\times a\times b\times b \\ 6a^3b^4\text{ = 2}\times3\times a\times a\times a\times b\times b\times b\times b \\ 12a^4b^4\text{ = 2 }\times2\times3\times a\times a\times a\times a\times b\times b\times b\times b \end{gathered}[/tex]From the above factorisation
The Greatest common factor is
[tex]\begin{gathered} G\mathrm{}C\mathrm{}F\text{ = 2}\times a\times a\times a\times b\times b \\ G\mathrm{}C\mathrm{}F=2a^3b^2 \end{gathered}[/tex]Therefore the greatest common factor is
[tex]2a^3b^2[/tex]Find the standard deviation for n = 10 and p = 0.6 when the conditions for the binomial distribution are met. (Round your answer to two digits after the decimal point.)
Answers
Given the values of n and p to be;
[tex]\begin{gathered} n=10 \\ p=0.6 \end{gathered}[/tex]We can calculate the standard deviation using the formula below;
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]substituting the given values;
[tex]\begin{gathered} \sigma=\sqrt[]{10\cdot0.6\cdot(1-0.6)} \\ \sigma=\sqrt[]{2.4} \\ \sigma=1.55 \end{gathered}[/tex]Therefore, the standard deviation for the distribution is;
[tex]\sigma=1.55[/tex]Determine the period PLEASE HELP
Answers
The period of the wave = 3 units of the x-variable.
From the Graph,
The period of a wave is the time taken to complete a cycle of motion of the wave
In the given figure, the graduations of the x-axis, which is the usually time axis = 1 unit
At the origin, (0, 0), the vertical displacement of the wave = 0
The maximum value of the wave function is between x = 0 and x = 1
The minimum value of the wave function is between x = 2 and x = 3
The time elapsed for two consecutive occurrences of the same result is called period.
At the point (3, 0) the value of the wave function is again 0, and a cycle of the wave is completed
Therefore, the period of the wave = 3 units of the x-variable.
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Answer:
2
Step-by-step explanation:
The Period goes from one peak to the next (or from any point to the next matching point).
How many of the justices were 65 or older in 2017?
Answers
The dot plot shows the frequency of the ages of the judges and each dot tells us that there is a judge of that age.
From 65 and beyond, we can count 5 dots meaning that we have 5 judges in that range.
OPTION D
What is the remainder when 2x2 - 3x + 5 is divided by x - 1?10-10-44
Answers
Explanation
Given the expression
[tex]f(x)=2x^2-3x+5[/tex]The remainder when it is divided by x-1 can be seen below.
[tex]\begin{gathered} r=2(1)^2-3(1)+5 \\ r=2-3+5 \\ r=4 \end{gathered}[/tex]Answer: 4
Coffee Shop PricesCup CostSmall $2Regular $4Large $5David and Jon are placing coffee orders for their friends.David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a $50 bill.Jon wants to know how much he spent on coffee.1. What is a good plan to find the amount Jon spent on coffee?2. Find how much Jon spent on coffee. Show the equations you used.3. Jamie says the equation 0 x $2 = $0 shows the amount Jon spent on small cups of coffee. Is he correct? Explain.4. Would David have enough money if he paid for his order with a $20 bill? Explain.3rd grade student
Answers
We are given the following details:
Small cup of Coffee = $2
Regular cup of Coffee = $4
Large cup of Coffee = $5
1.
Jon orders 4 fewer large cups than David as shown below. The amount he spent is shown below:
[tex]\begin{gathered} Jon=(10-4)\text{ }large\text{ }cups \\ Jon=6\text{ }large\text{ }cups \\ Jon=6\times5 \\ Jon=\text{\$}30 \end{gathered}[/tex]This means that Jon spent $30 on coffee
2.
The equation is shown below:
[tex]\begin{gathered} Jon=(10-6)\times\text{\$}5 \\ Jon=4\times\text{\$}5 \end{gathered}[/tex]3.
Jon bought zero small cups of coffee. This is represented as:
[tex]\begin{gathered} =0\times\text{\$}2 \\ =\text{ \$0} \end{gathered}[/tex]Hence, Jamie is correct
4.
David ordered 10 large cups of coffee as shown below:
[tex]\begin{gathered} David=10\times5 \\ David=\text{\$}50 \end{gathered}[/tex]If David paid for his order with a $20 bill, we have:
[tex]\begin{gathered} =\text{\$(}20-50) \\ =-\text{\$}30 \end{gathered}[/tex]That implies that $20 cannot cover David's order, he'd still be having a deficit of $30
10. Select all the expressions that have the
value of 9.
270 ÷ 3
250 ÷ 25
270 ÷ 30
207 ÷ 23
189 ÷ 21
Answers
Answer:
270 ÷ 30
207 ÷ 23
189 ÷ 21
These have a value of 9 just use a calculatorStep-by-step explanation:
River Rafting Company A costs $18 for a rental and has an
additional charge of $5 each hour. River Rafting Company B
costs $22 for a rental and has an additional charge of $3 each
hour. Let y represent the total cost and a represent the number
of hours. Which system of equations could you use to find
when the total cost of renting a raft will be the same?
Answers
Answer:
$28 on 2 hours of additional charges.
Step-by-step explanation:
Hello! Let's help you with your question here!
To begin, let's start writing these in terms of system of equations. Given your parameters we can split it up!
River Rafting Company A:
Here, we have a $18 cost for rental and an additional charge of $5 each hour. The $18 cost is essentially our flat rate, we have to pay this regardless and it's a one-time payment. The $5 each hour is our variable cost as we are unsure of how long people are going to be renting them for. So we can write the equation as:
[tex]y = 5a + 18[/tex]
River Rafting Company B:
Over on this side, we have a $22 cost for rental and an additional charge of $3 each hour. The explanation is the exact same as the previous one. We have a higher flat rate of $22 but a lower variable cost of $3 each hour. Therefore, the equation is:
[tex]y = 3a + 22[/tex]
Now that we have equations for both companies, we can solve using systems of equations to get y, since we are trying to get the total cost of both companies to be same. For this, let's solve with substitution.
Solve by Substitution:
Okay! Let's take [tex]y = 3a+22[/tex] (Equation 1) and substitute it into [tex]y = 5a+18[/tex] (Equation 2). To do this, we just essentially have substitute y in Equation 2 with the values that it equals to in Equation 1, so it becomes:
[tex]3a+22=5a+18[/tex]
Now, we solve for a, we move everything over to one side and then collect like terms. For this, I will be moving everything to the right. So it becomes as follows:
[tex]0 = 5a+18-3a-22[/tex]
[tex]0 = 2a - 4[/tex]
From here, we divide x and -4 by 2 to isolate a. We finally get [tex]a=-2[/tex]. Time cannot be negative which means it has to be [tex]a = 2[/tex] instead.
Now that we finally have the value of a, we can use that value and substitute it into Equation 1 to get the total cost y. So that would be:
[tex]y=3(2)+22[/tex]
[tex]y=28[/tex]
Let's try this for the second equation to verify that the cost are the same:
[tex]y=5(2)+18[/tex]
[tex]y=28[/tex]
Here, both y values are equal to 28. Therefore, you use solve by substitution to figure out that the total cost for both equals $28 when under the additional charge of 2 hours.
(Real-World Proportional Problems MC)
Three students have summer jobs. The proportional relationship between their pay and the hours they work is shown.
Student A:
Time (hours) 5 11
Pay (dollars) 63.75 140.25
Student B: $147.00 for 12 hours
Student C: The equation p = 12.5h, where p represents total pay and h represents hours worked
Which student is paid the most for 20 hours of work?
Answers
Student A paid the most for 20 hours of work.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
Given that;
Condition for A;
Time (hours) = 5 11
Pay (dollars) = $63.75 $140.25
Condition for B;
$147.00 for 12 hours.
Condition for C;
The equation, p = 12.5h
Where, p represents total pay and h represents hours worked
Now, For student A;
The amount of money raised for 1 hours of work will be;
⇒ $63.75 / 5
⇒ $12.75
So, The amount of money raised for 20 hours of work will be;
= $12.75 × 20
= $255
Hence, The amount of money raised for 20 hours of work = $255
For student B;
The amount of money raised for 1 hours of work will be;
= $147.00 / 12
= $12.25
Hence, The amount of money raised for 20 hours of work will be;
= $12.25 x 20
= $245
So, The amount of money raised for 20 hours of work = $245
For student C;
The amount of money raised for 1 hours of work will be;
p = 12.5h
p = 12.5 x 1
p = 12.5
Hence, The amount of money raised for 20 hours of work will be;
p = $12.5 x 20
p = $250
So, The amount of money raised for 20 hours of work = $250
Therefore,
Student A raised the least amount of money after walking 8 miles.
Learn more about the ratio visit;
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Answer: Student A, who is paid $255 for 20 hours of work
Step-by-step explanation: Since Student A gains $63.75 every 5 hours, and 5 x 4 = 20, then that means this $63.75 x 4 = $255 is logical and trustworthy
The triangles shown below are similar.Similar Help30Sole for
Answers
Here, we want to find the value of x
From the question, we have that the two triangles are similar
When two triangles are similar, the the ratio of their corresponding sides are equal
Thus, we have it that;
[tex]\begin{gathered} \frac{24}{30}\text{ = }\frac{8}{x} \\ \\ 24\text{ }\times\text{ x = 30}\times8 \\ x\text{ =}\frac{30\times8}{24} \\ x\text{ = 10} \end{gathered}[/tex]if 15 people with 225 total pounds of luggage plan to ride an elevator with 3000 pound weight limit write and solve an inequality to find the allowable average weight per person
Answers
The 15 people are transporting 225 pounds of luggage, this means that the total weight in the elavator is the weight of the 15 people added by the extra luggage.
[tex]\text{elevator load}=15\cdot w+225[/tex]Since the maximum load allowed in the elevator is 3000 pound, then the expression "15w+225" must be less than 3000.
[tex]15\cdot w+225<3000[/tex]To solve the inequality the first step is to subtract both sides by 225.
[tex]\begin{gathered} 15\cdot w+225-225<3000-225 \\ 15\cdot w<2775 \end{gathered}[/tex]Now we should divide both sides by 15.
[tex]\begin{gathered} \frac{15\cdot w}{15}<\frac{2775}{15} \\ w<185 \end{gathered}[/tex]The mean weight of the 15 people must be less than 185 pounds.
The recipe serves
six people. Find
the serving size
per person.
The serving is 24
Answers
Answer:
The serving size per person is 4
Step-by-step explanation:
The recipe serves six people. Find
The serving size per person is 24 ÷ 6 = 4.
What is the slope intercept equation for the following line.
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-2)}}} \implies \cfrac{-4 +2}{2 +2} \implies \cfrac{ -2 }{ 4 } \implies - \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-2)}) \implies y +2= -\cfrac{ 1 }{ 2 } (x +2) \\\\\\ y+2=-\cfrac{ 1 }{ 2 }x-1\implies {\Large \begin{array}{llll} y=-\cfrac{ 1 }{ 2 }x-3 \end{array}}[/tex]
Suppose that y varies directly as the square root of x, and that y = 45 when x = 196. What is y when x = 83? Round your answer to two decimal places if necessary
Answers
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
y=kx
In this problem we have
[tex]y=k\sqrt{x}[/tex]we have that
For y=45 x=196
step 1
calculate the constant of proportionality k
substitute the value of y and the value of x in the expression above
[tex]\begin{gathered} 45=k\sqrt{196} \\ 45=k(14) \\ k=\frac{45}{14} \end{gathered}[/tex]step 2
we have the expression
[tex]y=\frac{45}{14}\sqrt{x}[/tex]step 3
For x=83
substitute
[tex]\begin{gathered} y=\frac{45}{14}\sqrt{83} \\ y=29.28 \end{gathered}[/tex]Solve for the angles of the triangle described below. Express all angles in degrees and round to the nearest hundredth.a = 6, b = 6,C = 8l
Answers
ANSWER:
A = 48.19°
B = 48.19°
C = 83.62°
STEP-BY-STEP EXPLANATION:
Given:
a = 6, b = 6, c = 8
We can calculate the angles by means of the law of cosines, just like this:
[tex]A=\cos^{-1}\left(\frac{b^2+c^2-a^2}{2bc}\right)[/tex]We apply in each case to calculate the 3 angles, as follows:
[tex]\begin{gathered} A=\cos^{-1}\left(\frac{6^2+8^2-6^2}{2\left(6\right)\left(8\right)}\right)=\cos^{-1}\left(\frac{2}{3}\right) \\ \\ A=48.19^{\circ\:} \\ \\ B=\cos^{-1}\left(\frac{6^2+8^2-6^2}{2\left(6\right)\left(8\right)}\right)=\cos^{-1}\left(\frac{2}{3}\right) \\ \\ B=48.19^{\operatorname{\circ}} \\ \\ C=\cos^{-1}\left(\frac{6^2+6^2-8^2}{2\left(6\right)\left(6\right)}\right)=\cos^{-1}\left(\frac{1}{9}\right) \\ \\ C=83.62^{\circ\:} \end{gathered}[/tex]Therefore, the angles are the following:
A = 48.19°
B = 48.19°
C = 83.62°
3). What is the sale price for S45 sneakers, marked down 20% and then marked down another 25% to the nearest cent?
Answers
Given:
Original Price = $ 45
1st Mark down = 20 % ( this means you 're paying only 80% of the price)
2nd mark down = 25 % ( this means you 're paying only 75% of the price)
Required : Sale price of the sneaker after the 2nd markdown
Solution:
Sale price after the 1st mark down = Orignal Price x 80% or Original Price x ( 10
