Answer:
1 1/3 or 4/3
Step-by-step explanation:
1/6 + 1/6 = 2/6
simplified, it would be 1/3 then you add the one, and you get 1 1/3 or (written as a mixed number,) 4/3
Answer:
2
Step-by-step explanation:
Since the denominator is the same, we can add the numerators.
11/6 + 1/6 = 12/6
We can simplify this to 2.
So, the answer is 2.
A coach has $1280 in the budget to spend on team jackets. The team held a fundraiser and earned $1176. Each jacket costs $75. How many jackets can the coach Buy?
Pls Help
Answer: 32 jackets
Step-by-step explanation:
add 1280 to 1176 then divide the sum by 75
what times 5 gives me 1,000
Answer:
200
Step-by-step explanation:
To find that out, you divide 1,000 by 5.
1,000 ÷ 5 = 200
Could you please mark me as Brainliest? Thank you!
Answer: 200
Step-by-step explanation: 1000 divided by 5 = 200
Suppose you are doing a two sample test of means, and assume that the population variances are equal. We have the following data:
Sample 1: n1= 16, XX1 = 44, s1= 5
Sample 2: n2= 9, XX2 = 41, s2= 6
Find the test statistic.
t = 1.341
Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
Given that,
Assume you are conducting a two-sample test of averages and that the variances in the population are identical. The information below is ours:
Sample 1: n₁=16, x₁=44, and s₁=5.
Sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
We have to find the test statistic.
We know that,
n₁ = 16
x₁ = 44
s₁ = 5
n₂ = 9
x₂ = 41
s₂ = 6
We have
t= (x₂ - x₁)/√(n₁-1)s₁²+(n₂-1)s₂²/n₁+n₂-2(1/n₁+1.n₂)
t = 1.341.
Therefore, Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
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Jean is x years old and her younger brother Johnathan is y years old. What is the sum of their ages 5 years ago
The sum of their ages 5 years ago is x + y -10.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, Jean is x years old and her younger brother is y years old.
Age of Jean 5 years ago is:
x - 5
The age of Johnathan 5 years ago is:
y - 5
The sum of their ages 5 years ago is:
x - 5 + y - 5
= x + y -10
Hence, the sum of their ages 5 years ago is x + y -10.
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Denise works for a company where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes. What type of IT funding model is the company deploying?
chargeback
The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.
What is IT model funding?Traditional IT and project finance methods offer a key business risk and, if not modified, jeopardize the future of technology-based enterprises.
This excerpt from the whitepaper Changing the Finance Method by Keanen Wold, Levi Geinert, Shaun Norris, Charles Betz, Beth Dumke, Sam Guckenheimer, and Troy Magennis discusses that contradiction over how traditional financing methods handle ethical concerns and also what Agile and DevOps teams require to execute successfully.
Balancing the high-risk investment in innovation (research and development department) with regular business-as-usual responsibilities has always been difficult for organizations. Too much risk might, in the case of an unexpected failure, result in a business's dissolution; too little innovation could ultimately cause the company to be overtaken and lose market share to rivals and new upstarts.
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If units of a certain commodity are produced, then the marginal cost is dc/da = 9x^2+4x+15x ^1/4 + 10. Suppose the total cost of producing the 1st unit is 100. Calculate the total cost of producing the first 16 units. (calculus 1)
If a certain unit of a commodity is produced with a marginal cost of [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex], the cost of producing the first 126 units is 289.4
How to differentiate a function?
Differentiation is a way of showing rate of change of a function at a given time.
The given function [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex],
Differentiate with respect to x
[tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]
input the value 100 for the value of x,
This implies that [tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]
[tex]\frac{dc}{da}[/tex]=1800+4+[tex]\frac{15}{4}[/tex] x[tex]\frac{1}{\sqrt[4]{100^{3} } }[/tex]
[tex]\frac{dc}{da}=1800+4+\frac{15}{4}x\frac{1}{3.16}[/tex]
Simplifying further
[tex]\frac{da}{da} =1804+4.75[/tex]
[tex]\frac{dc}{da} =1808.75\\[/tex]
To produce the first 16 units,
[tex]\frac{1808.75}{100} }[/tex] x [tex]\frac{16}{1}[/tex]
The cost of producing the first 16 units is 289.4
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Football player one pushes against football player two, causing player two to slow down from moving any farther down the field. Which term best describes the work in this situation?
Negative work was done on player two.
Positive work was done on player two.
No work was done on either player.
Negative work was done on player one.
The work that has been done on player 2 by player 1 is a negative work. Option A.
What is work done?We define the work done as a situation in which the force that is applied moves a distance in the direction of the force. In this case we ought to know that a negative work is said to be done when the object is found to slow down at te application of the force. The meaning of this is that the force acts in such a way as to slow down motion which makes it a negative force.
For the fact that football player one pushes against football player two, causing player two to slow down from moving any farther down the field, a negative work is done.
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Which equation has the solution x = 5? Select each correct answer. Responses 32−4x=12 32 minus 4 x equals 12 25x+4=9 25 over x end fraction plus 4 equals 9 x5+5=6 x over 5 end fraction plus 5 equals 6 18−2x=9 18 minus 2 x equals 9 11 + 6x = 22
Answer:
32−4x=12,
25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and
x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)
Step-by-step explanation:
hope this help
Which ratio is equivalent to 3/15
1/3
3/5
1/5
15/3
Answer:
It should be 1/5
Since the fractional versions of the ratios are equal, the ratios are equivalent.
QUESTION 3
The triangle ABC is taken to triangle A'B'C' by a dilation. Select all of the scale factors for the
dilation that would result in an image that was smaller than the original figure.
A) 1/2 B) 8/9
C) 1
D) 3/2
E) 2
Find the difference between 54 and 9. Is the
answer even or odd?
Answer:
45, odd
Step-by-step explanation:
54-9=45
does the series converge? if the series does converge, find the sum. (if the quantity diverges, enter diverges.)
The given series [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] is convergence and the sum of the series is 33/28.
In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.
The given series is [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex].
Firstly we check the convergence of the given series.
When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.
We can write the series as:
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex]
As |0.3|<1 and |0.2|<1
Then [tex]\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n[/tex] is convergent.
So [tex]\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex] is also convergent.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right[/tex]
Series [tex]\sum_{n=1}^{\infty}(x)^{n-1}[/tex] converges to 1/x-1 for |x|<1.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}[/tex]
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}[/tex]
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 10/7 - 1/4
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 33/28
Hence, the sum of the given series is 33/28.
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The right question is:
Determine whether the series is convergent or divergent.
[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex]
If is is convergent, find the sum. (If the quantity diverges, enter diverges.)
in a sample of 62 swim instructors, 37 said that the butterfly stroke is the most difficult to teach. find the critical value used to test a claim that a majority of swim instructors think that the butterfly is the most difficult stroke to teach at the 1% significance level.
The critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84
Given that,
Of the 62 swim teachers who participated in the survey, 37 claimed that teaching the butterfly stroke is the most challenging. Find the criticial value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% level of significance.
This is right tailed test
Z [tex]\alpha[/tex] = Z 0.01 = 0.84 ( Using z table )
Therefore, the critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84
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i neeeeeeeed this answer to be right please
The measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that:
A circle:
The measure of the arc RMP = 360 - Arc RP
The measure of the arc RMP = 360 - 120 = 240 degrees
The measure of the angle RQP = 1/2[240 - 120]
The measure of the angle RQP = 60 degrees
In the second circle:
9(9 + x) = 15(15)
9 + x = 25
After solving we get:
x = 16
Thus, the measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.
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mary spent a total of $322.58 for a party. she spent $200.14 on food, plus an additional $30.61 for each hour of the party. how long was the party?
Answer: 4 hours
Step-by-step explanation:
322.58 - 200.14 = 122.44
122.44 divided by 30.61 = 4
Renata Corporation purchased equipment in 2018 for $328,400 and has taken $147,780 of regular MACRS depreciation. Renata Corporation sells the equipment in 2020 for $197,040.What is the amount and character of Renata's gain or loss?
The gain Renata Corporation got from the sale of equipment is $16420
The tax depreciation method used in the United States is called MACRS, or Modified Accelerated Cost Recovery System. In other words, the method used to determine your business's tax deductions based on the depreciation of your tangible (depreciable) assets is known as MACRS depreciation.
Equipment Book value =
Purchase price - MACRS depreciation
= $328, 400 - $147,780
=$1,80,620
Gain = sale price - Book value
= $197, 040 - $180620
=$ 16420
Gain up to total depreciation is to be treated as ordinary income, that is up to $147, 780. since the gain is $16,420 within depreciation, it is treated as ordinary income.
Renata Corporation has a gain of $16,420 of which $16, 420 is treated as ordinary income due to the section 1245 recapture
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Carlton is a project manager for a landscape design company. He is analyzing the duration of four current projects. Which graph best shows how many days each project has lasted? A. B. C. D.
Answer:i am pretty sure it is c
Step-by-step explanation:
this is because it says Which graph best shows how many days each project has lasted? and c is the only one that is talking about days
20 students selected macaroni and cheese and 16 students chose the cajun potato barrels. each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). which of the following prevents this study from being a well-designed experiment?
The students weren't assigned the treatments (new menu item) at random.
In an experiment, randomization refers to assigning volunteers randomly to the treatment. For example, we may define randomization as setting people to therapy at random.
The results are fair because randomization eliminates bias. To make the results of the experiment precise, it ensures that the groups created for experimenting are as similar to one another as possible.
In the given example, the menu items are not randomly assigned. Because the students were given a choice to choose a menu item instead of selecting the new menu item randomly. If randomly assigned all the new menu items will have an equal probability of being chosen.
Therefore, option b is the correct option.
The complete question is -
Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment?
a) There was no replication because students did not eat both menu items.
b) The treatments (new menu item) were not randomly assigned to the students.
c) An item that is currently on the menu should have been used as a control.
d) Students should not have been randomly selected.
e) There were no problems, and the study was a well-designed experiment.
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Which number set includes only RATIONAL numbers? O a O b O c Od {-4/5, 0, 0.121314..., 97/3) (-0.123123...., 0, n/2, V100, 77/4} (-66/7, 0, 0.13, V45, 98/5} (-2/3, 0, 0.321, 149, 101/3}
PLEASE HELP
The number form that includes only rational numbers are
(-2/3, 0, 0.321, √49, 101/3}
What is rational number?A rational number is one that has the form p/q, where p and q are both integers and q is not zero
Rational function means that the equation will be a fraction
examining the numbers
(-2/3, 0, 0.321, √49, 101/3}
-2/3 is already a fraction
0 = 0/1 hence can be written as a fraction
√49 = 7 = 7/1
101/3 already a fraction
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The volume of the circumscribed cylinder is 2154.04π cm^3. Find the radius of the sphere…show all work and steps.
The measure of the radius of the sphere is given as follows:
r = 359 cm.
How to obtain the volume of the cylinder?
The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h
Which is the base area given by πr² multiplied by the height h.
In the context of this problem, the parameters are given as follows:
The radius of the cylinder is the same as the radius of the sphere, which is of r.The height of the cylinder is twice the radius of the sphere, hence it is or 2r.The volume of the circumscribed cylinder is 2154.04π cm^3, hence the equation to solve for r is given as follows:
πr²h = 2154.04π
2πr³ = 2154.04π
2r³ = 2154.04
r = cube root of (2154.04/2)
r = 359.
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what is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? express your answer as a common fraction.
The ratio of the area of a square inscribed in a semicircle to the area of a square inscribed in a circle is 2/5.
What is a semicircle?
A semicircle in mathematics is a one-dimensional locus of points that makes up one-half of a circle. A semicircle's entire arc always measures 180 degrees. There is only one symmetry line in it.
For instance, if the radius is known, we can use the formula, which states that the area of a semicircle is equal to half that of a circle. As a circle's area is r2, Therefore, a semicircle's area is equal to 1/2(r2), where r is its radius. 3.14, or 22/7, is the value of.
Solution Explained:
Let's assume and take
The dimensions of the little square ABCD = 2 x 2 =4
of the little triangle's hypotenuse Radius of the semi-circle for BCG
H=sqrt(5) = The semicircle's radius
IHJK = 2sqrt is the diagonal of the huge square (5)
One side of the large square is IHJK when sin(45) x 2sqrt(5) = sqrt(10).
Therefore, the area of ABCD/area of IHJK is equal to 4/sqrt(10)2 = 2/5.
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Emma is going to invest in an account paying an interest rate of 5. 5% compounded annually. How much would emma need to invest, to the nearest hundred dollars, for the value of the account to reach $480 in 8 years?.
Emma would need to invest about $320 to increase her value by $480 over the course of 8 years.
We may use the compound interest formula to determine how much Emma would need to invest:
[tex]\mathrm{A = P(1 + r/n)^{(nt)}}[/tex]
Where:
A is equal to the final sum, in this case $480.
P is the principal sum, which represents the initial investment that we're looking for.
r = the yearly interest rate (0.055 in decimal form, or 5.5%)
n = the number of times the interest is compounded annually (in this case, n = 1 because it is compounded annually).
t = the number of years, in this instance 8 years.
Let's substitute the known values into the formula and solve for P:
[tex]\mathrm{480 = P(1 + 0.055/1)^{(1\times8)}}[/tex]
Simplifying:
[tex]480 = \mathrm P(1.055)^8[/tex]
Dividing both sides by (1.055)⁸:
[tex]\mathrm {P = \frac{480 }{ (1.055)^8}}[/tex]
P ≈ $480 / 1.50
P ≈ $320
Hence the amount to be invested is $320.
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Line a passes through the points (−5, −2) and (−5, −5), while line b passes through (0, 4) and (5, 4).
Which statement best describes the relationship between lines a and b?
A. a and b are intersecting.
B. a and b are parallel.
C. a and b are collinear.
D. a and b are perpendicular.
Based on the slopes of both lines, the relationship between both lines is: D. a and b are perpendicular.
What is the Relationship between Parallel lines or Perpendicular Lines?The relationship between two lines that are parallel is that they have the same slope, while the relationship between perpendicular lines is that their slopes are negative reciprocals of each other.
Find the slope of the line that passes through (-5, -2) and (-5, -5):
Slope (m) = change in y / change in x = (-5 -(-2)) / (-5 -(-5))
m = (-5 + 2) / (-5 + 5)
m = -3/0 [cannot divide, therefore, the slope is undefined).
The line is therefore a vertical line.
Find the slope of the line that passes through (0, 4) and (5, 4):
Slope (m) = change in y / change in x = (4 - 4) / (5 - 0)
m = 0/5
m = 0
This line is an horizontal line.
In conclusion, the relationship between a vertical and a horizontal line is that they are perpendicular to each other, therefore, the answer is: D. a and b are perpendicular.
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A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 19 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? (Round your answers to two decimal places.)
The dimensions of the rectangle that will maximize the area of the window are length, L = 3.41 feet and width, w = 3.41 feet
What rectangle dimensions will maximize the area of the window?
Given: Perimeter (P) = 19 feet
Perimeter of window = Perimeter of rectangle + Perimeter of semicircle
P = 2(2r + L) + πr
where r = radius of the semicircle and L = length of the rectangle
width(w) of the rectangle = 2r
Note: the diameter of the semicircle is the width of the rectangle
19 = 2(2r + L) + πr
19 = 4r + 2L + πr
2L = 19-4r-πr
L = 19/2 -2r- πr/2
Find the area (A) of the window:
A = Area of Rectangle + Area of Semicircle
A = 2rL + 1/2πr²
Put L into A = 2rL + 1/2πr²:
A = 2r(19/2 -2r- πr/2) + 1/2πr²
A = 19r - 4r² - πr² + 1/2πr²
A = 19r - 4r² - 1/2πr²
To maximize the area, differentiate both sides and set A' = 0
A = 19r - 4r² - 1/2πr²
A' = 19 - 8r - πr
0 = 19 - 8r - πr
8r + πr = 19
r(8 + π) = 19
r = 25/(8 + π)
width(w) = 2r
w = 2[19/(8 + π)]
w = 38/(8 + π)
w = 3.41 feet
put r = 19/(8 + π) into L = 25/2 -2r- πr/2:
L = 19/2 -2(19/(8 + π))- π(19/(8 + π))/2
L = 19/2 - 38/(8 + π) - 19π/2(8 + π)
L = [19(8 + π) - 19(2)- 19π] / [2(8 + π)]
L = 38/(8 + π)
L = 3.41 feet
Therefore, the dimensions of the rectangle are length of 3.41 feet and width of 3.41 feet
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19. For an overdue book, the school library
charges a 25¢ penalty, plus 5¢ for every
day the book is overdue. The town library
charges a 5¢ penalty, plus 10¢ for every
day the book is overdue. For what number
of days is the total fee at both libraries
the same?
Answer:
On the 4th day, the sum of penalties and charges will be the same in both the school library and the town library.
Step-by-step explanation:
School library
Penalty-25
Every day charge-5
City library
Penalty-5
Every day charge-10
Let the day when total fee at both libraries will be same be x
Total charge in school library-25+5x
Total charge in city library-5+10x
They both amount to be equal
evaluate the expression x(2 - 4y^2) when x = -2 and y = -2
Answer:
28
Step-by-step explanation:
substitute the given values into the expression
x(2 - 4y² )
= - 2(2 - 4(- 2)² )
= - 2(2 - 4(4))
= - 2(2 - 16)
= - 2(- 14)
= 28
Which equations are true equations? Select all correct answers. 48 ÷ 8 + 2³ = 5 + 3²/ 48 ÷ 8 + 2³ = 5 + 3² / 15052=30−42−12 150 /12 8⋅72−12=22−2⋅3
The equations out of the following that are true would be:
A) and B): [tex]48[/tex] ÷ [tex]8+2^3=5+3^2[/tex] ←(Options A and B were the same.)
The remaining two I am not certain if they are true or not. The way they were laid out made little to no sense. If you could maybe evaluate further on the other options, perhaps I can double check them for you and see if there are any other remainder options that are true. However, I know for certain that A and B are true.
a group of clerks must sort 1775 files. each clerk sorts at the constant rate of 30 files per hour. some of the clerks stop working at the end of the first hour; the same number of clerks stop working at the end of the second hour; and the same number of clerks stop working at the end of the third hour. the group finishes the sorting in 3 hours and 10 minutes. find the number of files sorted during the first one and a half hours of sorting.
The number of files sorted in the first one and a half hours of sorting is 945.
Here, we are given that a group of clerks must sort 1775 files.
Each clerk sorts at a constant rate of 30 files per hour.
Let the number of clerks who start working initially be x.
Thus, they will sort 30x files in the first hour.
After the first hour, let the number of clerks who stop working be a
Thus, the number of files sorted in the second hour will be 30(x - a)
Similarly, the number of files sorted in the third hour will be 30(x - 2a)x
In the last 10 minutes, the number of files sorted will be 5(x - 3a)
Thus, we can form the following equation-
30x + 30(x - a) + 30(x - 2a) + 5(x - 3a) = 1775
30x + 30x - 30a + 30x - 60a + 5x - 15a = 1775
95x - 105a = 1775
19x - 21a = 355
x = (355 + 21a)/ 19
since x and a both have to be integers, (355 + 21a) must be divisible by 19.
This is the case when a = 3
⇒ x = (355 + 21*3)/ 19
x = 418/ 9
x = 22
Now, the number of files sorted in first one and a half hours will be-
30x + 15(x - a)
= 30*22 + 15(22 - 3)
= 660 + 15*19
= 660 + 285
= 945
Thus, the number of files sorted in the first one and a half hours of sorting is 945.
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3. The function h(x) is a transformed function of f(x) = |x|. The transformation is as follows: 3 units vertical shift down, 2 units horizontal shift right.
a. Write the transformed equation, h(x).
b. Graph f(x) and h(x) on the same coordinate plane. Be sure to label the functions f(x) and h(x). This must be graphed by hand or by using the tools in Word. You may not use a web-based graphing program.
a. The transformed equation is given as follows: h(x) = |x - 2| - 3.
b. The graph of the two functions is shown by the image presented at the end of the answer.
What are translations?The translations are movements to the triangle in each of these directions:
Up.Down.Left.Right.The parent function in this problem is given as follows:
f(x) = |x|.
The first translation was a vertical translation three units down, hence we have that:
g(x) = f(x) - 3 = |x| - 3.
The second translation was a horizontal translation two units right, hence the have that the definition of the transformed equation h(x) is given as follows:
h(x) = g(x - 2) = |x - 2| - 3.
The graph of the functions is given by the image shown at the end of the answer, and the translations are verified on every point of the function, but especially the vertices.
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The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55degrees less than twice the medium angle, and the smallest angle measures 25 degrees less than the medium angle. Find the measures of each of the three angles.
Each of the three angles of the triangles whose sum of angles is 180 degree measures 75°, 65°, and 40°
What is meant by measurement of angles?An easy geometric instrument like a protractor is used to measure angles. A protractor is employed more frequently than a compass. Angle measurement is important for determining the precise angle. In geometry, there are several sorts of angles that we face in our daily lives, and we may measure angles using these tools.
Basic geometric instruments like a protractor and a compass are used to measure angles. These instruments aid in determining an angle's precise measurement. A protractor aids in producing an accurate angle measurement, while a compass aids in creating the angle. Angles can be measured in three different ways: in degrees, radians, and revolutions.
Here, we have
Let the largest angle be x degrees, the median y, and the smallest z.
x = 2y - 55
z = y - 25
x + y + z = 180
Substituting for x in the last equation:
2y - 55 + y + z = 180
3y + z = 235
From the second equation:
- y + z = -25 Subtract this from the last equation:
4y = 260
y = 65 degrees
z = 65 - 25 = 40 degrees.
and x = 180 - 65 - 40 = 75 degrees.
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