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sergiy2304 [10]
2 years ago
9

You are the administrator of an annual essay contest scholarship fund. This year a $80,000 college scholarship is being divided

between the top two contestants so that the winner receives four times as much as the runner-up. How much will each contestant receive (in dollars)? runner-up amount : winner amount:
Mathematics
1 answer:
Hatshy [7]2 years ago
7 0

Answer:

Runner Up Amount=$16,000

Winner Amount=$64,000

Step-by-step explanation:

Amount of the college's scholarship=$80,000

The fund is being divided between the top two contestants so that the winner receives four times as much as the runner-up.

Therefore: we can say it is being divided into 5 parts where the winner gets 4 parts and the runner up gets 1 part, i.e in the ratio 4:1.

Runner Up Amount=\dfrac{1}{5}X\$ $80,000=\$16000

Winner Amount=\dfrac{4}{5}X\$ $80,000=\$64000

The winner gets $64,000 and the runner up gets $16,000.

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Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine
NikAS [45]

Answer:

Using Geometry to answer the question would be the simplest:

Step-by-step explanation:

Remembering the formula for the area of a triangle which is A=\frac12bh. One can then tackle the question by doing the following:

Step 1 Find the y-intercepts

The y-intercepts are found by substituting in x=0.

Which gives you this when you plug it into both equations:

-y=1\\y=-1\\y=8

So the y-intercepts for the graphs are (0,-1)\\, and (0,8) respectively.

Now one has to use elimination to solve the problems by adding up the equations we get:

x-y=1\\2x+y=8\\3x=9\\x=3

Now to solve for the y component substitute:

2(3)+y=8\\y=2

Therefore, the graphs intersect at the following:

(3,2)

Now we have our triangle which is accompanied by the graph.

now to solve it we must figure out how long the base is:

b=8-(-1)\\b=9

The height must also be accounted for which is the following:

h=3

Now the formula can be used:

A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2

7 0
2 years ago
Read 2 more answers
What is the domain and range of the graph?
GREYUIT [131]

Answer:

Domain (0, ∞)

Range (-∞, ∞)

Step-by-step explanation:

The domain is the input values

The input is from 0 to infinity

Domain (0, ∞)

The range is the output values

The input is from negative infinity to infinity

Range (-∞, ∞)

5 0
2 years ago
Enlist education system found in Nepal​
Gelneren [198K]

Answer:

Education in Nepal was long based on home-schooling and gurukulas.[citation needed] The first formal school (Durbar School), established by Jung Bahadur Rana in 1853, was intended for the elite. The birth of Nepalese democracy in 1951 opened its classrooms to a more diverse population.[citation needed] Education in Nepal from the primary school to the university level has been modeled from the very inception on the Indian system, which is in turn the legacy of the old British Raj.[1]

Step-by-step explanation:

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8 0
3 years ago
A bag contains 5 red balls, 3 green balls, and 2 yellow balls. Find the sum of the probability of drawing a red ball, replacing
zalisa [80]
D would be the most reasonable because the whole set up adds up to 10 and you only have a chance of drawing all of the colors in a row

7 0
3 years ago
Read 2 more answers
Charlotte is working two summer jobs, making $7 per hour washing cars and making $15 per hour clearing tables. In a given week,
FrozenT [24]

Answer:

Claire must work 4 hours cleaning tables and 5 hours washing cars to earn more than $ 90.

Since Claire is working two summer jobs, making $ 7 per hour washing cars and making $ 15 per hour clearing tables, and in a given week, she can work at most 9 total hours and must earn a minimum of $ 90, to determine one possible solution the following calculation must be performed:

15 x 9 = 135

135 - 90 = 45

45/7 = 6.42

6 x 7 + 3 x 15 = 42 + 45 = 87

5 x 7 + 4 x 15 = 35 + 60 = 95

Therefore, at a minimum, Claire must work 4 hours cleaning tables and 5 hours washing cars to earn more than $ 90.

3 0
1 year ago
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