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Rzqust [24]
1 year ago
7

 A hiker is walking down a mountain. She walked​ 5,978 feet in 17 minutes. In that​ time, she descended​ 1,024 feet from the top

of the mountain. She then walked​ 3,972 feet in 7 minutes. In that​ time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.
Mathematics
1 answer:
Karo-lina-s [1.5K]1 year ago
5 0
First walk=descend of 1024 feet in 17 minutes
second walk=descend of 500 feet in 7 minutes

so in total she descended 1024+500=1524 feet in 7+17=24 minutes
as an average rate this equals 1524/24=63.5 feet/minute descended
or an average rate of -63.5 feet/minute in altitude (note the minus)
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Out of 498 applicants for a job, 187 have over 10 years of experience and 127 have over 10 years of experience and have a gradua
Kitty [74]

Answer:

the probability that randomly selected applicants over 10 years of experience is 0.6791

Step-by-step explanation:

The computation of the probability that randomly selected applicants over 10 years of experience is as follows:

Total would be

= 187 have 10 + years experience

Now

P(graduate | 10+) = (graduate and 10+ years experience) ÷ (10 + years of experience)

= 127 ÷ 187

= 0.6791

Hence, the probability that randomly selected applicants over 10 years of experience is 0.6791

3 0
1 year ago
It costs dylan $x$ dollars to buy $3$ tickets to the zoo. he discovers that if he were to buy $5$ tickets, he would receive a to
jonny [76]

So, if Dylan has x dollars and he bought 3 tickets with them, the tickets were priced at k dollars per ticket. If he bought 5 tickets with the x dollars and saved 12 total dollars, it would be the same as buying the tickets with x-12 dollars, so we have:

\frac{x}{3}=k\\ \frac{x-12}{5}=q

So, with this we have:

x=3k\\ x=5q+12

If we're looking for a number that satisfies these constraints, we can work with modular arithmetic. We have:

x\equiv 0 \pmod{3}\\ x\equiv 12 \pmod{5}

So, we can use the chinese remainder theorem here. So, we clearly have x=3k, which means:

3k\equiv12 \pmod{5} \implies\\ k \equiv 4 \pmod{5} \implies\\ k=5j+4

So, since we have x=3k, we also have x=3(5j+4)=15j+12.

So, clearly j=0 won't work so we should have j=1. That means our money per ticket for the five tickets is:

\frac{27-12}{5}=3

And our money per three tickets is:

\frac{27}{3}=9

This is easily verifiable. Three tickets needs 27 dollars and 5 tickets needs 15 dollars, which is 12 less than 27 dollars. So we have our money per three dollar ticket at 6 more than money per five dollar.

4 0
1 year ago
Read 2 more answers
Suppose that a person with a push mower can mow a large lawn in 5 ​hours, whereas the lawn can be mowed with a riding lawn mower
Reil [10]
------------------------------------------------------------------
Push Mower
------------------------------------------------------------------
It takes 5 hours to complete the job
1 hour = 1/5 of the job

------------------------------------------------------------------
Riding Lawn Mower
------------------------------------------------------------------
It takes 3 hours to complete the job
1 hour = 1/3 of the job

------------------------------------------------------------------
Push Mower + Riding Lawn Mower
------------------------------------------------------------------
1 hour = 1/5 + 1/3 
1 hour = 3/15 + 5/15 
1 hour = 8/15 of the job.

------------------------------------------------------------------
Calculate time needed to complete
------------------------------------------------------------------
8/15 of the job takes 1 hour
8/15 of the job = 1 hour 

------------------------------------------------------------------
Divide by 8/15 on both side
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8/15 ÷ 8/15 of the job = 1 ÷ 8/15 hour
Whole of the job = 1 x 15/8 hours
Whole of the job = 15/8 hours
Whole of the job = 1 7/8 hours

------------------------------------------------------------------
Answer: 1 7/8 hours
------------------------------------------------------------------

6 0
1 year ago
A middle school band has 45 sixth and seventh graders The ratio of sixth to seventh graders is 2 to 3 how many sixth graders are
AnnyKZ [126]

Answer:

  18

Step-by-step explanation:

There are 2+3 = 5 ratio units representing 45 band members, so each ratio unit represents 45/5 = 9 band members.

The 2 ratio units of sixth graders represent 2×9 = 18 sixth grade band members.

5 0
2 years ago
Montel collected 26 leaves for his science project. he wants to put 6 leaves on a page. which shows how many pages montel will n
MissTica
You divide 26 by 6, and you get 4 1/3, so I guess Montel will need 5 pages.
6 0
1 year ago
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