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Dafna11 [192]
2 years ago
6

Maury completed a bicycle race 1.5 hours faster than Vince at an average speed of 16 miles per hour. Vince completed the same ra

ce at an average speed of 12 miles per hour. How many miles was the race?
Mathematics
1 answer:
MAXImum [283]2 years ago
3 0
Let the time taken by Vince to complete the race was x hours. 
Maury completed the race 1.5 hours faster. This means Maury complete the race in (x - 1.5) hours.

Average Speed of Maury = 16 miles per hour
Average Speed of Vince = 12 miles per hour

Distance = Speed x Time.

For Maury:
Distance = 16(x - 1.5)

For Vince:
Distance = 12x

Since the distance covered by both was the same, we can equate the two equations as:

16(x - 1.5) = 12x
16x - 24 = 12x
4x = 24
x = 6 
This means Vince complete the race in 6 hours.

Distance = Speed x Time = 12 x 6 = 72 miles

Thus, the total distance of the race was 72 miles. 
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Which of these statements best describes the relation shown in Item 1?
Oksi-84 [34.3K]

Answer:

The relation is 'a function that is one-to-many'.

Step-by-step explanation:

From the table, we can see that element 10 i.e. y=10 in the range, corresponds to two elements i.e. x=-5, and x=5 in the domain.

In other words, the given table represents the many-to-one function as an element of the range y = 10 corresponds to more than one element in the domain.

Therefore, the relation is 'a function that is one-to-many'.

3 0
2 years ago
Find the common difference of the arithmetic sequence. 6,9.4,12.8,16.2
Blababa [14]

A sequence is said to be arithmetic if every couple of adjacent elements differ by the same number. If this is the case, that constant number is called the common difference.

This sequence is arithmetic, because the difference between every element and the previous one is

  • 9.4 - 6 = 3.4
  • 12.8 - 9.4 = 3.4
  • 16.2 - 12.8 = 3.4

So, the common differnece is 3.4, because every couple of adjacent terms differ by 3.4

8 0
2 years ago
You are in charge of a crew that inspects cars. Each car takes approximately 1/2 hour for 1 person to inspect. The normal crew h
jonny [76]

Answer:

Each inspectors NEEDS to work 20 hours in order to review 320 cars.

Step-by-step explanation:

The amount of time taken to inspect 1 car = 1/2 hr = 0.5 hr

The total people in crew are supposed to be 10

But 2 people are MISSING.

So, the total number of present people in crew = 10 - 2=  8

The total number of cars to be inspected  = 320 cars.

Since each car takes 0.5 hour to be reviewed.

So, the time required to review 320 cars =  320 x 05  = 160 hours.

So, the total hours needed to inspect all 320 cars = 160 hours

Now,as there are total 8 crew members.

\implies \textrm{The number of hours each inspector needs to work} = \frac{\textrm{Total working hours needed}}{\textrm{Toal number of inspectors}} \\= \frac{160}{8}  = 20

Hence , each inspectors NEEDS to work 20 hours in order to review 320 cars.

7 0
2 years ago
1) A 1.5 kg apple pie is sitting on the kitchen counter . If it has 13.44 J of gravitational potential energy, how tall is the c
vampirchik [111]

a)

Answer: 0.91 m

Explanation:

We know that,

P.E. = m g h

Where,

P.E = Potential energy

m = Mass of the object

g = acceleration due to gravity (9.8 m/s²)

It is given that, m = 1.5 kg

P.E. = 13.44 J

⇒ 13.44 = 1.5 kg × 9.8 m/s² × h

⇒ h = 0.91 m

Hence, apple sits om 0.91 m tall counter.

b)

Answer: 216 J

Explanation:

P.E. = m g h

Weight, mg = 120 N ( given)

height, h = 1.8 m ( given)

The energy possessed by the suitcase is due to virtue of its position (gravitational potential energy)

P.E. = 120 N × 1.8 m = 216 J

Hence, the energy possessed by the suitcase sitting on the counter is 216 J.

8 0
2 years ago
The three angle bisectors of ΔABC meet at P. Drag the vertices around to form different triangles, and then make a conjecture. W
DochEvi [55]
The answers are- 

XP=YP for an acute triangle

YP=ZP for an obtuse triangle

XP=YP For an obtuse triangle
5 0
2 years ago
Read 2 more answers
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