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solniwko [45]
3 years ago
5

Suppose that a cyclist began a 364 mi ride across a state at the western edge of the​ state, at the same time that a car traveli

ng toward it leaves the eastern end of the state. If the bicycle and car met after 6.5 hr and the car traveled 31.4 mph faster than the​ bicycle, find the average rate of each. The​ car's average rate is ___ mph. The​ bicycle's average rate is ___ mph. ​(Type an integer or a​ decimal.)
Mathematics
1 answer:
maw [93]3 years ago
6 0
The car's average rate  is 43.7 mph. The bicycle's average rate is 12.3 mph.

To get this solution, let the bicycle's average rate be (x) and the car's average rate be (x + 31.4) mph. 

Distance= Speed x Time
364 = (x + x + 31.4) 6.5
364 = (2x + 31.4) 6.5
364/6.5 = 2x + 31.4
56 = 2x + 31.4
56 - 31.4 = 2x
24.6 = 2x
24.6/2 = x
12.3 = x

x = 12.3 mph     
x+31.4 = 43.7 mph
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A bank paid 2.3% interest on a money market account. What is 2.3% written as a decimal
DochEvi [55]
1\%\ \ \rightarrow\ \  \frac{1}{100}=0.01 \\\\2.3\%\ \ \rightarrow\ \ x\\\\x= \frac{2.3\%\cdot0.01}{1\%} \ \ \ \Rightarrow\ \ \ x=0.023
7 0
3 years ago
Read 2 more answers
In triangle ABC segment DE is parallel to the side AC . (The endpoints of segment DE lie on the sides AB and BC respectively). F
Sophie [7]

Answer:

The length of DE is 14 cm.

Step-by-step explanation:

Given in triangle ABC segment DE is parallel to the side AC . (The endpoints of segment DE lie on the sides AB and BC respectively). we have to find the length of DE.

Given lengths are AC=20cm, AB=17cm, and BD=11.9cm

In ΔBDE and ΔBAC

∠BDE=∠BAC       (∵Corresponding angles)

∠BED=∠BCA       (∵Corresponding angles)

By AA similarity rule, ΔBDE~ΔBAC

∴their corresponding sides are in proportion

⇒ \frac{BE}{BC}=\frac{BD}{BA}=\frac{DE}{AC}

⇒ \frac{BD}{BA}=\frac{DE}{AC}

⇒ \frac{11.9}{17}=\frac{DE}{20}

⇒ DE=\frac{20\times 11.9}{17}=14cm

5 0
3 years ago
The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent.Find the single reduction the
Evgen [1.6K]

Answer:

40%  . The single reduction together is 40%.

Step-by-step explanation:

Let the bicycle cost is   x before reduced price.

First 25% is reduced  and again 20% further reduced.

Let the single reduction is y% if the two reduction together are equal.

Solution,

Case .1

reduction cost=x\times 25%%

=x\times 25/100

=x/4

The cost of bicycle after reduction of 25% is

=x-x/4=3x/4

cost of reduction further reduction of 20%      =3x/4\times 20%

=3x\times 20/(4\times 100)

=3x/20

The new cost of bicycle is further reduction of 20% is

=3x/4-3x/20

=\left ( 15x-3x \right )/20

=12x/20=3x/5

Case.2

if single reduction is done new cost of cycle is equal

x-x\times y%=3x/5

x\left ( 1-y/100 \right )=3x/5

\left ( 100-y \right )/100=3/5

100-y=60

y=40%

single reduction of a cycle is 40%

8 0
3 years ago
Goran made 6 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces
Tema [17]
    6b + 6p = 33.60              ; b=2.90

6(2.90) + 6p = 33.60

17.40 + 6p = 33.60
-17.40           -17.40

    6p = 16.20
     /6         /6

      p = 2.70

ANSWER: each pendant costs $2.70
5 0
3 years ago
A Ferris wheel can accommodate 35 people in 25 minutes. How many people can ride that Ferris wheel in 4 hours? What is the rate
Alex Ar [27]
336
60*4=240
35/25=1.4
1.4*240=336
7 0
4 years ago
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