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vladimir2022 [97]

2 years ago

13

Franklin rides his bike to the beach averaging 18mph. He rides home along the same route. What speed must he average on the way

home if he wants to average 21 miles per hour for the round trip?

1 answer:

Sedaia [141]2 years ago

8 0

<em>Answer:</em>

<em> 24 mph</em>

<em>Step-by-step explanation:</em>

<em>Hi there ! </em>

<em>Vm = 21mph</em>

<em>V1 = 18mph</em>

<em>V2 = ?</em>

<em>Vm = (V₁ + V₂)/2</em>

<em>2Vm = V₁ + V₂</em>

<em>V₂ = 2Vm - V₁</em>

<em>replace Vm ; V₁</em>

<em>V₂ = 2×21mph - 18mph</em>

<em>= 42mph - 18mph</em>

<em>= 24 mph</em>

<em>Good luck !</em>

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Page:<br>If A+B+C=180 , then prove that:cosA+cosB+cosC= 1+4SINA/2SINB/2SINC/2

lakkis [162]

Answer:

A + B + C = π ...... (1)

...........................................................................................................

L.H.S.

= ( cos A + cos B ) + cos C

= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C

= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C

= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }

= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }

= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }

= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }

= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)

= 1 + 4 sin(A/2) sin(B/2) sin(C/2)

= R.H.S. ............................. Q.E.D.

...........................................................................................................

In step (2), we used the Factorization formula

cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]

Step-by-step explanation:

6 0

2 years ago

Nathan is planning to ride his bike for 24 minutes.

Thepotemich [5.8K]

Answer:

who is nathan

Step-by-step explanation:

do u know her

3 0

2 years ago

Read 2 more answers

at the game, mrs. burns spent $45 for 4 soft pretzels, 3 bags of peanuts, and 8 bottles of water for snacks for the family. a bo

Irina18 [472]

Answer:

<u>The correct statements are A. The cost of a bottle of water is p – 0.75, C. The cost of a soft pretzel is $3.25. and D. The cost of a bag of peanuts is $4.00.</u>

Step-by-step explanation:

1. This is the information given to solve the case:

Amount spent by Mrs. Burns at the game = US$ 45

Detailed purchase done by Mrs. Burns = 4 soft pretzels, 3 bags of peanuts and 8 bottles of water.

Price of soft pretzel = p

Price of bag of peanuts = p + US$ 0.75

Price of bottle of water = p - US$ 0.75

2. This is the equation for solving the case:

4p + 3(p + 0.75) + 8(p - 0.75) = 45

4p + 3p + 2.25 + 8p - 6 = 45

4p + 3p + 8p = 45 + 6 - 2.25

15p = 48.75

p = 3.25

<u>The price of a soft pretzel is US$ 3.25, of a bag of peanuts is US$ 4 (3.25 + 0.75) and of a bottle of water is US$ 2.50 (3.25 - 0.75).</u>

3. Now, we have all the information necessary to analyze the statements.

A. The cost of a bottle of water is p – 0.75.<u> It's correct</u>.

B. The equation that represents this scenario is (p – 0.75) + (p – 0.75) + p = 45. <u>It's false.</u>

C. The cost of a soft pretzel is $3.25. <u>It's correct.</u>

D. The cost of a bag of peanuts is $4.00.<u> It's correct.</u>

E. The cost of 8 bottles of water is $26.00. <u>It's false. (8 * 2.50 = 20)</u>

<u>The correct statements are A. The cost of a bottle of water is p – 0.75, C. The cost of a soft pretzel is $3.25. and D. The cost of a bag of peanuts is $4.00.</u>

5 0

1 year ago

Read 2 more answers

Suppose that 3% of all athletes are using the endurance-enhancing hormone EPO (you should be able to simply compute the percenta

trapecia [35]

Answer:

Step-by-step explanation:

So there is a 3% probability that an athlete is using EPO .

The probability of showing positive on a test when you've used it is 0.99.

3% x 0.99= 2.97%

The probability of a positive result without EPO is 0.1

97% x 0,1 = 9,7 %

My guess is that 2.97% + 9,7% = 12.67% or 0.1267.

I don't know i may be wrong because you've put as an answer 0.0297 but if you like you may take only the first part of the answer.

6 0

2 years ago

Every year the United States Department of Transportation publishes reports on the number of alcohol related and non-alcohol rel

Damm [24]

Complete question:

The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.

Answer:

17,209

Step-by-step explanation:

The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.

Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.

The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :

From the graph:

Year - - - - - - - - - - Number of fatalities

2001 - - - - - - - - - - 17401

2002 - - - - - - - - - 17525

2003 - - - - - - - - - 17013

2004 - - - - - - - - - 16694

2005 - - - - - - - - - 16885

2006 - - - - - - - - - 17738

To get the average :

Sum of fatalities / number of years

(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6

= 103256 / 6

= 17209.333

Average number of alcohol related fatalities is 17,209 (to the nearest whole number)

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2 years ago