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nalin [4]
3 years ago
15

Jason runs the same distance each day. In one 7-day period he ran 40 1/4 miles. He knows that there is a proportional relationsh

ip between n, the number of days, and t, the total distance he runs. Tell whether each statement is True or False.
A. The relationship can be expressed as n=5.25t. True or False
B. The graph of the equation is a straight line through (0,0). True or False
C. The unit rate is 5.75. True or False
Mathematics
1 answer:
Harrizon [31]3 years ago
7 0
Jason runs the same distance each day. In one 7-day period he ran 40 1/4 miles. He knows that there is a proportional relationship between n, the number of days, and t, the total distance he runs. Tell whether each statement is True or False.
A. The relationship can be expressed as n=5.25t. True or False
B. The graph of the equation is a straight line through (0,0). True or False
C. The unit rate is 5.75. True or False





The answer is A
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spin [16.1K]
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anyanavicka [17]

Answer:

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8

Step-by-step explanation:

The sum you are trying to understand is this.

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}

Remember that in general when you have a geometric series  

\sum\limits_{n = 0}^{\infty} a*r^n you have that

\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}      and that equality is true as long as     |r| < 1.

Therefore here we have

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n        and   \big|\frac{-1}{15} \big| = \frac{1}{15} < 1

Therefore we can use the formula and

\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n =  \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16  = 15/8

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3 years ago
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Kipish [7]

6/319 = 0.0188087774

I used a calculator

or, just use long division

Have a great day!

Stay safe and healthy!

Happy holiday seasons!

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WILL GIVE BRAINLIEST ANSWER
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