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77julia77 [94]
2 years ago
8

A circular track is 1000 yards in circumference. Cyclists A, B, and C start at the same place and time, and race around the trac

k at the following rates per minute: A at 700 yards, B at 800 yards, and C at 900 yards. What is the least number of minutes it mus take for all three to be together again?
Mathematics
1 answer:
Lera25 [3.4K]2 years ago
6 0

Answer:

B gains 100 yards every minute. So, after 10 minutes, B has lapped A once.

C gains 100 yards on B every minute, so after 10 minutes C has lapped B.

Thus, after 10 minutes, A has gone 7 laps, B has gone 8 laps, C has gone 9 laps, and all are even again.

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Lola measures three buttons for a shirt she is making. one button is 1/8 inch, one is 3/8 inch, and one is 1/4 inch. the button
den301095 [7]

Answer: The first and last button will fit through the button hole.

Step-by-step explanation:

since we have given that

Size of first button is given by

\frac{1}{8}\ inch

Size of second button is given by

\frac{3}{8}\ inch

Size of third button is given by

\frac{1}{4}\ inch

The size of hole of the shirt is given by

\frac{2}{6}\ inch=\frac{1}{3}\ inch

So, the size of button must be smaller than the size of hole in the shirt to get fit .

Since we first make the denominator same , as L.C.M. of all denominators i.e.(8,8,4,and 3) is 24

So, Size of first button is given by

\frac{1}{8}\ inch=\frac{1\times 3}{8\times 3}=\frac{3}{24}\ inch

Similarly, Size of second button is given by

\frac{3}{8}\ inch=\frac{3\times 3}{8\times 3}=\frac{9}{24}\ inch

Similarly, Size of third button is given by

\frac{1}{4}\ inch=\frac{1\times 6}{4\times 6}=\frac{6}{24}\ inch

And, The size of hole of the shirt is given by

\frac{1}{3}\ inch=\frac{1\times 8}{3\times 8}=\frac{8}{24}

As we can see that

\frac{3}{24}

Hence, the first and last button will fit through the button hole.


7 0
1 year ago
Judy and Ramey together have 42 stuffed animals. Judy has 12 fewer animals than Ramey. How many stuffed animals does each girl h
Art [367]

Answer: Ramey has 27 and Judy has 15

Step-by-step explanation:

Just bc 27 + 15 is 42

7 0
1 year ago
Keenan gives Tisha half of his strawberries. Tisha keeps 4 of the strawberries she hit from Keenan and gives the rest to suvi. W
Darya [45]
Let’s say that Keenan give Tisha 8 of the 16 strawberries he had. So Tisha kept 4 of the 8 strawberries she got from Keenan and gave the rest to Suvi. The expression could be written like this: 16-8=8-4=4
8 0
1 year ago
Twice a year, for all four years of college, you used your credit card to pay for books and supplies, which amounts to $516 a se
mixer [17]

Answer:

$11,728

Step-by-step explanation:

Twice a year, for 4 years is 8 times

516×8 = 4128

Yearly for 4 years is 4 times

700×4 = 2800

Every month for 4 years is 48 times

100×48 = 4800

Minimum expenditure:

4128 + 2800 + 4800 = $11,728

4 0
1 year ago
Solve the equation y′ + 3y = t + e^(−2t).
Leni [432]
Hello,

I am going to remember:

y'+3y=0==>y=C*e^(-3t)

y'=C'*e^(-3t)-3C*e^(-3t)

y'+3y=C'*e^(-3t)-3Ce^(-3t)+3C*e^(-3t)=C'*e^(-3t) = t+e^(-2t)
==>C'=(t+e^(-2t))/e^(-3t)=t*e^(3t)+e^t
==>C=e^t+t*e^(3t) /3-e^(3t)/9

==>y= (e^t+t*e^(3t)/3-e^(3t)/9)*e^(-3t)+D
==>y=e^(-2t)+t/3-1/9+D
==>y=e^(-2t)+t/3+k


4 0
1 year ago
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