Simplify the expressions

Mandy and Jeff start running around the track in the same direction at the same time. Mandy runs one lap in 2 minutes and 30 sec

Savatey [412]

Answer:

At 8:52:30 am they will be side-by-side again

Step-by-step explanation:

Let s be the distance ran in one 1 lap.

Here Jeff runs one extra lap compared to Mandy for coming side by side again.

Mandy runs one lap in 2 minutes and 30 seconds = 150 s

Speed of Mandy, $=\frac{s}{150}$

Jeff runs one lap in 2 minutes and 15 seconds = 135 s

Speed of Jeff, $=\frac{s}{135}$

Let t be the time when Jeff run one extra lap,

That is

$t\times \frac{s}{135}-t\times \frac{s}{150}=s\\\\t\left ( \frac{1}{135}-\frac{1}{150}\right )=1\\\\t\times \frac{15}{135\times 150}=1\\\\t=1350s$

So after 1350 seconds Jeff comes side by side to Mandy,

They both start at 8:30 am

1350 s = 22.5 minutes = 22 minutes 30 seconds

Time = 8:52:30 am

3 0

3 years ago

Tai has a bag of different colored balloons. Without

nlexa [21]

Answer:

Step-by-step explanation:

A

8 0

3 years ago

Read 2 more answers

The next generation of miniaturized wireless capsules with active locomotion will require two miniature electric motors to maneu

Tresset [83]

Answer:

A. $\dfrac{28}{45}$

B. $\dfrac{16}{45}$

Step-by-step explanation:

Suppose 10 motors have been fabricated but that, in spite of tests performed on the individual motors, 2 will not operate satisfactorily when placed into a capsule. Then

there are 8 motors which operate satisfactorily when placed into a capsule;
there are 2 motors which do not operate satisfactorily when placed into a capsule.

To fabricate a new capsule, 2 motors will be randomly selected (that is, each pair of motors has the same chance of being selected).

A. The probability that both motors will operate satisfactorily in the capsule is

$P=\dfrac{C^8_2}{C^{10}_2}=\dfrac{\frac{8!}{2!(8-2)!}}{\frac{10!}{2!(10-2)!}}=\dfrac{8!}{6!}\cdot \dfrac{8!}{10!}=7\cdot 8\cdot \dfrac{1}{9\cdot 10}=\dfrac{56}{90}=\dfrac{28}{45}$

B. The probability that one motor will operate satisfactorily and the other will not is

$P=\dfrac{C^8_1\cdot C^2_1}{c^{10}_2}=\dfrac{\frac{8!}{1!(8-1)!}\cdot\frac{2!}{1!\cdot (2-1)!}}{\frac{10!}{2!(10-2)!}}=8\cdot 2\cdot \dfrac{2!\cdot 8!}{10!}=16\cdot \dfrac{2}{9\cdot 10}=\dfrac{32}{90}=\dfrac{16}{45}$

8 0

3 years ago

The plattsville glee club is sending 8 of its members to a singing contest in cincinnati, ohio. the cost will be $588 per person

natulia [17]

Solution:

we are goiven that

The cost is $588 per person.

we have been asked to find

How much will it cost for the entire group of 8 students to attend?

As we are give with the cost for one person, so for 8 person , we will multiply the given cost by 8.

Cost for the entire group of 8 students to attend $=588\times8=4704$ $

Hence the Cost for the entire group of 8 students to attend is 4704 $

5 0

3 years ago

The hypotenuse of a 30°-60°-90° triangle is 18. Find the lengths of the other sides.

Romashka-Z-Leto [24]

Answer:

9, 9√3

Step-by-step explanation:

The ratios of sides in a 30°-60°-90° triangle are ...

1 : √3 : 2

The shortest is half the longest. If the longest is 18, the others are 9, 9√3.

7 0

3 years ago

Simplify the expressions ​

Simplify the expressions