MATHEMATICS MIDDLE SCHOOL

A plane takes off at 6:00 am, traveling north at 270 miles per hour. A jet takes off at 7:00 am, traveling north at 460 miles per hour. At what time will the jet overtake the plane? (Round your answer to the nearest minute.)

Answers

Answer 1

Answer:

Answer:

The jet will overtake the plane at 8:25 am.

Step-by-step explanation:

The distance $D_p$ traveled by the plane after time $t$ since it took off is modeled by the equation

$D_p = 270t$

And the distance $D_j$ traveled by the jet after time $t$ since the plane took off is given modeled by the equation

$D_j =460t-460$ (we set this up such that at $t=1,$ $D_j= 0$ )

Now, the jet will overtake the plane when $D_j> D_p$ :

$460t-460> 270t$

$460t-270t> 460$

$190t>460$

$\boxed{t> 2.42\: hours }$

Which is 2 hours and 25 minutes after 6:00 am, or at 8: 25 am; therefore, the jet will overtake the plane at 8:25 am.

Answer 2

Answer:

Answer:

the answer is 8:25

Step-by-step explanation:

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Which is a good comparison of the estimated sum and the actual sum of 7 9/12 + 2 11/12?

Answers

7 9/12 = 7.75
2 11/12 = 2.917

So we can round both of these up.

7.75 rounds to 8
2.917 rounds to 3

8 + 3 = 11

So the estimated sum is 11.

7 9/12 + 2 11/12 = 10 2/3

So the actual sum is 10 2/3.

The estimated sum is a pretty good estimate to the original number.

7 9/12 + 2 11/12
((12*7)+9)/12+((12*2)+11)/12

93/12+35/12

128/12 divide by 2

(128/2)/(12/2)

64/6 divide by 2

(64/2)/(6/2)

32/3

10 2/3

Manny used 8 tenth-size parts to model 8/10. Ana used fewer parts to model an equivalent fraction. How does the size of a part in Ana's model compare to the size of a tenth-size part? Explain.

Answers

Alrighty, let's think of it like this: You are trying to fill a box with a bunch of sports balls. You have tiny little golf balls, and you have giant bowling balls. You need to fill this same box all the way up.

If you fill it with the tiny golf balls, you are going to need a whole lot of them!

If you are putting in bowling balls, only a few of them will fit, because they are so much bigger.

When it comes to your fraction, the box is the the number 8/10. That number will not change because we are not changing the size of the box.

We are just changing what we are filling it with. Manny, can fit 8 parts, or in this case balls, into the box.

It says Ana uses fewer parts, so she cannot fit as many in as Manny.

This means that Manny would have the golf balls, since he can fit more in than Ana, who must have the bowling balls.

So which is bigger? A bowling ball or a golf ball?

A bowling ball, which is what Ana has. So Ana's part will be bigger in size.

Ana's part is bigger

If 9(x − 9) = −11, then x = ?A. -92/9
B. -20/9
C. -11/9
D. -2/9
E. 70/9

Answers

$9(x - 9) =-11\n \n9x-9\cdot 9=-11\n \n9x-81=-11 \ \ |+81\n \n9x-81+81=-11+81\n \n9x=70 \ \ /:9\n \nx=(70)/(9)\n \nAnswer : \ E. \ \ 70/9$

$9(x - 9) = -11\n 9x-81=-11\n 9x=70\n x=(70)/(9)$

Captain Jessica has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Luis and his merciless band of thieves. The Captain has probability 4/9 of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability 1/4 .If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?

Answers

Answer: Probability that both the pirate and the Captain hit each other's ships is $(1)/(9)$

Step-by-step explanation:

since we have given that

Probability that the captain hits the pirate ship is given by

$(4)/(9)$

Probability that the pirate hits the Captains's ship is given by

$(1)/(4)$

So, we have to find the "Probability that both the pirate and the Captain hit each other's ship" is given by

$P(\text{Captain hits})* P(\text{ Pirates hit})\n\n=(4)/(9)* (1)/(4)\n\n=(1)/(9)$

Hence, probability that both the pirate and the Captain hit each other's ships is $(1)/(9)$

The probability that both the pirate and the Captain hit each other's ships is $(1)/(9)$ . This can be calculated by calculating the joint probability of both events.

What is joint probability?

A joint probability is a probability that two events will occur together and at the same time. Simply it is the probability that A occurs at the same time when B occurs. It can be calculated as:

$P(A and B) = P(A) * P(B)$ , where P(A and B) is the joint probability of A and B occurring together, P(A) is the probability of A, and P(B) is the probability of B.