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il63 [147K]
3 years ago
6

Runner A is initially 5.1 km west of a flagpole and is running with a constant velocity of 8.5 km/h due east. Runner B is initia

lly 4.1 km east of the flagpole and is running with a constant velocity of 7.4 km/h due west. How far are the runners from the flagpole when their paths cross? Answer in units of km.
Mathematics
1 answer:
Sati [7]3 years ago
8 0

Find the total distance between the two runners:

5.1 + 4.1 = 9.2 km apart.

We want to calculate the distance each runner does:

Runner A distance = X km, rate = 8.5 km/ hr.

Time = X / 8.5

Runner B distance = (9.2 - x) Total distance between the runners minus what runner A runs equals where they meet).

Rate = 7.4 km/hr.

Time = (9.2-x) / 7.4

Now to find where they meet set the two equations equal:

x / 8.5 = (9.2-x) / 7.4

Cross Multiply:

7.4x = 78.2 - 8.5x

Add 8.5x to both sides:

15.9x = 78.2

Divide both sides by 15.9:

x = 78.2 / 15.9

x = 4.918 = 4.9 km.

Since X is the distance runner A runs, subtract that from his distance from the flag pole:

5.1 - 4.9 = 0.2

The runners meet 0.2 km west of the flag pole.

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Below are I assume the choices, it can be found elsewhere:

A. 15x+10y≥250

B. x+y≤250

C. x+y≥20

D. 15x+10y≥20

E. x+y≤20

<span>F. 15x+10y≤250
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4 0
4 years ago
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Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable
alukav5142 [94]

Answer:

An ANOVA test

Step-by-step explanation:

You will use the ANOVA test, which is a test that compares the means of more than 2 samples.  Since the teacher used 3 test groups, she would have to use this test if she wanted to do a hypothesis test to determine if the means are equal.  

*This test only tells us if the means are equal, it won't say which is greater than the other.  You would have to do 3 individual hypothesis tests comparing 2 means at a time in order to determine that.

8 0
3 years ago
There are 50 roses in a tray. There is at least 1 red rose among any 24 randomly selected roses, and there is at least 1 white r
Darina [25.2K]

By using the second condition, we conclude that there are 23 white roses in the tray.

<h3>How many white roses are in the tray?</h3>

First, we know that there are a total of 50 roses in the tray, and we have the conditions:

  • <em>"There is at least 1 red rose among any 24 randomly selected roses"</em>
  • <em>"There is at least 1 white rose among any 28 randomly selected roses".</em>

The second statement means that, always that we take 28 roses, at least one of them is white. So, there are 27 roses in the tray that are not white.

Whit that in mind, if the 28th rose must be white, then all the remaining roses in the tray are white, this means that there are:

50 - 27 = 23 white roses.

If you want to learn more about counting.

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6 0
2 years ago
3(2a + 1) = -5(a + 6)
Lemur [1.5K]
3(2a+1)=-5(a+6)
First expand the brackets.
6a+3=-5a-30
Now add 5a to both sides.
11a+3=-30
Then subtract 3 from both sides.
11a=-33
Finally divide both sides by 11.
a=- 33/11
=-3
4 0
4 years ago
Please help me I need to get this done!!!
alukav5142 [94]

Answer:

y=-3x+4

Step-by-step explanation:

The question is asking for the equation in slope-intercept form. This is y=mx+b where m is the slope and b is the y-intercept.

The slope can be found by counting the units in between two points on the graph. Remember that slope is rise over run or y/x. Two points on the graph are (2,-2) and (1,1). The y is increasing by 3 while x is decreasing by 1. This means the slope is -3.

The y-intercept is where the line intersects with the y-axis. In this case, that point is (0,4). Therefore, b=4.

The final answer is y=-3x+4.

7 0
3 years ago
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