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julsineya [31]
3 years ago
14

9. start from 110 feet away, a person on a bicycle rides towards a checkpoint and then it passes it. the rider is traveling at a

constant rate of 30 feet per second. the distance between the bicycle and the checkpoint is given by the equation d=|110-3t|. at what times is the bike 40 feet away from the checkpoint?
A. 2.3 sec and 5 sec
B. 1.6 sec and 5 sec
C. 2.3 sec and 4.6 sec
D. 1.6 sec and 4.6 sec
Mathematics
1 answer:
Zinaida [17]3 years ago
8 0

Answer:

A. 2.3 sec and 5 sec

Step-by-step explanation:

We are given that start from 110 feet away, a person on a bicycle rides towards a checkpoint and then it passes it. the rider is traveling at a constant rate of 30 feet per second.

The distance between the bicycle and the checkpoint is given by the equation :

d=|110-30t|

Now we are required to calculate at what times is the bike 40 feet away from the checkpoint. So, substitute d = 40 in the equation

40=|110-30t|

40=110-30t     and    40= -110+30t

30t=110-40t     and   40+110=30t

30t=70               and   150=30t

t=\frac{70}{30}                   and   \frac{150}{30}=t

t=2.3                  and   5=t

Hence at 2.3 sec and 5 sec  the bike is 40 feet away from the checkpoint.

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Answer:

We conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.

Step-by-step explanation:

We are given that a particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000.

From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles.

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So, Null Hypothesis, H_0 : \mu \geq 50,000 miles   {means that deluxe tire averages at least 50,000 miles before it needs to be replaced}

Alternate Hypothesis, H_A : \mu < 50,000 miles    {means that deluxe tire averages less than 50,000 miles before it needs to be replaced}

The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about population standard deviation;

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