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Nat2105 [25]
2 years ago
13

Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 50 minutes. If she could increase her average s

peed by 1 km/hr, it would reduce her time around the loop by 7 minutes. How many kilometers long is the loop? (Round your answer to two decimal places.)
Mathematics
1 answer:
Iteru [2.4K]2 years ago
5 0

Answer:

67.84 km

Step-by-step explanation:

let her initial speed be 'u'

Time with speed u = 2 hours 50 minutes = 2.83 hours

Distance = speed × Time

therefore,

Distance = u × 2.83  ............(1)

when speed increase by 1 km/h

speed, v = u + 1

Time taken = 2 hours 50 minutes - 7 minutes

=  2 hours 43 minutes

= 2.7167 hours

Therefor,

Distance = ( u + 1 ) ×  2.7167 .............(2)

since, the distance in both the cases will be same

therefore,

from 1 and 2

u × 2.83 = ( u + 1 ) ×  2.7167

or

u × 1.0417 = u + 1

or

0.0417u = 1

or

u = 23.97 km/hr

Therefore,

Distance of loop = u × 2.83

= 23.97 × 2.83

= 67.84 km

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A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations al
NeX [460]

Complete Question

The complete qustion is shown on the first uploaded image

Answer:

The correct option is B

Step-by-step explanation:

From the question we are told that

      The sample size  is  n = 49

       The mean is  \mu  =  17ppb

       The standard deviation is \sigma =  14 ppb

Generally the standard error of this measurement is mathematically represented as

       \sigma_z  =  \frac{\sigma}{\sqrt{n} }      

substituting values

      \sigma_{\= x}  =  \frac{14}{\sqrt{49} }  

     \sigma_{\= x}  =  2ppb

Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )

Next is to find the z value

    z =  \frac{\mu -\sigma }{\sigma_{\= x}}

     z =  \frac{15-17}{2}

      z =  -1

Now checking the z-table for the z-score of  -1 we have  

      P(X

                       

       

     

5 0
2 years ago
Explain how u would use the integer tiles to find the quotient of -15 and 3
vova2212 [387]

Answer:

(-15)/3 = -5  

Step-by-step explanation:

(-15)/3

Assume that your positive tiles are yellow, and your negative tiles are red.

The question is asking, "if you take 15 red tiles and split them into three equal groups, how many will you have in each group?"

How can you model the first value of -15?  With 15 red tiles.

Let’s model how to divide the tiles into three equal groups by moving one tile at a time into three separate groups until all 15 tiles have been moved.

Step 1.

Start with 15 red tiles, as in the first picture.

Step 2.

Start by moving tiles one at a time to begin creating three new groups.

The middle picture shows the situation after you have moved the first three tiles.

Step 3.  

Continue moving tiles one at a time from the original group and stacking them evenly in the three new groups until you have no more tiles to move.  

The third picture shows the situation when you have finished.

How many red tiles are in each group?  There are five.

Is the answer positive or negative?  The answer is negative, because there are five red negative tiles in each group.

Conclusion? (-15)/3 = -5

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2 years ago
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D is the best choice because y would be the total amount of money he would have to pay. X would be the amount of hours he uses the phone and the hourly fee is 23 so it would be 23x. the flat fee was 16 so you just add that on to the hourly fee. The whole equation should be y = 23x + 16
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Answer:

Option D is correct

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2 years ago
WILL MARK BRANLIESTHELP ME PLZ
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I believe it’s 0.043
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2 years ago
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