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xenn [34]
3 years ago
6

A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose i

t is 6:30 am right now. At what time will both trains leave the station together?
Mathematics
1 answer:
Virty [35]3 years ago
7 0

Answer:

7:12 a.m

Step-by-step explanation:

Given that:

Train to New York city leaves station every 7 minutes

Train to Boston leaves station every 6 minutes

Current time = 6:30 a.m

Time both will leave station together is obtained by finding the least common multiple of 6 and 7

Multiples of ;

6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...

7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...

The least common multiple of 6 and 7 is 42.

Hence, both trains will leave the station together after 42 minutes ;

Current time + 42 minutes

6:30 a.m+ 42 minutes = 7:12 a.m

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2 years ago
The Consumer Price Index​ (CPI) is a measure of the change in the cost of goods over time. If 1982 is used as the base year of c
Mashcka [7]

Answer:

a) y = 3.8 x +100

b) Abs. change= |168.4-167.5|=0.9

So the calculated value is 0.9 points above the actual value.

Relative. Change =\frac{|168.4 -167.5|}{167.5}x100 =0.537%

And the calculated value it's 0.537% higher than the actual value.

c) For this case we can use the slope obtained from the linear model to answer this question, and we can conclude that the CPI is increasing at approximate 3.8 units per year.

Step-by-step explanation:

Data given

1982 , CPI=100

1986, CPI = 191.2

Notation

Let CPI the dependent variable y. And the time th independent variable x.

For this case we want to adjust a linear model givn by the following expression:

y=mx+b

Solution to the problem

Part a

For this case we can find the slope with the following formula:

m =\frac{CPI_{2006}-CPI_{1982}}{2006-1982}

And if we replace we got:

m =\frac{191.2-100}{2006-1982}=3.8

Let X represent the number of years after. Then for 1982 t = 0, and if we replace we can find b:

100 = 3.8(0)+b

And then b=100

So then our linear model is given by:

y = 3.8 x +100

Part b

For this case we need to find the years since 1982 and we got x = 2000-1982=18, and if we rpelace this into our linear model we got:

y = 3.8(18) +100=168.4

And the actual value is 167.5 we can compare the result using absolute change or relative change like this:

Abs. change= |168.4-167.5|=0.9

So the calculated value is 0.9 points above the actual value.

And we can find also the relative change like this:

Relative. Change =\frac{|Calculated -Real|}{Real}x100

And if we replace we got:

Relative. Change =\frac{|168.4 -167.5|}{167.5}x100 =0.537%

And the calculated value it's 0.537% higher than the actual value.

Part c

For this case we can use the slope obtained from the linear model to answer this question, and we can conclude that the CPI is increasing at approximate 3.8 units per year.

3 0
3 years ago
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