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Rasek [7]
3 years ago
5

You bike 1 mile the first day of your​ training, 1.3 miles the second​ day, 1.9 miles the third​ day, and 3.1 miles the fourth d

ay. If you continue this​ pattern, how many miles do you bike the seventh​ day?
On the seventh day you bike ____miles.
Mathematics
1 answer:
JulsSmile [24]3 years ago
7 0

Answer:

19.9 miles

Step-by-step explanation:

In this problem we have:

d_1=1 mi is the distance travelled during the 1st day

d_2=1.3 mi is the distance travelled during the 2nd day

d_3=1.9 mi is the distance travelled during the 3rd day

d_4=3.1 mi is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2

Which can be rewritten using the general formula:

d_{n+1}-d_n=2(d_n-d_{n-1})

This means that

d_{n+1}=d_n+2(d_n-d_{n-1})

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi

So, the  distance travelled on the 7th day is 19.9 miles.

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Joe will have eaten 24/30
Jane will have eaten 5/30
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3 years ago
. Isabella buys a 1.75 litre carton of apple juice. What is the largest number of 200 millilitre glasses that she can have from
Free_Kalibri [48]

Answer:

<em>The largest number of glasses of juice Isabella can have from the carton is 8.</em>

Step-by-step explanation:

<u>Ratios</u>

Knowing the total capacity of the carton of apple juice Ct, and the capacity of each glass Co, we can calculate how many glasses can be taken from the carton by finding the ratio:

\displaystyle n=\frac{Ct}{Co}

There are 1,000 milliliters in one liter, thus the carton has a capacity of

C t= 1.75*1,000 = 1,750 milliliters

Thus,

\displaystyle n=\frac{1,750}{200}

n=8.75

Since we cannot have 8.75 glasses, we round to the previous integer, then:

The largest number of glasses of juice Isabella can have from the carton is 8.

6 0
2 years ago
The population of a bacteria colony is growing exponentially, doubling every 6 hours. If there are 150 bacteria currently presen
marusya05 [52]

Answer:

If rounded to the nearest 10 bacteria, then it would be 500 bacteria.

Step-by-step explanation:

First multiply 150 by two in order to get 300, that leaves 4 hours to figure out. From there you can figure out the rest by seeing that 4 is 2/3 of 6. I converted it into the decimal number .66. Multiply 300 by .66 to get 198 and then add it to 300 to get 498. Then just round it up to the nearest 10 bacteria which leaves you with the final answer of 500 bacteria.

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3 years ago
In the given figure L1and L2 are two parallel sides . if the area of the rectangle PQRS is 60cm^2 then what is the area of the p
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Answer:

Step-by-step explanation:

Believe it or not, the two areas are the same.

The base of the rectangle is PQ

The height of the rectangle is PS

Now look at the parallelogram.

The base is PQ

The height is PS

The area has to be the same in both cases. There is no other way to interpret what is happening.

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3 years ago
I need help now assssssap
Andreyy89

Answer:

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Step-by-step explanation:

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2 years ago
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