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Delicious77 [7]
3 years ago
11

Matea recorded that water levels in one part of the river fell 1.05 millimeters per year for 2.48 years. Describe how you could

estimate the total variation in water level.
Mathematics
2 answers:
Mariulka [41]3 years ago
8 0

The decrease of the decimal rate -1.05 mm/year can be rounded to -1. You don’t need to round 2.48 because you’re multiplying by -1. Since -1.05 is negative and rounded to a greater value, the estimate could be adjusted to a slightly lesser value, maybe -2.5 or -2.6.



dusya [7]3 years ago
6 0
Round 1.05 mm to the nearest whole number the result is -1.1 then round 2.48 which the result will be equal to 3. The total variation in water level is -3.3
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EastWind [94]

We can employ a simple repeated decimal trick:

x=1.111\ldots

0.1x=0.111\ldots

\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9

###

Alternatively, we can compute the partial sum of the series.

\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}

S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}

0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}

\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}

\implies S_n=\dfrac{10}9-\dfrac9{10^n}

As n\to\infty, the second term vanishes and we're left with \dfrac{10}9. Notice that this is really just a more formal version of the earlier trick.

6 0
3 years ago
Read 2 more answers
Blake is 7 years older than Heather. In 7 years the sum of their ages will be 55. How old is Blake now?
Andreas93 [3]

Answer:

24 years old

Step-by-step explanation:

Let the age of Blake be x and the age of Heather by y then...

x=7+y

7+x+7+y=55

Notice we are adding additional 7s because the question states "in 7 years"

Simplify the second equation...

7+x+7+y=55

14+x+y=55

Subtract 21 from both sides

x+y=41

Solve using substitution (substitute 7+y for x since x = 7+y)

7+y+y=41

Combine like terms

2y+7=41

Subtract 7 from both sides

2y=34

Divide both sides by 2

y=17

x=7+17=24

Blake is 24 years old now

4 0
2 years ago
There are three blue marvels and five red marvels in a bag you randomly select a marble and put it it back in the back if you do
olga nikolaevna [1]

Answer:

25 times

Explanation:

Blue Marvels: 3

Red Marvels: 5

Total Marvels: 5 + 3 = 8 marvels

Probability: favorable outcomes/total outcomes

Probability - red marble =  5/8

After Doing 40 times:

= 5/8 × 40

= 25

7 0
2 years ago
Given the two relations, which one is a function and why is the other one not a function
Reil [10]

Answer:

The other one (number2) is not a function, because if you plot those points in a graph and use the line rule it shows that more than one point is aligned in that line.

Step-by-step explanation:

4 0
3 years ago
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ANSWERRR
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