Please look at the picture for the question

Estimate the following quantities without using a calculator. Then find a more precise result, using a calculator if necessary.

zubka84 [21]

Explanation:

a. It is so easy to double a number that no approximation is necessary.

31,000 × 200 = 3.1×10⁴ × 2×10² = 6.2×10⁶ exactly

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b. 6.2×10³ × 5.2×10⁶ ≈ 6×5×10⁹ = 3×10¹⁰ approximately

The approximation can be refined a bit by taking the ".2" into account:

6.2×10³ × 5.2×10⁶ ≈ (6×5 + .2×(6+5))×10⁹

= 32.2×10⁹ = 3.22×10¹⁰ approximately

Actual product: 3.224×10¹⁰.

For most purposes, the approximation is an adequate approximation, as it it within 10% of the actual value.

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c. 9×10⁶ -2.3×10⁴ ≈ 9×10⁶ approximately

A better approximation is to actually subtract an approximation of the smaller number:

9×10⁶ -2.3×10⁴ ≈ (9 - 0.02)×10⁶ ≈ 8.98×10⁶ approximately

The actual value uses all of the digits of the smaller number:

9×10⁶ -2.3×10⁴ ≈ (9 - 0.023)×10⁶ = 8.977×10⁶ exactly

As in part B, either approximation is adequate for most purposes, as the difference from the actual value is less than .3%.

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The accuracy required of an approximation, hence the work you expend improving accuracy, should depend on the need in the final application of the number. Often, approximations are used for budget or resource planning purposes where some "slop" is allowed or even expected.

They can also be used in engineering applications, where the error needs to be on the side of more safety (rather than less).

7 0

3 years ago

Look at each expression below. Is it equivalent to 42x - 56y? Select Yes or No for a. 40(2x-16y)

MrRa [10]

Answer:

A. no

Step-by-step explanation:

3 0

2 years ago

A broker had a taxable income of $77,050 last year. if she paid 10% of her income between $0 and $8350, 15% of her income betwee

stellarik [79]

10 percent is the same as saying 0.10 so we simply do this sum of all parts approach.
$(.10 \times8350)+(.15 \times(33950-8350)) + (.25\times(77050-33950))$

You should get an answer a bit over 15000 if you plug it into your calculator. Remember, you are taxing a certain amount of dollars at each percentage so don't get hung up on the structure of the taxes. This is why we are subtracting the smaller number from the bigger

5 0

3 years ago

Read 2 more answers

An orange punch is 45% juice and a mango punch is 20% juice. By combining the two, a company is making 500 L of a fruit punch th

AlekseyPX

Answer:

<h2>400 L of orange punch</h2>

Step-by-step explanation:

step one:

given data

orange punch is 45% juice and

mango punch is 20% juice.

amount of fruit punch to be made is

500 L of a fruit punch that is 40% juice.

Let x = the number of liters of orange punch in the fruit punch.

Then the number of liters of mango is 500 - x

The number of liters of orange + mango juice is

0.45x + 0.2(500 - x), and this must equal the number of liters

in the fruit punch, which is 0.4*500

0.45x + 100 - 0.2x = 200

solve for x

0.45x-0.2x+100-200=0

0.25x-100=0

0.25x = 100

x=100/0.25

x = 400 L

<u>400 L of orange punch</u>

6 0

2 years ago

Select the correct answer from each drop-down menu. Consider the table shown. x 1 2 3 4 5 f(x) 8 16 32 64 128 The average rate o

neonofarm [45]

Answer:

(1,3)

Step-by-step explanation:

I hope it will help u all

3 0

3 years ago