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emmainna [20.7K]
4 years ago
13

Jan walks 4 miles each week for one month.how many miles does she walk altogether

Mathematics
2 answers:
AveGali [126]4 years ago
4 0
16 miles if its 4 weeks. its 12 miles if its 3 weeks. its 20 miles if its 5 weeks
solniwko [45]4 years ago
3 0
I think it's 8 miles in one month if you round it I don't know what the exact decimal would be.
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Can someone answer all these questions for me?
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The solution to an absolute value inequality is shown on the graph below.
lawyer [7]

The solution to the absolute value inequality is (-3,-2)

<h3>How to determine the absolute inequality?</h3>

On the absolute value inequality, we have:

Interval = -3 to 2

The intervals are represented with open circles.

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Write down and simplify all the terms in the expansion of (1+3x)6.Using your results to estimate the value of (0.97)6correct to
Keith_Richards [23]

Answer:

(a)\ (1 + 3x)^6 = 728x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1

(b)\ (1 + 3(-0.01))^6 = 0.8330

Step-by-step explanation:

Given

(1 + 3x)^6

Solving (a): Expand

To do this, we make use of pascal triangle

When the exponent is 6, the factors are: 1, 6, 15, 20, 15, 6 and 1

As a rule, the exponent of 1 will start from 0 and then increase by 1 in each term while the exponent of 3x will start from 6 and then decrease by 1 in each term.

So, we have:

(1 + 3x)^6 = 1 * 1^0 * (3x)^6 + 6 * 1^1 * (3x)^5 + 15 * 1^2 * (3x)^4 + 20 * 1^3 * (3x)^3 + 15 * 1^4 * (3x)^2 + 6 * 1^5 * (3x)^1 + 1 * 1^6 * (3x)^0

Expand

(1 + 3x)^6 = 1 * (3x)^6 + 6 *  (3x)^5 + 15  * (3x)^4 + 20 *  (3x)^3 + 15 *  (3x)^2 + 6  * (3x)^1 + 1 * (3x)^0

(1 + 3x)^6 = 1 * 728x^6 + 6 *  243x^5 + 15  * 81x^4 + 20 *  27x^3 + 15 *  9x^2 + 6  * 3x + 1

(1 + 3x)^6 = 728x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1

Solving (b): (0.97)^6

Rewrite as:

(0.97)^6 = (1 - 0.03)^6

Express -0.03 as 3 * -0.01

(0.97)^6 = (1 + 3(-0.01))^6

So, by comparing:

(1 + 3x)^6 and (1 + 3(-0.01))^6

x = -0.01

Recall that:

(1 + 3x)^6 = 728x^6 + 1458x^5 + 1215x^4 + 540x^3 + 135x^2 + 18x + 1

This gives:

(1 + 3(-0.01))^6 = 728(-0.01)^6 + 1458(-0.01)^5 + 1215(-0.01)^4 + 540(-0.01)^3 + 135(-0.01)^2 + 18(-0.01) + 1

Using a calculator

(1 + 3(-0.01))^6 = 0.000000000728 -0.0000001458+ 0.00001215  -0.00054  + 0.0135 -0.18 + 1

(1 + 3(-0.01))^6 = 0.83297200492

(1 + 3(-0.01))^6 = 0.8330 --- approximated

4 0
3 years ago
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