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Rashid [163]
3 years ago
6

Maureen has a net spendable income of $2,100 per month. She sets up the following transportation budget for herself. 3. Transpor

tation (15% - 20%) 350 a. Car payments 150 b. Gas/Oil 120 c. Insurance 60 d. License/Registration 2 e. Taxes 5 f. Maintenance/Repair 50 What has Maureen done wrong?
Mathematics
2 answers:
algol133 years ago
7 0

Answer:

Given is : Maureen has a net spendable income of $2,100 per month.

Now, she sets up a 15 to 20% budget for transportation.

This means her should budget lie between

0.15\times1200=180 to 0.20\times1200=240 but she assigned $350 for this category.

Now adding up the sub- categories, we get:

150+120+60+2+5+50 =387

So, we can clearly see that the sub-categories cost more than the category itself.

Maureen has budgeted her transportation wrongly. Either she should increase the budget or she should cut out few dollars from the sub categories.

Aleksandr-060686 [28]3 years ago
4 0
She would need $387 dollars to cover her transportation budget. She will need to increase her transportation budget to cover the minimum recommended amount. hope this helps
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Answer:

x = 1/2 and x = 9/2

Step-by-step explanation:

To solve this equation: |2x-5|=4 we need two evaluate two cases:

|2x-5| = 2x-5 when x>5/2 ✅

|2x-5| = -2x+5 when x<5/2✅

Then, if x>5/2:

2x-5 = 4 ➡ x = 9/2

Then, if x>5/2:

-2x+5 = 4 ➡ x = 1/2

Then, the two solutions are:  x = 1/2 and x = 9/2

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Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))
Sonja [21]

Answer:

\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}

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We need to find \tan(a).

\sin^2(a)+\cos^2(a)=1 is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

(\frac{2}{3})^2+\cos^2(a)=1

\frac{4}{9}+\cos^2(a)=1

Subtract 4/9 on both sides:

\cos^2(a)=\frac{5}{9}

Take the square root of both sides:

\cos(a)=\pm \sqrt{\frac{5}{9}}

\cos(a)=\pm \frac{\sqrt{5}}{3}

The cosine value is positive because a is a number between -\frac{\pi}{2} and \frac{\pi}{2} because that is the restriction on sine inverse.

So we have \cos(a)=\frac{\sqrt{5}}{3}.

This means that \tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}.

Multiplying numerator and denominator by 3 gives us:

\tan(a)=\frac{2}{\sqrt{5}}

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

\tan(a)=\frac{2\sqrt{5}}{5}

Let's continue on to letting b=\cos^{-1}(\frac{1}{7}).

Let's go ahead and say what the restrictions on b are.

b is a number in between 0 and \pi.

So anyways b=\cos^{-1}(\frac{1}{7}) implies \cos(b)=\frac{1}{7}.

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of b.

\cos^2(b)+\sin^2(b)=1

(\frac{1}{7})^2+\sin^2(b)=1

\frac{1}{49}+\sin^2(b)=1

Subtract 1/49 on both sides:

\sin^2(b)=\frac{48}{49}

Take the square root of both sides:

\sin(b)=\pm \sqrt{\frac{48}{49}

\sin(b)=\pm \frac{\sqrt{48}}{7}

\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}

\sin(b)=\pm \frac{4\sqrt{3}}{7}

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This implies:

\sin(b)=\frac{4\sqrt{3}}{7}

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Multiplying both top and bottom by 7 gives:

\frac{4\sqrt{3}}{1}= 4\sqrt{3}.

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\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}

\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}

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\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}

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Answer:

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Step-by-step explanation:

Given data

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