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2 years ago

The railing of a wheelchair ramp is parallel to the ramp. Find x and y in the diagram.

Mathematics

1 answer:

yKpoI14uk [10]2 years ago

5 0

Given:

The wheel chair ramp is parallel to the ramp.

To find:

The value of x and y.

Solution:

If two lines are parallel, then the alternate interior angles are congruent.

4x° + 6y° = 86° --------- (1)

Similarly,

5x° + 6y° = 94°

Subtract 5x° from both sides.

5x° + 6y° - 5x° = 94° - 5x°

6y° = 94° - 5x° --------- (2)

Substitute (2) in (1).

4x° + 94° - 5x° = 86°

94° - x° = 86°

Subract 94° on both sides.

94° - x° - 94° = 86° - 94°

- x° = 86° - 94°

- x° = -8°

Multiply by -1 on both sides, we get

x = 8

Substitute x = 8 in (2).

6y° = 94° - 5(8)°

6y° = 54°

Divide by 6 on both sides, we get

y = 6

The value of x is 8 and y is 6.

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2 years ago

A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean le

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Answer:

$1000-1.96\frac{2}{\sqrt{4}}=998.04$

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

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$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$1000-1.96\frac{2}{\sqrt{4}}=998.04$

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2 years ago

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Answer:

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Step-by-step explanation:

Purchasing Cost = 28,000$

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Total Depreciation:

Total Depreciation over 5 years (60 Months) = Purchasing Cost - Salvage Value

Total Depreciation over 5 years (60 Months) = 28,000 - 3,000

Total Depreciation over 5 years (60 Months) = 25,000$

Monthly Depreciation:

Using the unity method we have monthly depreciation by dividing the total depreciation by the total no. of months as below:

Total Depreciation over a single month =25,000/60

Total Depreciation over a single month = 416.67$ (Monthly Depreciation)

Depreciation till December 31, Year 1

As from September 1, Year 1 to December 31, Year 1, its been 3 months therefore total depreciation will be = 3 * Monthly Depreciation

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2 years ago

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