Which of the functions graphed below could be defined by a cubic equation?

A point x is 34m due to east of a point Y . The bearing of a flagpole from x and Y are N18°W And N40°E respectively .

Murljashka [212]

Answer:

The distance of flag post from Y is 38.13 m

Step-by-step explanation:

Consider point Y at the intersection of both lines as shown below. Now the point X lies 34 meter from point Y in east direction.

Now flag pole at point X lies at a bearing of N18°W. That is at point X from north, flag post makes an angle of 18° towards west.

Similarly flag pole at point Y lies at a bearing of N40°E. That is at point Y from north, flag post makes an angle of 40° towards east.

Consider ∆ AXY as right angle triangle. Therefore measure of angle FXY is,

$\angle AXY=\angle AXF+\angle FXY$

$\therefore 90 \degree=18\degree+\angle FXY$

$\angle FXY=72\degree$

Consider ∆ BYX as right angle triangle. Therefore measure of angle FYX is,

$\angle BYX=\angle BYF+\angle FYX$

$\therefore 90 \degree=40\degree+\angle FYX$

$\angle FYX=50\degree$

Refer attachment 1.

From diagram consider the triangle FYX. To find the third angle that is ∠YFX can be calculated by using angle sum property of triangle.

∠YFX+∠FYX+∠FXY=180°

∠YFX+50°+72°=180°

∠YFX=58°

Refer attachment 2.

Now the distance FY can be calculated using sin rule as follows,

$\frac{\sin X}{FY}=\frac{\sin F}{YX}=\frac{\sin Y}{FX}$

Substituting the values,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}=\frac{\sin 50}{FX}$

Simplifying first two terms,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}$

Cross multiplying,

$34\times\sin 72=FY\times \sin 58$

$\dfrac{34\times\sin 72}{\sin 58}=FY$

$FY=38.13$ m

7 0

1 year ago

Below is a graph of the Murphys' annual expenses. How much will the Murphys' pay in state/local taxes if their gross annual

Murrr4er [49]

Answer:

the answer is C: 2,500.80

Step-by-step explanation:

3 0

1 year ago

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Orange M&M’s: The M&M’s web site says that 20% of milk chocolate M&M’s are orange. Let’s assume this is true and set

SOVA2 [1]

Answer:

The correct option is (A).

Step-by-step explanation:

Let X = number of orange milk chocolate M&M’s.

The proportion of orange milk chocolate M&M’s is, p = 0.20.

The number of candies in a small bag of milk chocolate M&M’s is, n = 55.

The event of an milk chocolate M&M being orange is independent of the other candies.

The random variable X follows a Binomial distribution with parameter n = 55 and p = 0.20.

The expected value of a Binomial random variable is:

$E(X)=np$

Compute the expected number of orange milk chocolate M&M’s in a bag of 55 candies as follows:

$E(X)=np$

$=55\times 0.20\\=11$

It is provided that in a randomly selected bag of milk chocolate M&M's there were 14 orange ones, i.e. the proportion of orange milk chocolate M&M's in a random bag was 25.5%.

This proportion is not surprising.

This is because the average number of orange milk chocolate M&M’s in a bag of 55 candies is expected to be 11. So, if a bag has 14 orange milk chocolate M&M’s it is not unusual at all.

All unusual events have a very low probability, i.e. less than 0.05.

Compute the probability of P (X ≥ 14) as follows:

$P(X\geq 14)=\sum\limits^{55}_{x=14}{{55\choose x}0.20^{x}(1-0.20)^{55-x}}$

$=0.1968$

The probability of having 14 or more orange candies in a bag of milk chocolate M&M’s is 0.1968.

This probability is quite larger than 0.05.

Thus, the correct option is (A).

4 0

2 years ago

Suppose that a person with a push mower can mow a large lawn in 5 hours, whereas the lawn can be mowed with a riding lawn mower

Reil [10]

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Push Mower
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It takes 5 hours to complete the job
1 hour = 1/5 of the job

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Riding Lawn Mower
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It takes 3 hours to complete the job
1 hour = 1/3 of the job

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Push Mower + Riding Lawn Mower
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1 hour = 1/5 + 1/3
1 hour = 3/15 + 5/15
1 hour = 8/15 of the job.

------------------------------------------------------------------
Calculate time needed to complete
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8/15 of the job takes 1 hour
8/15 of the job = 1 hour

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Divide by 8/15 on both side
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8/15 ÷ 8/15 of the job = 1 ÷ 8/15 hour
Whole of the job = 1 x 15/8 hours
Whole of the job = 15/8 hours
Whole of the job = 1 7/8 hours

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Answer: 1 7/8 hours
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6 0

1 year ago

What is the length of Line segment A B? Round to the nearest tenth. Triangle A B C is shown. Angle A C B is a right angle and an

amm1812

C=90°, A=75°, b=AC=19, x=AB

Without a figure, we see AC is adjacent to angle A, so

cos A = AC/AB = b/x

x = b/cos A = 10 / cos 75° ≈ 38.637

Answer: 38.6

3 0

1 year ago

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