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3 years ago

Find four consecutive integers such that the sum of the second and fourth is 132

Mathematics

1 answer:

Ulleksa [173]3 years ago

7 0

Remark

As long as the representation shows the numbers come one after another, you can get x to be anything.

Givens

x Can be the second number

x - 1 Can be the first number

x + 1 Can be the third number

x + 2 Can be the fourth number

Equation

x + x + 2= 132

Solution

2x + 2 = 132

2x = 130

x = 65

So the 4 numbers are 64 65 66 67

Check

The second and fourth numbers added together = 65 + 67 = 132

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3 years ago

A person on a runway sees a plane approaching. The angle of elevation from the runway to the plane is 11.1° . The altitude of th

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Answer:

The horizontal distance from the plane to the person on the runway is 20408.16 ft.

Step-by-step explanation:

Consider the figure below,

Where AB represent altitude of the plane is 4000 ft above the ground , C represents the runner. The angle of elevation from the runway to the plane is 11.1°

BC is the horizontal distance from the plane to the person on the runway.

We have to find distance BC,

Using trigonometric ratio,

$\tan\theta=\frac{Perpendicular}{base}$

Here, $\theta=11.1^{\circ}$ ,Perpendicular AB = 4000

$\tan\theta=\frac{AB}{BC}$

$\tan 11.1^{\circ} =\frac{4000}{BC}$

Solving for BC, we get,

$BC=\frac{4000}{\tan 11.1^{\circ} }$

$BC=\frac{4000}{0.196}$ (approx)

$BC=20408.16$ (approx)

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3 years ago

Mr. Barnett’s test is normally distributed with a mean of 65 with a standard deviation of five points what is the probability th

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Answer: 2.5%

Step-by-step explanation:

Mean score = 65

Standard deviation = 5

Score (x) = >75

Z-score = [(score - mean) ÷ standard deviation]

Z - score = [(75 - 65) ÷ 5]

Z - score = 10 ÷ 5 = 2

P(score higher than 75) = 100 - 95 = 5/2 = 2.5%

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2 years ago