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Ilia_Sergeevich

1 month ago

6

You are in charge of a crew that inspects cars. Each car takes approximately 1/2 hour for 1 person to inspect. The normal crew h

as 10 people, but this crew is missing 2 people. If you have 320 cars that need to be inspected, how many hours will each of the inspectors need to work?

1 answer:

Inessa [12.5K]1 month ago

7 0

Answer:

Each inspector MUST work 20 hours to complete the review of 320 cars.

Step-by-step explanation:

To inspect one car, the time taken is 1/2 hour, or 0.5 hours.

Originally, there are expected to be 10 crew members.

However, 2 crew members are ABSENT.

This leaves a total of 8 crew members available for the task.

For the 320 cars needing inspection, each taking 0.5 hours:

Thus, the total time required to inspect all 320 cars equals 320 x 0.5 = 160 hours.

Therefore, a total of 160 hours is necessary to inspect all 320 cars.

Given that there are 8 inspectors now available.

$\implies \textrm{The number of hours each inspector needs to work} = \frac{\textrm{Total working hours needed}}{\textrm{Toal number of inspectors}} \\= \frac{160}{8} = 20$

Consequently, each inspector MUST work 20 hours to review 320 cars.

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Two boats start their journey from the same point A and travel along directions AC and AD, as shown below: ABC is a right triang

Inessa [12570]

*Refer to the image attached below

Answer:

346.4 ft

Step-by-step Explanation:

The distance between the boats, CD = BD - BC

Using trigonometry, find the length of BD in triangle ∆ABD and also calculate the length of BC in triangle ABC.

Length of BD in triangle ABD:

Opposite side to <30° = 300 ft

Adjacent side = BD

$tan(30) = \frac{300}{BD}$

$BD*tan(30) = 300$

Divide both sides by tan(30)

$\frac{BD*tan(30)}{tan(30)} = \frac{300}{tan(30)}$

$BD = 519.6 ft$ (rounded to nearest tenth)

Length of BC in triangle ABC:

Opposite side to <60° = 300 ft

Adjacent side = BC

$tan(60) = \frac{300}{BC}$

$BC*tan(60) = 300$

Divide both sides by tan(60)

$\frac{BC*tan(60)}{tan(60)} = \frac{300}{tan(60)}$

$BC = 173.2 ft$ (rounded to nearest tenth)

The distance, CD, between the boats is calculated as BD - BC

= 519.6 - 173.2 = 346.4 ft

4 0

1 month ago

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A set of angles has a ratio of 5 to 2. If the larger angle measures 105 degrees then what is the measure of the smaller angle

babunello [11817]

ratio 5:2

105, ___

5x = 105 → x = 21

2x = ____ → 2(21) = 42

Result: 42°

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25 days ago

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Write an absolute value equation to satisfy the given solution set shown on a number line.

babunello [11817]

IX - 4I ≤ 4

Step-by-step explanation:

The number line indicates that the possible values of x fall within the range:

0 ≤ x ≤ 8

We aim to create an absolute value equation to encompass this set of potential solutions.

An example of such an equation is:

IX - 4I ≤ 4

To form this, we find the midpoint M of our set, which is 4 in this case.

Then, we write:

Ix - MI ≤ IMI

It's important to note my use of the inclusive sign, as the filled dots indicate that the endpoints x = 0 and x = 8 are part of the solution, differing from empty dots which denote an open set requiring < > signs.

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16 days ago

Finally, you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V s

tester [12383]

Answer:

w and y are the knights

Step-by-step explanation:

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1 month ago

Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number

tester [12383]

Answer:Part a) $2,50,18$

Part b) When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , the result is an integer.

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For $x=2$

$\sqrt{2}*\sqrt{2}=\sqrt{4}=2$ -----> the product results in an integer

thus

The number $x=2$ could potentially be Jenny's favorite positive integer

2) For $x=50$

$\sqrt{50}*\sqrt{2}=\sqrt{100}=10$ -----> the product results in an integer

thus

The number $x=50$ could potentially be Jenny's favorite positive integer

3) For $x=18$

$\sqrt{18}*\sqrt{2}=\sqrt{36}=6$ -----> the product results in an integer

thus

The number $x=18$ could potentially be Jenny's favorite positive integer

Part B)

1) For $x=2$

$\sqrt{2}/\sqrt{2}=\sqrt{1}=1$ -----> the outcome is an integer

2) For $x=50$

$\sqrt{50}/\sqrt{2}=\sqrt{25}=5$ -----> the outcome is an integer

3) For $x=18$

$\sqrt{18}/\sqrt{2}=\sqrt{9}=3$ -----> the outcome is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she obtains an integer as a result.

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18 days ago