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lord [1]
4 years ago
14

A central angle measuring 120° intercepts an arc in a circle whose radius is 3.

Mathematics
1 answer:
Kisachek [45]4 years ago
5 0

Answer:

6.28

Step-by-step explanation:

The length of arc which subtends an angle \alpha at the center of a circle is given by \alpha r where r is the radius of circle.

______________________________

given

the central angle of arc is  120°

\pi = 180\\120 = (\pi /180)* 120\\120 = 2/3\pi

we will use value of \pi as 3.14

r = 3

Length of this arc is

2/3( \pi *3) = 2\pi \\=2*3.14 = 6.28

The length of the arc to the nearest hundredth of unit is 6.28

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The airport security randomly selected 36 suitcases from the security line. Of these bags, they screened 8 suitcases. Based on t
castortr0y [4]

The ratio of suitcases to screened suitcases is 36:8. The second ratio is 180:?.

--

180 is 5 times 36 which can be proven by dividing 180 by 36.

180 ÷ 36 = 5

Multiply 5 by 8 to find the amount of suitcases that would be screened if there were 180 total suitcases.

5 × 8 = 40

The first ratio is 36:8, and with a scale factor of 5 we get the second equivalent ratio 180:40.

<h2>Answer:</h2>

<u>Forty suitcases</u><u> will be screened.</u>

I hope this helps :)

4 0
3 years ago
You started the trail with 500lbs. of food. You now have 282lbs. of food. What percentage of your starting amount do you have le
mestny [16]

Answer:

43.6%

Step-by-step explanation:

500-282=218

218/500=0.436

0.436=43.6%

3 0
3 years ago
A little shop sells Christmas toys. The wholesale price for each toy in a consignment of 50 toys was $5.5. Half of this quantity
laila [671]

Answer:

Profit = \$250

Step-by-step explanation:

Given

Number of Toys = 50

Unit Cost Price = $5.5

Unit Selling price = $15

Required

Determine the profit after sales

First, we need to determine the total cost price;

Cost\ Price = Number\ of\ toy *\ Unit\ cost\ price

Cost\ Price = 50 * \$5.5

Cost\ Price = \$275

First, we need to determine the total sales;

____________________________________________________

Half of the toy was sold at $15;

Half\ of\ the\ toy = \frac{1}{2} * 50

Half\ of\ the\ toy = 25

Sales = \$15 * 25

Sales = \$375

____________________________________________________

Two-fifth of the remaining was sold at half of the sales price

From the above calculation;

Remaining\ Toy = 50 - 25

Remaining\ Toy = 25

<em></em>

<em>Calculating Two-fifth of the remaining:</em>

\frac{2}{5} * 25

= \frac{50}{5}

= 10

<em>Calculating half of the sales price:</em>

\frac{1}{2} * \$15

\$7.5

This means that 10 toys were sold for $7.5

Sales = 10 * \$7.5

Sales = \$75

____________________________________________________

The remaining was sold at one-third of the sales price

From the above calculations (1 & 2);

Remaining\ Toy = 50 - 25 - 10

Remaining\ Toy = 15

<em>Calculating </em>one-third <em>of the sales price:</em>

\frac{1}{3} * \$15

\$5

This means that 15 toys were sold for $5

Sales = 15 * \$5

Sales = \$75

____________________________________________________

Now the total sales can be calculated;

Total\ Sales = \$375 + \$75 + \$75

Total\ Sales = \$525

Profit = Total\ Sales -\ Cost\ Price

Profit = \$525 -\$275

Profit = \$250

3 0
3 years ago
I need help in this!!!!!
Nostrana [21]

Answer:

B.) m∠3 would need to be doubled

Step-by-step explanation:

since AC and BD are parrallel, the angles would have to match up - meaning - if the m∠6 side is doubled then the m∠3 side need to be doubled as well -

hope this helps!!

3 0
3 years ago
Read 2 more answers
If ΔABC, BC = 12.35, AC = 8.75 centimeters, and m∠B = 37°, what are m∠A and m∠C in two decimal places?
Lesechka [4]
We apply the sine rule here:
a/sin(A) = b/sin(B) = c/sin(C)
The side opposite to angle B is AC
The side opposite to angle A is BC
The side opposite to angle C is AB
8.75/sin(37) = 12.35/sin(A)
A = 58.15°
The sum of the three angles is 180°
Angle C = 180 - 58.15 - 37
Angle C = 84.85°
The answer is B
4 0
3 years ago
Read 2 more answers
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