- 12. What is the greatest common factor of 120 and 84?

Mathematics

2 answers:

sweet [91]3 years ago

7 0

Answer:

12 (the third one is the greatest common factor of 120 and 84)

inna [77]3 years ago

7 0

Answer:

Step-by-step explanation:

factors of 120. 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,80,120

factors of 84: 1,2,3, 4,6,7,12,14,28,42,84

greatest common factor=12

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Alexis washes 10 1/2 windows in 3/4 hours. At this rate, how many windows can she wash in one hour?

Zepler [3.9K]

Alexis can wash a total of 14 windows in 1 hour

<h3><u>Solution:</u></h3>

Given that Alexis washes $10\frac{1}{2}$ windows in $\frac{3}{4}$ hours

<u><em>To find: </em></u>number of windows washed in one hour

To simplify the calculations we will convert the given mixed fraction to improper fraction

$\begin{array}{l}{=10 \frac{1}{2}} \\\\ {=\frac{2 \times 10+1}{2}} \\\\ {=\frac{21}{2}=10.5}\end{array}$

Hence, to wash 10.5 windows, Alexis takes 0.75 hours

Let "n" be the number of windows washed in 1 hour

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"n" windows ⇒ 1 hour

By cross-multiplication we get,

$n \times 0.75 = 10.5 \times 1$

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Thus Alexis can wash 14 windows in one hour

4 0

3 years ago

in circle O the radius is 4ft and the measure of minor arc ab is 120 degrees find the length of minor arc ab to the nearest inte

KIM [24]

Answer:

$8\:\text{ft}$

Step-by-step explanation:

The length of the arc is proportional to the degree measure it in encompasses. Since there are 360 degrees in a circle and the arc is 120 degrees, the arc's length will be $\frac{120}{360}=\frac{1}{3}$ of the circle's length (circumference).

The circumference of a circle is given by $2\pi r$ , where $r$ is the radius of the circle. Therefore, the circumference of the circle is $2\pi(4)=8\pi$ . As we found earlier, the length of the arc is $\frac{1}{3}$ of this circumference. Therefore, the arc's length is $8\pi\cdot \frac{1}{3}=\frac{8\pi}{3}$ .