A) 6 B) 15 C) 20 D) 24 E) 30

For a circle with a radius of 6 feet, what is the measurement of the central angle (in degrees) that intercepts an arc

geniusboy [140]

Answer: The central angle measures 135 degrees

Step-by-step explanation: We have been given an arc with length 9pi/2 feet and a radius of 6 feet. The arc is shown in the attached diagram (please see attachment). The central angle subtended by this arc is at point O and has been labeled angle X.

So if the diagram shows arc AB with length 9pi/2 and radius AO with length 6, we can use the formula to compute “Length of an arc” to arrive at the missing angle.

Length of an arc = X/360 x 2pi x radius

Substituting for the known values, our formula can now be re-written as

9pi/2 = X/360 x 2pi x6

By cross multiplication we now have

9pi/2pi x 6 = 2X/360

We simplify as much as possible by dividing all like terms, hence pi divides pi on the left side of the equation. Also 2 divides 360 on the right side of the equation.We now arrive at,

9/12 = X/180

Simplify even further and we have

3/4 = X/180

By cross multiplication we now have

(3 x 180)/4 = X

540/4 = X

135 = X

Therefore the central angle that intercepts the arc measures 135 degrees.

6 0

4 years ago

at best buy they have a 60"tv that sells for $1999 and is on sale for 20% off. the sales tax is 8.8%. what is the final cost

sweet [91]

I believe the answer is $1,458.47

6 0

3 years ago

Joanne buys a rug with an areas of 35/4 square meters. The length of the rug is 7/2 meters, What is the width , in meters, of th

natita [175]

$\bf \textit{area of a rectangle}\\\\
A=l\cdot w\quad 
\begin{cases}
l=length\\
w=width\\
-----\\
A=\frac{35}{4}\\\\
l=\frac{7}{2}
\end{cases}\implies \cfrac{35}{4}=\cfrac{7}{2}w\implies \cfrac{\quad \frac{35}{4}\quad }{\frac{7}{2}}=w
\\\\\\
\cfrac{35}{4}\cdot \cfrac{2}{7}=w\implies \cfrac{35}{14}=w\implies 2\frac{7}{14}=w$

6 0

3 years ago

(2 pts) Amid students in a certain Capstone group, 60% have taken Linear Algebra , 50% have taken Calculus 3 , and 30% hav

Reil [10]

Answer:

a. 0.6

b. 0.5

Step-by-step explanation:

Let A be the event that student takes algebra and C be the event that student takes Calculus 3.

P(A)=0.60

P(C)=0.5

P(A and C)=0.30

a.

We have to find P(A/C).

P(A/C)=P(A and C)/P(C)=0.3/0.5=0.6

Thus, if someone took Calculus 3, the probability that he/she took Linear Algebra too is 0.6 or 60%

b.

We have to find P(C/A)

P(C/A)=P(A and C)/P(A)=0.3/0.6=0.5

Thus, if someone took Linear Algebra, the probability that he/she took Calculus 3 too is 0.5 or 50%

4 0

3 years ago

A student skipped a step when she tried to convert 18 hours into seconds,

gladu [14]

Answer:

The conversion of minutes to seconds is skipped in multiple-step conversion.

Step-by-step explanation:

Given:

To convert 18 hours into seconds.

Now, to get the conversion ratio skip in this multiple-step conversion.

First we need to convert hours into minutes:

1 hour = 60 minutes.

So, 18 hours = $18\times 60 minutes$

= $1080 minutes$ .

Then, we convert minutes into seconds:

1 minute = 60 seconds.

So, 1080 minutes = $1080\times 60 seconds$

= $64800 seconds$ .

Thus, 18 hours = 64800 seconds.

As given in question the conversion from hours to seconds is there but the conversion of minutes to second is not there it is skipped so the result is incorrect.

Therefore, the conversion of minutes to seconds is skipped in multiple-step conversion.

5 0

3 years ago