Please show the work so I can learn the steps.

There are 24 students in a class. if 16 are boys, what fraction of the students are boys?

pshichka [43]

Answer:

2/3 is the fraction of students who are boys.

Step-by-step explanation:

First of all, a fraction consists of two parts: The denominator and the numerator. The denominator is the whole, while the number is a part of the whole (and sometimes above).

1. Since in your question, there are 24 students in total in the class, the denominator will be 24.

2. You said that 16 of them are boys, so 16 is the numerator.

3. In a fraction, it will be 16/24.

4. 16/24 can be simplified into 2/3 since both 16 and 24 can be divided by 8.

So our final answer is 2/3.

3 0

1 year ago

Write an equation of the perpendicular bisector of the line segment whose endpoints are (−1,1) and (7,−5)

icang [17]

The equation is $y = \frac{3}{2} x - \frac{11}{2}$

<u>Explanation:</u>

We have to first find the mid-point of the segment, the formula for which is

$(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$

So, the midpoint will be $(\frac{-1+7}{2} , \frac{1-5}{2} )\\\\$

= $(3,-2)$

It is the point at which the segment will be bisected.

Since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula $\frac{y_2-y_1}{x_2-x_1}$

The slope is $\frac{-5-1}{7+1}$ = $-\frac{2}{3}$

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of $-\frac{2}{3}$ is $\frac{3}{2}$

To write an equation, substitute the values in y = mx + c

WHere,

y = -1

x = 3

m = 3/2

Solving for c:

$-1 = \frac{3}{2} X 3 + c\\\\-1 = \frac{9}{2}+c\\ \\c = \frac{-2-9}{2} \\\\c = \frac{-11}{2}$

Thus, the equation becomes:

$y = \frac{3}{2} x - \frac{11}{2}$

7 0

3 years ago

After a 5% discount, a telephone bill is $79.50. How much was the bill originally?

ICE Princess25 [194]

The original bill is $ 83.475

7 0

3 years ago

Karyn proofreads 15 pages in 2 hours for $40.

OLEGan [10]

Hi there.

Since she reads 15 pages in 2 hours, all we have to do to find out how much she reads in 1 hour is divide.

15/2 = 7.5

7.5 pages/hour

Same applies to the pay

40/2 = 20

$20/hour

Karyn proofreading rate is 7.5 pages per hour. Karyn receives on average $20 per hour.

~

8 0

3 years ago

Read 2 more answers

The interior of a regular polygon is 5 times the exterior angle

densk [106]

Step-by-step explanation:

The interior angle of a polygon is given by

$\frac{(n - 2) \times 180}{n}$

The exterior angle of a polygon is given by

$\frac{360}{n}$

where n is the number of sides of the polygon

The statement

The interior of a regular polygon is 5 times the exterior angle is written as

$\frac{(n - 2) \times 180}{n} = 5( \frac{360}{n} )$

Solve the equation

That's

$\frac{180n - 360}{n} = \frac{1800}{n}$

Since the denominators are the same we can equate the numerators

That's

180n - 360 = 1800

180n = 1800 + 360

180n = 2160

Divide both sides by 180

The interior angle of the polygon is

$\frac{(12 - 2) \times 180}{12} = \frac{10 \times 180}{12} \\ = \frac{1800}{12}$

The answer is

Interior angle + exterior angle = 180

From the question

Interior angle = 150°

So the exterior angle is

Exterior angle = 180 - 150

We have the answer as

The polygon has 12 sides

The name of the polygon is

<h2>Dodecagon</h2>

Hope this helps you.

6 0

2 years ago