Let <em>A</em>, <em>B</em>, and <em>C</em> denote the sets of students that have taken calculus, sociology, and Spanish, respectively.
We're given that consists of 187 students.
We want to find the size of , given that
• <em>A</em> has 61 students;
• <em>B</em> has 78;
• <em>C</em> has 72;
• has 15;
• has 20; and
• has 13.
Using the inclusion/exclusion principle, we have
where |<em>X</em>| denotes the size of the set <em>X</em>. Plug in all the known sizes:
so 24 students have taken all three classes.
Simplify 3/5p tp 3p/5
4 + 2p = 10(3p/5 - 2)
Expand
4 + 2p = 6p - 20
Subtract 2p from both sides
4 = 6p - 20 - 2p
Simplify 6p - 20 - 2p to 4p - 20
4 = 4p - 20
Add 20 to both sides
4 + 20 = 4p
Simplify 4 + 20 tp 24
24 = 4p
Divide both sides by 4
24/4 = p
Simplify 24/4 to 6
6 = p
Switch sides
<u>p = 6</u>
Answer:
x = 22°
y = 26°
z = 48°
Step-by-step explanation:
∠PQS and ∠QSR is a pair of alternate interior angles
plus PQ is parallel to SR
then
x = 22°
SPR is an isosceles triangle then m∠PRS = 66°
Therefore x + y = 180-(66+66) = 180-132 = 48
then y = 48 - x = 48-22 = 26
finally, z = x + y = 48
<h2>
<u>SLOPE</u></h2>
<h3>
</h3>
» What is the slope of the line passing through the points (-1, – 7) and (-9, - 2)?
<h3>
</h3>
— — — — — — — — — —
<h3>
</h3>
<h3>
</h3>
<h3>
</h3>
_______________❦︎_______________
Hey there!
Let us take Michael's score as ' x '
Let us take Kathryn's score as ' y '
Michael - 70 less than twice Kathryn's
x = 2y - 70
y = y
Add them, we get , 425
2y - 70 + y = 425
3y - 70 = 425
3y = 495
y = 495/3
y = 165
Kathryn's score = 165
Michael - 2 ( 165 ) - 70
= 260
Hope it helps!