Answer: 12 students
Step-by-step explanation:
Let X and Y stand for the number of students in each respective class.
We know:
X/Y = 2/5, and
Y = X+24
We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:
(Y-x)/(X+x) = 1
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We can rearrange X/Y = 2/5 to:
X = 2Y/5
The use this value of X in the second equation:
Y = X+24
Y =2Y/5+24
5Y = 2Y + 120
3Y = 120
Y = 40
Since Y = X+24
40 = X + 24
X = 16
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Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:
(Y-x)=(X+x)
(40-x)=(16+x)
24 = 2x
x = 12
12 students must transfer to the more difficult, very early morning, class.
Company A has a sales position with a yearly salary of $42,000. Company B has a similar sales position with a slary of $39,000 plus 1% conmission on yearly sales.
Let x be the amount of yearly sales
Company A has a sales position with a yearly salary of $42,000.
yearly salary = 42,000
Company B has a similar sales position with a salary of $39,000 plus 1% commission on yearly sales.
1% is 0.01
yearly salary = 39,000+ 0.01x
yearly sales is the salary at company A greater than the salary and conmission at company B
A > B
42000 > 39000+ 0.01x
We solve the inequality
39000+ 0.01x < 42000
Subtract 39000 on both sides
0.01x < 3000
divide by 0.01
x> 300,000
For yearly sales > $300,000, the salary at company A greater than the salary and commission at company B
Answer:
A) Ms. Swift can conclude that hey are similar, because line E,C,A is collinear, and they both are right triangles.
B) 158.3ft
Step-by-step explanation:
A) Having a collinear line makes the triangles similar, and because of their collinear line they are both right triangles.
B) The question tells you DE is 103 ft. You take 76ft and Square it giving you 5776ft You then take 103 and square it giving you 10609ft adding them together gives you 16385ft you take the square root of it and it gives you the hypotenuse of triangle CDE. To get the hypotenuse of triangle ABC you take The expression (AB/DE)=(BC/CD)=(AC/EC) step one (AB/DE)=(94ft/76ft)=AC/DE) step two (103ft/127ft)=(94ft/76ft)=(AC/DE) third step (103ft/127ft)=(94ft/76ft)=(128ft/158.3)
I truly hope this helps! :)
Answer: B. 254.34 cm^2
Step-by-step explanation:
The area of a circle is pi times the radius squared.
Using the diameter we have to find the radius.
The diameter is two times the radius meaning that the radius is half the diameter.
18/ 2 = 9
The radius will be 9 cm
Now using the formula v= pi * r^2 , input the value for pie and the radius and solve for v the volume
v = 3.14 * 9^2
v= 3.14 * 81
v = 254.34 cm^2
