Answer:
60
Step-by-step explanation:
We are given the triangles are congruent, that means the angles are the same measurement
<A = <X
<B = <Y
<C = <Z
We know A = 50 so X = 50
We know <Y = 70 so < B = 70
The three angles of a triangle add to 180
<A + <B + <C = 180
Substituting into the equation
50 + 70 + <C = 180
Combining like terms
120 + <C =180
Subtracting 120 from each side
120-120 +<C =180-120
<C = 60
Remark
The way you have to set this up is to take the new number for the males and put it over the total for the males and females. The new number for the males / total = 3/5.
Step One
Find the total number of females
100 + 160 = 260 when 100 females have been added to the study.
Step Two
Find the number of males
The total number of males = 240 + x where x is the number of males to be added.
Step Three
Find the total for both
260 + 240 + x = Total
500 + x = Total.
Step Four
Find the ratio of males to total
(240 + x) / (500 + x) = 3/5
Step Five
Cross multiply and solve
(240 + x)*5 = (500+x)*3
1200 + 5x = 1500 + 3x Subtract 1200 from both sides.
5x = 1500 - 1200 + 3x
5x = 300 + 3x Subtract 3x from both sides.
5x - 3x = 300
2x = 300 Divide by 2
x = 300 / 2
x = 150
Check
(240 + 150 ) / (500 + 150) = ? 3/5
390 / 650 = ? 3/5
39/65 = ? 3/5 Divide the top and bottom on the left by 13
3/5 = 3/5 and it checks.
The answer is Y = -1/3x + 1
Answer:
the probability that 0≤x≤1/2 and 1/4≤y≤1/2 is 3/64 (4.68%)
Step-by-step explanation:
assuming that X and Y are independent variables for the probability density function f(x,y) :
f(x,y) = 4*x*y for 0≤x≤1 and 0≤y≤0
f(x,y) = 0 elsewhere
then the probability is calculated through:
P(x,y)= ∫f(x,y) dx dy = ∫4xy dx dy
for 0≤x≤1/2 and 1/4≤y≤1/2 we have
P(0≤x≤1/2,1/4≤y≤1/2 ) = ∫4xy dx dy = ∫4xy dx dy = 4*∫x dx ∫y dx = 4*[((1/2)²/2-0²/2)] *[(1/2)²/2-(1/4)²/2)] = 1 * 1/4 * (1/4-1/16) = 1 * 1/4 * 3/16 = 3/64
then the probability that 0≤x≤1/2 and 1/4≤y≤1/2 is 3/64 (4.68%)
Answer: 17/2
Step-by-step explanation: 16 divided by 2 is eight and a half is left over so add it
Hope this helps go answer my question! :)