X = 5/3 and m∠SPY = 8 1/3°.
Since PQ bisects the angle, the two angles formed by the bisector are equal:
11/2x - 5 = 4x - 5/2
We will first multiply everything by 2 to eliminate the fractions:
(11/2x)*2 - 5*2 = 4x*2 - (5/2)*2
11x - 10 = 8x - 5
Subtract 8x from each side:
11x - 10 - 8x = 8x - 5 - 8x
3x - 10 = -5
Add 10 to both sides:
3x - 10 + 10 = -5 + 10
3x = 5
Divide both sides by 3:
3x/3 = 5/3
x = 5/3
Now we will plug this in for x in both smaller angles and add them together to find the measure of ∠SPY:
11/2(5/3) - 5 + 4(5/3) - 5/2
55/6 - 5 + 20/3 - 5/2
We will rewrite everything using a denominator of 6:
55/6 - 30/6 + 40/6 - 15/6 = (55-30+40-15)/6 = 50/6 = 8 2/6 = 8 1/3°
Can't see it the equation is to blurry.
Answer:
Option A
Step-by-step explanation:
By applying Pythagoras theorem in ΔABC,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
AC² = AB² + BC²
AC² = 6² + 5²
AC = 
Similarly, by applying Pythagoras theorem in ΔACD,
AD² = AC² + CD²
(10)² =
+ x²
x² = 100- 61
x² = 39
x = √(39)
Option A will be the answer.
Answer:
The probability is
Step-by-step explanation:
From the question we are told that
The proportion that live with their parents is 
The sample size is n = 125
Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution
i.e

Now the mean is evaluated as



Generally the proportion that are not staying with parents is

= > 
The standard deviation is mathematically evaluated as



Given the n is large then we can use normal approximation to evaluate the probability as follows

Now applying continuity correction

Generally



So for the z - table


X=8 I’m not that to sure but hope i helped!