His friends ate 1/2 of 3/4..." of " means multiply
1/2 * 3/4 = 3/8
so his friends ate 3/8 of the bag of popcorn
Answer:
a. [ 0.454,0.51]
b. 599.472 ~ 600
Step-by-step explanation:
a)
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=410
Sample Size(n)=850
Sample proportion = x/n =0.482
Confidence Interval = [ 0.482 ±Z a/2 ( Sqrt ( 0.482*0.518) /850)]
= [ 0.482 - 1.645* Sqrt(0) , 0.482 + 1.65* Sqrt(0) ]
= [ 0.454,0.51]
b)
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Samle Proportion = 0.482
ME = 0.04
n = ( 1.96 / 0.04 )^2 * 0.482*0.518
= 599.472 ~ 600
Step-by-step explanation:
sin 0 = opposite ÷ hypothenus
sin 0 = 3 / 5
3 / 5 = x / 15
5 × n = 15
n = 3
x = 3 × 3 = 9
y = use pythagoras
= 12
tan 0 = opposite ÷ adjacent
tan 0 = 9/12
Answer:
all real numbers
continuous function
Step-by-step explanation:
y = -2x is a straight line which extends infinitely in both directions
linear equations are continuous functions
Let c = angle TPS
This angle adds to angle 'a' to get a+c = 90. We know these angles are complementary because triangle PQR is a right triangle. The acute angles of a right triangle add to 90.
We also know that b+c = 90 for similar reasons. Triangle PST is a right triangle.
So we have these two equations
a+c = 90
b+c = 90
If we were to subtract straight down then we would end up with
a-b = 0
which solves to
a = b
after adding b to both sides
