3.2m casts 1.54m shadow.
3.2÷1.54= 160/77 (2.077922077922...)
50.75 × 160/77= 105.454545...
105m to the nearest meter.
3.5x-10>-3 add 10 to both sides
3.5x>7 divide both sides by 3.5
x>2
... now for the other inequality:
8x-9<39 add 9 to both sides
8x<48 divide both sides by 3
x<6
So we have x>2 and x<6, so the compound inequality is:
2<x<6 and this means that the solution set is:
x=(2, 6)
1/2y^2=1/2x^2+8. The curve's slope at (x,y) is x/y, so dy/dx=x/y. To solve this differential equation, rearrange it to: y*dy=x*dx, and by integrating both sides, we get 1/2y^2=1/2x^2+C (some constant). Plug in (0,4) into this equation, 8=0+C, so C=8. The curve's equation is 1/2y^2=1/2x^2+8.
Answer:
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportions, the mean is 
and the standard deviation is 
In this problem, we have that:
.
So
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Answer:
x = -1
Step-by-step explanation:
AB + BC = AC = 28
the way from A to C goes through B.
so, the total way of A to C is the sum of the way from A to B and then from B to C.
=>
(5x + 10) + (2x + 25) = 28
7x + 35 = 28
7x = -7
x = -1
