Answer:
We have strong evidence that on average, students study less than 150 minutes per night during the school week
Step-by-step explanation:
Normal distribution:
mean μ₀ = 150
Sample:
Sample size n = 272
Sample mean x = 141
Sample standard deviation s = 66
The standard error of the sample mean SE = σ /√n
SE = 66/√272
SE = 66 / 16,49
SE = 4
Test Hypothesis:
Null hypothesis H₀ x = μ₀
Alternative hypothesis Hₐ x < μ₀
z(s) test statistics is:
z(s) = ( x - μ₀ ) / s/√n
z(s) = - 9 /4
z(s) = - 2,25
p-value for that z(s) p-value = 0,0122
Then for α = 0,05 p-value < 0,05
We are in the rejection region we need to reject H₀
Answer:
The width is 8 units
Step-by-step explanation:
This is a variation problem we are to work with.
Length is inversely proportional to width, let length be l and width be w
modeling the statement mathematically, we have lw = k where k is the proportionality constant
Now let’s get k from l = 12 and w = 6
k = 12 * 6 = 72
Now for the second rectangle also;
lw = k given l = 9
9w = 72
w = 72/9
w = 8
I will try to get back to you a little later
If you move the negative on the left side of the second equation over to the right side, then we can see that the equation is equivalent to
.
Remember that an equation
represents a line with slope
and y-intercept
. Since both equations given have a slope of -2, but have different y-intercepts, they are
parallel.
Answer: 14+5x
Step-by-step explanation:
(18+8x) - (4+3x)
18+8x-4-3x
14+5x
