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:
7
Step-by-step explanation:
The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.
In the given range, there are 7 such boards:
4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28
Answer: The tree was 27 feet tall
Step-by-step Explanation: First of all Sally was standing 30 feet away from the tree and she looks up at an angle of elevation of 38 degrees to the top of the tree. With this bit of information we can determine that a right angled triangle has been formed with the reference angle as 38 degrees, the side facing it as h (the height of the tree) and the adjacent side as 30. We shall apply the trigonometric ratio as follows;
Tan 38 = opposite/adjacent
Tan 38 = h/30
0.7813 = h/30
0.7813 x 30 = h
23.4 = h
We remember at this point that Sally’s eyes were 4 feet above the ground. What we have just calculated is the height of the tree from “4 feet above the ground” (where her eyes were). Hence the actual height of the tree is calculated as 23.4 plus 4 which gives us 27.4
Therefore the tree was 27 feet tall (approximately to the nearest foot)
Answer:
-41/80, -45/80, -48/80, -51/80, -55/80, -59/80
Step-by-step explanation:
-4/8, -3/4 = -4/8, -6/8
= -40/80, -60/80
∴ Rational numbers between -40/80 and -60/80 = -41/80, -45/80, -48/80, -51/80, -55/80, -59/80.
Answer:
1/6 = 16.67%
Step-by-step explanation:
There are a total of 24 m&ms. The probability of picking an m&m that has a quantity of 4 is 4/24 = 1/6 = 16.67%
