Answer:
37.5% are male
62.5% are female
Step-by-step explanation:
in total 120 teachers (45 male+75 female)
therefore:
for male
120 - 100%
45 - x% (we need to find x)
by using the butterfly method (or cross multiply) we get:
120x=100*45
x=4500/120=37.5% (male teachers)
we do the same for female but instead of using 45 we will use 75(the quantity of female theachers in school)
120x=100*75
x=7500/120=62.5%
Answer:
a: z = -1.936
b: 0.0265
d: z < -1.645
Reject H0 if z < -1.645
Step-by-step explanation:
We are given:
H0: µ = 20
HA: µ < 20
n = 60, sample mean: 19.6, σ = 1.6
Since the alternate hypothesis has a < sign in it, it is a left tailed test. The < or > sign in the alternate hypothesis points towards the rejection region.
For a: We need to calculate the test statistic for our situation. This is done with a z-score formula for samples.
For b: we need to use the z-score table to look up the p-value for the score we calculate in part a. The p-value is 0.0265. This means that there is only about a 2.65% chance that the sample values were a result of random chance.
For d: Since the significance level is 0.05, and this is a one tailed test, we have a critical value of z < - 1.645. This means that if the z-score we calculate in part a is less than -1.645, we will reject the null hypothesis
See attached photo for all the calculations!
Answer: 
Step-by-step explanation:
By definition, Direct proportion equations have the following form:

Where "k" is the constant of proportionality.
In this case you know that the distance (in meters) that an ant can travel varies directly with the amount of time (in hours) the ant spends walking.
With this information you can write the following equation:

According to the exercise, the constant of proportionality is:

Therefore, substituting the value of the constant of proportionality into the equation, you get that the equation that represents the proportional relationship between "d" and "t" is:

Answer:
higher
Step-by-step explanation:
add all of these numbers, if the sum is positive it is higher, if the sum is negative it is lower
32-10+13-25=10, this is positive so it is higher
Answer:
6.2
Step-by-step explanation:
Although there's multiple ways to solve this problem, my method will be to simply find the area for the full triangle (the empty + orange triangles) and subtract the area of the smaller, empty triangle.
Now, you that area for a triangle is 1/2*base*height.
To find the measurements for the full triangle, you must add up the bases for the two smaller triangles:

Height is the same for both triangles so Height total = 4 ft.
Now the total area can be calculated:
Area total= 1/2* base_total * height_total
Area total = 1/2 * 5ft * 4 ft
Area total = 20 / 2 = 10 ft squared
Lastly, subtract the area of the empty triangle from the total triangle to find the orange triangle.
Area Empty Triangle = 1/2 * base_empty * height_empty
Area Empty Triangle = 1/2 * 1.9ft * 4 ft = 7.6 ft / 2 = 3.8 ft squared
Area total - Area empty = 10ft^2 - 3.8ft^2 = 6.2 ft squared