Answer:
95.15%
Step-by-step explanation:
We have that the mean (m) is equal to 20, the standard deviation (sd) 3
They ask us for P (x <25)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / sd
We have all these values, replacing we have:
z = (25 - 20) / (3)
z = 1.66
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <1.66) = 0.9515
Which means that the probability that it arrives before 25 minutes is 95.15%
Answer:
B, the one with the line and shaded the top on the right side. (The one that goes to 7 on the x axis).
Step-by-step explanation:
First I find which graph as y -intercept of -3, which is all of them.
Next, I find with graph has a slope of 1/3. (rise 1 run 3). Only B and D has a slope of 1/3 (The ones that has a less steep graph. )
Then, I use the coordinate (0,0) to see which side the graph shades. I plug it into the inequality. (0)≥1/3(0)-3. Solve. Is 0 greater than -3. YES! so we shade the part where (0,0) is shaded which is B.
Answer: x ≥ 0
Step-by-step explanation:
First, let's define the symbols used:
a < x (this means that a is strictly smaller than x)
a > x (this means that a is strictly larger than x)
a ≤ x (this means that a is smaller than or equal to x)
a ≥ x (this means that a is larger than or equal to x)
Now we have the statement "x is no less than 0"
Then x can be equal to zero, or larger than zero, but never smaller than zero.
Looking at the symbols above, we know that we need to use:
x ≥ 0
(this is equivalent to the statement)
Answer:
8
Step-by-step explanation:
Let's just call the number x for simplicity.
So, 7x is 8 less than x².
Putting this into an equation would look like this
x² - 8 = 7x
It looks like we'll have to factor this to solve. Before we do that we need to move the 7x to the left side so that everything is together.
x² - 7x -8 = 0
Now, we can proceed. To factor we first need to find the factors of -8.
The factors of -8 are
-2 ⋅ 4, -4 ⋅ 2, -1 ⋅ 8, 1 ⋅ -8.
We need to find the pair of factors that adds up to -7. The only ones that do are -1 and 8.
So now that we have these we can create a pair of binomials using them. This will give us the factored form of this equation.
( x + 1 ) ( x - 8 )
To find the solutions we will have to set them to 0 and solve each of these binomials individually.
x - 1 = 0
x = 1
So, one of the solutions is 1. It's not the one we want, since it's positive.
x - 8 = 0
x = 8
This is the one we want since it is positive.
