Step-by-step explanation:
On the straight line where x is located on, we can identify that the line is equal to 180⁰.
180⁰ = 125⁰ + 30⁰ + x⁰
<u>Find</u><u> </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>x</u><u>.</u>
<u>Subtract 155 from both sides:</u>
The unknown measurement (x) equals 25⁰.
Answer:
36
Step-by-step explanation:
If you set the equation up, it would be n + 5 = 41. If you subtract the 5 from both sides to get n by itself, you get n = 36.
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If , then .
Let's simplify that.
Distribute with :
Combine the end like terms :
Use identity for :
Combine like terms and :
We are given .
So we have that .
The vertex happens at .
Compare to to determine .
Let's plug it in.
So the coordinate is 5.
Let's find the corresponding coordinate by evaluating our expression named at :
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is where the vertex is .
Let's put into this form.
We are given .
We will need to complete the square.
I like to use the identity .
So If you add something in, you will have to take it out (and vice versa).
So we have in vertex form is:
.
The vertex is (3,-6).
So if we are dealing with the function .
This means we are going to move the vertex of right 2 units to figure out the vertex of which puts us at (3+2,-6)=(5,-6).
The coordinate was not effected here because we were only moving horizontally not up/down.
Answer:
(I am assuming this is just approximation since there are no other numbers, just to be clear :))
Algebra: about 450 students
Geometry: about 250 students
Calculus: about 50 students
Answer:
17.76 pounds
Step-by-step explanation:
The first thing we have to do is resort to the normal distribution table (attached image).
To find the smallest annual per capita consumption of ice cream that can be in the top 25% of consumption, we must find when the probability of z is equal to = 1 - 0.25 = 0.75
Find the z value when the probability 75%, i.e .:
z = invNorm (0.75) = approximately 0.675
To find the value, we apply the following formula:
x = z * sd + m
where sd is the standard deviation 3.5 and m the mean that is 15.4, knowing these values, we replace:
x = 0.675 * 3.5 + 15.4
x = 17.76
That is, the smallest annual consumption under these conditions is 17.76 pounds.