Since it is a cube, all sides lengths are the same.
Surface area = 2lw+2lw+2hw
if you substitute all the sides for 13 you get
2(169) three times
so you multiply and get 338 three times so you do 338x3 which is 1014 cm
its messy to explain so i attached a photo
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the graph is 0 because the line tangent to the point is horizontal. We can find the rate of change by taking the derivative of the function.
y' = 2ax + b
Now that we where the derivative, we can set it equal to 0.
2ax + b = 0
We also know that at the extreme value, x = -1/2. We can plug that in as well.
The 2 and one-half cancel each other out.
Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.
a(-0.5)^2 + a(-0.5) + 10 = 0
0.25a - 0.5a + 10 = 0
-0.25a = -10
a = 40
b = 40
To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.
80x + 40
Our critical number is x = -1/2. We need to plug a number that is less than -1/2 and a number that is greater than -1/2 into the derivative.
LESS THAN:
80(-1) + 40 = -40
GREATER THAN:
80(0) + 40 = 40
The rate of change of the graph changes from negative to positive at x = -1/2, therefore the extreme value is a minimum.
4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.
y' = 2ax + 1
2a(3) + 1 = 0
6a = -1
a = -1/6
So now plug the a value and x=3 into the original function to find the extreme value.
(-1/6)(3)^2 + 3 + 3 = 4.5
The extreme value is 4.5
Answer:
6 bars on the histogram
2 of the bars represent 12+students with complete paintings
the actual fraction is 2 out of 6 I believe
Step-by-step explanation:
Answer:
Option C
Step-by-step explanation:
Given that for a random sample of 20 houses selected from a city showed that the mean size of these houses is 1880 square feet with a standard deviation of 320 square feet.
X, the sizes of houses is Normal
Hence sample mean will be normal with
Mean = 1880
and std dev = 
For 90% confidence interval critical value for t with degree of freedom 19 is
1.328
Confidence interval upper bound
= mean + margin of error
= 
Option C is right
Answer:
10 units
Step-by-step explanation:
Area of a triangle is 
= Area
where h is the height, and b is the base
We can substitute these values into the area equation and get:
Multiply both sides by 2:
x * 10 = 100
Divide both sides by 10:
x = 10
The missing side is 10 units long
