The dimensions of the box formed will be:
width: 20 - 2x
length: 40 - 2x
height: x
Volume = width x length x height
1500 = x(20 - 2x)(40 - 2x)
1500 = x(800 + 4x² - 120x)
1500 = 4x³ - 120x² + 800x
0 = 4x³ - 120x² + 800x - 1500
0 = x³ - 30x² + 200x - 375
Solving the cubic equation:
x = 5 (only integer root)
Length = 30 cm
Width = 10 cm
Height = 5 cm
Answer:
B) 112°
Step-by-step explanation:
After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:
2·56° = 112°
_____
In the attached, lines l and m are separated by 56°, as required by the problem statement.
Answer:
251.65 Millimeters rounded to the hundredths place.
Step-by-step explanation:
The formula for the area of a circle is A=π×r^2.
Step 1: Find r, or the radius, which is half the diameter. In this case, it is 8.95.
Step 2: Square the radius that you get. In this case, the answer is 80.1025.
Step 3: Multiply the past number by π on your calculator. Some teachers allow 3.14 but be certain that your teacher allows it. In this case, π×80.1025=251.649425534
Step 4: You've got your answer! Hope this helps!
Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the lifetime for a TV of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability like this:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.