9. The experimental probability that it will rain on any given day in Houston Texas is about 15%.
Thus, out of 365 days, 15% of that are the predicted days the it will rain in the Place.
=> 365 days is the total number of days in a year
=> 15% is the predicted days to rain
=> 365 * .15 = 54.75
Since this is a decimal number, let’s round this off to 55 days.
Why 55 because the value of tenths is more than 5.
Answer:
Yes, the sum of any two sides is greater than the third.
Step-by-step explanation:
To determine whether the provided sides are the sides of a triangle check if the sum of two sides is more than the third side.
The length provided are: 8.5, 13 and 19.1.
- Consider the sides 8.5 and 13:
The sum is:
This sum is greater than the third side 19.1
- Consider the sides 8.5 and 19.1:
The sum is:
This sum is greater than the third side 13
- Consider the sides 13 and 19.1:
The sum is:
This sum is greater than the third side 8.5
Thus, the sides 8.5, 13 and 19.1 are sides of a triangle.
Answer:
x=3
x=−3
Step-by-step explanation:
2x^2 - 5 = 13
Subtract 13 from both sides.
2x^2 - 5 - 13 = 0
Subtract 13 from −5 to get −18.
2x^2 - 18 = 0
Divide both sides by 2.
x^2 - 9 = 0
Consider x^2−9. Rewrite x^2−9 as x^2−3^2. The difference of squares can be factored using the rule: a^2−b^2=(a−b)(a+b).
(x−3)(x+3)=0
To find equation solutions, solve x−3=0 and x+3=0.
x=3
x=−3
Probability = (number of ways to succeed) / (total possible outcomes) .
The total possible results of rolling two dice is
(6 on the first cube) x (6 on the second one) = 36 possibilities.
How many are successful ? I need you to clarify something first.
You said that the 'second die' shows an odd number. When a pair
of dice is rolled, the problem usually doesn't distinguish between them.
And in fact, you said that they're "tossed together" (like a spinach and
arugula salad ?) so I would understand that they would lose their identity
unless they were, say, painted different colors, and we wouldn't know
which one is the second one.
Oh well, I'll just work it both ways:
First way:
Two identical dice are tossed.
The total is 5 and ONE cube shows an odd number.
How can that happen ?
1 ... 4
4 ... 1
3 ... 2
2 ... 3
Four possibilities. Probability = 4/36 = 1/9 = 11.1% .
=======================================
Second way:
A black and a white cube are tossed together.
The total is 5 and the white cube shows an odd number.
How can that happen:
B ... W
4 .... 1
2 .... 3
Only two possibilities. Probability = 2/36 = 1/18 = 5.6% .
Answer:
17) MC(x) = 35 − 12/x²
18) R(x) = -0.05x² + 80x
Step-by-step explanation:
17) The marginal average cost function (MC) is the derivative of the average cost function (AC).
AC(x) = C(x) / x
MC(x) = d/dx AC(x)
First, find the average cost function:
AC(x) = C(x) / x
AC(x) = (5x + 3)(7x + 4) / x
AC(x) = (35x² + 41x + 12) / x
AC(x) = 35x + 41 + 12/x
Now find the marginal average cost function:
MC(x) = d/dx AC(x)
MC(x) = 35 − 12/x²
18) x is the demand, and p(x) is the price at that demand. Assuming the equation is linear, let's use the points to find the slope:
m = (40 − 50) / (800 − 600)
m = -0.05
Use point-slope form to find the equation of the line:
p(x) − 50 = -0.05 (x − 600)
p(x) − 50 = -0.05x + 30
p(x) = -0.05x + 80
The revenue is the product of price and demand:
R(x) = x p(x)
R(x) = x (-0.05x + 80)
R(x) = -0.05x² + 80x
