Answer: f(2) = 4
Step-by-step explanation:
F(x) and g(x) are said to be continuous functions
Lim x=2 [3f(x) + f(x)g(x)] = 36
g(x) = 2
Limit x=2
[3f(2) + f(2)g(2)] = 36
[3f(2) + f(2) . 6] = 36
[3f(2) + 6f(2)] = 36
9f(2) = 36
Divide both sides by 9
f(2) = 36/9
f(2) = 4
Answer:
9.33 feet = 111.96 inches
Step-by-step explanation:
If we have similar triangles, the rate between matching sides is the same.
So the length of the smaller ladder (18 ft) over the length of the taller ladder (24 ft) is equal to the distance from the bottom of the smaller ladder to the tree (7 ft) over the distance from the bottom of the taller ladder to the tree (x ft):
18 / 7 = 24 / x
x = 7 * 24 / 18
x = 9.33 feet
To find this measure in inches, we just need to multiply by 12:
x = 9.33 * 12 = 111.96 inches
Answer:
Correct choice is B
Step-by-step explanation:
All given options represent quadratic function. Let the equation of this quadratic function be

Then
1. 
2. 
3. 
Solve the system of two equations:

Then

Thus, the equation of the function is

Note that


Answer:
At least 202.44 mm in the top 15%.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:

How many yearly mm of rainfall would there be in the top 15%?
At least X mm.
X is the 100-15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.




At least 202.44 mm in the top 15%.
Given :
For the school's sports day, a group of students prepared 12 1/2 litres of lemonade. At the end of the day they had 2 5/8 litres left over.
To Find :
How many litres of lemonade were sold.
Solution :
Initial amount of lemonade, I = 12 1/2 = 25/2 litres.
Final amount of lemonade, F = 2 5/8 = 21/8 litres.
Amount of lemonade sold, A = I - F
A = 25/2 - 21/8 litres
A = 9.875 litres
Therefore, 9.875 litres of lemonade were sold.
Hence, this is the required solution.