The equation of the sphere centered at 0, and radius 4 is:
,
note that this equation describes exactly the points of the surface of the square. That is, this is an EMPTY sphere.
The solid sphere, that is the points on the surface and all points in the inside, are given by :
since we want the left part of the solid part, picture 2, we add the condition x<0,
thus "the solid left (x < 0 is left) hemisphere of a sphere of radius 4 centered at the origin" is given by the system of inequalities:
Answer:
A) 0.0107
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 440 seconds and a standard deviation of 40 seconds.
This means that 
Find the probability that a randomly selected boy in secondary school can run the mile in less than 348 seconds.
This is the p-value of Z when X = 348. So
has a p-value of 0.0107, and thus, the correct answer is given by option A.
<h3>
Answer: f(x) = x + 13 </h3>
This is the same as y = x+13
=============================================================
Explanation:
Let's find the slope
I'll use the first two rows as the (x1,y1) and (x2,y2) points
m = (y2-y1)/(x2-x1)
m = (19-18)/(6-5)
m = 1/1
m = 1
The slope is 1.
Now apply the point slope formula and solve for y
y - y1 = m(x - x1)
y - 18 = 1(x - 5)
y - 18 = x - 5
y = x-5 + 18
y = x + 13
f(x) = x + 13 is the final answer
As a check, note how something like x = 5 leads to...
f(x) = x+13
f(5) = 5+13 ... replace x with 5
f(5) = 18
We see that x = 5 leads to f(x) = 18. That verifies the first row. I'll let you check the remaining three rows.
The equation y = x+13 has slope 1 and y intercept 13.
Complete question is;
Multiple-choice questions each have 5 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.
Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC), where C denotes a correct answer and W denotes a wrong answer.
P(WWWWC) =
Answer:
P(WWWWC) = 0.0819
Step-by-step explanation:
We are told that each question has 5 possible answers and only 1 is correct. Thus, the probability of getting the right answer in any question is =
(number of correct choices)/(total number of choices) = 1/5
Meanwhile,since only 1 of the possible answers is correct, then there will be 4 incorrect answers. Thus, the probability of choosing the wrong answer would be;
(number of incorrect choices)/(total number of choices) = 4/5
Now, we want to find the probability of getting the 1st 4 guesses wrong and the 5th one correct. To do this we will simply multiply the probabilities of each individual event by each other.
Thus;
P(WWWWC) = (4/5) × (4/5) × (4/5) × (4/5) × (1/5) = 256/3125 ≈ 0.0819
P(WWWWC) = 0.0819
