Answer:
(
, 
) and (1, 8 )
Step-by-step explanation:
To find the points of intersection equate f(x) and g(x), that is
3x² + 5 = 4x + 4 ( subtract 4x + 4 from both sides )
3x² - 4x + 1 = 0 ← in standard form
(3x - 1)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
3x - 1 = 0 ⇒ 3x = 1 ⇒ x =
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 functions for corresponding y- coordinates.
Substituting into g(x), then
g(1) = 4(1) + 4 = 4 + 4 = 8 ⇒ (1, 8 )
g( ) = 
+ 4 = ⇒ (, )
Answer:
Step-by-step explanation:
The three step test for continuity states that a function ƒ(x) is continuous at a point x = a if three conditions are satisfied:
- f(a) is defined.
- The limit of ƒ(x) as x approaches a exists.
- The limit of ƒ(x) as x approaches a is equal to f(a).
(i) Left-hand limit = right-hand limit.
Pass. The limit from either side is 8.
(ii) Left-hand limit = limit.
Pass. If the limits from either direction exist, the limit exists.
(iii) Limit as x ⟶ ∞ is not part of the three-step test.
(iv) Limit as x ⟶ 1 exists. Pass.
(v) f(1) is defined.
FAIL. f(1) is not defined.
(vi) Limit as x ⟶ ∞ is not part of the three-step test.
(vii) Passing the three-step test is not a step in the test.
(viii) The limit as x ⟶ 1 does not equal f(1).
FAIL. f(1) is undefined.
The steps in the three-step test for which the function fails are 
.
Hello there! So the speed goes up in 6 seconds, maintains for 8 seconds, and then holds for 20 seconds. When something is resting, the line stays straight horizontally for that 20 seconds. B and C are eliminated, because there is no break for C and B does not show the speed accurately. Really, the fish would speed up to 2.5 m/s in 6 seconds, then it maintains that speed, and slows down. D shows a constant speed, which the speed isn't constant, so D is out. A is the only one that represents the scenario properly. The answer is A.
Answer:
As we can see the deviation is proportional to the value of n and if n increase then the deviation increases too. So then the deviation would be larger when n gets larger.
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
We can define the following random variable X ="Number of heads in n tosses of a coin".
We assume that the coin is fair and then 
for any trial so then we can model X with the following distribution:
For this distribution the mean and variance are given by:
And the deviation would be just the square root of the variance and we got:
Does this standard deviation get larger or smaller when n gets larger?
As we can see the deviation is proportional to the value of n and if n increase then the deviation increases too. So then the deviation would be larger when n gets larger.
Answer:
3/4
Step-by-step explanation:
The mean of a data set is synonymous with the average. To find the mean, add up all the values in the data set and then divide by the number of elements.
From the table, there is 12 values. Thus, add up all the 12 values and then divide by 12:
Simplify:
Reduce:
Therefore, the mean of the data set is 3/4.
For the data set, this means that the average person guesses the temperature too high by about 3/4°F.
(Note: the symbol of x with a bar over it denotes the mean of a set)
