Hello from MrBillDoesMath!
Answer:
96 degrees
Discussion:
The base angles of an isosceles triangle are equal and a triangle has 180 degrees. In our case this means that
42 + 42 + (measure of vertex angle) = 180
84 + (measure of vertex angle) = 180 => (subtract 84 from both sides)
84 - 84 + (measure of vertex angle) = 180- 84 =>
(measure of vertex angle) = 180- 84 = 96
Thank you,
MrB
Answer:
g(x) = x+1
Step-by-step explanation:
Informally, you can see that the function h(x) takes the root of a value that is 1 more than the value under the same radical in f(x). This suggests that adding 1 to x in f(x) will give you h(x). That is, ...
h(x) = f(x+1) = f(g(x))
so
g(x) = x+1
_____
More formally, you can apply the inverse of the function f(x) to the equation ...
h(x) = f(g(x))
f^-1(h(x)) = f^-1(f(g(x))) . . . inverse function applied
f^-1(h(x)) = g(x) . . . . . . . . . simplified
Now f^-1(x) can be found by solving for y in ...
x = f(y)
x = ∛(y+2) . . . . . . . . . definition of f(y)
x^3 = y+2 . . . . . . . . . cube both sides
x^3 -2 = y = f^-1(x) . . . subtract 2 from both sides
So, f^-1(h(x)) is ...
f^-1(h(x)) = g(x) = (∛(x+3))^3 -2 = x+3 -2
g(x) = x+1
Answer:
51 74
Step-by-step explanation:
x = smaller
x +23 = larger
added together (x + x+23) equal to 28 less than 3x = 3x-28
x + x+23 = 3x-28 subtract 2x from both sides of the equation
23 = x -28 add 28 to both sides
51 = x then the larger = 51 + 23 = 74
Answer:
Step-by-step explanation:
1) 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".
2) Solution to the problem
The probability in favor of the regulation based on the recent survey is:
Let X the random variable of interest "Number of favor respondents about the regulation", on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And we want to find this probability:
If we use X= "Number of respondednts opposed to the regulation we got the same answer", but on this case p = 1-0.68=0.32, and we want this probability:
Answer:
The sample proportion of successful procedures is 0.962.
Step-by-step explanation:
The sample proportion of successful procedures is the number of successfiç procedures divided by the total number of procedures.
In this problem:
158 procedures, of which 152 were successful. So
p = 152/158 = 0.962
The sample proportion of successful procedures is 0.962.
