Answer:
- P (blue or too big) = 11 / 12
Explanation:
A two way table permits to represent the situation clearly and find the answser is an easy way.
The two way table is that results from the given information is:
Initial information:
Blue Green Total
Fit well 4 1 ?
Too big ? ? ?
Total 5 7 12
Now by subtraction and addition you can fill the unknown fields:
Blue Green Total
Fit well 4 1 5
Too big 1 6 7
Total 5 7 12
Now, you can see that there are 5 blue and 7 too big shirts, but the total number of them is 5 + 7 - 1 (because one of the too big shirts is also blue).
Then, the number of shirts being blue or too big is 5 + 7 - 1 = 11.
And the probability is :
- P(blue or too big) = number of blue or too big / total number of shirts
- P (blue or too big) = 11 / 12 ← answer
You can also realize that there is only 1 green shirt that fits well, and that is the only option of not being blue of too big, so 1 /12 is the probability of not being blue or too big, and its complement (being blue or too big) is 1 - 1/12 = 11 / 12.
Answer:
Anton's definition is not valid.
Step-by-step explanation:
We have been given that Anton defines an acute angle as an angle that is not obtuse. We are asked to find whether Anton's definition is valid or not.
We know that an angle is known as acute angle whose measure is greater than 0 and less than 90 degrees.
We also know that an angle is known as obtuse angle whose measure is greater than 90 degrees and less than 180 degrees.
We know that a right triangle is neither acute nor obtuse. Since Anton hasn't mentioned a right triangle to his definition, therefore, his definition is not valid.
Answer:
g(f(-1)) = 2
Step-by-step explanation:
f(x) = 2 + x
g(x) = 3 - x
if you need to find g(f(-1)); find f(-1) first
f(-1) = 2 + (-1) = 1
f(-1) =1; now plug this into g(1)
g(1) = 3 - 1 = 2
Answer:
A) (2x − 7) (4x² + 14x + 49)
C) (3x + 5) (9x² − 15x + 25)
Step-by-step explanation:
Sums and differences of cubes factor as:
a³ + b³ = (a + b) (a² − ab + b²)
a³ − b³ = (a − b) (a² + ab + b²)
8x³ − 343 is a difference of cubes.
(2x)³ − 7³
(2x − 7) (4x² + 14x + 49)
27x³ + 125 is a sum of cubes.
(3x)³ + 5³
(3x + 5) (9x² − 15x + 25)
