Answer:
1.) Yes
2.) Yes
Step-by-step explanation:
Given that
n = k(k + 7)
If k is a positive integer and n = k(k + 7), is n divisible by 6 ?
(1) k is odd. Yes.
Let assume that k = 3
Then, n = 3(3 + 7)
n = 3 × 10
n = 30.
30 is divisible by 6.
(2) When k is divided by 3, the remainder is 2. That is,
Let k = 5
Then,
5/3 = 1 remainder 2
Substitute k into the equation
n = k(k + 7)
n = 5(5 + 7)
n = 5 × 12
n = 60
And 60 is divisible by 6.
Therefore, the answer to both questions is Yes.
Option A:
The probability that Everett and Finley end up with an even number and a blue disk is
.
Solution:
Given data:
Everett is rolling a block with numbers = {1, 2, 3, 4, 5, 6}
Finley is drawing one disk from basket with colors = {blue, red, yellow}
Total number of numbers = 6
Total number of colors = 3





Divide numerator and denominator by the common factor 3.


Option A is the correct answer.
Hence the probability that Everett and Finley end up with an even number and a blue disk is
.
Answer:
65/72
Step-by-step explanation:
cot is simply cosine over sine or the tangant flipped
the cos (c)=65/97
sin (c) = 72/97
cot would be (65/97)/(72/97)
How do you divide fractions? By multiplying the reciprocal!
cot would be 65/97 * 97/72
the 97s cross out.
65/72
Answer:

Step-by-step explanation:
The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.
The volume of the square prism is given by
, where
is the base length and
is the height. Substituting given values, we have: 
The volume of a trapezoidal prism is given by
, where
and
are bases of the trapezoid,
is the length of the height of the trapezoid and
is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (
) multiplied by the trapezoid's height (
).
Substituting given values, we get:

Therefore, the total volume of the composite figure is
(ah, perfect)
Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

Answer:they got it
Step-by-step explanation: