Answer:
The common difference is -1/2
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant and is called the common difference
we have
a1=2/3
a2=1/6
a3=-1/3
a4=-5/6
so
a2-a1=1/6-2/3=-1/2
a3-a2=-1/3-1/6=-1/2
a4-a3=-5/6-(-1/3)=-5/6+1/3=-1/2
therefore
The common difference is -1/2
This problem states that there are 5 trophies and the problem requires to determine the number of ways Naomi can line up her trophies. In this case, the formula using counting is 5 * 4 * 3 * 2 * 1. there is a decreasing trend as the number of trophies chosen to line up next is decreased by one each time. The answer is 120 ways.
Answer:
5.19%
Step-by-step explanation:
The amount of an account (A) earning simple interest rate r for time t on principal P is ...
A = P(1 +rt)
Filling in the given values and solving for r gives ...
6000 = 5500(1 +r(21/12))
12/11 = 1 + r(7/4) . . . . . . . . . . divide by 5500, simplify fractions
1/11 = r(7/4) . . . . . . . . subtract 1
4/77 = r . . . . . . . . . . . multiply by 4/7
r ≈ 0.051948 ≈ 5.19%
You will be earning about 5.19% annual simple interest.
The last one is correct
A translation of 6 units down a rotation and then a reflection
good luck
First problem: draw a line segment through the vertex R and a point C on PQ such that the segment is perpendicular to PQ, thus forming an altitude of the triangle. This new segment CR, the new segment CP, and PR form a 30-60-90 right triangle, where the measure of angle PCR is 90 degrees. CR then occurs with PR in a ratio of
to 2, so
and this can be considered the height of a triangle whose base is PQ. The area is then
Second problem: the sum of the interior angles of any triangle is 180, so the measure of the missing angle must be 180 - 20 - 35 = 125 degrees. By the law of sines, the length of the missing side (call it
) satisfies
Use Heron's formula to find the area of the triangle:
where
is the area,
are the lengths of the sides, and
is the half the perimeter of the triangle. Then the area is about
square feet. Convert to square yards:
then round up to 7 square yards. At a price of $12.50 per square yard, the total price will be $87.50.