Answer:
C
Step-by-step explanation:
There's a property of cyclis quadrilaterals that say that opposite sides will add up to 180
so we have

which is option c
Answer:
A darts player practices throwing a dart at the bull’s eye on a dart board. Her probability of hitting the bull’s eye for each throw is 0.2.
(a) Find the probability that she is successful for the first time on the third throw:
The number F of unsuccessful throws till the first bull’s eye follows a geometric
distribution with probability of success q = 0.2 and probability of failure p = 0.8.
If the first bull’s eye is on the third throw, there must be two failures:
P(F = 2) = p
2
q = (0.8)2
(0.2) = 0.128.
(b) Find the probability that she will have at least three failures before her first
success.
We want the probability of F ≥ 3. This can be found in two ways:
P(F ≥ 3) = P(F = 3) + P(F = 4) + P(F = 5) + P(F = 6) + . . .
= p
3
q + p
4
q + p
5
q + p
6
q + . . . (geometric series with ratio p)
=
p
3
q
1 − p
=
(0.8)3
(0.2)
1 − 0.8
= (0.8)3 = 0.512.
Alternatively,
P(F ≥ 3) = 1 − (P(F = 0) + P(F = 1) + P(F = 2))
= 1 − (q + pq + p
2
q)
= 1 − (0.2)(1 + 0.8 + (0.8)2
)
= 1 − 0.488 = 0.512.
(c) How many throws on average will fail before she hits bull’s eye?
Since p = 0.8 and q = 0.2, the expected number of failures before the first success
is
E[F] = p
q
=
0.8
0.2
= 4.
Answer:
2,436 students
Step-by-step explanation:
At a 90% confidence level, the z-score is 1.645 and the confidence interval is given by:

Where s is the standard deviation, and n is the sample size.
If they want the length of their confidence interval to be no greater than 0.2, it must be no further than 0.1 from the mean 'X':

Rounding up to the next whole number, the sample size should be 2,436 students.
we have
the equation of the line is 
the points are

<u>Method 1</u>
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
or 
In this problem we have a direct variation
The constant of proportionality k is equal to the slope of the line

so

therefore
<u>the answer is</u>
the slope of the line is equal to

<u>Method 2</u>
we know that
the formula to calculate the slope between two points is equal to

we have

substitute in the formula



therefore
<u>the answer is</u>
the slope of the line is equal to

we know that
1) scale factor is equal to 
2) The ratio of the perimeters of the triangles is equal to the ratio of the measures of the sides
3) the longest side of ∆ABC=[scale factor]*the longest side of ∆DEF
the longest side of ∆ABC=
the longest side of ∆ABC=
units
the answer part a) is
the longest side of ∆ABC is
units
Part b)
The ratio of the area of ∆ABC to the area of ∆DEF is equal to the scale factor squared
so
![[scale factor]^{2} =(\frac{1}{10})^{2} \\ \\ =\frac{1}{100} \\ \\ =0.01](https://tex.z-dn.net/?f=%20%5Bscale%20factor%5D%5E%7B2%7D%20%3D%28%5Cfrac%7B1%7D%7B10%7D%29%5E%7B2%7D%20%5C%5C%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B100%7D%20%5C%5C%20%5C%5C%20%3D0.01%20)
therefore
the answer part b) is
The ratio of the area of ∆ABC to the area of ∆DEF is 