Answer:
a) By graphing just one interval of length . b) Infinite number of angles, c) Infinite times.
Step-by-step explanation:
Any function is periodical when:
,
Where is the period of the function. The periodicity of the function allows us to limit the graphing of the function to just an interval of one period and according to the definition, you can expect same output with n different angles (infinite number of angles and same output infinite times).
Answer:
y =
Step-by-step explanation:
A line with a slope of zero is a horizontal line parallel to the x- axis.
The equation of a horizontal line is
y = c
where c is the value of the y- coordinates the line passes through.
Here the line passes through (0, ) with y- coordinate
, thus
y = ← equation of line
Answer:
(a) $1,020 or more = 0.2358
(b) Between $880 and $1,130 = 0.7389
(c) Between $830 and $940 = 0.3524
(d) Less than $770 = 0.0294
Step-by-step explanation:
We are given that According to M/PF Research, Inc. report, the average cost of renting an apartment in Minneapolis is $951.
Suppose that the standard deviation of the cost of renting an apartment in Minneapolis is $96 and that apartment rents in Minneapolis are normally distributed.
<em>Let X = apartment rents in Minneapolis</em>
So, X ~ Normal()
The z score probability distribution for normal distribution is given by;
<em> </em> Z = ~ N(0,1)
where, = average cost of renting an apartment = $951
= standard deviation = $96
(a) Probability that the price is $1,020 or more is given by = P(X $1,020)
P(X $1,020) = P(
) = P(Z
0.72) = 1 - P(Z < 0.72)
= 1 - 0.76424 = 0.2358
<em>The above probability is calculated by looking at the value of x = 0.72 in the z table which gives an area of 0.76424.</em>
<em />
(b) Probability that the price is between $880 and $1,130 is given by = P($880 < X < $1,130) = P(X < $1,130) - P(X 880)
P(X < $1,130) = P( <
) = P(Z < 1.86) = 0.96856
P(X $880) = P(
) = P(Z
-0.74) = 1 - P(Z < 0.74)
= 1 - 0.77035 = 0.22965
<em>The above probability is calculated by looking at the value of x = 1.86 and x = 0.74 in the z table which gives an area of 0.96856 and 0.77035 respectively.</em>
<em />
Therefore, P($880 < X < $1,130) = 0.96856 - 0.22965 = 0.7389
<em />
(c) Probability that the price is between $830 and $940 is given by = P($830 < X < $940) = P(X < $940) - P(X 830)
P(X < $940) = P( <
) = P(Z < -0.11) = 1 - P(Z
0.11)
= 1 - 0.5438 = 0.4562
P(X $830) = P(
) = P(Z
-1.26) = 1 - P(Z < 1.26)
= 1 - 0.89617 = 0.10383
<em>The above probability is calculated by looking at the value of x = 0.11 and x = 1.26 in the z table which gives an area of 0.5438 and 0.89617 respectively.</em>
<em />
Therefore, P($830 < X < $940) = 0.4562 - 0.10383 = 0.3524
(d) Probability that the price is Less than $770 is given by = P(X < $770)
P(X < $770) = P( <
) = P(Z < -1.89) = 1 - P(Z
1.89)
= 1 - 0.97062 = 0.0294
<em>The above probability is calculated by looking at the value of x = 1.89 in the z table which gives an area of 0.97062.</em>