The reason is rooted in the angle addition postulate. If we have the scenario where TR is a line intersecting segment VS at point R, we can establish that by applying the angle addition postulate, we can deduce that x is equal to 30. In option (1), which uses the substitution property of equality, this condition cannot be utilized correctly here. Option (3) involving the subtraction property of equality does not apply either. Lastly, option (4) regarding the addition property of equality is also inappropriate for deriving the value of x.
Answer:
B. The triangle.
Step-by-step explanation:
The number of sides decreases by one as you progress down the list.
The equation that demonstrates a proportional relationship, maintaining a constant of proportionality equal to 14, is: Here, and are proportional with a constant of proportionality of 14.
Answer:
Answer and Explanation:
We have:
Population mean,
μ
=
3
,
000
hours
Population standard deviation,
σ
=
696
hours
Sample size,
n
=
36
1) The standard deviation for the sampling distribution:
σ
¯
x
=
σ
√
n
=
696
√
36
=
116
2) By the central limit theorem, the sampling distribution's expected value matches the population mean.
Thus:
The expected value of the sampling distribution equals the population mean,
μ
¯
x
=
μ
=
3
,
000
The standard deviation of the sampling distribution,
σ
¯
x
=
116
The sampling distribution of
¯
x
is roughly normal due to a sample size greater than
30
.
3) The likelihood that the average lifespan of the sample falls between
2670.56
and
2809.76
hours:
P
(
2670.56
<
x
<
2809.76
)
=
P
(
2670.56
−
3000
116
<
z
<
2809.76
−
3000
116
)
=
P
(
−
2.84
<
z
<
−
1.64
)
=
P
(
z
<
−
1.64
)
−
P
(
z
<
−
2.84
)
=
0.0482
In Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)
4) The probability of the average life in the sample exceeding
3219.24
hours:
P
(
x
>
3219.24
)
=
P
(
z
>
3219.24
−
3000
116
)
=
P
(
z
>
1.89
)
=
0.0294
In Excel: =NORMSDIST(-1.89)
5) The likelihood that the sample's average life is lower than
3180.96
hours:
P
(
x
<
3180.96
)
=
P
(
z
<
3180.96
−
3000
116
)
=
P
(
z
<
1.56
)
=
0.9406
629.20 divided by 520 equals 1.21
Power of 6V1.21 equals 1.0323
Interest rate is 3.23
