Step-by-step explanation:
Given that,
We have to find the value of m∠E.
Here, two sides are equal, thus it is an isosceles triangle. As the two sides are equal, so their angles must be equal. So, ∠E and ∠D will be equal. Let us assume the measures of both ∠E and ∠D as x.
→ Sum of all the interior angles of ∆ = 180°
→ ∠E + ∠D + ∠F = 180°
→ 116° + x + x = 180°
→ 2x = 180° – 116°
→ 2x = 64°
→ x = 64° ÷ 2
→<u> x = 32°</u>
Henceforth,
→ m∠E = x
→ m∠E = 32°
~
Answer:
Option B) 9.1
Step-by-step explanation:
We are given the following in the question:
Average score = 490.4
Standard deviation = 63.7
Sample size, n = 49
Formula:
Putting values, we get,
Standard error =
Thus, the correct answer is
Option B) 9.1
Answer:
A 98% confidence interval for the mean assembly time is [21.34, 26.49] .
Step-by-step explanation:
We are given that a sample of 40 times yielded an average time of 23.92 minutes, with a sample standard deviation of 6.72 minutes.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~
where, = sample average time = 23.92 minutes
s = sample standard deviation = 6.72 minutes
n = sample of times = 40
= population mean assembly time
<em> Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation. </em>
<u>So, a 98% confidence interval for the population mean, </u><u> is;
</u>
P(-2.426 < < 2.426) = 0.98 {As the critical value of z at 1% level
of significance are -2.426 & 2.426}
P(-2.426 < < 2.426) = 0.98
P( <
<
) = 0.98
P( <
<
) = 0.98
<u>98% confidence interval for</u> = [
,
]
= [ ,
]
= [21.34, 26.49]
Therefore, a 98% confidence interval for the mean assembly time is [21.34, 26.49] .
Answer:
226.4 m³.
Step-by-step explanation:
The volume of a right cone with a circular base is:
,
where
The radius of the circular base is one-half its diameter.
.
.