Bill earns an annual salary of $65 000. He receives a pay rise of 13.5%, how much does he earn after the increase?
2 answers:
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Answer:
The mean for the sample mean distribution is 297 minutes.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
Using the Central Limit Theorem for Means, what is the mean for the sample mean distribution?
The mean is the same as the population mean, that is, 297 minutes.
Vic's cookies having a ratio of flour to butter of 250/170 contains less
butter than Imani's cookies, 750/630, what Vic will think is therefore;
(A) Imani's cookies have too much butter
<h3>Which method can be used to evaluate the cookies?</h3>
The quantity of flour per 170 grams of butter in Vic's cookies = 250 grams
The amount of flour Imani uses for every 630 grams of butter = 750 grams
Required:
What Vic will think about the amount of butter in Imani's cookies
Solution;
Imani's cookies contains more cookies than Vic's cookies, what Vic will
think of the amount of butter in Imani's cookies is therefore;
(A) Imani's cookies have too much butter
Learn more about fractions here:
<span>Copy the diagram and show how sec θ, csc θ, and cot θ relate to the unit circle.
The representation of the diagram is shown if Figure 1. There's a relationship between </span>sec θ, csc θ, and cot θ related the unit circle. Lines green, blue and pink show the relationship.
a.1 First, find in the diagram a segment whose length is sec θ.
The segment whose length is sec θ is shown in Figure 2, this length is the segment
, that is, the line in green.
a.2 <span>Explain why its length is sec θ.
We know these relationships:
(1)
(2) </span>
<span>
(3) </span>
<span>
Triangles </span>ΔOFC and ΔOBD are similar, so it is true that:
<span>
</span>∴
<span>
b.1 </span>Next, find cot θ
The segment whose length is cot θ is shown in Figure 3, this length is the segment
, that is, the line in pink.
b.2 <span>Use the representation of tangent as a clue for what to show for cotangent.
</span>
It's true that:
But:
Then:
b.3 Justify your claim for cot θ.
As shown in Figure 3, θ is an internal angle and ∠A = 90°, therefore ΔOAR is a right angle, so it is true that:
c. find csc θ in your diagram.
The segment whose length is csc θ is shown in Figure 4, this length is the segment
, that is, the line in green.
The representation of the diagram is shown if Figure 1. There's a relationship between </span>sec θ, csc θ, and cot θ related the unit circle. Lines green, blue and pink show the relationship.
a.1 First, find in the diagram a segment whose length is sec θ.
The segment whose length is sec θ is shown in Figure 2, this length is the segment
a.2 <span>Explain why its length is sec θ.
We know these relationships:
(1)
(2) </span>
<span>
(3) </span>
<span>
Triangles </span>ΔOFC and ΔOBD are similar, so it is true that:
</span>∴
b.1 </span>Next, find cot θ
The segment whose length is cot θ is shown in Figure 3, this length is the segment
b.2 <span>Use the representation of tangent as a clue for what to show for cotangent.
</span>
It's true that:
But:
Then:
b.3 Justify your claim for cot θ.
As shown in Figure 3, θ is an internal angle and ∠A = 90°, therefore ΔOAR is a right angle, so it is true that:
c. find csc θ in your diagram.
The segment whose length is csc θ is shown in Figure 4, this length is the segment