Answer:


Step-by-step explanation:
To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.
a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

we can substitute the value of sec(θ) in this equation:

and solve for for cos(θ)

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by
b) since right triangle is mentioned in the question. We can use:

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:
- length of the adjacent side = 1
- length of the hypotenuse = 52
we can find the third side using the Pythagoras theorem.




- length of the opposite side = √(2703) ≈ 51.9904
we can find the sin(θ) using this side:


and since 

Answer:
(a) 1, 2, 3, 6, 8
Step-by-step explanation:
Given


Required
The sequence of hours worked each day
<em>See attachment for options</em>
From the question, we understand that:

This means that, the middle number is 3 (when sorted)
So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively
Next, is to determine the mean of (a) and (d)
The mean of a data is calculated as:

So, we have:
(a)



(d)



Option (a) is true, because it has:


Answer:
<em>* Siobhan's profit at the grocery store ⇒ $ 10.8 *</em>
Step-by-step explanation:
See below;
Priya's 40% profit in the grocery store ⇒ 40/100 * 9 = 2/5 * 9 = 18/5 ⇒ $ 3.6,
Priya's profit at the grocery store ⇒ 9 + 3.6 ⇒ $ 12.6,
Siobhan's 15% of Priya's profit from the store ⇒ 15/100 * 12.6 = $ 1.8
Siobhan's profit at the grocery store ⇒ 12.6 - 1.8 = $ 10.8
<em>* Siobhan's profit at the grocery store ⇒ $ 10.8 *</em>