Answer:
Option C is correct.
Step-by-step explanation:
We need to find reference angle and signs of sinФ, cosФ and tanФ
We know that 
is equal to 150°
and 150° is in 2nd quadrant.
So, Ф is in 2nd quadrant.
And In 2nd quadrant sine is positive, while cos and tan are negative
The reference angle Ф' is found by: π - Ф
=> Ф = 5π/6
so, Reference angle Ф' = π - 5π/6
Ф' = 6π - 5π/6
Ф' = π/6
So, Option C Θ' = pi over 6; sine is positive, cosine and tangent are negative is correct.
Answer:
(115.2642, 222.7358).
Step-by-step explanation:
Given data:
type A: n_1=60, xbar_1=1827, s_1=168
type B: n_2=180, xbar_2=1658, s_2=225
n_1 = sample size 1, n_2= sample size 2
xbar_1, xbar_2 are mean life of sample 1 and 2 respectively. Similarly, s_1 and s_2 are standard deviation of 1,2.
a=0.05, |Z(0.025)|=1.96 (from the standard normal table)
So 95% CI is
(xbar_1 -xbar_2) ± Z×√[s1^2/n1 + s2^2/n2]
=(1827-1658) ± 1.96×sqrt(168^2/60 + 225^2/180)
= (115.2642, 222.7358).
Answer:
192 orders
Step-by-step explanation:
All robots are working simultaneously, so each robot takes 10 minutes to do their orders. They are all identical, so they take an equal amount of time to do each order, meaning 20 ÷ 5 = 4. Each robot takes 10 minutes to do 4 orders.
If there are eight robots working for 60 minutes, each robot can make six times as many orders, compared to when they were working for 10 minutes. 4 x 6 = 24. There are eight robots, so 24 x 8 = 192 orders.
Answer:
ok what u need?
Step-by-step explanation:
In ∆FDH, there are two slash marks in two of its legs. This indicates that this triangle is isosceles. If a triangle is isosceles, then it will have two congruent sides and therefore have two congruent angles.
In ∆FDH, angle D is already given to us as the measure of 80°. We can find out the measure of the other angles of this triangle by using the equation:
80 + 2x = 180
Subtract 80 from both sides of the equation.
2x = 100
Divide both sides by 2.
x = 50
This means that angle F and angle H in ∆FDH both measure 50°.
Now, moving over to the next smaller triangle in the picture is ∆DHG. In this triangle, there are also two legs that are congruent which once again indicates that this triangle is isosceles.
First, we have to solve for angle DHG and we do that by using the information obtained from solving for the angles of the other triangle.
**In geometry, remember that two or more consecutive angles that form a line will always be supplementary; the angles add up to 180°.**
In this case angle DHF and angle DHG are consecutive angles which form a linear pair. So, we can use the equation:
Angle DHF + Angle DHG = 180°
50° + Angle DHG = 180°.
Angle DHG = 130°.
Now that we know the measure of one angle in ∆DHG, we can use the same method as the previous step for solving the missing angles. Use the equation:
130 + 2x = 180
2x = 50
x = 25
The other two missing angles of ∆DHG are 25°. This means that the measure of angle 1 is also 25°.
Solution: 25°
