Answer:
x = 65.03°
Step-by-step explanation:
To solve for x, we have to apply trigonometric ratio.
Recall: SOH CAH TOA
From the diagram, we know the following:
Reference angle = x
Hypotenuse = 45
Adjacent = 19
Since we know the Hyp and Adj, we would apply CAH, which is:
Cos x = Adj/Hyp
Plug in the values
x = 65.0250346°
x = 65.03° (nearest hundredth)
Recall that for all t,
cos²(t) + sin²(t) = 1
Now,
x = 5 cos(t) - 7 ⇒ (x + 7)/5 = cos(t)
y = 5 sin(t) + 9 ⇒ (y - 9)/5 = sin(t)
so that substituting into the identity above, we get
((x + 7)/5)² + ((y - 9)/5)² = 1
which we can rewrite as
(x + 7)²/25 + (y - 9)²/25 = 1
(x + 7)² + (y - 9)² = 25
and this is the equation of a circle centered at (-7, 9) with radius 5.
26% is the answer to your question
1 is 28
2 is 13, 84, 85
Figure both by the Pythagorean Theorem<span />
Answer: 0.0241
Step-by-step explanation:
This is solved using the probability distribution formula for random variables where the combination formula for selection is used to determine the probability of these random variables occurring. This formula is denoted by:
P(X=r) = nCr × p^r × q^n-r
Where:
n = number of sampled variable which in this case = 21
r = variable outcome being determined which in this case = 5
p = probability of success of the variable which in this case = 0.31
q= 1- p = 1 - 0.31 = 0.69
P(X=5) = 21C5 × 0.31^5 × 0.69^16
P(X=5) = 0.0241
