Answer:
Length of side AB = 5.6 cm
Step-by-step explanation:
From the figure attached.
In right triangle ABC,
m∠ABC = 62°
m(BC) = 12 cm
By applying Cosine rule in this triangle,
Cos62° = 
Cos62°= 
0.46947 = 
AB = 12 × 0.46947
AB = 5.63
≈ 5.6 cm
Therefore, length of side AB = 5.6 cm
Here is your answer
B. (12,30)
REASON:
Given,
.......(i)
.......(ii)
Putting the value of y from eq.i in eq.ii we get




Putting x=12 in eq.i we get



So,

Hence answer is (12,30) in which x=12 and y=30
HOPE IT IS USEFUL
Answer:
Nat's salary after 3 years = 976562.5 $
Explanation:
Salary of Nat = $500,000
Raise in salary for next three years = 25 % = 0.25
Salary of Nat after 1 year = 500,000 + 0.25 * 500,000 = 625000 $
Salary of Nat after 2 years = 625000 + 0.25 * 625000 = 781250 $
Salary of Nat after 3 years = 781250 + 0.25 * 781250 = 976562.5 $
So, Nat's salary after 3 years = 976562.5 $
Easy Method;
No of years considering = 3
Initial salary = $500,000
Rate of increase = 0.25
Final salary
$
Nat's salary after 3 years = 976562.5 $
By the Pythagoras theorem, in a right triangle with the sides being a and b,
a² + b² = Hypotenuse²
Hypotenuse² = 4² + 4²
Hypotenuse² = 16 + 16 = 2*16
Hypotenuse = √2 * √16
Thus, hypotenuse = 4√2
Answer:
The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the zscore that has a pvalue of
.
For this problem, we have that:

95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:

The upper limit of this interval is:

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).