63720 i just did the math
cos θ = 
, sin θ = 
, cot θ = 4/7, sec θ = 
, cosec θ = 
<h3>What are trigonometric ratios?</h3>
Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin θ: Opposite Side to θ/Hypotenuse
Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos
Cos θ: Adjacent Side to θ/Hypotenuse
Sec θ: Hypotenuse/Adjacent Side & 1/cos θ
Analysis:
tan θ = opposite/adjacent = 7/4
opposite = 7, adjacent = 4.
we now look for the hypotenuse of the right angled triangle
hypotenuse = 
= 
= 
sin θ = opposite/ hyp = 
Rationalize, x 
= 
But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.
Therefore, sin θ = -
cos θ = adj/hyp = 
By rationalizing and knowing that cos θ is negative, cos θ = -
cot θ = 1/tan θ = 1/7/4 = 4/7
sec θ = 1/cos θ = 1/ = -
cosec θ = 1/sin θ = 1/
=
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For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.
- A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x].
- The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable.
- Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).
- Mean(μ) = (1+2+3+4+5+6)/6
- Mean(μ) = 21/6
- Mean(μ) = 3.5
- The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'.
- A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'.
- σ² = E[X²]−μ²
- σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²
- σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²
- σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²
- σ² = (91/6) - (3.5)²
- σ² = 15.167-12.25
- σ² = 2.917
- σ = √2.917
- Standard deviation (σ) = 1.708
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Working out the expression 7(3ˣ) is first to calculate the value of 3ˣ then multiply the answer to 7.
For example, let x = 2
Then 7(3ˣ) = 7(3²) = 7 × 9 = 63
With the same value of x = 2, calculating 21ˣ = 21² = 441, which isn't the same answer with the expression 7(3ˣ)
30% of 47.50 is 14.25 so the amount payed the person payed in total would be 33.50
0.30 x 47.50 = 14.25
47.50 - 14.25 = 33.50
