6 x 2 minus 20 because 6 x 2 is in parenthesis so it comes first
Answer:
b
Step-by-step explanation:
Answer:
The new mean = 3 × (the old mean) = 150
The new standard deviation is also = 3 × (The old standard deviation) = 15
Step-by-step explanation:
µ = 50 and σ = 5
The mean is the sum of variables divided by the number of variables.
Mean = (Σx)/N = µ = 50
x = each variable
N = number of variables
If each variable changed to 3x
Mean becomes
Mean = (Σ(3x))/N = 3 (Σx)/N = 3 × µ = 3 × 50 = 150.
The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.
The standard deviation measures the rate of spread of the data set around the mean.
Standard deviation = σ = √[Σ(x - µ)²/N]
x = each variable
µ = mean
N = number of variables
If each variable changed to 3x
Recall µ changed to 3µ
Standard deviation = σ = √[Σ(3x - 3µ)²/N]
σ = √[Σ 3² (x - µ)²/N] = √[(3²)Σ(x - µ)²/N] = 3×√[Σ(x - µ)²/N] = 3 × σ = 3 × 5 = 15
If every score is multiplied by 3, it is logical to reason that the average of the new set of numbers also is 3× the old average.
And the new set of numbers spread out similarly around this new mean, only that the new space of spread is now 3× the old one.
Answer:
8
Step-by-step explanation:
The conjugate of - 2 + 2i is - 2 - 2i, hence
(- 2 + 2i)(- 2 - 2i) ← expand factors using FOIL
= 4 + 4i - 4i - 4i² [ note i² = - 1 ]
= 4 + 4
= 8
For any quadratic functions, ax² + bx + c, we can easily find the x-coordinate of its vertex through the use of the formula below.

where a and b are the coefficients of the function. For f(x), we have a = -1 and b = -16. Thus, we have


Since we now have the x-coordinate of the vertex, we can just easily substitute 8 into f(x) as shown below.


Thus, the
vertex of f(x) is (8, 60). The vertex of the function shows the maximum value that the function can reach. For this particular case, the vertex represents the
maximum profit that the shop owner could earn.The x-intercepts of the function are the values of x when f(x) is zero. By equation f(x) with zero, we can solve the quadratic equation to find the x-intercepts as shown below.





From this, we can see that the x-intercepts are
(6, 0) and (10, 0). We just discussed that the x-intercepts are the values of x when y is zero. So, for this case it means that the shop does not earn a profit if they sell 6 or 10 candles. Basically, the x-intercepts represent the
number candles sold if the shop wants to break even.