If the 4x2 is actually 4x^2 then the answer is
-(4x+3x-24)
Answer:
Step-by-step explanation:
if he rode 4 miles in 20 minutes
1h=20*3=60 min
4*3=12 miles/hour
Answer:
0 < y ≤ 72.
Step-by-step explanation:
We are given the maximum length of the tray is 12 inches. This implies that;
x + 5 ≤ 12
x ≤ 7
Therefore, the maximum value of x is 7 inches. The maximum width will thus be;
x - 1 = 7 - 1 = 6 inches.
The maximum area, y, will thus be;
Area = length * width
Area = 12 * 6 = 72
The reasonable domain will thus be;
0 < y ≤ 72.
The area is simply between 0 and 72. The area of any object can not be negative.
Answer:
The simplest form is tan(4x)
Step-by-step explanation:
* Lets revise the identity of the compound angles
- 
- 
* Lets solve the problem
- Let 9x = 5x + 4x
∴ tan(9x) = tan(5x + 4x)
- Use the rule of the compound angle
∵ 
⇒ (1)
∵ 
⇒ (2)
∵ tan(9x) = equation (2)
- Substitute (2) in (1)
∴ 
- Multiply up and down by (1 - tan(5x)tan(4x))
∴ ![\frac{tan(5x)+tan(4x)-tan(5x)[1-tan(5x)tan(4x)]}{1-tan(5x)tan(4x)+tan(5x)[tan(5x)+tan(4x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%285x%29%2Btan%284x%29-tan%285x%29%5B1-tan%285x%29tan%284x%29%5D%7D%7B1-tan%285x%29tan%284x%29%2Btan%285x%29%5Btan%285x%29%2Btan%284x%29%5D%7D)
- Simplify up and down
∴ 
∴ ![\frac{tan(4x)+tan^{2}(5x)tan(4x)}{[1+tan^{2}(5x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%284x%29%2Btan%5E%7B2%7D%285x%29tan%284x%29%7D%7B%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D)
- Take tan(4x) as a common factor up
∴ ![\frac{tan(4x)[1+tan^{2}(5x)]}{[1+tan^{2}(5x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%284x%29%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D%7B%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D)
- Cancel [1 + tan²(5x)] up and down
∴ The answer is tan(4x)
Answer: a) margin of error = 61.25, b) sample size when margin of error is 45 = 30
Step-by-step explanation:
The formulae to get the margin of error of a confidence interval is given as
Margin of error = critical value * (σ/√n)
Where σ = population standard deviation = 125
n = sample size = 16
Critical value =Zα/2 = 1.96 ( this is so because we are performing a 95% confidence level test then level of significance (α) will be 5% and since our test is of two values, it will be 2 tailed).
Margin of error = 1.96 * (125/√16)
Margin of error = 1.96 * 125/4
Margin of error = 1.96 * 31.25
Margin of error = 61.25
Question b)
Margin of error = 45
Critical value =Zα/2 = 1.96
Population standard deviation = σ = 125
Sample size =n =??
By recalling the formulae
Margin of error = critical value * (σ/√n)
45 = 1.96 * (125/√n)
45 = (1.96 * 125)/√n
45 = 245/√n
45 * √n = 245
√n = 245/ 45
√n = 5.444
n = (5.444)²
n= 29.64 which is approximately 30.
