Answer:
z = 1.960
Step-by-step explanation:
The sample proportion is:
p = 715 / 2684 = 0.2664
The standard error is:
σ = √(pq/n)
σ = √(0.266 × 0.734 / 2684)
σ = 0.0085
For α = 0.05, the confidence level is 95%. The z-statistic at 95% confidence is 1.960.
The margin of error is 1.960 × 0.0085 = 0.0167.
The confidence interval is 0.2664 ± 0.0167 = (0.2497, 0.2831).
The upper limit is 28.3%, so the journal can conclude with 95% confidence that the true percentage is less than 29%.
Answer:
y= -2/3x-3
Step-by-step explanation:
The formula for slope-intercept form is y=mx+b. m=Slope. b=y-intercept. Therefore the equation would be y= -2/3x-3
Answer:
V = 84.78 ft^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = 3.14 ( 3)^2 (3)
V = 3.14 *9(3)
V = 84.78 ft^2
Answer:
Adjacent, b = 5.3 units
Step-by-step explanation:
Let the length of sides of the triangle be;
- Opposite side = a
- Adjacent side = b
- Hypotenuse side = c
From the right-angle triangle, we can deduce the following data;
Hypotenuse, c = 8
Opposite, a = 6
To find the length of the adjacent (third) side, we would have to apply Pythagorean' theorem.
From Pythagorean theorem;
c² = a² + b²
Substituting into the formula, we have;
8² = 6² + b²
64 = 36 + b²
Rearranging the equation (collecting like terms), we have;
b² = 64 - 36
b² = 28
Taking the square root of both sides, we have;
b = √28
<em>Adjacent, b = 5.3 units</em>
Probably the easiest way to do this is to use synthetic division. We already know one of the zeros of the quadratic so we can use that number to find the other zero. If the point is (4, 0), then when y = 0, x = 4. Thus, 4 is a zero. Put 4 outside the "box" and put the coefficients from the quadratic inside, like this: 4 (1 -1 -12). Draw a line and bring down the first one under it. Multiply that 1 by the 4 to get 4. Put that 4 up under the -1 and add to get 3. Multiply 3 by 4 to get 12. Put that 12 up under the -12 and add to get 0. The numbers left under the line are the coefficients for the next polynomial, called the depressed polynomial, and this polyomial is one degree less than the one we started with. Those coefficients are 1 and 3. Therefore, the polynomial is x + 3 = 0. That means that the other zero, or x-intercept, is x = -3.
