Given:
n = 150, sample size
Denote the sample proportion by q (normally written as
).
That is,
q = 60/150 = 0.4, sample proportion.
At the 96% confidence level, the z* multiplier is about 2.082, and the confidence interval for the population proportion is
![q \pm z^{*}[ \frac{q(1-q)}{ \sqrt{n} } ]](https://tex.z-dn.net/?f=q%20%5Cpm%20z%5E%7B%2A%7D%5B%20%5Cfrac%7Bq%281-q%29%7D%7B%20%5Csqrt%7Bn%7D%20%7D%20%5D)
That is,
0.4 +/- 2.082* √[(0.4*0.6)/150]
= 0.4 +/- 0.0833
= (0.3167, 0.4833)
= (31.7%, 48.3%)
Answer: The 96% confidence interval is about (32% to 48%)
Answer:
(6 + m²)(6 + m²) . . . . . . . lower left selection
Step-by-step explanation:
When in doubt, you can multiply out the offered factorizations and see which one gives you the given expression.
___
A lot of math is about pattern matching. The given trinomial has first and last terms that are perfect squares. The first term is the square of 6. The last term is the square of m². The middle term is double the product of these two square roots: 2·(6m²) = 12m².
This pattern matches the special form of the square of a binomial:
(a + b)² = a² + 2ab + b²
This special form is useful to commit to memory (at least while you're in math classes in school).
So, when you see 6² + 2·6·m² + (m²)², you can recognize that it is the square ...
(6 + m²)²
When this is written out in the way the answer choices are written, it looks like ...
(6 + m²)(6 + m²)
90 × 7 = 630 , it's not hard, it's easy
Answer:
<em>The helicopter is 27.38 m far off the ground</em>
Step-by-step explanation:
The drawing shown in the image below has all the measures and variables needed to solve the problem.
We need to find R, the height of the helicopter. We'll use the law of sines to find the length of side a.
The angle X is the measure needed to complete 180°:
X = 180° - 54° - 62° = 64°
Solving for a:
Calculating:
a = 31.11 m
Now using the sine ratio in the right triangle to the left side:
Solving for R:
R=31.11*0.88
R = 27.38 m
The helicopter is 27.38 m far off the ground
Answer:
<em>4(y+2) = 3(x+4) and 4y - 3x = 4</em>
Step-by-step explanation:
The equation of the line in point slope form is expressed as;
y - y0 = m(x-x0)
m is the slope
(x0, y0) is the point on the line
Given the equation 3x - 4y = 7
Rewrite in slope intercept form
-4y = -3x+7
y = 3/4 x - 7/4
Slope = 3/4
Slope of the required line will also be 3/4 since they are parallel lines
Substitute the slope and the point into the equation above;
y - y0 = m(x-x0)
y +2 = 3/4 (x+4)
4(y+2) = 3(x+4)
4y + 8 = 3x+12
4y - 3x = 12-8
4y - 3x = 4
<em>Hence the required equations are 4(y+2) = 3(x+4) and 4y - 3x = 4</em>
