Answer:
b. It will decrease by a factor of 2
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence interval 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
The lower end of the interval is given by:
The upper end of the interval is given by:
The length of the interval is the subtraction of the upper end by the lower end, so it is:
This means that the length is inverse proportional to the square root of the size of the sample.
So, if the sample size is multiplied by 4, the length of the interval is going to decrease by a factor of 2.
Answer:
the length of the hypotenuse must be 10.
Step-by-step explanation:
This is a right triangle, so we can apply the Pythagorean Theorem.
6² + 8² = 10² so the length of the hypotenuse must be 10.
Answer:
<h2>x = 12</h2><h2 /><h2>y = 4√3</h2>
Step-by-step explanation:
<u>To find x we use cosine</u>
cos∅ = adjacent / hypotenuse
x is the adjacent
8√3 is the hypotenuse
cos 30 = x / 8√3
x = 8√3 cos 30
<h3>x = 12</h3>
<u>To find y we use sine</u>
sin∅ = opposite / hypotenuse
y is the opposite
8√3 is the hypotenuse
sin 30 = y / 8√3
y = 8√3 sin 30
<h3>y = 4√3</h3>
Hope this helps you
Answer:
K = 43
Step-by-step explanation:
We'll begin by determining the gradient of the equation 5y + 4x = 8. This can be obtained as follow:
5y + 4x = 8
Rearrange
5y = 8 – 4x
5y = –4x + 8
Comparing 5y = –4x + 8 with y = mx + c, the gradient m is –4
Next, we shall determine the gradient of the line perpendicular to the line with equation 5y = 8 – 4x.
This can be obtained as follow:
For perpendicular lines, their gradient is given by:
m1 × m2 = – 1
With the above formula, we can obtain the gradient of the line as follow:
m1 × m2 = – 1
m1 = –4
–4 × m2 = – 1
Divide both side by –4
m2 = –1/–4
m2 = 1/4
Finally, we shall determine the value of k as follow:
Coordinate => (k, 4) and (3, –6)
x1 coordinate = k
y1 coordinate = 4
x2 coordinate = 3
y2 coordinate = –6
Gradient (m) = 1/4
m = (y2 – y1) / (x2 – x1)
1/4 = (–6 – 4) / (3 – K)
1/4 = –10 /(3 – K)
Cross multiply
3 – K = 4 × –10
3 – K = –40
Collect like terms
– K = – 40 –3
–k = –43
Divide both side by – 1
K = –43/–1
k = 43
