In the lab, Leila has two solutions that contain alcohol and is mixing them with each other. Solution A is alcohol and Solution
1 answer:
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Answer:
a) n =1623
b)
Step-by-step explanation:
1) Notation and definitions
random sample taken
estimated proportion of customers are not satisfied with the service provided by the local dealer
Confidence =0.96 or 96%
Me= 0.02 represent the margin of error
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Part a
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 96% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=1623
Part b
The margin of error is given by:
So then if w replace the value of n obtained from part a we got:
Answer:
9) y = -200x + 1200
11) slope = -2
15) $2,450
16) 9 days
Step-by-step explanation:
9) Given the two points from the graph:
Let (x₁, y₁) = (0, 1200)
(x₂, y₂) = (1, 1000)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (1000 - 1200)/(1 - 0)
m = -200/1
m = -200
The slope of the line is -200.
Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis. Upon observing the graph, it shows that the line crosses at point (0, 1200). The y-coordinate of this ordered pair is the value of the y-intercept, b = 1200.
Therefore, the linear equation in slope-intercept form is y = -200x + 1200.
<h3>11) Given the points, (5, -18) and (-4, 0): </h3>Let (x₁, y₁) =(5, -18)
(x₂, y₂) = (-4, 0)
Substitute these values into the following <u>slope formula</u>:
m = (y₂ - y₁)/(x₂ - x₁)
Therefore, the slope of the line is -2.
<h3>15) Solve:</h3>Given the fixed fee of $200, and the $150 per hour after the initial meeting:
We can represent these in slope-intercept form:
y = 150x + 200
y = total cost for the Attorney's services
x = number of hours worked.
The y-intercept in this given problem is $200, which represents the flat fee charged for the initial meeting. While the slope in this equation is $150, which is the hourly rate that an Attorney charges his clients after the initial meeting.
If an Attorney works for 15 hours, then:
Let x = 15, and substitute its value into the equation to find the total cost:
y = 150x + 200
y = 150(15) + 200
y = 2,250 + 200
y = 2,450
Therefore, a client will pay a total of $2,450 for an Attorney's 15 hours of work.
<h3>16) Solve: </h3>Given the water level on a Lake of 165 inches after a rainstorm, and the water level's receding rate of 3 inches per day:
We can establish the following linear equation to model this given problem:
L = -3d + 165
Where:
L = represents the water level of the Lake
d = number of days that the water level recedes
In order to find the number of days it will take before the water level recedes to 84 inches:
Substitute the value of L = 84 into the equation:
L = -3d + 165
84 = -3d + 165
Subtract 165 from both sides:
84 - 165 = 3d + 165 - 165
-27 = -3d
Divide both sides by -3:
9 = d
Therefore, it will take 9 days for the water level to be at 84 inches.
Answer:
Option 4 -
Step-by-step explanation:
To find : Which set of rational numbers is arranged from least to greatest?
Solution :
The set of rational numbers are
Writing all number in one form,
Now, -1.4<-0.5<0.2<3
From least to greatest the set of natural numbers are
So,
Therefore, option 4 is correct.