Answer: 16 1/2
Step-by-step explanation:
It's easiest to multiply improper fractions and then to convert them back into mixed numbers, so 4 1/2 would become 9/2 and 3 2/3 would become 11/3. = 99/6. Now just simplify to 33/2 and then convert back into a mixed number. 16 1/2
Answer:
61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.
Step-by-step explanation:
Given : We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.
To find : How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters?
Solution :
At 95% confidence the z-value is z=1.96
The sample mean is within 3 minutes of the population mean i.e. margin of error is E=3 minutes
The population standard deviation is s=12 minutes
n is the number of sample
The formula of margin of error is given by,
Substitute the value in the formula,
Squaring both side,
Therefore, 61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.
Answer:
8 suits
Step-by-step explanation:
Divide 30 m by 3 m , or 30 ÷ 3.75 , then
30 ÷ 3.75 = 8
Then 8 suits can be made from 30 m of cloth
Answer:
The solution is (0, 2) or x = 0, y = 2.
Step-by-step explanation:
Solving a system of linear equations graphically entails graphing the lines and then finding the point where the lines intersect. This point of intersection will be the solution to the system of equations.
Getting these linear equations into slope-intercept form (y = mx + b, where m is the line's slope and b is the line's y-intercept) makes them a lot easier to graph, so let's make sure that both lines are in slope-intercept form.
The first line isn't in slope-intercept form, so we can rewrite it as:
x + y = 2
y = -x + 2 (Subtract x from both sides of the equation to isolate y)
The second line technically isn't in slope-intercept form, so we can rewrite it as:
y = 2 - 3x
y = -3x + 2 (Commutative Property of Addition)
Now, we can graph the lines to find the solution to the system.
To graph y = -x + 2, draw a line with a slope of -1 (since m = -1) and a y-intercept of (0, 2) (since b = 2). This is the red line on the graph.
To graph y = -3x + 2, draw a line with a slope of -3 (since m = -3) and a y-intercept of (0, 2) (since b = 2). This is the blue line on the graph.
Looking at the graph below, we see that the lines intersect at (0, 2), so this is our answer.
To check if this point is a solution to the system of equations, simply substitute the x and y-coordinates of the point into the equations. If the point satisfies all of the equations, then it is a solution to the system.
In (0, 2), x = 0, and y = 2. Substituting these values into the first equation gives us 0 + 2 = 2, which simplifies to 2 = 2. This is a true statement, so (0, 2) satisfies the first equation. Substituting x = 0 and y = 2 into the second equation gives us 2 = 2 - 3 * 0, which simplifies to 2 = 2. This is also a true statement, so (0, 2) satisfies the second equation, and therefore is a solution to the system of linear equations. Hope this helps!
