Answer:
(7,4)
Step-by-step explanation:
The midpoint formula is expressed as:
M(X, Y) = {(x2+x1)/2, (y2+y1)/2
Given the coordinates of the midpoint
M(2.5, -1.5)
Endpoint A(-2, -7)
Required
Endpoint B
From the formula;
X = x2+x1/2
Given
X = 2.5, x1 = -2
Get x2
2.5 = -2+x2/2
5 = -2+x2
x2 = 5+2
x2 = 7
Also
Y = y2+y1/2
-1.5 = -7+y2/2
-3 =-7+y2
y2 = -3+7
y2 = 4
Hence the coordinate of the endpoint B (x2,y2) is (7,4)
Answer:
Compute the cost of driving for two different job options.
Driving costs 0.50 dollars per mile. Driving occurs 250 days per year.
Job 1
Miles each way 5
What is the cost of driving?
Job 2
Miles each way 50
What is the cost of driving?
Answer:
The new rate should be $56.67 per day
Step-by-step explanation:
Proportion states that the two fractions or ratios are equal.
As per the statement:
Normal rate per day = $45
To find the new rate:
Let new rate be x per day
By definition of proportion:
By cross multiply we have;
Divide both sides by 100 we get;
Simplify:
x = $56.7
Therefore, the new rate should be $56.7 per day
We are going to make simultaneous equations.
x will be our $3 ice cream and y will be our $5 ice cream
Equation1 ---- x + y = 50 (the sum of all the ice creams they sell)
Equation 2 ---- 3x + 5y = 180 Sum of all the $3 and $5 ice creams is $180
Since we can't solve for both variables we will put one of the variables in terms of the other.
Take x+y=50 and subtract y from both sides. (I could have done subtracted x - it did not matter). Now we have x= ₋ y +50 (negative y +50)
Now I am going to take equation 2 and replace the x with -y +50
3 (-y +50) + 5y = 180
Now I will use the distributive law on the 3 and what's in the parentheses:
-3y + 150 + 5y = 180
Now I will combine like terms (the -3y and the 5y)
2y + 150 = 180
Now subtract 150 from both sides of the equation
2y = 30
Divide both sides by 2
and get y= 15 They sold 15 ice creams that cost $5 each
Since equation 1 is x+y=50 we can replace y with 15
x + 15 = 50 Now subtract 15 from both sides x = 35
Since x represents the $3 ice creams, they sold 35 of those.
Check:
35 X 3 = $105
15 x 5 = + <u>75
</u> $180
Answer:
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
Step-by-step explanation:
We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.26.
The standard error of the proportion is:
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the population proportion is (0.192, 0.328).
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
