Answer:
Step-by-step explanation:
Amanda bought g gallons of paint for $16.55 per gallon and t pints of paint thinner for $5.97 per pint
Total amount = rate per gallon times gallons + rate per pint times pints
amanda bought 8 gallons of paint and 3 pints of paint thinner
g=8 and t=3, substitute the values and find total cost
Answer:
Yes. There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.
Step-by-step explanation:
The sample of the remaining toothpaste is: [.53, .65, .46, .50, .37].
This sample has a size n=5, a mean M=0.502 and standard deviation s=0.102.
The 10% of the advertised content is:
Hypothesis test for the population mean:
The claim is that the remaining toothpaste is significantly is less than 10% of the advertised net content.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 4 degrees of freedom and t=-2.148, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.049) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.
We are given a system of linear programming problem as follows:
Max 5A + 5B
s.t. A ≤ 100---------------(1)
B ≤ 80-------------(2)
2A+4B ≤400-------------(3)
which is given by:
A+2B ≤ 200
and A,B≥0
This means that the solution to this LPP will lie in the first quadrant.
( Since, both the variables A and B are greater than or equal to zero)
Now, we consider that A is represented by the x axis and B by y-axis.
We know that the optimal solution always exist at the boundary point.
Hence, by plotting these inequalities in the graph we get the boundary points as:
(0,0) , (0,80) , (100,0) , (100,50) and (40,80)
Now, we will check at which boundary point the optimal function is maximized .
Point Value of optimal function( 5A+5B)
(0,0) 0
(0,80) 400
(100,0) 500
(100,50) 750
(40,80) 600
The maximum value is obtained at (100,50).
and the value of the optimal solution is: 750
