Jacques wants to make up packs of $0.45 comic books mixed with $0.75 ones to sell at $9.00 per pack. The number of $0.45 comic b
1 answer:
Answer:
The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books
Step-by-step explanation:
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
In this case, the unknowns or unknown variables are:
x: number of $ 0.45 comic books
y: number of $ 0.75 comic books
Jacques wants to make up packs of $0.45 comic books mixed with $0.75 ones to sell at $9.00 per pack. Then the equation that represents this situation is:
x*0.45 + y*0.75= 9
On the other side, the number of $0.45 comic books is 4 more than the number of $0.75 comic books. Then the equation that represents this situation is:
x+4=y
The system of equations to solve is:
One way to solve a system of equations is the substitution method, which consists of solving one of the unknowns in one of the equations and substituting its value in the next.
In this case we directly replace the expression of the variable and of the second equation in the first:
x*0.45 + (x+4)*0.75= 9
Solving:
x*0.45 + 0.75*x + 4*0.75= 9
1.2*x + 3=9
1.2*x= 9-3
1.2*x= 6
x= 6÷ 1.2
x=5
Replacing this value in the expression x+4=y you get:
5 +4=y
9=y
<u><em>The number of each type in the pack is 5 of $0.45 comic books and 9 of $0.75 comic books</em></u>
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Answer:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean temperature actually its NOT significant less then 22 at 1% of signficance.
(D) P-val=0.021, fail to reject the null hypothesis
Step-by-step explanation:
1) Data given and notation
represent the mean for the temperatures
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less than 22C, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
We can calculate the degrees of freedom like this:
Since is a one left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean temperature actually its NOT significant less then 22 at 1% of signficance.
The best option would be:
(D) P-val=0.021, fail to reject the null hypothesis
Answer:
The equation of the line that passes through the point (4,7) and has a slope of 0 will be:
Step-by-step explanation:
As we know the equation of a line in a slope-intercept form of an equation is
Here,
- m is the slop
- b is the y-intercept
so
substituting the point (4,7) and slope m=0
Therefore, the equation of the line that passes through the point (4,7) and has a slope of 0 will be: