Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- an
1 answer:
Answer:
There are 18 nickels and 52 dimes in the jar
Step-by-step explanation:
First establish the variables of x and y
x = number of nickels.
y = numer of dimes.
Then develope the system of two linear equations with two variables.
The first equation can result from adding the number of nickels and dimes which result will be 70 coins then
x + y = 70
The second equation is related with the value, so if we multiply the number of nickels by its value and add it with the number of dimes by its value we will have $6.10 then we have:
0.05x + 0.1y = 6.10
Now we have the two equations and we are going to solve them by the elimination method
x + y = 70
0.05x + 0.1y = 6.10
We are going to eliminate x then we have to multiply by -0.05 in both sides of the first equation and we are going to leave the second equation the same but in the first line to make easier the process.
0.05x + 0.1y = 6.10
(x+y)(-0.05) = 70*(-0.05)
0.05x + 0.1y = 6.10
<u>-0.05x -0.05y = -3.50</u> (now do the operation)
0 +0.05y = 2.60
y =
y = 52
We have 52 dimes.
Now replace in the initial equation the y value
x + 52 = 70
x = 70 - 52
x = 18
We have 18 nickels
Then in the jar we have 52 dimes and 18 nickels
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Answer: -2/7
Step-by-step explanation:
To find the slope, you use the formula .
Now, we know the slope is -2/7.
Answer:
a)
b) Since we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.
Because Type I error " is the rejection of a true null hypothesis".
c)
d) For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054
And we can use this formula:
And if we solve for n we got:
Step-by-step explanation:
Previous concepts and data given
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".
We can calculate the sample mean and deviation with the following formulas:
represent the sample mean
represent the sample standard deviation
n=5 represent the sample selected
significance level
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less than 90, 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)
z-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:
Part a
P-value
First we need to calculate the degrees of freedom given by:
Then since is a left tailed test the p value would be:
Part b
Since we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.
Because Type I error " is the rejection of a true null hypothesis".
Part c
We want this probability:
The best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
Part d
For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054
And we can use this formula:
And if we solve for n we got: