Answer:
Side =
Step-by-step explanation:
Given that,
Area of a square room is 125 square feet
We need to find the length of one side of the room.
The area of a square shaped room is given by :
Where, x is side of the square room
So, the side of the room is .
Answer:
Step-by-step explanation:
Given
Required
Find p, when
We have:
Express as equation
Make k the subject
When:
When , we have:
Answer:
z = -0.139
The data provide evidence that this particular meets the government regulation
Step-by-step explanation:
To determine if the the data provide evidence that this particular meets the government regulation, we need to define a null and alternative hypothesis as:
H0: m = 0.3
H1: m > 0.3
where m is the population mean NOX emission.
Then, we need to find the appropriate statistic. So, taking into account that the model follows a Normal distribution with standard deviation equal to 0.05, the statistic is equal to:
where x is the mean of the sample, m is 0.3 g/mi, s is the population standard deviation and n is the size of the sample.
Therefore, replacing x by 0.298, m by 0.3, s by 0.05 and n by 12, we get that the test statistic is:
Finally, we need to find the p-value using the normal distribution table as:
p-value = P(z > -0.139 ) = 0.4443
So, taking into account that the p-value is big value, we can conclude that we don't reject H0. It means that the data provide evidence that this particular meets the government regulation.
Answer:
Answer 1.
Step-by-step explanation:
The complete question is:
The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 3 centered at the origin. Which statement is correct?
1. The image of the line has the same slope as the pre-image but a different y-intercept.
2. The image of the line has the same y-intercept as the pre-image but a different slope.
3. The image of the line has the same slope and the same y-intercept as the pre-image.
4. The image of the line has a different slope and a different y-intercept from the pre-image.
Recall that a dilation by a scale factor r centered at the origin takes a point (x,y) and maps it to the point (r*x,r*y).
Consider also a line of equation . From this equation, the slope of the line is given by the number
and the y-intercept is given by
.
Consider the given equation 3x-5y =4. If we replace (x,y) with (3x,3y), we get
which is equivalent to
Note that comparing the equations 3x-5y=4 and the values of a and b are equal but the value of c is different. This means that they have the same slope but a different y-intercept.