Scale Factor (K) = (new length/measure)/ (original length/measure)
for x-coordinate = 8/2 = 4
for y-coordinate = 16/4 = 4
K=4, expansion
K is the representation of "scale factor". Scale factor is the ratio of the lengths involved of the similar figures. It can be used to identify the kind of dilation, whether it is contraction or expansion. If the Scale Factor is greater than 1, then that means expansion and if it is less than 1, then it signifies contraction.
Answer:
a. We reject the null hypothesis at the significance level of 0.05
b. The p-value is zero for practical applications
c. (-0.0225, -0.0375)
Step-by-step explanation:
Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.
Then we have
,
,
and
,
,
. The pooled estimate is given by
a. We want to test
vs
(two-tailed alternative).
The test statistic is
and the observed value is
. T has a Student's t distribution with 20 + 25 - 2 = 43 df.
The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value
falls inside RR, we reject the null hypothesis at the significance level of 0.05
b. The p-value for this test is given by
0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.
c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)
, i.e.,
where
is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So
, i.e.,
(-0.0225, -0.0375)
The following are prices for a 25 inch T.V. found in different stores around Roseville: 100,98,121,111,97,135,136,104,135,138,18
Vlad1618 [11]
There are 14 values above. The mean of these 14 numbers is calculated by dividing their sum by 14 which will give us an answer of 117.07 or ~117. The smallest of these values is 69 which is 48 units to the left of the average. The largest value is 189 which is 72 units to the right of the average. Therefore, in this distribution, the values are skewed to the right.
Answer: 2 markers.
Step-by-step explanation:
1. You know that she gives 12 markers to Mr. Cooke, then the rest among is:
29 markers-12 markers=17 markers
2. She divides the rest among 5 other teachers and each one of them get the same number of markers. So, you need to divide 17 markers by 5 teachers as following:
17 markers/5=3.4 markers
3. But the number of marker each one teacher has can't be a decimal number, so this number must be: 3 markers for each teacher.
3. The number of markers that will be left over is:
17 markers-(5*3 markers)=2 markers