Answer:
The new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)
Step-by-step explanation:
The rectangle ABCD on the grid shown is attached below.
From the grid, it is clear that the coordinates of point D are (-4, -4)
i.e. D(-4, -4)
As we are told that the figure is to be dilated from the origin.
A dilation tends to stretch or shrink the original figure, depending upon scale factor.
When we dilate a figure from the origin by any scale factor, the new coordinates of the image can be obtained by multiplying the scale factor with the coordinates of the original object/figure.
As the the coordinates of point D are (-4, -4). If we dilate the figure by a scale factor of 1/2, the new new coordinates of point D would be:
P(x, y) → P'(1/2x, 1/2y)
D(-4, -4) → D'(-4/2, -4/2) or D'(-2, -2)
Therefore, the new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)
Answer:
Step-by-step explanation:
Given that a group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below.
Data set is as ollows:
70 79 38 63 44 23 62 61 67 50 61 70 94 87 65
H0: mu = 60 sec
Ha: mu not equals 60 sec
Mean diff = 2.27
Test statistic = 2.27/SE =0.4815
p value =0.6376
Since p>0.05, we accept null hypothesis
i.e. there is statistical evidence to say that students are reasonably good at estimating one minute
Answer:
Tuesday z-score was 3.26.
Tuesday was a significantly good day.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
A score is said to be significantly high if it has a z-score higher than 1.64, that is, it is at least in the 95th percentile.
In this problem, we have that:
On Tuesday, the store sold $34,885.21 worth of goods. Find Tuesday's z-score.
This is Z when
Tuesday z-score was 3.26.
Was Tuesday a significantly good day?
A z-score of 3.26 has a pvalue of 0.9994. So only 1-0.9994 = 0.0006 = 0.06% of the day are better than Tuesday.
So yes, Tuesday was a significantly good day.
Answer:
The standard deviation of the number of rushing yards for the running backs that season is 350.
Step-by-step explanation:
Consider the provided information.
The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards.
Here it is given that mean is 790 and 1637 is 2.42 standard deviations above the mean.
Use the formula:
Here z is 2.42 and μ is 790, substitute the respective values as shown.
Hence, the standard deviation of the number of rushing yards for the running backs that season is 350.