Your friend is trying to grow her hair as long as her cousin’s hair. The table shows their hair lengths y (in inches) in differe
1 answer:
<span>Given the
table that shows the hair lengths y (in inches) of your friend and her cousin in different months x.
Month Friends Hair(in) Cousins Hair(in)
3 4 7
8 6.5 9.
To solve for the cousins hair, recall that the equation of a line is given by
y = mx + c
From the table,
7 = 3m + c . . . (1)
9 = 8m + c . . . (2)
(1) - (2) ⇒ -2 = -5m
Substituting for m into equation (1) gives:
Therefore, the equation representing the growth of the cousin's hair is given by y = 1.2x + 5.8
</span>
Month Friends Hair(in) Cousins Hair(in)
3 4 7
8 6.5 9.
To solve for the cousins hair, recall that the equation of a line is given by
y = mx + c
From the table,
7 = 3m + c . . . (1)
9 = 8m + c . . . (2)
(1) - (2) ⇒ -2 = -5m
Substituting for m into equation (1) gives:
Therefore, the equation representing the growth of the cousin's hair is given by y = 1.2x + 5.8
</span>
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Answer:
So on this case the 95% confidence interval would be given by (0.2789;3.055)
The 95% confidence interval to judge whether the two indeners result in different measurements is?
Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.
Step-by-step explanation:
We have the following dataset:
specimen 1 2 3 4 5 6 7 8 9
Steel Ball 51 57 61 70 68 54 65 51 53
Diamond 53 55 63 74 69 56 68 51 56
If we calculate the differences diamond-steel ball we have this datase:
d: 2, -2, 2, 4, 1, 2, 3, 0, 3
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
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".
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that
.
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (0.2789;3.055)
The 95% confidence interval to judge whether the two indeners result in different measurements is?
Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.
<u>Given</u>:
The length of the segment of the chord DB is 8.2 units.
The length of the segment AB is 6.9 units.
The length of the radius AC be x units.
We need to determine the value of x.
<u>Length of BC:</u>
Since, we know the property that, "if a radius is perpendicular to the chord, then it bisects the chord".
Thus, applying the above property, we have;
DB ≅ BC
8.2 = BC
Thus, the length of BC is 8.2 units.
<u>Value of x:</u>
Since, ∠B makes 90°, let us apply the Pythagorean theorem to determine the value of x.
Thus, we have;
Substituting the values, we have;
Thus, the value of x is 10.7 units.
Hence, Option A is the correct answer.
