Rachel, Nancy, and Diego were in fishing competition. Rachel's fish was 7/8 foot long, Nancy's fish was 1/4 foot long, and Diego
1 answer:
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Answer:
number of successes
number of failure
The criteria are met
A
The sample proportion is
B
C
What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from the true population proportion will not more than 4.4%
Ci
D
This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%
E
Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time
F
Yes our result would support the claim because
Step-by-step explanation:
From the question we are told that
The sample size is
The sample proportion is
Generally the number of successes is mathematical represented as
substituting values
Generally the number of failure is mathematical represented as
substituting values
for approximate normality for a confidence interval criteria to be satisfied
Given that the above is true for this survey then we can say that the criteria are met
Given that the confidence level is 95% then the level of confidence is mathematically evaluated as
Next we obtain the critical value of from the normal distribution table, the value is
Generally the margin of error is mathematically represented as
substituting values
=>
What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from the true population proportion of those that are happy by more than 4.4%
The 95% confidence interval is mathematically represented as
substituting values
The upper limit of the 95% confidence interval is
The lower limit of the 95% confidence interval is
This 95% confidence interval mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit is 95%
Given that 50% of the population proportion lie with the 95% confidence interval the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time
Yes our result would support the claim because
Answer:
Given: In triangle XYZ, , XY=13x-21 , YZ=8x-6 and XZ=x+4.
If two angles are congruent if and only if, they measure the same number of degrees.
therefore, from the given condition; .
Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.
Therefore, the triangle XYZ is an isosceles triangle, as the base angle and
are equal and the sides opposite to these angles are also equal i.e, XY=YZ.
Since, we have XY=YZ ,
⇒ 13x-21 =8x-6 or
13x-8x=21-6 or
5x=15
Simplify:
x=3
Therefore, the sides of an isosceles triangle are:
XY = 13x-21 = = 39-21 = 18 unit ,
YZ = 8x-6 = = 24-6 =18 unit,
and XZ = x+4 = 3+4 =7 unit.
Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.
As W is the midpoint(i.e, it divide the sides into two equal halves),
XW=WZ = unit
Now, use the Pythagorean theorem, to find the altitude WY.
⇒
Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;
⇒
Simplify:
or
On simplify we get;
WY=17.65 unit(approx.)
The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; .
⇒
⇒ (approx) or
Therefore, the angle .
The sum of the measure of the angle in the triangle is 180 degree.
In triangle XYZ.
Since
then,
⇒
Simplify:
.
Therefore, the measure of each angle are: and
