Help 15 points!!!!!!!!!!!!!!!!!!!!!
1 answer:
Answer:
see explanation
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan A = =
=
, then
∠ A = (
) ≈ 41° ( to the nearest degree )
The sum of the angles in the triangle = 180° , then
∠ B + 41° + 90° = 180°
∠ B + 131° = 180° ( subtract 131° from both sides )
∠ B = 49°
Using Pythagoras' identity in the right triangle
AB² = BC² + AC² = 7² + 8² = 49 + 64 = 113 ( take square root of both sides )
AB = ≈ 10.6 ( to the nearest tenth )
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Answer:
<em>n = 6 </em>
Step-by-step explanation:
2.3 × = (1 × 10³)(2.3 ×
)
(1 × 10³)(2.3 × ) = (1)(2.3) × (10³)(
) = 2.3 ×
2.3 × = 2.3 ×
⇒ 3 + n = 9 ⇒ <em>n = 6</em>
The equation of the line in point-slope form is given by:
Where,
(xo, yo): point that belongs to the line
m: slope of the line
The slope is given by:
Substituting values:
Rewriting:
Now we choose an ordered pair:
Substituting values we have:
We now rewrite the equation in its standard form:
Where,
b: cut with the y axis.
We have then:
Answer:
point-slope form:
or
standard form
Where,
(xo, yo): point that belongs to the line
m: slope of the line
The slope is given by:
Substituting values:
Rewriting:
Now we choose an ordered pair:
Substituting values we have:
We now rewrite the equation in its standard form:
Where,
b: cut with the y axis.
We have then:
Answer:
point-slope form:
or
standard form
Answer:
So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.
Step-by-step explanation:
Previous concepts
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 population proportion have the following distribution
Solution to the problem
The margin of error for the proportion interval is given by this formula:
(a)
If solve n from equation (a) we got:
(b)
The margin of error desired for this case is equivalent to 2% points
For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is
In order to find the critical value we need to take in count that we are finding the margin of error for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
Now we have all the values needed and if we replace into equation (b) we got:
So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.