Answer:
Step-by-step explanation:
Recall the mnemonics SOH CAH TOA.
SOH means the Sine ratio is Opposite over Hypotenuse.
This implies that;
The side opposite to angle A is 4cm and the hypotenuse is 5cm.
Which choice is NOT a way to find 7 ÷ 3? A- 1/3 of 7 B- 7 × 1/3 C- 1/7 of 3 D- 7/3
2 answers:
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Answer:
a) Null and alternative hypothesis
b) Test statistic t=-1.565
P-value = 0.0612
NOTE: the sample size is n=65.
c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
d) Null and alternative hypothesis
Test statistic t=-1.565
Critical value tc=-1.669
t>tc --> Do not reject H0
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=65.
The sample mean is M=30.15.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
<u>Critical value approach</u>
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At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.
As the test statistic is greater than the critical value, it falls in the acceptance region.
The null hypothesis failed to be rejected.
Therefore the point P is at 3.46 cm from O and it lies on the angle bisector of ∠XOY
<h3>What is an Angle Bisector ?</h3>The ray that bisects the angle into half is called Angle Bisector.
It is given that ∠XOY = 60 degree
the length of OX = 4.5 cm
OY =5 cm
The point M is on OX such that
OM = 2 MX
so The M is at 3 cm from O
The point P lies in the acute angle such that the distance between point P and OX and OY is always same and at 3 cm from M
According to the angle bisector theorem converse states that if a point is in the interior of an angle and is at equal distance from the sides then it lies on the bisector of that angle.
As it can be seen from the image that a point equidistant from the rays , at 3 cm from M will be at
By Pythagoras Theorem
3² +3² = OP²
OP = 2 = 3.46 cm from O
To know more about Angle Bisector
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