Given: circle k(O) with diameter AB and CD ⊥ AB Prove: AD·CB=AC·CD
1 answer:
Answer:
Hence it is proved that AD.CB=AC.CD
Step-by-step explanation:
Given:
A circle with diameter AB and CD perpendicular to AB.
To Prove:
AD.CB=AC.CD
Solution:
Construct a circle with diameter AB and CD perpendicular AB
To get perpendicular Diameter AB ,point C must be on Y-axis with passing through center getting CD as radius of circle.
<em>(Refer the Attachment)</em>
<em>Now</em><em>,</em>
we get two triangles, as ADC and CDB
So
Side(AD)=side(BD)
CD is common side
and Angle(ADC)=angle(BDC)
<em>Using S-A-S test to triangles are similar </em>
<em>So their corresponding sides are in proportion </em>,
AD/BD=AC/BC
therefore
AD*BC=AC*BD
as BD=CD ........................... ( both are radius of the circle).
AD*BC=AC*CD
Hence it is required Proof.
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Answer:
We accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.
Step-by-step explanation:
Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit.
This means that the null hypothesis is:
The production group believes that the mean weight has changed.
This means that the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
12 is tested at the null hypothesis:
This means that
They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces.
This means, respectibely, that
Value of the test statistic:
Pvalue of the test:
We are testing if the mean is different from a value, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.42.
Looking at the z-table, z = 2.42 has a pvalue of 0.9922
1 - 0.9922 = 0.0078
2*0.0078 = 0.0156
What conclusion can we make from the appropriate hypothesis test at the .01 level of significance?
0.0156 > 0.01. This means that at the 0.01 level, we accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.