State the slope and y-intercept of the graph y = 3x - 10.
1 answer:
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The relationship between the lengths of the sides of a right triangle are
given by Pythagoras theorem.
- Part A: <u>ΔABC is similar to ΔADC</u>
- Part B: ΔABC and ΔADC are similar according <u>AA similarity postulate</u>
- Part C: <u>DA = 6</u>
Reasons:
Part A:
∠A = 90°
Segment AD ⊥ Segment BC
Location of point D = Side BC
Part A: In triangle ΔABC, we have;
∠A = 90°, ∠B = 90° - ∠C
In triangle ΔADC, we have;
∠ADC = 90°, ∠DAC = 90° - ∠C
∴ <u>ΔABC is similar to ΔADC</u> by Angle-Angle, AA, Similarity Postulate
Part B: The triangles are similar according to <u>AA similarity postulate</u>,
because two angles in one triangle are equal to two angles in the other
triangle and therefore, by subtraction property of equality, the third angle
in both triangles are also equal.
Part C: The length of DB = 9
The length of DC = 4
Required: Length of segment DA
In triangle ΔABD, we have;
∠BDA = 90°= ∠ADC
∠DAC ≅ ∠B by Congruent Parts of Congruent Triangles are Congruent
Therefore;
ΔABD ~ ΔADC by AA similarity, which gives;
=
Which gives;
= 4 × 9 = 36
= √(36) = 6
<u> = 6</u>
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Answer:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is lower than 20, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0