Ask question

Ask question

All categories

2 years ago

3

Consider the diagram and proof by contradiction. Given: △ABC with AB ≅ AC Since it is given that AB ≅ AC, it must also be true t

hat AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that ________.

2 answers:

olasank [31]2 years ago

7 0

Answer:

The conclusion is ∠B and ∠C are congruent.

Step-by-step explanation:

Given a △ABC with AB ≅ AC

Since AB ≅ AC implies AB=AC.

Now as given assumption ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other and if

m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem.

and if m∠B < m∠C, then AC < AB by the same reason.

As we know if in a triangle two sides are equal then the triangle becomes an isosceles triangle

Since triangle is isosceles then the angles opposite to equal sides are equal i.e

if AB=AC then ∠B = ∠C in △ABC

which is contradiction to the assumption that ∠B and ∠C are not congruent.

Therefore, it can be concluded that

∠B and ∠C are congruent.

miss Akunina [59]2 years ago

4 0

Answer:

∠B and ∠C

Step-by-step explanation:

You might be interested in

Refer to table 28-6. what is the u-2 measure of labor underutilization?

mafiozo [28]

Bvgdgmhmgjm,jh,,,,,,,,,,,,,,,,,

4 0

2 years ago

The average weight of a chicken egg is 2.25 ounces with a standard deviation of 0.2 ounces. You take a random sample of a dozen

n200080 [17]

Answer:

$P(\bar X$

$P(\bar X$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sigma)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

On this case $\bar X \sim N(2.25,\frac{0.2}{\sqrt{12}})$

Solution to the problem

We want this probability:

$P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X$

$P(\bar X$

5 0

2 years ago

A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st

maxonik [38]

Answer:

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

$p_v =2*P(z>1.413)=0.158$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance

Step-by-step explanation:

Data given and notation

$\bar X=5.0611$ represent the sample mean

$\sigma=0.2803$ represent the population standard deviation for the sample

$n=42$ sample size

$\mu_o =5$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ 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 true mean is different from 5, the system of hypothesis would be:

Null hypothesis: $\mu = 5$

Alternative hypothesis: $\mu \neq 5$

If we analyze the size for the sample is > 30 but and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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:

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(z>1.413)=0.158$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance

8 0

2 years ago

Please help me with this question

natulia [17]

what's up

Seek understand, to be understood!

To get the answer we need the formula or source.

The question in another way if 4cm=1.2km, what is the 10cm=--------

first, you have to use the crisscross.

4cm=1.2km

10cm= x it is variable

then, 4xx= 1.2kmx10cm

4x=12km

4x/4= 12/4

x=3km

4 0

2 years ago

The manager suggests that Darryl should purchase the deli’s bread from Store D because they sell the most loaves of bread for th

stealth61 [152]

Answer:

yes

Step-by-step explanation:

because it sells the best price

5 0

2 years ago

Read 2 more answers