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3 years ago

Look at the picture below

Mathematics

2 answers:

Lelu [443]3 years ago

7 0

Answer: Phillip is correct. The triangles are not congruent.

How do we know this? Because triangle ABC has the 15 inch side between the two angles 50 and 60 degrees. The other triangle must have the same set up (just with different letters XYZ). This isn't the case. The 15 inch side for triangle XYZ is between the 50 and 70 degree angle.

This mismatch means we cannot use the "S" in the ASA or AAS simply because we don't have a proper corresponding pair of sides. If we knew AB, BC, XZ or YZ, then we might be able to use ASA or AAS.

At this point, there isn't enough information. So that means John and Mary are incorrect, leaving Phillip to be correct by default.

Note: Phillip may be wrong and the triangles could be congruent, but again, we don't have enough info. If there was an answer choice simply saying "there isn't enough info to say either if the triangles are congruent or not", then this would be the best answer. Unfortunately, it looks like this answer is missing. So what I bolded above is the next best thing.

spayn [35]3 years ago

4 0

Answer:

Phillip states that the triangles are not congruent.

Step-by-step explanation:

Assume for a second the triangles are congruent.

Then the angles are equal

<A =< X

<B= <Y

<C = <Z

Then

Triangle ABC = Triangle XYZ

from this information

AB = XY

and BC = YZ

and CA = ZX

but the only other piece of information we have is CA = 15 and XY = 15

If this is true then CA = ZX = 15 and AB = XY = 15

That would make this an isosceles triangle (AB = AC)

so angles B and C would have to be equal, but they are not.

So these two triangles cannot be congruent.

You might be interested in

Simplify 7.2x10^3/1.8x10^7

spayn [35]

To simplify and solve this equation we must follow PEMDAS.

P=Parentheses

E=Exponents

M=Multiplication (from left to right)

D=Division (from left to right)

A=Addition

S=Substraction

We begin the process.

10^3=1000

10^7=10000000

New equation looks like this:

7.2*1000/1.8*10000000

We then multiply

7.2*1000= 7200

7200/1.8=4000

4000*10000000= 40000000000

So our final answer is 40000000000.

Hope this helps!

P.S. I forgot this was scientific notation and I solved it a different way. But both ways give the same answer. Let me know if you want the other method.

3 0

3 years ago

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

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". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$