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2 years ago

The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:

Mathematics

1 answer:

ratelena [41]2 years ago

8 0

Answer:∠JML ≅ ∠QJM

Alternate Interior Angles Theorem

Step-by-step explanation:

Here, Given: JKML is a parallelogram,

That is, JK ║ ML and JM ║ KL

Prove: ∠ MLK ≅ ∠ KJM and ∠ JML ≅ ∠ LKJ

Extend segment JM beyond point and draw point P (Construction)

∠ MLK ≅ ∠ PML ( Alternate Interior Angles Theorem)

∠ PML ≅ ∠KJM ( Corresponding Angles Theorem )

⇒ ∠ MLK ≅ ∠ KJM ( By transitive property of equality )

Extend segment JK beyond point J and draw point Q, by Construction.

∠JML ≅ ∠QJM ( Alternate Interior Angles Theorem)

∠ QJM ≅ ∠ LKJ ( Corresponding Angles Theorem )

⇒ ∠JML ≅ ∠ LKJ ( By transitive property of equality )

Thus, the opposite angles of parallelogram JKLM are congruent.

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1 year ago

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g A modal class in a histogram is the class that includes a. the largest number of observations. b. the smallest observation in

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Answer:

a. the largest number of observations.

Step-by-step explanation:

The mode is the variable in a data that has the highest frequency. Which implies that it occurs more than other variables.

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2 years ago

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Alex17521 [72]

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

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And we can find this probability using the complement rule, the normal standard table or excel and we got:

$P(z>0.686)=1- P(Z$

c) $P(46.8-1.5*1.75$

And we can find this probability with this difference:

$P(-1.5$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.5$

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".

Part a

Let X the random variable that represent the velocities of a population, and for this case we know the distribution for X is given by:

$X \sim N(46.8,1.75)$

Where $\mu=46.8$ and $\sigma=1.75$

We are interested on this probability

$P(X$

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

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

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

$P(X$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

Part b

$P(X>48)=P(\frac{X-\mu}{\sigma}>\frac{48-\mu}{\sigma})=P(Z>\frac{48-46.8}{1.75})=P(z>0.686)$

And we can find this probability using the complement rule, the normal standard table or excel and we got:

$P(z>0.686)=1- P(Z$

Part c

$P(46.8-1.5*1.75$

And we can find this probability with this difference:

$P(-1.5$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.5$

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2 years ago

What values of b satisfy 3(2b + 3)2 = 36?

meriva

What values of b satisfy 3(2b+3)^2 = 36

we have
3(2b+3)^2 = 36
Divide both sides by 3
(2b+3)^2 = 12
take the square root of both sides
( 2b+3)} =(+ /-) \sqrt{12} \\ 2b=(+ /-) \sqrt{12}-3

b1=\frac{\sqrt{12}}{2} -\frac{3}{2}
b1=\sqrt{3} -\frac{3}{2}

b2=\frac{-\sqrt{12}}{2} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}
therefore

the answer is
the values of b are
b1=\sqrt{3} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}

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Answer:

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