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4 years ago

How can a regular hexagon be folded to show that it has reflections symmetry

2 answers:

6 0

It can be folded by the up covering the down, it can be folded by the left or the right covering one another, you can even do it diagonally. Any angle of the hexagon covering the one on the opposite side will show reflections symmetry.

evablogger [386]4 years ago

3 0

You have to fold it straight in half.

You might be interested in

The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard

PtichkaEL [24]

Answer:

a) $X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

b) $P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

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

$P(Z>1.5)=1-P(Z$

c) $P(X$

$P(Z$

d) $P(60$

$P(-0.167$

e) IQR = 75.13-50.87=24.26

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 amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

$X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

Part b

We are interested on this probability

$P(X>90)$

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:

$P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

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

$P(Z>1.5)=1-P(Z$

Part c

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:

$P(Z$

Part d

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

$P(60$

And we can find this probability with this difference:

$P(-0.167$

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

$P(-0.167$

Part e

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.75$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.674$

And if we solve for a we got

$a=63 -0.674*18=50.87$

So the value of height that separates the bottom 25% of data from the top 75% is 50.87.

Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674

$z=0.674$

And if we solve for a we got

$a=63 +0.674*18=75.13$

And then the IQR = 75.13-50.87=24.26

3 0

3 years ago

Find the integral of √(x² +4) W.R.T x

Allushta [10]

Answer:

$\frac{x}{2} *\sqrt{x^{2} +4}$ + $\frac{1}{2}$ *LN(| $\frac{x+\sqrt{x^{2} +4} }{2}$ |) +C

Step-by-step explanation:

we will have to do a trig sub for this

use x=a*tanθ for sqrt(x^2 +a^2) where a=2

x=2tanθ, dx= 2 sec^2 (θ) dθ

this turns $\int\limits {\sqrt{x^{2}+4 } } \, dx$ into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ

the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1

then it simplifies into integral(4*sec^3 (θ)) dθ

you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C

then you will need to rework your functions of θ back into functions of x

tanθ will resolve back into $\frac{x}{2}$ (see substitutions) while secθ will resolve into $\frac{\sqrt{x^{2} +4} }{2}$

sec(θ)= $\frac{\sqrt{x^{2} +4} }{2}$ is from its ratio identity of hyp/adj where the hyp. is $\sqrt{x^{2} +4}$ and adj is 2 (see tan(θ) ratio)

after resolving back into functions of x, substitute ratios for trig functions:

= $\frac{x}{2} *\sqrt{x^{2} +4}$ + $\frac{1}{2}$ *LN(| $\frac{x+\sqrt{x^{2} +4} }{2}$ |) +C

3 0

3 years ago

I am greater than 54 fewer tens than 90?

Lubov Fominskaja [6]

In all cases, we will let x represent the number.
1) 54 tens = 540
90 - 540 = -450
x > -450

2) x < 36 and x > 24
24 < x < 36

3) 8 tens and 5 ones = 80 + 5 = 85
x > 85

4) x > 27
x < 33
And the value in the ones place is less than the value in the tens place, so
30 ≤ x ≤ 32

6 0

3 years ago

Of the clients at Hunter's salon, 27 clients have red hair and 57 clients have hair in other colors.What is the probability that

sleet_krkn [62]

Answer: 27/84

simplified answer: 9/28

5 0

3 years ago

0.000387 in scientific notation

jasenka [17]

Answer:

0.000387 = 3.87 × 10^-4

8 0

3 years ago