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3 years ago

1) A regular hexagon is mapped onto itself every time it is rotated

1 answer:

5 0

A regular hexagon has angles that measure 360/6=60°, between 0° and 360°, the multiples of this angle is 120°, 180°, 240°, 300°. Thus when the hexagon is rotated through this angles, it will be mapped onto itself. When rotated through any other angle, the same result won't be possible.
Thus we conclude that the hexagon it's mapped into itself every time it is rotated.

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2) A company used 24 lemons to make 4 bottles of lemonade. Write an equation that

boyakko [2]

Answer:

Step-by-step explanation:

4 0

3 years ago

8x-2=4+5x<br><br> Solve for x

DochEvi [55]

$8x-2=4+5x\ \ \ |add\ 2\ to\ both\ sides\\8x=6+5x\ \ \ \ |subtract\ 5x]\ from\ both\ sides\\3x=6\ \ \ \ |divide\ both\ sides\ by\ 3\\\boxed{x=2}$

4 0

3 years ago

Read 2 more answers

The surface area of the triangular prism pictured below is 204 square centimeters. What is the height of the prism?

Fudgin [204]

The picture in the attached figure

we know that
surface area=2*area of the base+perimeter*height

area of the base=area of the triangle
area of the base=3*4/2----> 6 cm²

perimeter of the base=perimeter of triangle
perimeter=3+4+5----> 12 cm
height=x cm

surface area=2*6+12*x
surface area=204 cm²
12+12*x=204
12*x=204-12
12*x=192
x=192/12
x=16 cm

the answer is
16 cm

6 0

3 years ago

You went to the mall with $80. You spent 25% of your money on a pair of shorts and 65% of the remainder on sandals. How much did

swat32

25% of 80 is 20
65% of 20 is 13
Your answer is 13

4 0

3 years ago

Read 2 more answers

At Pike Place Fish Market in Seattle, customers can purchase a variety of different types of seafood. One type of seafood sold a

allsm [11]

Answer:

$z=1.28$

And if we solve for a we got

$a=3.6 +1.28*0.8=4.624$

So the value of height that separates the bottom 90% of data from the top 10% is 4.624.

So then the best answer for this case would be:

C. 4.64

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".

Solution to the problem

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

$X \sim N(3.6,0.8)$

Where $\mu=3.6$ and $\sigma=0.8$

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

$P(X>a)=0.1$ (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 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

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:

$z=1.28$

And if we solve for a we got

$a=3.6 +1.28*0.8=4.624$

So the value of height that separates the bottom 90% of data from the top 10% is 4.624.

So then the best answer for this case would be:

C. 4.64

8 0

3 years ago