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Pie
3 years ago
9

FRQ 1

Mathematics
1 answer:
Reptile [31]3 years ago
5 0

Answer:

a) The number of visits between the patrons who buys the season passes shows higher frequency than those who did not buy season passes, in general. However, the minimum value of 1 visit is present for both cases.

b) The mean visits of the patrons are just PARAMETERS. If you want to test your hypothesis using hypothesis testing, the statistics are the z or t scores comparing the parameters (means).

c) The proportion who would have paid less are those with 2 or fewer visits because they would only just paid $82 instead of $100.

Number of patrons with 2 or fewer visits: 16

Total number of patrons who bought season passes: 30

Proportion who would've paid less = 16/30 = 0.5333

Step-by-step explanation:

I just did it

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The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
2 years ago
1. Which of these transformations are isometries? The diagrams are not drawn to scale.
lisov135 [29]

In math, an isometry is a congruent transformation in which the distance (or length) and the angle is preserved or remains the same even after the transformation.

The transformation can be translation, rotation, reflection, etc.

Let us not use this definition of isometry to answer our question, one at a time.

(I) In here, as we can see the distances 10 and 5 and the angle 43 degrees has been preserved. So, <u>this is an isometry.</u>

(II) In here, distances have been halved, so this is<u> not an isometry</u>, even though the angles have been preserved.

(III) In here, the corresponding distances and the angles have been preserved. So, <u>this is an isometry.</u>

6 0
3 years ago
What is the value of x?
Westkost [7]

Answer:

x is equal to 20 in this picture.

Step-by-step explanation:

In order to find this, we need to note that these two angles will be equal to each other. Now we can put their values equal to each other and solve for x.

3x + 50 = 6x - 10

50 = 3x - 10

60 = 3x

20 = x

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3 years ago
Which equation represents a linear function that has a slope of 5 and a y-interceptof-6?
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Answer:

y=5x-6

Step-by-step explanation:

Comparing y=5x-6 with y=mx+c,the slope is 5 and y intercept is-6

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2 years ago
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JulijaS [17]
Area of the 2 right triangles =2 (1/2 x 1.5 x 2 ) = 3 in²

Area of the 3 rectangles = (1.5 + 2 + 2.5) x 11 = 66 in²

Total Surface area = 3 + 66 = 69 in²

Answer:  69 in²
3 0
3 years ago
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