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AnnyKZ [126]
2 years ago
7

A school has 2000 students a survey finds that 36 students out of a random sample of 80 student's are bilingual the margin of er

ror for the survey is +4% find the interval in which the total number of bih Guam students is most likely to lie
Mathematics
1 answer:
SVETLANKA909090 [29]2 years ago
5 0

Answer:

(820 ; 980)

Step-by-step explanation:

Given :

Sample size, n = 80

Number of bilingual from sample = 36

Sample proportion, phat = x / n = 36 / 80 = 0.45

Margin of Error = 4% = 0.04

Interval = sample proportion ± margin of error

0.45 ± 0.04

(0.41 ; 0.49)

(0.41 * 2000 ; 0.49 * 2000)

(820 ; 980)

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3000 %

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-4n - 5

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Which number below best represents a depth of two meters below the ground?
Slav-nsk [51]

Answer:

-2

Step-by-step explanation:

We usually start measuring the height from the ground, so basically the positive direction is above the ground, for example  2 is the best number which represents 2m above the ground.

So the negative sign represents the depth below the ground.

7 0
1 year ago
Robert has available 400 yards of fencing and wishes to enclose a rectangular area. Express the areaAof the rectangle as a funct
solong [7]

Answer:

The answer is below

Step-by-step explanation:

a)Given that the length of fencing available is 400 yards. This means that the perimeter of the rectangle is 400 yards.

the perimeter of a rectangle is given as:

Perimeter = 2(length + width) = 2(l + w)

Hence;

400 = 2(l + w)

200 = l + w

l = 200 - w

The area of a rectangle is given as:

Area = length × width

Area = (200 - w) × w

Area = 200w - w²

b) For a quadratic equation y = ax² + bx + c. it has a maximum at x = -b/2a

Hence, for the area = 200w - w² a=-1, b = 200, the maximum width is at:

w = -b/2a = -200/2(-1) = -200/-2 = 100

A width of 100 yard has the largest area

c) l = 200 - w = 200 - 100 = 100 yards

Area = l × w = 100 × 100 = 10000 yd²

The maximum area is 10000 yd²

7 0
3 years ago
Polygons ABDC and A′B′D′C′ are shown on the following coordinate grid:
weeeeeb [17]

Answer: A

Step-by-step explanation:

Let's first review how turning about the origin changes a point's coordinates:

After rotating and translating some points, one can see the following pattern:

  • 180° Rotation: (x,y) -> (-x,-y)
  • 90° Clockwise Rotation: (x,y) -> (y, -x)
  • 90° Counter-clockwise Rotation: (x,y) -> (-y, x)
  • Translation <em>a</em> units to the left: (x, y) -> (x-a, y)

Using these patterns will make it much easier to find the correct series of transformations than graphing each one.

A: A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

Using the patterns found above, this set of transformations would make (x,y) move first to (-y, x), then (-y-1, x).

  • A(2,-2) -> A'(1,2)
  • B(4,-2) -> B'(1,4)
  • D(5,-3) -> D'(2,5)
  • C(1,-3) -> C'(2,1)

B: A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin

This would make (x,y) move first to (x-1,y), then to (-y, x-1)

  • A(2,-2) -> A'(2, 1)
  • B(4,-2) -> B'(2,3)
  • D(5,-3) -> D'(3,4)
  • C(1,-3) -> C'(3,0)

C: A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

This would make (x,y) move first to (y, -x), then (y-1, -x)

  • A(2,-2) -> A'(-3, -2)
  • B(4,-2) -> B'(-3,-4)
  • D(5,-3) -> D'(-4, -5)
  • C(1,-3) -> C'(-4, -1)

D: A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin

This would make (x,y) move first to (x-1,y), then (y, -x+1)

  • A(2,-2) -> A'(-2, -1)
  • B(4,-2) -> B'(-2, -3)
  • D(5,-3) -> D'(-3, -4)
  • C(1,-3) -> C'(-3, 0)

Therefore, the answer is A, as only it correctly matches to polygon A'B'D'C'.

5 0
2 years ago
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