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Studentka2010 [4]
3 years ago
14

In a recent​ poll, 44​% of survey respondents said​ that, if they only had one​ child, they would prefer the child to be a boy.

Suppose you conducted a survey of 150 randomly selected students on your campus and find that 71 of them would prefer a boy.
​(a) Use the normal approximation to the binomial to approximate the probability​ that, in a random sample of 150 ​students, at least 71 would prefer a​ boy, assuming the true percentage is 44​%.
​(b) Does this result contradict the​ poll? Explain.
Mathematics
1 answer:
viva [34]3 years ago
5 0

Answer:

a) The probability that 71 of 150 will prefer boy child is 71/150 or 0.47

b) The result contradicts the poll actual percentage is 47.33% which is 3.33% more than the poll predicted

Step-by-step explanation:

If 71 out of 150 prefer boy child

The probability that the 71 will prefer boy child is

= 71/150

The actual percentage is

(71/150)*100%

= 47.33%

This contradicts the poll as this is more than the poll predicted. That means Less than 71 of 150 actually preferred boy child.

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a (1,4) b (-1,2) c (5,-2) are the vertices of triangle abc find the sum of coordinates of the point where the right bisector of
zmey [24]

Answer:

3.

Step-by-step explanation:

Find the midpoint of BC:

midpoint = (-1+5)/2, (2-2)/2 = (2, 0).

The slope of BC = (2 - -2) / (-1-5) = -2/3.

Find the equation of the right bisector of BC:

The slope = -1 / -2/3 = 3/2.

y-y1 = m(x-x1)

y - 0 = 3/2(x - 2)

y = 3/2x - 3.

Now find the equation of the median through C:

The midpoint of AB = (1 - 1)/2, (4+2)/2

= (0, 3).

The equation of the median:

The slope = (-2-3) / (5-0)

= -1.

The equation is:

y - 3 = -1(x - 0)

y -3 = -x.

Now we find the point of intersection by solving the 2 equations:

y - 3 = -x

y = 3/2x - 3

y = -x + 3

So:

3/2x - 3 = -x + 3

3/2x + x = 6

5/2 x = 6

x = 12/5.

y =  -12/5 + 3

= -12/5 + 15/5

= 3/5.

The sum of the coordinates = 12/5 + 3 /5

= 15/5

= 3.

3 0
3 years ago
Can help me complete this problem please :c
FrozenT [24]

Answer:

112.5 deg

Step-by-step explanation:

First we find the area of the entire circle.

A = pi * r^2

A = pi * (4 m)^2

A = 16pi m^2

The entire circle has area = 16pi m^2.

The sector has area 5pi m^2.

Now we find the fraction the area of the sector is of the entire circle.

fraction = (5pi m^2)/(16pi m^2) = 5/16 = 0.3125

The full circle has a central angle of 360 deg, the entire circle.

The measure of the central angle of the arc of the sector is the same fraction of the entire circle.

measure of sector angle = 0.3125 * 360 deg = 112.5 deg

4 0
3 years ago
Read 2 more answers
You are designing a miniature golf course and need to calculate the surface area and volume of many of the objects that will be
laiz [17]
a. To solve the first part, we are going to use the formula for the surface area of a sphere: A=4 \pi r^2
where
A is the surface area of the sphere
r is the radius of the sphere
We know from our problem that r=5ft; so lets replace that value in our formula:
A=4 \pi (5ft)^2
A=314.16ft^2

To solve the second part, we are going to use the formula for the volume of a sphere: V= \frac{4}{3}  \pi r^3
Where
V is the volume of the sphere
r is the radius 
We know form our problem that r=5ft, so lets replace that in our formula:
V= \frac{4}{3}  \pi (5ft)^3
V=523.6ft^3

We can conclude that the surface area of the sphere is 314.16 square feet and its volume is 523.6 cubic feet.

b. To solve the first part, we are going to use the formula for the surface area of a square pyramid: A=a^2+2a \sqrt{ \frac{a^2}{4} +h^2}
where
A is the surface area
a is the measure of the base
h is the height of the pyramid 
We know form our problem that a=8ft and h=12ft, so lets replace those value sin our formula:
A=(8ft)^2+2(8ft) \sqrt{ \frac{(8ft)^2}{4} +(12ft)^2}
A=266.39ft^2

To solve the second part, we are going to use the formula for the volume of a square pyramid: V=a^2 \frac{h}{3}
where
V is the volume 
a is the measure of the base
h is the height of the pyramid
We know form our problem that a=8ft and h=12ft, so lets replace those value sin our formula:
V=(8ft)^2 \frac{(12ft)}{3}
V=256ft^3

We can conclude that the surface area of our pyramid is 266.39 square feet and its volume is 256 cubic feet.

c. To solve the first part, we are going to use the formula for the surface area of a circular cone: A= \pi r(r+ \sqrt{h^2+r^2}
where
A is the surface area
r is the radius of the circular base
h is the height of the cone
We know form our problem that r=5ft and h=8ft, so lets replace those values in our formula:
A= \pi (5ft)[(5ft)+ \sqrt{(8ft)^2+(5ft)^2}]
A=226.73ft^2

To solve the second part, we are going to use the formula for the volume os a circular cone: V= \pi r^2 \frac{h}{3}
where
V is the volume
r is the radius of the circular base
h is the height of the cone 
We know form our problem that r=5ft and h=8ft, so lets replace those values in our formula:
V= \pi (5ft)^2 \frac{(8ft)}{3}
V=209.44ft^3

We can conclude that the surface area of our cone is 226.73 square feet and its surface area is 209.44 cubic feet.

d. To solve the first part, we are going to use the formula for the surface area of a rectangular prism: A=2(wl+hl+hw)
where
A is the surface area
w is the width
l is the length 
h is the height
We know from our problem that w=6ft, l=10ft, and h=16ft, so lets replace those values in our formula:
A=2[(6ft)(10ft)+(16ft)(10ft)+(16ft)(6ft)]
A=632ft^2

To solve the second part, we are going to use the formula for the volume of a rectangular prism: V=whl
where
V is the volume 
w is the width
l is the length 
h is the height
We know from our problem that w=6ft, l=10ft, and h=16ft, so lets replace those values in our formula:
V=(6ft)(16ft)(10ft)
V=960ft^3

We can conclude that the surface area of our solid is 632 square feet and its volume is 960 cubic feet.

e.  Remember that a face of a polygon is a side of polygon.
    - A sphere has no faces.
    - A square pyramid has 5 faces.
    - A cone has 1 face.
    - A rectangular prism has 6 faces.
Total faces: 5 + 1 + 6 = 12 faces

<span>We can conclude that there are 12 faces in on the four geometric shapes on the holes.
</span>
f. Remember that an edge is a line segment on the boundary of the polygon.
   - A sphere has no edges.
   - A cone has no edges.
   - A rectangular pyramid has 8 edges.
   - A rectangular prism has 12 edges.
Total edges: 8 + 20 = 20 edges

Since we have 20 edges in total, we can conclude that your boss will need 20 brackets on the four shapes.

g. Remember that the vertices are the corner points of a polygon.
   - A sphere has no vertices.
   - A cone has no vertices.
   - A rectangular pyramid has 5 vertices.
   - A rectangular prism has 8 vertices.
Total vertices: 5 + 8 = 13 vertices

We can conclude that there are 0 vertices for the sphere and the cone; there are 5 vertices for the pyramid, and there are are 8 vertices for the solid (rectangular prism). We can also conclude that your boss will need 13 brackets for the vertices of the four figures.

7 0
3 years ago
CAN SOMEBODY HELP. Unscramble the words to correctly to state a fact.
qaws [65]

Answer:

Cells create usable energy through Cellular Respiration.

Step-by-step explanation:

If you think about it, cellular respiration is the way cells make their food, or usable energy. Therefore, the answer would be up above-------------------------^^

5 0
3 years ago
5TH GRADE LEVEL QUESTION: look at photo and answer.
k0ka [10]

Answer 11/20

Step-by-step explanation:

6 0
3 years ago
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