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storchak [24]
3 years ago
5

01:49:1

Mathematics
1 answer:
Keith_Richards [23]3 years ago
6 0

Answer:

The correct option is C:

C) The representative sample contained more girls than boys.

Step-by-step explanation:

It is given that a random sample is chosen from a total students of 160 students. The sample can be of 10,15 or any small numbers of students as compared to 160. However, a sample cannot be of 160 students as it is defined as a population in this case.

A random sample is always unbiased. Which means that the sample chosen should have around the same proportion of girls to boys as it is in the population of 160.

We know that:

Total boys in 160 = 65

Total girls in 160 = 95

Proportion of girls to boys = 95/65 = 1.462

Which means that for every 1 boy, there are 1.462 of girls.

The same ratio is held in a random sample, hence the total number of girls will be greater than boys

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An airplane flies with a constant speed of 620 miles per hour. How long will it take to
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Answer:

30 minutes

Step-by-step explanation:

Alright lets start by laying out what the problem gives us :

A plane flies 620 mph.

It is asking how long it will take to travel 310 miles.

We need to give our answer in minutes or hours.

So lets take mph and look at the full meaning "Miles per hour"

An hour has 60 minutes in it.

So really it is saying miles per 60 minutes as well as miles per hour

So you could say the plane is traveling 620 miles every 60 minutes.

So now lets look at the number 310.

Just looking at it I can tell you that 310 looks very close to half of 620, in fact it is exactly half!

So lets divide the 620 mph by the 310 miles it is asking and we get 2! Proving that 310 is half of 620.

Alright now lets divide both the number of miles and number of minutes :

620 miles per 60 minutes

divided by 2 both miles and minutes

310 miles per 30 minutes

So this is your answer. After this you get that it would take 30 minutes to travel 310 miles in a plane going 620 miles per hour!

I hope this helps and I could help you understand it. :)

If you have any questions feel free to comment or dm me.

7 0
2 years ago
(1 point) If p(x) and (x) are arbitrary polynomials of degree at most 2, then the mapping =p(-1)q(-1) + p(070) +p(3)q(3) defines
Ainat [17]

If p(x) and q(x) are arbitrary polynomials of degree at most 2 then

||p||||q|| = 26(\sqrt{640}) and angle between p(x) and q(x) is 0.233.

Given that

<p,q> = p(-1)q(-1) + p(0) q(0) + p(3)q(3)

and p(x) = 2x²+ 6 , q(x)= 4x²-4x

then the values of p and q at x = -1,0,3 are given as;

x = -1,

p(-1) = 2(-1)² + 6 = 8   ,    q(-1) = 4(-1)² - 4(-1) = 8

x = 0,

p(0) = 2(0)² + 6 = 6   ,    q(0) = 4(0)² - 4(0) = 0

x = 3,

p(3) = 2(3)² + 6 = 24  ,  q(3) = 4(3)²- 4(3) = 24.

<p,q> = p(-1)q(-1) + p(0)q(0) + p(3)q(3)

         = (8)(8) + (6)(0) + 24(24)

         = 64 + 0 + 576

<p,q> = 640

Now we have to find ||p|| ||q||, for this we'll find ||p|| and ||q||

||p|| = \sqrt{ < p,p > }

     = \sqrt{8(8) + 6(6) + 24(24)}

     = \sqrt{676}

||p|| = 26

and

||q|| = \sqrt{ < q,q > }

      =\sqrt{8(8) + 0(0) + 24(24)}

||q||  =\sqrt{640}

∴||p||||q|| = 26(\sqrt{640\\)

Now we have to find angle between p(x) and q(x),

∴ α = cos⁻¹\frac{ < p,q > }{||p||||q||}

      = cos ⁻¹ \frac{640}{26(\sqrt{640}) }

      = cos ⁻¹ \frac{4\sqrt{10} }{13}

  α  = 13.34°

In radian

α = 0.233.

To know more about Inner product here

brainly.com/question/14185022

#SPJ4

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