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3 years ago

47 / 101 Marks

Mathematics

1 answer:

Citrus2011 [14]3 years ago

7 0

Answer:

Step-by-step explanation:

I’m assuming that A has a side of 15 cm and has a volume of 400 cm.

Using our volume formula:

(15/10)^3 = (400/x)

(3/2)^3 = 400/x <— simplify

27/8 = 400/x

27x = 3200

so the volume of B is 3200/27 or about 118.52cm^3

(if I assumed the wrong side lengths please tell me!)

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PLEASE HELP I NEED THIS ASAP ! 100 POINTS!!

Finger [1]

Answer:

Part A: The population are the American adult citizens, excluding the ones from Alaska and Hawaii. The population is the people which the sample is trying to represent, as a hole.

The sample is a portion of this population, and in this case is represented by a randomly selected amount of people whose response to the interview has been selected.

Part B: The sample here has been selected in two steps. The first step is the one that we must pay attention to: the numbered list of one million responses from around the US (excluding Alaska and Hawaii). Because these responses were obtained by an online survey, the sample looks like a convenience sampling, as it depends on the availability and willingness from participants to take part of the study (is not compulsory for everyone, so not everyone is going to response, then there are people that is not going to be represented by). The second step is the random selection of a part of the previous responses. This last part will ensure that, the individuals that took part of the group that was interviewed, are well represented in the results.

Part C: As it was mentioned, there is a selection bias, because the information from the sample comes from a specific group of people that has certain features that may not represent all American adults citizens. For example, the opinion of those people who do not use internet, will not be considered (and they may be a large number of persons). This situations weaken the conclusions obtained in the study, as they are not representative of the hole population.

Step-by-step explanation:

6 0

2 years ago

When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100

ser-zykov [4K]

Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the future value FV.

In order to see the rule of formation, let's see the value (in $) for the first few years

End of year 0

1,000

End of year 1(capital + interest + new deposit)

1,000*(1.09)+10

End of year 2 (capital + interest + new deposit)

(1,000*(1.09)+10)*1.09 +10 =

$\bf 1,000*(1.09)^2+10(1+1.09)$

End of year 3 (capital + interest + new deposit)

$\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)$

and we can see that at the end of year 50, the future value is

$\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}$

The sum

$\bf 1+1.09+(1.09)^2+...+(1.09)^{49}$

is the sum of a geometric sequence with common ratio 1.09 and is equal to

$\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356$

and the future value is then

$\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564$

The present value PV is

$\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62$

rounded to the nearest hundredth.

5 0

3 years ago

Consider the equation r = 5 sin(theta). Use the drop-down boxes to complete the sentences.

Alecsey [184]

9514 1404 393

Answer:

circle
y-axis
5 units

Step-by-step explanation:

It can be helpful to actually see the graph. For 0 ≤ θ ≤ π, a circle is developed above the x-axis, symmetrical about the y-axis (θ=π/2). For π ≤ θ ≤ 2π, the same circle is traced again in the same direction (CCW), as values of r are negative for those angles.

The circle has a radius of 2.5, centered at (0, 2.5), so the diameter is 5 units. The length of the diameter is the farthest distance between any two points on a circle.

8 0

3 years ago

Please help me w this an explain how you got it!.

pishuonlain [190]

Answer:

Vertex → (2, 4)

Step-by-step explanation:

Quadratic equation has been given as,

y = -x² + 4x

We rewrite this equation in the form of a function as,

f(x) = - x² + 4x

By comparing this equation with the standard quadratic equation,

y = ax² + bx + c

a = -1 and b = 4

Vertex of the parabola represented by this equation is given by $[-\frac{b}{2a}, f(\frac{-b}{2a})]$

x coordinate = $-\frac{4}{2(-1)}$

= 2

y-coordinate = f(2)

= - (2)² + 4(2)

= -4 + 8

= 4

Therefore, vertex of the given function is (2, 4)

6 0

2 years ago

Antonia is saving for a video game. On the first day, she saves two dollars in her piggy bank. Each day after that, she doubles

ehidna [41]

Answer:

64 dollars

Step-by-step explanation:

1st day= $2

2nd day= $4

3rd day= $8

4th day= $16

5th day= $32

6th day= $64

5 0

2 years ago

Read 2 more answers