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3 years ago

Form a polynomial using numbers -4,4,2 with a degree of 3

Mathematics

1 answer:

shtirl [24]3 years ago

3 0

These three roots are sufficient to enable us to form a 3rd degree polynomial:

f(x) = (x+4)(x-4)(x-2) = (x^2 - 16)(x-2) = x^3 - 2x^2 - 16x + 32 (answer)

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Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

2 years ago

A triangle has side lengths of

Angelina_Jolie [31]

Answer:

3 is the right one

Step-by-step explanation:

Simple math you know

3 0

2 years ago

Guys, this is important!! My assignment is worth 100 points. (not the question but the assignment!) Solve this graph for me and

galben [10]

Answer:

I think it goes like this : 20:4=5 so there's five monsters in the room

Step-by-step explanation:

if that's the case of this question it should go like this:

9(rooms)×5(monsters per room)= 45 monsters

30(monsters):5(monsters per room)=6 rooms

13(rooms)×5(monsters per room)=65 monsters

35(monsters):5(monsters per room)=7 rooms

I hope you do well in your assignment.

I hope I helped at least a little!

8 0

2 years ago

What number times it self 3 times equals 729

katrin2010 [14]

729 ÷ 3 = 243
so if you do 243 × 3 = 729
so your answer will be 243

3 0

3 years ago

Only answer if u know the answer

Dmitriy789 [7]

Answer:

Angle C = 142 degrees

Step-by-step explanation:

A+B = 90

B+C = 180

Rearrange first equation to get B = 90-A

Plug this into the second equation:

90-A + C = 180

C = A + 90

Plug in A, C = 52 + 90 = 142

8 0

2 years ago