consider the bevariate data below about Advanced Mathematics and English results for a 2015 examination scored by 14 students in a particular school.The raw score of the examination was out of 100 marks.
Questions:
a)Draw a scatter graph
b)Draw a line of Best Fit
c)Predict the Advance Mathematics mark of a student who scores 30 of of 100 in English.
d)calculate the correlation using the Pearson's Correlation Coefficient Formula
e) Determine the strength of the correlation

​

Answer:

(a) (C U D) = {k, m, y, z}

(b) C ∩ D = {z}

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Answer:

Step-by-step explanation:

If Charles is 22 years older, he will be double Danielle's age when she is 22. If that is 10 years from now, Danielle is 12 and Charles is 34.

Answer:

10

Step-by-step explanation:

these are small bags (just as comment), so in real life the cost of using bags would add significantly to the price of the apples.

anyway, so we need to find how many units of 3/5 pounds do we need to get 6 pounds ?

3/5 × x = 6

3 × x = 30

x = 10

she buys 10 bags to get 6 pounds.

Answer:

2 13/15 miles

Step-by-step explanation:

Hey there!

Well first we need to find the distance between Lancaster and Hillsdale and Lancaster to Silvergrove.

9 + 7 13/15

= 16 13/15

LS is just 14 miles.

Now we can do,

16 13/15 - 14

= 2 13/15 miles

Hope this helps :)

Answer:

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

Step-by-step explanation:

Given

Range: = 1 to 100 (Inclusive)

Required

Determine the notation that represents the perfect square in the given range

Represent the range with P

P = 1 to 100

Such that the perfect squares will be P² and integers

In set notation, integers are represented with Z

The set notation becomes

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

The [tex]\leq[/tex] shows that 1 and 100 are inclusive of the set

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Take

[tex]u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x[/tex]

[tex]\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3[/tex]

Then

[tex]\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C[/tex]

[tex]=\boxed{\dfrac49x^3(3\ln x-1)+C}[/tex]

The required integration is,

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

The given integral is,

∫4x² lnx dx

Using integration by parts, choose u and dv.

In this case, we choose u = lnx and dv = 4x²dx.

Using the formula for integration by parts, we have:

∫ u dv = uv - ∫ v du

Substituting the values of u and dv, we get:

∫4x² lnx dx = (lnx) (∫ 4x² dx) - ∫ [(d/dx)lnx] (∫4x² dx) dx

Simplifying the first term using the power rule of integration, we get:

∫ 4x² dx = (4/3)x³ + C₁

For the second term, we need to evaluate (d/dx)lnx,

Which is simply 1/x. Substituting this value, we get:

∫ [(d/dx)lnx] (∫4x² dx) dx = ∫ [(1/x) ((4/3)x³ + C₁)] dx

Simplifying this expression, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - ∫ [(4/3)x³/x] dx

Using the power rule of integration again, we get:

∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C

Where C is the constant of integration.

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Answer:

[tex]\boxed {\boxed {\sf 120 \ units^2}}[/tex]

Step-by-step explanation:

We are asked to find the area of a triangle. The formula for calculating this is:

[tex]a= \frac{1}{2} bh[/tex]

This is a right triangle, so the base and height are the legs of the triangle. The 2 smallest sides are the legs because the longest side is the hypotenuse. Since the side lengths are 10, 26, and 24, the base and height must be 10 units and 24 units.

Substitute these values into the formula.

[tex]a= \frac{ 1}{2} ( 10 \ units)(24 \ units)[/tex]

Multiply the numbers in parentheses.

[tex]a= \frac{1}{2}(240 \ units^2)[/tex]

Multiply by 1/2 or divide by 2.

[tex]a= 120 \ units^2[/tex]

The area of the triangle is 120 units squared.

9514 1404 393

Answer:

  (x, y) = (4, -4)

Step-by-step explanation:

A graphing calculator makes graphing very easy. The attachment shows the solution to be (x, y) = (4, -4).

__

The equations are in slope-intercept form, so it is convenient to start from the y-intercept and use the slope (rise/run) to find additional points on the line.

The first line can be drawn by staring at (0, -2) and moving down 1 grid unit for each 2 to the right.

The second line can be drawn by starting at (0, 2) and moving down 3 grid units for each 2 to the right.

The point of intersection of the lines, (4, -4), is the solution to the system of equations.

Answer:

Step-by-step explanation:

The answer is that 1 variable is allowed to change. The others are held at a constant.

An example would be the growth of a poinsettia. These Christmas plants are very touchy. They respond badly to too much water or not enough water. So you keep the amount of dirt, the amount of sunlight, the amount of support that each plant receives as a constant.

The amount of water is what you change in one of the plants. The one plant (or a few) will measure the growth of the plant.

So the last answer is the one you want.

Answer: 22,103

Step-by-step explanation:

Compound interest is the interest calculated on the initial principal and the accumulated interest.

The amount in the account at the end of two years is $22,050.

Compound interest is the interest calculated on the initial principal and the accumulated interest.

We have,

Principal = $20,000

Rate = r = 5%

It is compounded yearly.

Time = t = 2 years.

The formula for the amount having compound interest:

A = P [tex]( 1 + \frac{r}{n} )^{nt}[/tex]

A = 20,000 [tex](1 + \frac{5}{100\times1})^{2\times1}[/tex]

A = 20,000 ( 1 + 5/100 )²

A = 20,000 ( 105/100 )²

A = (20,000 x 105 x 105) / (100 x 100)

A = 2 x 105 x 105

A = $22,050

Thus the amount in the account at the end of two years is $22,050.

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Answer:

- 8p - 80

Step-by-step explanation:

Given

4(- 15 - 3p) - 4(- p + 5) ← distribute both parenthesis

= - 60 - 12p + 4p - 20 ← collect like terms

= - 8p - 80

Answer:

-8p -80

Step-by-step explanation:

4(-15-3p)-4(-p+5)

Distribute

-60 -12p +4p -20

Combine like terms

-60-20 -8p +4p

-80-8p

-8p -80

Answer:

D

Step-by-step explanation:

The true statement is:

The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

As, per the graph and table is:

From the graph of f(x):

Axis of symmetry will be at x = 2

The maximum value of f(x) = 10

From the table of g(x):

Axis of symmetry will be at x = 2

The minimum value of g(x) = 4

thus, The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.

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Answer:

30

Step-by-step explanation:

If we have 4 integers that have an average of 9, then all the numbers will add up to [tex]9\cdot4=36[/tex].

If we want the greatest number possible, the other 3 need to be the lowest possible.

Since they are all different, the lowest possible values of the first 3 numbers are 1, 2, and 3.

[tex]1 + 2 + 3 = 6[/tex]

[tex]36 - 6 = 30[/tex]

So 30 is the greatest value of one of the integers.

Hope this helped!

Answer:

0.9938

Step-by-step explanation:

We can find this probability using a test statistic.

The test statistic to use is the z-scores

Mathematically;

z-score = (x-mean)/SD/√n

from the question, x = 119 , mean = 117 , SD = 6.4 and n = 64

Plugging these values in the z-score equation above, we have;

z-score = (119-117)/6.4/√64

z-score = 2/6.4/8

z-score = 2.5

The probability we want to find is;

P(z < 2.5)

we can get this value from the standard normal distribution table

Thus; P(z < 2.5) = 0.99379

Which to four decimal places = 0.9938

Answer:

P = 3x - 4

Step-by-step explanation:

Side 1 = x - 3

Side 2 = x

Side 3 = 2 + (Side 1) = 2 + x - 3 = x - 1

Perimeter = 20 in

Perimeter = Side 1 + Side 2 + Side 3

Perimeter = (x - 3) + (x) + (x - 1)

Perimeter = x - 3 + x + x - 1

Perimeter = 3x - 3 - 1

Perimeter = 3x - 3 - 1

Perimeter = 3x - 4

P = 3x - 4

Answer:

A 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .

Step-by-step explanation:

We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                             P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of defective items = [tex]\frac{24}{200}[/tex] = 0.12

            n = sample of items = 200

            p = population proportion  of defective items

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                      of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

  = [ [tex]0.12-1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] , [tex]0.12+1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] ]

 = [0.075, 0.165]

Therefore, a 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1

[tex]\\ \sf \longmapsto 4+10(x-1)=3[/tex]

[tex]\\ \sf \longmapsto 4+10x-10=3[/tex]

[tex]\\ \sf \longmapsto 10x-6=3[/tex]

[tex]\\ \sf \longmapsto 10x=3+6[/tex]

[tex]\\ \sf \longmapsto 10x=9[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{9}{10}[/tex]

Answer:

Here's what I get  

Step-by-step explanation:

h = 0.5d + 4

A function rule tells you how to convert an input value (x) into an output value (y).

Your function rule is

ƒ(x) = 0.5x + 4

An easy way to represent your function is to make a graph.

The easiest way to make a graph is to make a table containing some inputs and their corresponding outputs.  

Here's a typical table.

[tex]\begin{array}{cc}\textbf{x} &\textbf{y} \\0 & 4 \\2 & 5 \\4 & 6 \\6 & 7\\6 & 8 \\\end{array}[/tex]

The graph is like the one below.

Complete Question

Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?

a.

The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen’s d.

b.

The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.

c.

The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen’s d.

d.

The larger sample is less likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.

Answer:

The Cohen's d value is  [tex]d = 0.895[/tex]

The  correct option is b

Step-by-step explanation:

From the question we are told that

   The  sample mean of  each population is  [tex]M = 84[/tex]

    The  variance of each  population is  [tex]s^2 = 20[/tex]

    The  first sample size is  [tex]n_1 = 10[/tex]

    The  second  sample size is  [tex]n_2 = 20[/tex]

The  null hypothesis is  [tex]H_o : \mu = 80[/tex]

   Generally the standard deviation is mathematically evaluated as

            [tex]s = \sqrt{20 }[/tex]

=>         [tex]s = 4.47[/tex]

  The first test statistics is evaluated as

            [tex]t_1 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_1} } }[/tex]

    =>    [tex]t_1 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{10} } }[/tex]

   =>     [tex]t_1 = 2.8298[/tex]

  The second  test statistics is evaluated as

           [tex]t_2 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_2} } }[/tex]

=>       [tex]t_2 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{20} } }[/tex]

=>       [tex]t_2 = 4.0[/tex]

The sample with the larger test statistics (sample  size) will more likely reject the null hypothesis

Generally the Cohen's d value is mathematically evaluated as

          [tex]d = \frac{M - \mu }{s }[/tex]

  =>     [tex]d = \frac{ 84 - 80 }{4.47 }[/tex]    

=>         [tex]d = 0.895[/tex]

Given that the the sample mean and  sample size are the same for both sample the Cohen's d value will be  the same      

Answer:

Average rate of change of the function will be = (-1.5)

Step-by-step explanation:

Average rate of change of a function f(x) is determined by the formula,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex] If a < x < b

We have to find the average rate of change of a function g(t) between the interval [-3, 1]

From the given table,

For t = -3,

g(-3) = 6

For t = 1,

g(1) = 0

Therefore, average rate of change of the function in the given interval

= [tex]\frac{g(1)-g(-3)}{1-(-3)}[/tex]

= [tex]\frac{0-6}{1+3}[/tex]

= [tex]-\frac{3}{2}[/tex]

= - 1.5

Answer:

Hey there!

The area of a rectangle is the length times width.

Thus, we can write the equation, 600=30w.

Solving for the width, we get that the width is equal to 20 ft.

Let me know if this helps :)

Answer:

20 feet across.

Step-by-step explanation:

You will have to do a simple equation solve.

x is how many feet across the court is.

* could be our multiplying sign

600 = 30*x

Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.

That leaves 20 = x.

So it is 20 feet across.

Answer:

hkkr

need school the long said

Answer:

That would indicate 20.0 ml

id appreciate a rating thanks XP

Answer: 0.10299,0.1037  ,0.1038 ,0.9

Step-by-step explanation:

In all the numbers we could see that 0.9 is the greatest because it has the greatest tenth value. The rest three have the same tenth value which is one and the same hundredth value which is 0 so we will compare the numbers using  their thousandth values.

In the numbers 0.1038,0.10299, 0.1037   The first one has a thousandth value of 3, the second one has a thousandth value of 2, and the third one has a thousandth value of 3. Which means the first and the second have the same thousandths value so using their last numbers which is 8  and 7 , 8 is greater than 7  so  0.1038  is greater than 0.1037 and 0.10299.  The same way 0.1037 is greater than 0.10299.

So to order them from least to greatest,

0.10299 will be first

0.1037  will be second  

0.1038  will be the third  

0.9  will be the last.

Look where the parabola crosses the x axis. This is where the x intercepts are located. The term "x intercept" is the same as "root" and also the term "zero".

Answer:

the value of the test statistic is calculated as "T - distribution" with the formula;

t = (x-bar - μ)/(s/√n)

Step-by-step explanation:

We are told that the standard deviation is unknown. But normally, we use a z-distribution if the standard deviation is known.

However, in a hypothesis test for a population mean where the population standard deviation is unknown is still conducted in the same way like we do when we know the population standard deviation. The only difference in this case is that we will use the t-distribution rather than the standard normal z-distribution.

The t-distribution formula used is;

t = (x-bar - μ)/(s/√n)

Answer:

Hello,

Answer

[tex]\sigma=457,95...[/tex]

Step-by-step explanation:

p(z<a)=0.9

p(z<1.29)=0.9015

p(z<1.28)=0.8997

using linear interpolation: with 4 decimals

p(z<1.282)<0.9

[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]

Answer:

4.2

Step-by-step explanation:

f varies inversly with L can be translated matimatically as:

● f = k/L

It takes 7 pounds of pressure to break a 3 feet long board.

Replace f by 7 and L by 3.

● 7 = k/3 => k=7×3=21

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's find tge length of a board that takes 5 pounds of pressure to be broken.

● 5 = k/L

● 5 = 21/L

● L = 21/5 = 4.2

So the board is 4.2 feet long