Simplify ( 7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3

Answer:

[tex]\log_{10}\sqrt{a} -\dfrac{3}{4}=\dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]

Step-by-step explanation:

Given:

[tex]x=\dfrac{\sqrt{10a\sqrt{0.1}}}{10}[/tex]

Therefore:

[tex]\implies \log_{10}x=\log_{10}\left(\dfrac{\sqrt{10a\sqrt{0.1}}}{10} \right)[/tex]

[tex]\textsf{Apply the log quotient law}: \quad \log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay[/tex]

[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-\log_{10}10[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-1[/tex]

[tex]\textsf{Apply radical rule: $\sqrt{ab}=\sqrt{a}\sqrt{b}$, \quad assuming $a \geq 0,\;b\geq 0$}[/tex]

[tex]\implies \log_{10}\left(\sqrt{10}\sqrt{a}\sqrt{\sqrt{0.1}}}\right)-1[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \log_{10}\sqrt{10} + \log_{10}\sqrt{a} + \log_{10}\sqrt{\sqrt{0.1}}}\right)-1[/tex]

Rewrite the radicals:

[tex]\implies \log_{10} \left(10\right)^{\frac{1}{2}} + \log_{10}\sqrt{a} + \log_{10}\left(0.1\right)^{\frac{1}{4}\right)-1[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \dfrac{1}{2}\log_{10} 10 + \log_{10}\sqrt{a} + \dfrac{1}{4}\log_{10}0.1-1[/tex]

[tex]\textsf{Apply log laws}: \quad \log_aa=1 \quad \textsf{and} \quad \log_a\dfrac{1}{a}=-1[/tex]

[tex]\implies \dfrac{1}{2}(1) + \log_{10}\sqrt{a} + \dfrac{1}{4}(-1)-1[/tex]

[tex]\implies \dfrac{1}{2}+ \log_{10}\sqrt{a} -\dfrac{1}{4}-1[/tex]

[tex]\implies \log_{10}\sqrt{a} -\dfrac{3}{4}[/tex]

If you want to simplify further:

[tex]\implies \log_{10}\left(a\right)^{\frac{1}{2}} -\dfrac{3}{4}[/tex]

[tex]\implies \dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]

Answer:

56

Step-by-step explanation: 10a+10 0.1 -=

We cannot conclude that the percentage of people in New York who would vote for the incumbent president is different from 53%.

The correct answer is B) Do not reject H0.

What is a null hypothesis in probability?

The null hypothesis is a typical statistical theory that suggests that no statistical relationship and significance exists in a set of given single observed variables, between two sets of observed data and measured phenomena.

In this situation, the null hypothesis H0 is that the percentage of people in New York who would vote for the incumbent president is equal to 53%. The alternative hypothesis Ha is that the percentage of people in New York who would vote for the incumbent president is different from 53%.

The test statistic for this hypothesis test is z = -1.60. This means that the sample result of 45% is 1.60 standard deviations away from the hypothesized value of 53%.

The p-value is the probability of observing a test statistic as extreme as or more extreme than the one observed, given that the null hypothesis is true. In this case, the p-value is 0.1090, which is greater than the significance level of 0.10.

Since the p-value is greater than the significance level, we do not have sufficient evidence to reject the null hypothesis.

Hence, we cannot conclude that the percentage of people in New York who would vote for the incumbent president is different from 53%.

The correct answer is B) Do not reject H0.

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If the number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Then, the answer is 210 .

In the question ,

it is given that ,

number 22 is divided into 22 individual items ,

the three categories in which these items are placed are x₁, x₂ and x₃ .

x₁ + x₂ + x₃ = 22    .....equation(1)

(x₁ - 1) + (x₂ - 1) + (x₃ - 1) = 22 - 3 = 19

let a = x₁ - 1 , b = x₂ - 1  and c = x₃ - 1 .

Hence , a + b + c = 19    ....equation(2)

Now , because the number of solution of equation(1) excluding zero will be equal to the number of solutions of equation(2) including the zero .

So , we subtracted 1 from x₁, x₂ and x₃ respectively .

Now , we have to divide 19 into 3 parts where any part can be zero also or any part is a whole number .

For Example : let us have 19 apples , which must be divided into 3 parts by placing 2 J's among 19 A's .

Now we have reduced the problem to such that we have to find the permutation of 19 A's and 2 J's that is 21 characters in which every permutation is a solution .

So , the  number of ways of arranging 21 characters in which 19 are same(A)  and 2 are same (J)

= 21!/(2! * 19!)

= 21*10 = 210

It means there are 210 non negative integral solutions of a+b+c = 19 .

It means total positive solutions of x₁ + x₂ + x₃ = 22  is 210 .

Therefore , the number of solution to the equation is 210 .  

The given question is incomplete , the complete question is

Start by thinking of the number 22 as divided into 22 individual items and the variables x₁, x₂, and x₃ as three categories into which these items are placed. since each [tex]x_{i}[/tex] is a positive integer, start by placing one item in each category and distribute the remaining items among the categories. The number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. Thus, the answer is ______  .

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Therefore , [tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.

The probability of winning is actually closer to 1/3 (25/72). Carnival game operators want you to think that a game is fair like I did, so that you will play. If you knew that the probability of winning a game was only about 1/3, most likely you would not waste your money.

Mathematical descriptions of the likelihood that an event will occur or that a claim will be true are called probabilities.

Here,

[tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.

Therefore , [tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.

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The lengths of the right-angled triangle are 6 and 8.

A right-angled triangled is a triangle that has one of its angles equal to 90°. The sum of the other two interior angles is also equal to 90°.

The Pythagoras theorem relates the three sides of a right-angled triangle through a simple equation. According to the Pythagoras theorem,

hypotenuse^2 = base^2 + opposite^2

Let base = b, so opposite = b + 2

So,

10^2 = b^2 + (b+2)^2

100 = b^2 + b^2 + 4b + 4

100 = 2b^2 + 4b + 4

50 = b^2 + 2b + 2

b^2 + 2b - 48 = 0

solving this quadratic equation gives, b = 6 and b = -8. Since length cannot be negative, the base is 6 feet and the opposite is 8 feet.

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The rate of change of the average price of the new car is $274.50 per year.

The rate of change of the average price of the new car is a function of the change in average price over the years and the change in the number of years.

Rate of change = change in the average price / change in the number of years

Rate of change = (price in 2002 - price in 1994)  / difference in the number of years

Rate of change = (19,126 - 16,930) / (2002 - 1994)

Rate of change = 2196 / 8

Rate of change = $274.50

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Answer:

3

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=2x+1\\g(x)=x^2-3\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

The given composite function f o g(-2) means to substitute the function g(-2) in place of the x in function f(x):

[tex]\begin{aligned}(f \circ g)(-2)&=f[g(-2)]\\&=2[g(-2)]+1\\&=2(2^2-3)+1\\&=2(4-3)+1\\&=2(1)+1\\&=2+1\\&=3\end{aligned}[/tex]

Answer: Rise over Run

Step-by-step explanation: Take the change in the x coordinates, and divide by the change in y coordinates.

For example, to find slope when given 2 coordinates:

(2,5)     (5, 10)

The change in the x coordinates is 3, because from 2-->5 it moves 3 places to the right. (run)

The change in the y coordinates is 5, because from 5-->10 it moves 5 places upwards. (rise)

Use rise/run.

Rise= 5 (change in y coordinate)

Run = 3 (change in x coordinate)

5/3 is the slope.

On questions like #6, the slope is -3. That is because the equation for slope is y=mx+b.

m is the coefficient of the x, so -3 is the slope.

Likewise, the slope of #2 is 7. The slope of #10 is 3/4.

The acute angle of intersection is  5.2°.

What is acute angle?

Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.

The direction vector normal to the plane is ...

 n = (1, 1, 3)

The direction vector of the line is ...

 m = (1, -3, 1)

Then the angle θ between them can be found from the dot product:

 n•m = |n|·|m|·cos(θ)

 (1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)

 1 = 11·cos(θ)

 θ = arccos(1/11) ≈ 84.8°

This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, the line and plane must intersect.

 acute angle = 90° -84.8° = 5.2°

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Answer:

Step-by-step explanation:

The sum of (2.25 x 10^19) and (6.7 x 10^17) is (2.317 x 10^19).

To find the sum of these two numbers, we first need to line up the decimal points and add the numbers as we would with any other addition problem:

2.25 x 10^19

+ 6.7 x 10^17

Then, we can carry the 1 and add the numbers:

2.25 x 10^19

6.7 x 10^17

2.317 x 10^19

The sum of these two numbers is 2.317 x 10^19, which is equal to choice B.

The probability that a randomly selected bike is green given that the bike has road bike tires is 0.66

Given :

Nellie is shopping for a new bicycle. She is most interested in color and type of tires.

Probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event .

From the table given :

Total number of 6 road bikes = 4

Total road bikes = 2 + 4 = 6

Probability = 4 / 6

= 2 / 3

= 0.66

Hence the  probability that a randomly selected bike is green given that the bike has road bike tires is 0.66 .

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The  program for a  given rectangular matrix m,  if an element of m is equal to 0, sets that element's entire row and column to 0

def zeroify_matrix(m):  

rows = len(m)  

cols = len(m[0])  

rows_to_zeroify = []  

cols_to_zeroify = []  

for i in range(rows):

  for j in range(cols):

  if m[i][j] == 0:  

 rows_to_zeroify.append(i)  

cols_to_zeroify.append(j)  

for i in range(rows):  

for j in range(cols):

  if i in rows_to_zeroify or j in cols_to_zeroify:

   m[i][j] = 0  

return m

It is coded in python for the given problem of recreating a rectangular matrix, for a single element to be 0, the whole row nad column will contain zero elements.

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Answer:

Adults: 134

Senior: 241

Step-by-step explanation:

Known

Number of adult tickets sold: x

Revenue from adult tickets: $11x

Number of senior tickets sold: y

Revenue from senior tickets: $8y

From the problem, we found the equation [tex]y = 2x - 27[/tex] and 3,402 = 11x + 8y

Combining the two equation:

[tex]3,402 = 11x + 8(2x-27)\\3,402 = 11x + 16x - 216\\3,402 + 216 = 27x\\27x = 3,618[/tex]

Divided both side by 27

[tex]x = 134[/tex]

Since

[tex]y = 2x - 27[/tex]

Inserting the value of x,

[tex]y = 2(134) -27\\y = 268 - 27\\y = 241[/tex]

So, there are 134 adult tickets sold and 241 senior tickets sold.

Answer:

6y

Step-by-step explanation:

What can you remove form the left side that makes this a false equation?

It's 6y. So place 6y on the right side.

6y + 13 = 6y + 8

Subtract 6y from both sides.

13 = 8

Since 13 = 8 is a false statement, the equation 6y + 13 = 6y + 8 has no solution.

Answer: 6y

Step-by-step explanation:

i did the iready and got it right

its 6y

Null Hypothesis: H0: There is an equal distribution of contralateral and ipsilateral tumors in the population.Ha: There is not an equal distribution of contralateral and ipsilateral tumors in the population.

1) Calculate the observed value:

The observed value is 26 out of 41 cases.

2) Calculate the expected value:

The expected value is 20.5 out of 41 cases.

3) Calculate the test statistic:

The test statistic is (26-20.5)/sqrt(20.5) = 2.44

4) State the critical value:

The critical value for a two-sided test with a significance level of 0.05 is 1.96.

5) The test statistic (2.44) is greater than the critical value (1.96), so we reject the null hypothesis and conclude that there is not an equal distribution of contralateral and ipsilateral tumors in the population.

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The time that it will take for Kiran to run 6 meters is; 2 seconds

A function table is defined as a visual table that has columns and rows that display the function with regards to the input and output.

Now, the coordinates of the function table are given as;

(0, 0), (3, 1), (6, 2), (9, 3.2), (12, 3.8), (15, 4.6), (18, 6), (21, 6.9), (24, 8.09), (27, 9)

Now, the graph shows that the y-axis represents  the time, t, he took to run various distances, d which is represented on the x-axis.

Now, we want to find the time that it takes Kiran to run 6 meters. From the graph and table attached, it is seen to be 2 seconds.

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The function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.

Given, the lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours.

That is, 5.231(e/1000)f(x) x > 0. I

f 30 light bulbs having this lifetime distribution are placed on test.

we have to find the probability that 10 or fewer of these light bulbs survive to time 1200.

as, we have to find the expression for the function f(x) so that 10 or fewer of the given light bulbs survive to time 1200.

f(x) = 1/1000×e^(-x/1000)

So, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.

Hence, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.

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Answer:

42

Step-by-step explanation:

To simplify the expression -7x3x(-2)x(-5)x(-1), we need to apply the rules of exponentiation and multiplication.

First, we note that the terms -7, -2, -5, and -1 are all negative numbers, which means that they will be multiplied together to give a positive result.

Next, we apply the rule that says that any term raised to the power of 0 is equal to 1. Since -1 raised to the 0 power is 1, this means that the expression -7x3x(-2)x(-5)x(-1) is equivalent to -7x3x(-2)x(-5)x1.

Next, we apply the rule that says that any term raised to the power of 1 is equal to itself. Since 3 raised to the 1 power is 3, and 5 raised to the 1 power is 5, this means that the expression -7x3x(-2)x(-5)x1 is equivalent to -7x3x(-2)x5x1.

Finally, we apply the rule that says that the product of any number and its multiplicative inverse (or reciprocal) is equal to 1. Since the reciprocal of 5 is 1/5, this means that the expression -7x3x(-2)x5x1 is equivalent to -7x3x(-2)x(1/5)x1.

We can now use the rules of multiplication to simplify the expression further. Since any number multiplied by 1 is equal to itself, this means that the expression -7x3x(-2)x(1/5)x1 is equivalent to -7x3x(-2)x(1/5).

Next, we use the rule that says that the product of two negative numbers is a positive number. This means that the expression -7x3x(-2)x(1/5) is equivalent to 7x3x2x(1/5).

Finally, we can apply the rules of exponentiation and multiplication to evaluate the expression. Since any number raised to the power of 1 is equal to itself, this means that the expression 7x3x2x(1/5) is equivalent to 7x3x2. We can then multiply these terms together to get the final result:

7x3x2 = 42

Therefore, the simplified expression is equal to 42.

The equation of the line that includes CD, in slope-intercept form, is: B. y = -4/3x + 2.

To write the equations of two lines that are parallel or perpendicular to each other, recall that parallel lines have the same slope (m), while perpendicular lines have slopes that are negative reciprocals.

The slope of y = 3/4x - 11 is 3/4. The negative reciprocal of 3/4 is -4/3. Therefore, the slope of AB that is perpendicular to the graph of y = 3/4x - 11 is, m = -4/3.

Since the CD is parallel to AB, then CD will have the same slope of, m = -4/3.

To write the equation of the line that includes CD, substitute m = -4/3 and (a, b) = (-6, 10) into y - b = m(x - a):

y - 10 = -4/3(x + 6)

Rewrite in slope-intercept form:

y - 10 = -4/3x - 8

y = -4/3x - 8 + 10

y = -4/3x + 2

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Given inputs A, B, C, D, E, design a CMOS circuit to implement the logic function: Y(not) = A(B+C) + D + E has  5-c-mos, 5-pmos total 10 mos transistors

this can be realize by takeing three c-mos in parallel which gives ABC ,two c-mos are series which is in serires with

another c-mos whic gives D(A+B), now connect ABC and D(A+B) in series

the out put will be (ABC + D(A+B) )'

so we require total 6-mos and 6-pmos total 12mos transistors

F = AC + BD

pull down

this can be realize by takeing two c-mos in series which gives AB ,two cmos are in series

which whic gives BD, now connect AC and BD in parallel

pull up

this can be realize by takeing two c-mos in parallel which gives Ac ,two c-mos are in parallel

which whic gives BD, now connect AC and BD in series

the output is (AC+BD)'

to avoid the complement we have to connect the output to c-mos inverter then we get AC+BD

so we require 5-nmos, 5-pmos total 10 mos transistors

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The likelihood or the probability is 121, or 8.33%.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

We must make a table for easier comprehension in order to determine the P(x=4);

Refer to the attachment for table:

There are three different ways that P(x=4) can occur based on the table. Out of 36 possible results (6 x 6 = 36), they are (1,3), (2,2), and (3,1). As a result, the chance of the event is 363; it is then reduced to 121, or 8.33%.

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Answer:

<CYZ = 60 degrees

Step-by-step explanation:

CY = CZ  ==> both segments are radiuses of the circle since they both have

                     a CenterPoint at Point C and a point touching the edge of the

                     circle

CY = YZ  ==> Since CY=CZ and YZ=CZ, CY also equal YZ. In addition, this

                     means that CY, YZ, and CZ are all radiuses of the circle

Hence, CY = YZ = CZ.

Since all sides of the triangle are equal, that means that all angles of the triangle are equal as well:

<CYZ + <CZY + <YCZ = 180  ==> 180 is the total degrees in a triangle

<CYZ + <CYZ + <CYZ = 180  ==> all angles have the same measure

3 * <CYZ = 180  ==> solve for <CYZ

(3 * <CYZ)/3 = 180/3 ==> divide by 3 on both sides to isolate <CYZ

<CYZ = 60 degrees

Answer: [tex]\angle CYZ=60^{\circ}[/tex]

Step-by-step explanation:

[tex]\overline{CZ}=\overline{CY}[/tex] (radii of a circle)

[tex]\implies \overline{YZ}=\overline{CZ}=\overline{CY}[/tex]

[tex]\therefore \angle CYZ=60^{\circ}[/tex] (equilateral triangle)

The 92.5% of confidence interval for the percentage of adults is

(-1.176 ,  1.342).

as per given in the question,

The total number of adults (n) is 649

The number of smokers (x) = 54

the probability of getting a smoker is P =x/n

=> P = 54/649

=> 0.083

not getting a smoker is

1 - P = 1-0.083

=> 0.916

At 92.5% confidence level the Z critical value is ,

[tex]\alpha[/tex] = 1 - 92.5%

=> 1 - 0.925

=> 0.075

[tex]\alpha[/tex] / 2 = 0.075/ 2

=> 0.0375

now,

for the two tail test

Z[tex]\alpha[/tex]/2

= Z(0.0375)

= 1.7805

Margin of error

E = [tex]Z\alpha / 2 * \sqrt{( p * (1 - p) / n)}[/tex]

= 1.780 [tex]\times (\sqrt{((0.083 \times 0.916 ) / 649)}[/tex]

= 1.2596

A 92.5 % confidence interval for population proportion p is ,

P- E < P < P + E

0.083- 1.259 < P < 0.083 + 1.259

-1.176 < p < 1.342

(-1.176 ,  1.342) is the interval

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To correct a number to 3 decimal places, we need to round it to the nearest thousandth. The number 45.7395 is already very close to 45.740, which is the nearest thousandth. Therefore, we can round 45.7395 to 45.740, which is the correct answer to 3 decimal places.

The two plans will cost the same when Yolanda has driven 233 miles distance. That is, $70 + (0.30 x 233) = $233 = 0.80 x 233.

To find out how many miles Yolanda needs to drive for the two plans to cost the same, we need to set up an equation. The equation should calculate the total cost of each plan. For the first plan, the total cost is the initial fee plus the cost of the miles driven. For the second plan, the total cost is just the cost of the miles driven. We can then set the two equations equal to each other and solve for the number of miles distance driven. The final result is that Yolanda needs to drive 233 miles for the two plans to cost the same.

Plan 1: C = F + (D × CPM)

Plan 2: C = (D × CPM)

Plan 1 = Plan 2

F + (D × CPM) = (D × CPM)

F = 0

D × CPM = D × CPM

D = 233

Therefore, Yolanda needs to drive 233 miles for the two plans to cost the same.

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The equation has one repeated irrational number solution. thus Option A is correct.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given equation is the quadratic equation by

[tex]-4x^2+ 24x-36=0[/tex]

We need to determine the number and type of solutions.

Noted that If the discriminant equals zero, the equation has one repeated rational number solution.

Since we know that If the discriminant is positive, then the equation has two real solutions.

And If the discriminant is negative, then the equation has two imaginary solutions.

To Calculate the discriminant of the equation [tex]-4x^2+ 24x-36=0[/tex] by substituting a= -4, b= 24  and c= -36 into the discriminant formula:

Since the discriminant equals zero, it follows that the equation has one repeated irrational number solution x = 3

The equation has one repeated irrational number solution.

Option A is correct.

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Answer:

Domain: 0<=x<=500

Range: 0<=y<=250

Step-by-step explanation:

I'm not sure if this is what you asked for. She spend 2 minutes reading 1 page, there are 250 pages, therefore: 250*2=500

the range is simply the total pages

Hope this help!

The least squares line , y = mx + b form from given data is y = ( -32/100 )x + ( -39/100).

We have an equation of line is

y(x) = mx + b --(1)

given data, (-2, 1), (2, 1),(-1,-1), (0,-2), (2,-2) and (-2, 1)

plugging each point on above equation we get, 1 = -2m + b ; 1 = 2m + b ; -1 = -m + b ; -2 = 0m + b ;

-2 = 2m +b ; 1 = -2m + b

The above equations can be written in matrix form as,

[ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] [ m ; b]

= [ 1 ; 1 ; -1 ; -2 ; -2 ; 1]

AX = B

X = (Aᵀ A)⁻¹ AᵀB where Aᵀ is transpose of matrix A and (Aᵀ A)⁻¹ is inverse of (Aᵀ A).

AᵀA = [ -2 2 -1 0 2 -2 ; 1 1 1 1 1] [ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] = [ 17 -1 ; -1 6 ]

so, X = [ 17 -1 ; -1 6 ] ^-1 [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]

let [ 17 -1 ; -1 6 ] = P

[ 17 -1 ; -1 6 ]⁻¹ = adj.P/det P

det P = 17×6 - 1 = 101

P⁻¹ = 1/101 [ 6 1 ; 1 17 ]

Now, X = 1/101 [ 6 1 ; 1 17 ] [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]

=> X = 1/101[ 6 1 ; 1 17 ] [ -5 ; -2 ]

=> X = 1/101 [ -32 ; -39] = [ -32/100 ; -39/100 ]

=> [ m ; b ] = [ -32/100 ; -39/100 ]

=> m = -32/100 , b = -39/100

then, y = mx + b

=> y = ( -32/100 )x + ( -39/100)

Hence, the required equation is

y = ( -32/100 )x + ( -39/100).

To learn more about least squares line , refer :

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