A study was conducted to investigate whether a new drug could significantly reduce pan in people with arthritis. From a group of 500 people with arthritis 250 were randomly assigned to receive the drug (group 1) and the remaining people were assigned a placebo (group 2). After one month of treatment, 225 people in group 1 reported pain relief and 150 people in group 2 reported pain relief Let Pe represent the combined (or pooled) sample proportion for the two samples. Have the conditions for inference for testing the difference in population proportions been mel? (A) No. The people in the study were not selected at random (6) (B) No. The number of people in the study was too large compared with the size of the population (C) No. The normality of the sampling distribution cannot be assumed because Pe times each sample size is not sufficiently large (D) No. The normality of the sampling distribution cannot be assumed because I - Pe times each sample size is not sufficiently large 6 (E) Yes. All conditions for inference have been met

Answer:

Step-by-step explanation:

Integer=8

negative fraction= -1/2

positive fraction= 1/9

negative decimal=-0.4

positive decimal= 0.8

Multiply both sides by \(x^{-3}\) to get a homogeneous equation.

\((2xy^2 - x^3) \, dy + (y^3 - 2yx^2) \, dx = 0 \\\\ \implies \left(2\dfrac{y^2}{x^2} - 1\right) \, dy + \left(\dfrac{y^3}{x^3} - 2\dfrac yx\right) \, dx = 0\)

Substitute \(y=vx\) and \(dy = x\,dv + v\,dx\). This makes the equation separable.

\((2v^2 - 1) (x\,dv + v\,dx) + (v^3 - 2v) \, dx = 0\)

\(x (2v^2 - 1) \,dv + (2v^3 - v) \, dx + (v^3 - 2v) \, dx = 0\)

\(x (2v^2 - 1) \,dv + (3v^3 - 3v) \, dx = 0\)

Separate the variables.

\(x (2v^2 - 1) \, dv = (3v - 3v^3) \, dx\)

\(\dfrac{2v^2-1}{3v-3v^3} \, dv = \dfrac{dx}x\)

\(\dfrac13 \dfrac{1 - 2v^2}{v(v-1)(v+1)} \, dv = \dfrac{dx}x\)

Expand the left side into partial fractions.

\(\dfrac{1-2v^2}{v(v-1)(v+1)} = \dfrac av + \dfrac b{v-1} + \dfrac c{v+1} \\\\ \dfrac{1-2v^2}{v(v-1)(v+1)} = \dfrac{a(v^2-1) + bv(v+1) + cv(v-1)}{v(v-1)(v+1)} \\\\ 1-2v^2 = (a+b+c) v^2 + (b-c) v - a\)

Solve for the coefficients \(a,b,c\).

\(\begin{cases} a + b + c = -2 \\ b-c = 0 \\ -a = 1 \end{cases} \implies a=-1, b=c=-\dfrac12\)

Thus our equation becomes

\(\left(-\dfrac1{3v} - \dfrac1{6(v-1)} - \dfrac1{6(v+1)}\right) \, dv = \dfrac{dx}x\)

Integrate both sides.

\(\displaystyle \int \left(-\dfrac1{3v} - \dfrac1{6(v-1)} - \dfrac1{6(v+1)}\right) \, dv = \int \dfrac{dx}x\)

\(\displaystyle -\frac13 \ln|v| - \frac16 \ln|v-1| - \frac16 \ln|v+1| = \ln|x| + C\)

Solve for \(v\) (as much as you can, anyway).

\(\displaystyle -\frac16 \left(2\ln|v| + \ln|v-1| + \ln|v+1|\right) = \ln|x| + C\)

\(\displaystyle \ln\left|\frac1{\sqrt[6]{v^2(v^2-1)}}\right| = \ln|x| + C\)

\(\displaystyle \frac1{\sqrt[6]{v^4-v^2}} = Cx\)

\(\sqrt[6]{v^4-v^2} = \dfrac Cx\)

\(\left(\sqrt[6]{v^4-v^2}\right)^6 = \left(\dfrac Cx\right)^6\)

\(v^4-v^2 = \dfrac C{x^6}\)

Put the solution back in terms of \(y\).

\(\left(\dfrac yx\right)^4-\left(\dfrac yx\right)^2 = \dfrac C{x^6}\)

\(y^4 - x^2y^2 = \dfrac C{x^2}\)

\(\boxed{x^2y^4 - x^4y^2 = C}\)

which is about as simple as we can hope to get this.

Answer:

dlgSHJKAGDHFDKFKDK

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given the translation rule

(x, y ) → (x - 4, y + 2 )

This means subtract 4 from the original x- coordinate and add 2 to the original y- coordinate, that is

a point (4 , - 4 ) → (4 - 4, - 4 + 2 ) → (0, - 2 )

The resulting graph would result in moving input x by --4  horizontally and Output y by +2 vertically.

Translations are defined by saying how much a point is moved to the left/right and up/down. Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically.

Given the point  (x - 4, y + 2), we can clearly observe that the graph would move vertically by +2 units while the input will be in the -ve x-axis direction from right to left and thus will move negatively by -4.

Hence, The resulting graph would result in moving input x by --4  horizontally and Output y by +2 vertically.

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The price at which Berkshire Hathaway close on the previous day based on the table is $199,740.

The closing price of stock means the final trading price at which a particular stock or security is traded on given trading day. It is the last recorded price of a stock when market closes for the day.

The closing price is an important indicator used in financial markets to evaluate the performance and value of a stock. It serves as a reference point for investors, analysts and traders to assess the overall market sentiment and make investment decisions.

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Answer:

65° + 127° + 140° = 332°

360° - 332° = 28° (measure of missing interior angle)

28° + c = 180°, so c = 152°.

The value of angle C is 152°

A quadrilateral is a four-sided polygon, which means it is a closed shape with four straight sides. The sum of the angles in a quadrilateral is always 360 degrees.

To solve the given problem, find the missing angle using the sum of angles and find the angle C with the 4th angle of the Quadrilateral.

Here we have

A quadrilateral with angles 65°, 140°, 127°

Let 'x' be the missing angle

As we know the sum of angles in a quadrilateral is 360°

=>  65° + 140° + 127° + x = 360°

=>  332° + x = 360°

=>  x = 28°  

Here ∠C + 28° = 180°   [ Sum of Linear angles ]  

=> ∠C = 180° - 28°

=> ∠C = 152°

Therefore,

The value of angle C is 152°

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Answer:

8.5

Step-by-step explanation:

51/6=8.5

9514 1404 393

Answer:

  (9x -4)/(x^2 -4)

Step-by-step explanation:

Perhaps you intend the sum ...

  7x/(x^2 -4) +2/(x +2)

  \(=\dfrac{7x}{(x+2)(x-2)}+\dfrac{2}{x+2}=\dfrac{7x+2(x-2)}{(x+2)(x-2)}\\\\=\boxed{\dfrac{9x-4}{x^2-4}}\)

Answer:

7 and 7

Step-by-step explanation:

It is asking, what 2 numbers when added together equal 14, but when you multiply them together get the largest number that you can.

7+7 = 14

7*7= 49 which is the largest number you can get.

I hope this helped <3

Answer: 105 chips

Step-by-step explanation:

minute 1: 15 chips

minute 2: 30 chips

minute 3: 45 chips

minute 4: 60 chips

minute 5: 75 chips

minute 6: 90 chips

minute 7: 105 chips

or you could do 15 x 7 = 105

105 chips in 7 minutes

Answer:

5.25 litres.

Step-by-step explanation:

6 bottles * 3.5 litres = 21 litres of juice total.

21 / 4 = 5.25 litres per person.

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }\)

Answer: -48 yd

Step-by-step explanation:

11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).

Step-by-step explanation:

the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the

let's firstly convert the mixed fraction to improper fraction and proceed from there.

\(\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div \left(\cfrac{3}{8}\div \cfrac{1}{2} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{8}\cdot \cfrac{2}{1} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{4} \right) \\\\\\ \cfrac{9}{4}\cdot \left(\cfrac{4}{3} \right)\implies \cfrac{9}{3}\cdot \cfrac{4}{4}\implies 3\cdot 1\implies \text{\LARGE 3}\)

Answer:

1,2,5,and 6

Step-by-step explanation:

I did the assignment

Answer:

A

Step-by-step explanation:

6 is less than 14 obviously.

95% of adult males have diastolic blood pressure readings that are at least 62 mmHg

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 80 mmHg and the standard deviation is 9 mmHg.

95% fall within two standard deviations.

2*9=`18

80 - 18 = 62 mmHg

Therefore, 95% of adult males have diastolic blood pressure readings that are at least 62 mmHg.

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We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

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The transformations that change the domain of a function are given as follows:

The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.

Hence we must look at transformations that change the values of x of the function, which are given as follows:

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The maximum number of zeroes in a generic equation with the form axe? + bx4 + cx3 + dx2 is 5.

a) \($ax^{5}\)

b) Factor 2x3 - 9x2 + 7x + 6  is

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

c) x = -b / 2a

Replace x by -2, from the vertex:

-2 = -b / 2a

Solve for b:

-b = -4a

Or

b = 4a

By evaluating the equation with the vertex's x-value, we can determine the y-value from the vertex:

y = ax2 + 4ax - 6

Simplify, 6 for y, and -2 for x:

6 = a(-2)2 + 4a(-2) - 6

6 = 4a - 8a - 6

solve for a:

a = -3

Simplifying the above equation,

b = 4a, b = -12

The value for a is -3.

The value for b is -12

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Answer:

The four first terms are:

\(7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}\)

Step-by-step explanation:

The function is:

\(f(x)=7xe^{x}\)

The Taylor series around a is given by:

\(F(x)=\sum^{\infty}_{n=0} \frac{f^{n}(a)(x-a)^{n}}{n!}\)

The first 4 terms will be:

\(F(x)=f(0)+\frac{f^{'}(0)(x)}{1}+\frac{f^{''}(0)(x)^{2}}{2}+\frac{f^{'''}(0)(x)^{3}}{6}\)  

Let's find first the derivatives:

\(f'(x)=7(xe^{x}+e^{x})\)

\(f'(0)=7(0e^{0}+e^{0})=7\)

\(f''(x)=7xe^{x}+7e^{x}+7e^{x}=7xe^{x}+14e^{x}\)  

\(f''(0)=14\)  

\(f'''(0)=21\)

\(f''''(0)=28\)    

\(F(x)=0+\frac{7(x)}{1}+\frac{14(x)^{2}}{2}+\frac{21(x)^{3}}{6}+\frac{28(x)^{4}}{24}\)

Therefore, the four first terms are:

\(7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}\)

I hope it helps you!

So the Taylor series for the function informed will be:

\(7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}\)

The function is:

\(f(x)= 7e^xx\)

The Taylor series around a is given by:

\(f(x)= \sum \frac{f^n (a) (x-a)^n }{n!}\)

The first four terms will be:

\(F(x)=f(0)+\frac{f'(0)(x)}{1}+\frac{f''(0)(x)^2}{2} + \frac{f'''(0)(x)^3}{6}\)

Let's find first the derivaties:

\(f'(x)= 7(e^xx+e^x)\\f'(0)= 7\\f''(x)= 7e^xx+14e^xx\\f''(0)=14\\f'''(0)= 21\\f''''(0)= 28\)

\(F(x)= 0+\frac{7x}{1}+\frac{14x^2}{2}+\frac{21x^3}{6}+\frac{28x^4}{24}\)

Therefore, the four first terms are:

\(7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}\)

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If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Answer:

-1519 4/5

-1519.8

-7599/5

Step-by-step explanation:

Answer:

41° and 49°

Step-by-step explanation:

Complementary angles are angles that sum up to 90°.

Let x represent the smaller angle, then the bigger angle will be represented with x + 8:

x + x + 8 = 90°

2x + 8 = 90°

2x = 82°

x = 41° this is the measure of smaller angle, then the bigger angle wpis 49°

The answer is:

Work/explanation:

If two angles are complementary, their measures add to 90°.

So we can set up an equation to find the angles. Let the unknown angle be w, and its complement will be w + 8:

w + w + 8 = 90

Combine like Terms

2w + 8 = 90

2w = 82

w= 41

The other angle measures 8° more than the measure of w:

41 + 8 = 49

Answer:

A.

Step-by-step explanation:

Whenever you decide exponents, you actual subtract them

Taking the first part

\( \frac{21 {m}^{42} }{3 {m}^{21} } \)

21 divided by 3 is 7, right

Now the small numbers, 42 divided by 21. Since they are exponents, we do 42 minus 21. Making it 21.

You'd do the same for n and p, ending up with A

Recall that

Var[aX + bY] = a ² Var[X] + 2ab Cov[X, Y] + b ² Var[Y]

Then

Var[3X - 7Y] = 9 Var[X] - 42 Cov[X, Y] + 49 Var[Y]

Now, standard deviation = square root of variance, so

Var[3X - 7Y] = 9×6² - 42×2 + 49×8² =  3376

The general result is easy to prove: by definition,

Var[X] = E[(X - E[X])²] = E[X ²] - E[X]²

Cov[X, Y] = E[(X - E[X]) (Y - E[Y])] = E[XY] - E[X] E[Y]

Then

Var[aX + bY] = E[((aX + bY) - E[aX + bY])²]

… = E[(aX + bY)²] - E[aX + bY]²

… = E[a ² X ² + 2abXY + b ² Y ²] - (a E[X] + b E[Y])²

… = E[a ² X ² + 2abXY + b ² Y ²] - (a ² E[X]² + 2 ab E[X] E[Y] + b ² E[Y]²)

… = a ² E[X ²] + 2ab E[XY] + b ² E[Y ²] - a ² E[X]² - 2 ab E[X] E[Y] - b ² E[Y]²

… = a ² (E[X ²] - E[X]²) + 2ab (E[XY] - E[X] E[Y]) + b ² (E[Y ²] - E[Y]²)

… = a ² Var[X] + 2ab Cov[X, Y] + b ² Var[Y]

Answer:

$460.955 ≈ $460.96  

Step-by-step explanation:

A work week is 8 hours × 5 days = 40 hours per week.   Pete worked 44 hours and 30 minutes which is 44.5 hours.  This tells you that Pete worked 40 hours at regular paid and 4.5 hours of overtime at a rate is his amount per hour plus half of his amount per hour). So Pete earns $14.79 per hour for overtime rate  ($9.86 + $4.93 = $14.79) .

Earning for the week:  40 × $9.86 + 4.5 × $14.79

                                  = $394.40 + $66.555

                                  =  $460.955 ≈ $460.96