Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:
rev: 12_26_2015_QC_CS-36924
t distribution with df = 81.
t distribution with df = 82.
t distribution with df = 41.
t distribution with df = 80.

The solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

What is a quadratic equation?

Any equation of the form  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

x = [-b± (√b²-4ac )] / 2a

The quadratic equation:

x²+6x+9=20

x²+6x -11 = 0

a = 1, b = 6, c = -11

x₁,₂ = [-6±√6² - 4.1.(-11)]/2(1)

x = -3 + 2√5 , x = -3 - 2√5

Thus, the solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

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As per the sampling, the resulting values of

(a) Single sample design

(b) two independent samples

(c) matched pairs

What is meant by sampling?

In math, sampling is the process of selecting the group that you will actually collect data from in your research.

Here we have find in Which design the following situations all require inference about a mean or means.

By looking into the given statement,  (a) You want to estimate the average age of your store’s customers.

Here this is a single sample design and the only sample we need here is the store’s customers.

Where as (b) You do an SRS survey of your customers every year. One of the questions on the survey asks about customer satisfaction on a seven-point scale with the response 1 indicating “very dissatisfied’’ and 7 indicating “very satisfied.’’ You want to see if the mean customer satisfaction has improved from last year.

In this is the two independent samples design. Because in this case we compare the customer satisfaction of two groups of customers. And the first group is the customers from last year and the other is the group from this year.

Finally, (c) You ask an SRS of customers their opinions on each of two new floor plans for your store.

Here we have a matched-pair design in this case because one group of people gave opinions on two new floor plans.

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To find the angular speed in rpm, we need to use the formula for tangential speed, which is the speed at which an object moves along a circular path. The formula for tangential speed is:

v = r * omega

where v is the tangential speed, r is the radius of the circle, and omega is the angular speed.

In this case, we are given that v = 25 mph and r = 15 feet. We can solve for omega by dividing both sides of the equation by r:

omega = v / r

Substituting the given values, we get:

omega = 25 mph / 15 feet

To convert the units of speed from mph to feet per second, we need to use the conversion factor that 1 mph is equal to 5280/3600 feet per second. We can use this conversion factor to rewrite the expression for omega in terms of feet per second:

omega = (25 mph * (5280/3600)) / 15 feet

This simplifies to:

omega = 0.7222 feet/second

Next, we need to convert the angular speed from feet per second to rpm. To do this, we need to use the formula for converting from linear speed to angular speed, which is:

omega = (v * 60) / (2 * pi * r)

where v is the linear speed, r is the radius of the circle, and omega is the angular speed in rpm.

In this case, we are given that v = 0.7222 feet/second and r = 15 feet. We can solve for omega by plugging these values into the formula and simplifying:

omega = (0.7222 feet/second * 60) / (2 * pi * 15 feet)

= 0.7222 feet/second * 60 / (2 * pi * 15 feet)

= 0.7222 * 60 / (2 * pi * 15)

= 4.3332 / (2 * pi * 15)

= 0.2821 / (pi * 15)

Therefore, the angular speed in rpm is 0.2821 / (pi * 15), or approximately 0.0046 rp

Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05. Therefore, the null hypothesis should not be rejected.

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

An assertion used in statistical inference experiments is known as the alternative hypothesis. It is indicated by Ha or H1 and runs counter to the null hypothesis. Another way to put it is that it is only a different option from the null. An alternative theory in hypothesis testing is a claim that the researcher is testing.

One less than the confidence level, or 0.01, is the test's level of significance. The null hypothesis is not rejected since the p-value of 0.05 exceeds the level of significance of 0.01.

Therefore, the null hypothesis should not be rejected.

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The inequality is: h less than equal to 2 That is the Numbers written in order from least to greatest going across

To find:

The values that make the given inequality true.

We have,

h less than equal to 2

It means the value of h must be less than or equal to 2.

In the given options, the list of numbers which are less than or equal to 2 is

-6, -3, -1, 1, 1.9, 1.99, 1.999, 2

The list of numbers which are greater than 2 is

2.001, 2.01, 2.1, 3, 5, 7, 10

Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.

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The 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is expressed as f(x) ≈ P3(x) = a₀ + a₁(x - 4) + a₂(x - 4)² + a₃(x - 4)³.

Here, a₀, a₁, a₂, and a₃ are the coefficients that need to be calculated. To find these coefficients, we must use the Taylor series formula and the derivatives of f(x) evaluated at 4.

The Taylor series formula is Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!) (x-a)² + (f'''(a)/3!) (x-a)³ + ... +[tex](f^(n)(a)/n!) (x-a)^n[/tex].

The derivatives of f(x) evaluated at 4 are f'(4) = 1/2, f''(4) = -1/8, f'''(4) = -1/16.

Using these values, the coefficients of the 3rd-order Taylor polynomial can be calculated as a₀ = 2, a₁ = 1/2, a₂ = -1/8, and a₃ = -1/16.

Therefore, the 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is P3(x) = 2 + (1/2)(x - 4) - (1/8)(x - 4)² - (1/16)(x - 4)³.

Using this polynomial to approximate √14.03, we have P3(14.03) = 2 + (1/2)(14.03 - 4) - (1/8)(14.03 - 4)² - (1/16)(14.03 - 4)³ ≈ 3.76401097.

Therefore, the approximation of √14.03 using the 3rd-order Taylor polynomial is 3.76401097 to 8 decimal places.

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Answer:

b. temperature

Step-by-step explanation:

It is the measure of average kinetic energy of motion or K.E of a single particle in a system.

Answer:

[tex]r = \frac{3}{4}[/tex]

Step-by-step explanation:

Geometric sequence formula: [tex]a_n = a_1 r^{n-1}[/tex]

From the provided sequence, we know that the first term is -4

The second term is -3

Inserting to value to the formula

( n = 2, since we are using the value of the second term)

[tex]a_2 = -4 * r^{2-1}\\[/tex]

[tex]-3 = -4 * r[/tex]

[tex]r = \frac{-3}{-4}[/tex]

[tex]r = \frac{3}{4}[/tex]

Answer:

(-∞, -4)

Step-by-step explanation:

11x > 4(1+3x)

11x > 4*1+4*3x  ==> distribute 4 to 1 and 3x using the distribution property

11x > 4 + 12x  ==> simplify

11x-12x > 4 + 12x-12x  ==> isolate x by subtracting 12x on both sides

-x > 4

x < -4  ==> when dividing by a negative number, switch the inequality sign

x < -4 can also be written as -∞ < x < -4

This is because x is greater than -∞ but can never equal -∞.

-∞ < x < -4 ==> (-∞, -4)

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Answer:

Triangle RST rises 4 units and runs 8 units.

Triangle XYZ rises 3 units and runs 6 units.

The slope of line b is 1/2.

Step-by-step explanation:

Triangle RST rises 4 units and runs 8 units.

Triangle XYZ rises 3 units and runs 6 units.

The slope of line b is 1/2.

(2, 0) and (8, 3)

m = 3-0/8-2

m = 3/6

m = 1/2

As per the 95% confidence interval for the population mean is (31.042, 42.958).

What is meant by confidence interval?

In math, A normal distribution with a mean, μ  and standard deviation, σ  is used to estimate the confidence interval for the unknown population mean.

Here we have given that the random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations.

And we need to find the 95% confidence interval for ju for each of these situations.

Here we are given the following data:

   • Sample size, n=70

   • Sample mean, ¯x=37

   • Population standard deviation, σ=20

Then the 95% confidence interval for the population mean is defined as:

=> x±z0.01/2×σ√n

Here by applying Excel function for the confidence coefficient: 

=> NORM.INV(0.01/2,0,1)

Then we get,

=> 37±2.58×20√75(31.042, 42.958)

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The percentage of the business that James owns, given the amount he invested into the partnership, is 5 %

To find the percentage of the business that James owns, you first need to find the total amount invested into the business by all the partners. That amount is :

= 10, 000 + 10, 000 + 90, 000 + 90, 000

= $ 200, 000

The percentage of the business owned by James is :
= Amount invested by James / Total amount invested by partnership

= 10, 000 / 200, 000

= 5 %

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The resulting probability is 100%

How to calculate probability?

The general formula to calculate the probability is

=> P(B) = (n(B)/N(S)

where,

P(B) is the probability of an event 'B'.

n(B) is the number of favorable outcomes of an event 'B'.

n(S) is the total number of events occurring in a sample space.

Given,

A woman visits four different places: A, B, C, and D. If, at a given time, she is at point A, then the next hour she will be at point D with 100 percent probability. If she is at point B, then she will be at point A in an hour (with 100 percent probability) If she is at point C, then she will be at point A or B, with equal probabilities (that is, 50 percent each). If she is at point D, then she will be at point B or C with equal probability.

Here we have given that,

Number of places = 4 (A, B, C, D)

Initial point = A

Point D probability = 100%

For Point B to A probability = 100%

For point C to A or B probability = 50%

For point D to B and C probability = 50%

Now, here we need to find the probabilities that the woman will be at.

Like the women will spend three hours of travelling in the point A, B and C, then the probability of the points are calculated as,

=> 1 + 0.5 + 0.5 - 1

=> 2 - 1 = 1

Therefore, the resulting probability is 100%.

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The correct answer is c. The null hypothesis would be rejected at both the 0.05 and 0.01 levels.

A p-value is a probability of obtaining a result that is at least as extreme as the one observed in the sample data, given that the null hypothesis is true. The smaller the p-value, the less likely it is that the observed result occurred by chance, and the more likely it is that the null hypothesis is false.

In this case, the p-value of 0.002 is less than both the 0.05 and 0.01 significance levels, which means that it is highly unlikely that the observed result occurred by chance if the null hypothesis is true. Therefore, the null hypothesis should be rejected at both the 0.05 and 0.01 levels.

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If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94

As we can see here,

20N force which is passing through the center O will not produce any torque about point O

For 30N force which is acting at 45 angles with the x−axis, its x−component will pass through the origin, hence its horizontal component will also not cause any torque about O

Hence, torque because of 20N force which is acting in a tangential direction :

τ1=r⊥F=0.1×30=3N-m

Torque produced by y component of 30N force acting at angle 45:

τ2=r⊥F=0.05×30sin45∘

=0.05×30×1/√2=1.5/√2Nm⨀

Torque produced by 20N force acting in negative y direction:

τ3=r⊥×F=0.05×20

τ=1Nm⨀

Hence, the Net torque produced on O

τnet=τ1+τ2+τ3

τnet=−3+(1.5/√2)+1

τnet=−0.94Nm

or

|τnet|=0.94Nm

So  If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94

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Answer:

The answer would be 12.

The equation would be (25/5)+7

Step-by-step explanation:

To solve this problem, first divide 25 by 5.

25/5=5

Now, add 7 to 5 for your answer.

The answer would be 12.

The equation would be (25/5)+7

Hope this helps! Have a great day! :D

25÷5=5

5+7=12

12 is your answer

The number as a product of two fractions is 4/2 * 1/5

From the question, we have the following parameters that can be used in our computation:

Fractions = 2/5

To express it as a product of two fractions, we start with the following equation (first split)

Fractions = 2/1 * 1/5

Express 2 as 4/2

So, we have the following representation

Fractions = 4/2 * 1/5

Hence, the fraction products is 4/2 * 1/5

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The domain and range of the given function is a set of al real numbers and as such;

Domain : (-∞,∞)

Range : (-∞,∞)

We are given the function as f(x)= -3x+7.

In order for us to sketch the graph of this given function, we need to make a function table

Lets assume some random number for x  and find out f(x)

x                f(x) = -3x + 7

-2                 -3(-2) + 7 = 13    

-1                 -3(-1) + 7 = 10

0                 -3(0) + 7 = 7

1                  -3(1) + 7 = 4

We now plot the points as shown in the graph attached

Domain is defined as the set of all x values for which the function is defined while Range is defined as the set of all y values for which the function is defined

In this case, there is no restriction for x  and y and as such the domain and range is a set of all real numbers

Domain : (-∞,∞)

Range : (-∞,∞)

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Complete question is;

Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -3x + 7

The simplified expression of [(b - 3)/(b² + 2b)] + [b/(4b + 8)] is (b² - 12 + 4b)/[(4b)(b + 2)]

From the question, we have the following parameters that can be used in our computation:

[(b-3)/(b^2+2b)]+[b/(4b+8)]

Rewrite the exponents

[(b - 3)/(b² + 2b)] + [b/(4b + 8)]

So, we have

(b - 3)/(b² + 2b) + b/(4b + 8)

Factor out b and 4

(b - 3)/b(b + 2) + b/4(b + 2)

Factor out 1/(b + 2)

1/(b + 2) * ((b - 3)/b + b/4)

So, we have

1/(b + 2) * (4(b - 3) + b²)/(4b)

This gives

1/(b + 2) * (4b - 12 + b²)/(4b)

Rewrite as

1/(b + 2) * (b² - 12 + 4b)/(4b)

Lastly, we have

(b² - 12 + 4b)/[(4b)(b + 2)]

Hence, the solution is (b² - 12 + 4b)/[(4b)(b + 2)]

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Both triangles are congruent by the SAS congruence theorem.

The congruence statement is, ΔBDC ≅ ΔBDA.

The SAS stands for side-angle-side theorem, which means that if we can show that two triangles have two corresponding congruent sides and one pair of corresponding congruent included angle, then both triangles are congruent.

From the information given, we can state the following:

AB ≅ CB, which is one pair of corresponding congruent sides [given]

Angle ABD ≅ angle CBD, which is one pair of corresponding included congruent angles [given]

BD ≅ BD, also one pair of corresponding congruent sides [reflexive property of congruence]

Therefore, we can conclude based on the above information that:

ΔBDC ≅ ΔBDA by the SAS congruence theorem.

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The distance between the satellite and tracking station at 12:03 p.m is 1271.55 miles.

Given that :

TS = 1000 miles

Orbital time = 2 hours

Let T be tracking station.

     S be satellite position.

     R be a satellite position at 12:03 p.m

Time = 12:03 - 12:00 = 3 min

SR = Satellite speed × time

Orbital distance = 2πR

                           = 2π(4000 + 1000)

                           = 10000 π miles

Orbital speed =  [tex]\frac{satellite distance}{satellite time}[/tex]

                       = [tex]\frac{10,000\pi }{2}[/tex]

                       = 5000 π miles/hour

                       = [tex]\frac{5000 \pi }{60}[/tex] miles/min

Distance SR  = Orbital speed × time

                      = [tex]\frac{5000 \pi }{60}[/tex] × 3

                      = 250 π miles

Using pythagoras theorem in triangle TSR

      [tex]TR^{2}[/tex] = [tex]TS^{2} + SR^{2}[/tex]

             = [tex]\sqrt{TS^{2} + SR^{2} }[/tex]

             = [tex]\sqrt{1000^{2} + 250 \pi ^{2} }[/tex]

        TR = 1271.55 miles

Therefore, the distance between the satellite and tracking station at 12:03 p.m is 1271.55 miles.

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The cumsum function returns the cumulative sum of an array whose size is not 1 from the dataset that is imported from Walmart.

Create an array of the number of stores in each state along with the date opened. You can then use the cumsum option to find the total number of stores Walmart has over the states.

For instance, to find cumulative sum of integers 1 to 6, we have

A = 1:6;

B = cumsum(A)

It yields the output:

1, 3, 6, 10, 15, 21

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To get the coordinate of point R partitioned by the ratio 3:5, the required

What is partition

To divide (something, as a country) into two or more territorial pieces with distinct political standing is to divide it into parts or shares. to divide or separate by a partition (such as a wall), frequently used with off.

formula will be given as [tex]M(x, y)=\left(\frac{a x_1+b x_2}{a+b}, \frac{a y_1+y_2}{a+b}\right)[/tex]M(x, y) = (ax1+bx2/a+b, ay1+by2/a+b)

The midpoint rule

From the given statement, we have the following information

Point Q = (-14, 0)

Point S = (2, 0)

R = (x, y)

To get the coordinate of point R partitioned by the ratio 3:5, the required formula will be given as M(x, y) = (ax1+bx2/a+b, ay1+by2/a+b)

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The simplified form of an expression is the expression written in its simplest form, usually achieved by combining like terms and removing unnecessary parentheses.

To take 10% of something, move the decimal point one spot to the left

Examples:

If x and y be  i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero.

Yes, x y are x y independent studysoup.

Here  x and y be i.i.d. unif(0, 1)

The i.i.d stands for independent and identically distributed

unif means that the uniformly distributed

Here x and y are i.i.d unif (0,1)

The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable

Here we have to find the covariance of x + y and x - y

According to the properties of covariance

Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0

Because Cov(x, x) = Cov (y, y)

Cov(y, x) = Cov(x, y)

Therefore, the covariance of x+y and x - y is 0.

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The null and alternative hypothesis of the number models are

H₀ : There is no difference among the means of four samples models.

H₁ : There is difference among the means of four samples models.

Given that,

Many photocopiers are used by a large marketing company, several of each of the four models. The office manager calculated for each machine the typical amount of minutes per week that it is out of commission due to repairs over the previous six months, yielding the following information:

Model g: 56 61 68 42 82

Model h: 74 77 92 63 54

Model k: 25 36 29 56 44

Model m: 78 105 89 112 61

We have to find the null and alternative hypothesis.

We know that,

So,

H₀ : There is no difference among the means of four samples models.

H₁ : There is difference among the means of four samples models.

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The estimated regression equation for the given data is y = 17.49 + 1.0334x.Create a 95% confidence interval for the median entertainment spending for all cities with $89/day room rates.

a. Estimate the amount of money that will be spent on entertainment in a city with a $89 daily hotel fee (to 2 decimals).

$106.55

b. Create a 95% confidence interval for the average entertainment spending for all cities with $89 daily room rates (to 2 decimals).

($102.61, $110.49)

c. A hotel in Chicago costs $128 on average per night. Create a 95% prediction interval for Chicago's entertainment spending (to 2 decimals).

($132.42, $143.75)

The estimated regression equation for the given data is y = 17.49 + 1.0334x. For a particular city that has a daily room rate of $89, the predicted amount spent on entertainment is $106.55. The 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 is ($102.61, $110.49). For Chicago, which has an average room rate of $128, the 95% prediction interval for the amount spent on entertainment is ($132.42, $143.75).

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The length of the rectangle is 1.054 units and the width of the rectangle is 4.72 units.

Length times width equals the area of a rectangle. Let's assume that x represents length and y represents width. To determine the dimensions of the rectangle, we must apply y values to the area formula, differentiate with respect to x, and then set differentiate to zero.

Parabola: [tex]y=5-x^{2}[/tex]

The equation of parabola indicates that it opens down and the axis of symmetry is x=0. So we can take the vertices of the rectangle on the x-axis as [tex]A=(-x,0)[/tex] and [tex]D=(x,0)[/tex]). The other two vertices above the x-axis on the parabola will be [tex]B=(-x, 5-x^{2} )[/tex] and [tex]C=(x,5-x^{2} )[/tex]

Dimensions of the rectangle will be,

[tex]x-(-x)=2x[/tex] and [tex](5-x^{2} )[/tex]

Area of the rectangle (A) = [tex]2x(5-x^{2} )[/tex]

Area function when differentiated (A′) = [tex]2x(-2x)+(5-x^{2} )(2)[/tex]

A′= [tex]-4x^{2} + 10 -2x^{2}[/tex]

A′= [tex]-6x^{2} +10[/tex]

Critical points for maxima and minima ⟹ [tex]-6x^{2} +10=0[/tex]

                                                               ⟹ [tex]10=6x^{2}[/tex]

                                                               ⟹ [tex]x^{2} = \frac{10}{6}[/tex]

                                                               ⟹ [tex]x= \sqrt \frac{10}{6}[/tex]

                                                               ⟹ [tex]x=[/tex] ±[tex]0.527[/tex]

Maximum area of 2X2 rectangle(square)

A= [tex]2*0.527(5- 0.527^{2} )[/tex] = [tex]4.97[/tex] [tex]units^{2}[/tex]

Length = 2x = 1.054 units

Width = [tex](5-x^{2} )[/tex] = 4.72 units

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