In testing the difference between the means of two normally
distributed populations, assuming equal variance of the
populations, if u1 = u2 = 50, n1 = 10, and n2 = 13, the degrees of
freedom for the t

The scatterplot that would be approximately follow a straight line is c.) a plot of log y against x.

Taking the logarithm of y transforms the model to log y = log 2.7 + x log 0.316, which is a linear function of x. Therefore, plotting log y against x would result in a linear relationship, where the slope of the line is the logarithm of 0.316 and the intercept is the logarithm of 2.7.

The other options do not result in a linear relationship when plotted. A plot of y against x would result in a curve, a plot of y against log x would result in an exponential curve, a plot of log y against log x would result in a power law relationship. Therefore, the correct answer is c).

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Answer:

B

Step-by-step explanation:

by a rule of angles in parallel lines we have that

angle 4 + angle 5 =180

so we have

(3x+15)+(2x-10)=180

(3+2)x+(15-10)=180

5x+5=180

5(x+1)=180

x+1=36

x=36-1

x=35

Answer:

B. 35

Step-by-step explanation:

<4 and <5 are supplementary angles and their sum is = 180°

3x + 15 + 2x - 10 = 180 add like terms

5x + 5 = 180

5x = 175

x = 35

The value of sin 150° is -1/2. and cos 150° is √3/2 (note that it is negative because it is in the second quadrant).

We can use the unit circle to find the exact values of sin 150° and cos 150°.

First, let's consider sin 150°. Since 150° is in the second quadrant, we know that sin 150° is negative. Also, we know that the sine function is periodic with a period of 360°, which means that sin 150° is equal to sin (150° - 360°) = sin (-210°). Now we can use the reference angle of 30° (since 210° is 30° past the 180° mark in the second quadrant) to find the exact value of sin 150°:

sin 150° = sin (-210°) = -sin 30° = -1/2

Therefore, sin 150° is -1/2.

Next, let's consider cos 150°. Since 150° is in the second quadrant, we know that cos 150° is negative. Also, we know that the cosine function is periodic with a period of 360°, which means that cos 150° is equal to cos (150° - 360°) = cos (-210°). Now we can use the reference angle of 30° to find the exact value of cos 150°:

cos 150° = cos (-210°) = cos 30° = √3/2

Therefore, cos 150° is √3/2 (note that it is negative because it is in the second quadrant).

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Answer:

\(V=\frac{32}{3} \pi\)

Step-by-step explanation:

We first need to know the formula to find the volume of a sphere.

The formula to find the volume of a sphere is:

(Where V is the volume and r is the radius of the sphere)

If the radius of the sphere is 2, then we can insert that into the formula for r:

Therefore the answer is \(V=\frac{32}{3} \pi\).

Answer:

¿Qué distancia recorre con 1.000 pasos? Multiplicas: 7/8 ×1000 = 7000 / 8 = 875 m. ¿Cuántos pasos debe dar para recorrer una distancia de1400 m.? Divides: 1400 ÷ (7/8) = (1400×8) / 7 = 1600 pasos.

Step-by-step explanation:

Answer:

∠B = 55

Step-by-step explanation:

∠A + ∠B + ∠C = 180  {Angle sum property}

35 + ∠B + 90  = 180

        ∠B + 125 = 180

                  ∠B = 180 - 125

                  ∠B = 55

The question mentions obtaining the iterative Cochrane-Orcutt estimates using data related to barium. It also asks whether the Prais-Winsten and Cochrane-Orcutt estimates are similar and whether such similarity was expected.

The Cochrane-Orcutt method is a procedure used for estimating parameters in a time series regression model when there is serial correlation in the error terms. It involves using an iterative process to estimate an autoregressive model. The Prais-Winsten method is a similar approach that addresses serial correlation in a time series regression model.

Without specific data related to barium or the estimated coefficients, it is not possible to determine the similarity between the Prais-Winsten and Cochrane-Orcutt estimates in this context. However, both methods aim to address the issue of serial correlation, and thus, their estimates are expected to be similar in terms of addressing this specific problem.

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Answer:

option d. perimeter of quadrilateral=35

The environment changed in such a way that, "guppies with small spots had a better chance of survival and reproduction, leading to an increase in their population and a decrease in the population of guppies with large spots".

Over many generations, guppies with small spots had a survival advantage in the river because the rocks on the river bottom became smaller. This made guppies with small spots harder for larger fish to see and catch, increasing their chances of survival and reproduction.

As a result, more guppies with the small spot gene passed it on to their offspring, leading to an increase in the population of guppies with small spots. At the same time, the population of guppies with large spots decreased as they were more visible to predators and had a lower chance of survival. This process of natural selection led to a change in the frequency of different traits within the population of guppies.

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The value of X and y using substitution method for the quadratic equation given above would be = -3.6 and - 2.8 respectively.

The equations given are;

2x - 7y = 13. ----> equation 1

3x + y = 8 --------> equation 2

From equation 2 make y that subject of formula;

y = 8 - 3x

Substitute y = 8 - 3x into equation 1

2x - 7(8 - 3x) = 13

2x - 56 - 21x = 13

-19x = 13+56

-19x = 69

X = -69/19

X = - 3.6

Substitute X = -3.6 into equation 2

3(-3.6) + y = 8

y= 8 - 10.8

= - 2.8

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If we choose to use a diameter of 201 for the experiment, the strength will be 786.6596.

Given, the experiment in which weld diameter and shear strength (in pounds) were measured for five distinct spot welds on steel produced the data that is included.

The gathered information and the regression equation are shown below.

Strength = -941.6992 + 8.5988×Diameter

we have to calculate the predicted y-hat value for the diameter value of 201.

Now, we are given the regression equation with the strength and diameter as the variables.

now, when we put the diameter equal to 201, the strength will be

Strength = -941.6992 + 8.5988×Diameter

Diameter = 201

Strength = -941.6992 + 8.5988×201

Strength = -941.6992 + 1,728.3588

Strength = 786.6596

So, the value of the strength be 786.6596

Consequently, the strength value when the diameter is 201 be, 786.6596.

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The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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The length of an arc is given by the formula:

We are provided with the following;

Thus, we have:

Hence, the degree measure is 72 degrees

Answer: 36

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

it helps to organize and categorize large amounts of information, making it more accessible and manageable. This organizational structure helps users to locate specific codes and information efficiently. indexing system True.

The National Codes index lists entries under one main term, which is usually a broad topic or subject area. Under each main term, there may be several subentries that provide more specific details or categories related to the main term. This type of indexing system allows users to quickly and easily find information related to a specific topic, without having to search through an entire document or database. Additionally, it helps to organize and categorize large amounts of information, making it more accessible and manageable.

In the index of the National Codes, entries are listed under one main term to ensure easy navigation and understanding of the content. This organizational structure helps users to locate specific codes and information efficiently.

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Answer:

\( \dfrac{3a^2 + 3b}{a^2 - b^2} \)

Step-by-step explanation:

You can try factoring the numerator and denominator.

\( \dfrac{3a^2 + 3b}{a^2 - b^2} = \dfrac{3(a^2 + b)}{(a + b)(a - b)} \)

Nothing cancels out, so the expression is simplified as given.

Answer: \( \dfrac{3a^2 + 3b}{a^2 - b^2} \)

The COVID-19 pandemic led to significant changes in the grocery business. As restaurants closed their doors to all but take-out orders, grocery store revenues increased by approximately 10%. This increase in demand resulted in significant operational changes for grocery stores.

including expanded hours, increased staffing, and the implementation of strict health and safety protocols. Retailers also invested heavily in e-commerce capabilities to accommodate the increase in online orders. Furthermore, the pandemic has also impacted consumer behavior, as customers stockpiled items and made fewer trips to the store, opting instead for bulk purchases.

As the pandemic continues, the grocery industry will continue to evolve to meet consumer demands and changing economic conditions. In the future, we may see further investments in e-commerce capabilities, increased attention to health and safety protocols, and continued efforts to cater to shifting consumer preferences.

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Answer:

$0.75 per bottle is the unit cost per bottle

The two nonparallel vectors and the coordinates of a point in the plane with parametric equations is a = <2, 1, -1> = 2i + j -k and

b = <3, -5, 2> = 3i -5j + 2k.

Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude. As a result, vectors are shown as arrows and have starting and ending points. It took 200 years for the idea of vectors to develop. Physical quantities like displacement, velocity, acceleration, etc. are represented by vectors.

Additionally, the development of the field of electromagnetic induction in the late 19th century marked the beginning of the use of vectors. For a better understanding, we will explore the concept of vectors in this section along with their characteristics, formulae, and operations while utilising solved examples.

r(s, t) = < x, y, z> = < 2s+3t, s-5t, -s+2t >

r(s, t) = < x, y, z> = < 0+2s+3t, 0+s-5t, 0-s+2t >

r(s, t) = < x, y, z> = < 0+0+0, s(2, 1, -1), t(3, -5, 2) >

In parametric form for following:

a = <2, 1, -1> = 2i + j -k

b = <3, -5, 2> = 3i -5j + 2k

and point P(\(x_0,y_0,z_0\)) = P(0, 0, 0)

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Answer:

V= 1/3 pi*r^2*

Step-by-step explanation:

The reason the volume of a cone involves using the fraction 1/3, is because it takes three cones to fill up a cylinder. So, if the volume of a cylinder is pi*r^2*h, and a cone is 1/3 the size, then the volume of a cone(which uses the same formula) has to have the 1/3rd in front.

Answer:

V=πr2h

Step-by-step explanation:

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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The expected payoff from rolling the die is 0 usd.

According to the given question.

A die is rolled.

So, the possiblbe outcomes for a dice = {1, 2, 3, 4, 5, 6}

⇒ Total number of outcomes = 6

Also, it is given that

If a die is roll to a 1 or 2, we win 2usd and if it rolls to 3, 4, 5, or 6 we lose 1 usd.

As, we know that "Probability denotes the possibility of the outcome of any random event". And probability of any event can be calculated as

P(E) = total number of favorable outcomes/ Total number of outcomes

So,

The probability that die rolls 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3

And, the probability thet die rolls 3, 4, 5, or 6

= 1/6 +  1/6 + 1/6 + 1/6

= 4/6

= 2/3

Therefore, the excepted payoff from rolling this die

= \(2\times\frac{1}{3} - 1\times\frac{2}{3}\)

\(= \frac{2}{3} - \frac{2}{3}\)

= 0 usd

Hence, the expected payoff from rolling the die is 0 usd.

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The concentration of sugar in the tank after 11 minutes will be 1.8 pounds per gallon.

We are given the concentration function C(t) = 7 + (3t/100) + 15t, where t represents the time in minutes.

To find the concentration after 11 minutes, we substitute t = 11 into the function:

C(11) = 7 + (3(11)/100) + 15(11)

      = 7 + (33/100) + 165

      = 7 + 0.33 + 165

      = 172.33

Therefore, the concentration of sugar in the tank after 11 minutes is approximately 172.33 pounds per gallon.

Note: It's important to pay attention to units while performing calculations. In this case, the concentration is given in pounds per gallon, and the time is given in minutes.

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Answer:

SEE BELOW

Step-by-step explanation:

INTERRIOR ANGLES

3.

∠A + ∠B + ∠C = 180

(180 - 103) + (3x - 14) + (3x + 9) = 180

6x = 180 - 77 + 14 - 9

x = 108 / 6

x = 18

m∠ACB = (3x - 14)

             = 3(18) - 14

             = 40

m∠ABC = (3x + 9)

              = 3(18) + 9

              = 63

-------------------------------

INTERRIOR ANGLES

4.

∠A + ∠B + ∠C = 180

(180 - 97) + (2x + 2) + (14x - 1) = 180

16x = 180 - 83 - 2 + 1

x = 96 / 16

x = 6

m∠BCA = 2x + 2

             = 2(6) + 2

             = 14

m∠ABC = 14x - 1

             = 14(6) - 1

             = 83

-------------------------------

EXTERIOR ANGLES

5.

∠B

180 - 15x + 20

15x = 180 + 20

   x = 200/15

   x = 13.33

∠C

180 - 9x + 10  

9x = 190

 x = 190/9

 x = 21.11

∠E

180 - 17x + 2

17x = 182

  x = 182/17

  x = 10.706

m∠BEF = 17x + 2

             = 17 (10.706) + 2

             = 184

m∠ABC = 15x + 20

             = 15(15.33) + 20

             = 220

-------------------------------

EXTERIOR ANGLES

6.

first solve x by adding all the interior angles = 180

∠B + ∠E + ∠C = 180

2x + x + 93 = 180

3x = 180 - 93

x = 87/2

x = 43.5

m∠BEC = 360 - x

             = 360 - 43.5

             = 316.5

m∠ABC = 180 - 2x

             = 180 - 2(43.5)

             = 93

The age of the twins is 9 if the Johnson twins were born eight years after their older sister.

When a ratio, such as p:q, is used to express age, qx and px are taken into account. The current age will be (xn) years if you assume the current age to be x. If you're assuming that x is the age you are now, then 1/n of your age will be equivalent to (x/n) years.

What are known as age problems are one use for linear equations. The ages of two separate persons (or objects), both present and future (or past), are typically compared for solving age-related problems. These issues typically seek to determine the current age of each subject.

Let the age of twins be x

The age of older sister be x+8

x(x)(x+8) = x + x + (x+8)+1422

x²(x+8) = 3x+1430

x³+8x² = 3x+1430

x³+8x²- 3x-1430=0

x=9.2045≈9

Therefore, the age of the twins is 9

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Answer:

67

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

x + 55 = 90 (Right angle triangle)

x = 90 - 55

x = 35

Please mark as brainliest.

Answer:

19m, A

Step-by-step explanation:

Work = Force x distance

so rearrange to get:

distance = Work ÷ Force

distance = 665÷35

distance = 19m

Answer:

If 55 + 5x = 0 then x = -11

Step-by-step explanation:

To find x just get it by itself

55 + 5x = 0

subtract 5x

55 = -5x

then divide by -5

-11 = x