For the following scores: 15,14,9,10,15,12,14,11,13. 14,13,14,12,14,13,13,12,11 Organize the scores in a frequency distribution table. If there are rows in the table below the minimum value of X , leave the unused rows at the bottom. Based on the frequencies, identify the shape of the distribution. The distribution is with of scores. Last question: The distribution is (negatively skewed, positively skewed, or roughly symmetrical) with (no distinct piles, two piles, or one pile) of scores.

Model B is appropriate since the relationship between x and log y is linear. Hence, option E is the correct answer to this question.

The conclusion can be made based on the residual plot of Model B, which shows a linear pattern, indicating a good fit between the model and the data.

On the other hand, the residual plot of Model A shows a non-linear pattern, suggesting that the relationship between x and y may not be well-represented by a linear model.

By taking the logarithm of one or both of the variables, it may be possible to linearize the relationship and obtain a better model fit. Here, Model B, which models the relationship between x and log y, appears to be the more appropriate model.

Read more about the Residual plot:

brainly.com/question/27733055

#SPJ4

The complete question is -

Two variables, x, and y, were measured for a random sample of 25 subjects, and two separate regression models were fit to the data. The least squares estimation of the parameters in Model A yielded the following equation and residual plot. The least squares estimation of the parameters in Model B yielded the following equation and residual plot. Which of the following conclusions is correct?

(a) Model A is appropriate since the relationship between x and y is linear.

(b) Model B is appropriate since the relationship between x and y is linear.

(c) Model A is appropriate since the relationship between log x and log y is linear.

(d) Model A is appropriate since the relationship between log x and y is linear.

(e) Model B is appropriate since the relationship between x and log y is linear.

Answer:

Step-by-step explanation:

35 + 0.18 *x miles ≤ 71

x ≤ 200

0.18 *x miles ≤ 71 - 35

35≤ 71 - 0.18 *x miles

Charles should hire 20 workers for each hour.

To determine the optimal number of workers to hire, Charles needs to compare the marginal cost and marginal benefit of each additional worker.

The marginal benefit of each worker is the additional number of drinks they can produce multiplied by the average selling price per drink. The marginal cost is the hourly wage of each worker multiplied by the number of hours they work.

Initially, the marginal benefit of the first worker is 20 drinks * $3/drink = $60.

The marginal cost is $15/worker * 8 hours = $120.

The second worker has a marginal benefit of 18 drinks * $3/drink = $54.

The marginal cost is still $120.

For each additional worker hired, the marginal benefit decreases by 2 drinks * $3/drink = $6, while the marginal cost remains constant at $120.

Charles should hire workers as long as the marginal benefit is greater than the marginal cost.

Once the marginal benefit is equal to or less than the marginal cost, it is no longer profitable to hire more workers.

Therefore, Charles should hire workers until the marginal benefit is equal to the marginal cost, which occurs when the marginal benefit is $120.

To find out how many workers will provide a marginal benefit of $120, we set the marginal benefit equal to $120 and solve for the number of workers:

$6 * n = $120

$n = 20

For more questions on marginal benefit

https://brainly.com/question/8136407

#SPJ4

The quadrilateral ABCD is a parallelogram as the opposite sides are equal but not a rectangle because all the interior angles are not right angles.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

To make any conclusion about the quadrilateral we have to look at the lengths of each side by the distance formula [tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

AB = [tex]\sqrt{(4 - 0)^2 + (2 - 8)^2[/tex].

AB = [tex]\sqrt{16 + 36[/tex].

|AB| = √52.

Similarly, |DC| = √52.

So, AB = DC.

Now, |AD| = √85 and |BC| = √85.

So, AD = BC.

Therefore, The lengths of the opposite sides are equal so it is a parallelogram.

Now, To be a rectangle DC ⊥ CB.

Slope(DC) = 6/- 4 = - 3/2.

Slope(CB) = - 6/ - 7 = 6/7.

So The quadrilateral ABCD is a parallelogram.

learn more about quadrilaterals here :

https://brainly.com/question/29934291

#SPJ1

Answer:

p=0.83 g/cm3

Step-by-step explanation:

Density = Mass ÷ Volume

So,

Density = 25 g ÷ 30 cm³ = 0.83 g/cm³ (rounded to the nearest hundredth place).

The project start date for the project is 2/12/23.

In order to calculate the start date for the project, in excel, the WORKDAY Function is used. The WORKDAY Function is found under Excel Date and Time functions. The function provides a date that is N working days in the future or in the past. Working days exclude weekends and any dates identified as holidays.

The formula is: ‘=WORKDAY(start_date,days,[holidays]). The start_date (which represents the start date) and days (which represents the number of workdays to be added) are required fields. The [holiday] (which represents the array of dates that are included as workdays) is an optional field. In the given case, the formula used will be WORKDAY(G2, 0, C3:C13) and the project start date will be 2/12/23. Note that the start date of the first phase will be the same as start of the project.

Learn more about Project start date:

https://brainly.com/question/12310554

#SPJ4

Kyle needs 0 mL of the 24% solution and 42 mL of the 18% solution to make 20% acid solution.

percentage, a relative value indicating hundredth parts of any quantity.

Let's call the amount of 24% solution used x, and the amount of 18% solution used y.

We can set up two equations to represent the concentration of the mixture and the total volume of the mixture:

Concentration equation: (0.24 x + 0.18 y) / (x + y) = 0.20

Volume equation: x + y = 42 mL

we can substitute 42 mL for y in the volume equation and solve for x:

y = 42 mL

x = 42 - y = 42 - 42 = 0 mL

So, Kyle needs 0 mL of the 24% solution and 42 mL of the 18% solution to make 20% acid solution.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

As per the above given triangles the value of x is 45°.

Three-line segments joined end to end form the geometric shape of a triangle, which exists in two dimensions. These line segments are each referred to as a side, and the three locations where the sides converge are known as vertices. The type of triangle is determined by the angles between the sides and their lengths. Triangles can be classified as being equilateral, isosceles, scalene, right, or acute. The fact that a triangle's internal angles always add up to 180 degrees is just one of the intriguing characteristics of triangles. Triangles are a crucial idea in geometry and mathematics because they can provide the foundation for more complicated shapes and structures.

According to question:

[Since angles made by same chord on circumference are equal]

Sum of angles of triangle is 180°

47°+88°+x=180°

135+x=180

x=45°

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

The length of the unknown leg is given as follows:

x = 2.

The possible mistake is given as follows:

C. He did not square the length of the given leg.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

For this problem, we have that:

Hence the unknown leg is obtained as follows:

2.1² + x² = 2.9².

4.41 + x² = 8.41²

x² = 4

x = 2.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

The polynomial function for the number of ships in thousands that visited the port in a given year is

The polynomial is found by substituting the values of x and the function that has same value as in the table is the correct function

The function P(x) = 2.3x² + 0.2x + 1.8 gave the correction option, this can be ascertained using

x = 1

P(1) = 2.3 * 1² + 0.2 * 1 + 1.8 = 4.2

x = 2

P(2) = 2.3 * 2² + 0.2 * 2 + 1.8 = 8.2

x = 3

P(3) = 2.3 * 3² + 0.2 * 3 + 1.8 =  14.1

Learn more about polynomials at:

https://brainly.com/question/15702527

#SPJ1

The result after the point is translated is (-5, -5)

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

Point = (-9, -2)

The transformation rule is given as

translation left 4 units and down 3 units

Mathematically, this is represented as

(x, y) = (x + 4, y - 3)

So, we have

Image = (-9 + 4, -2 -3)

Evaluate

Image = (-5, -5)

Hence, the image is (-5, -5)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

The third-degree polynomial function that has an output of 1,025 when x=5, and has zeros −20 and −4i is:

f(x) = 4.55(x + 20)(x² - 16)

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

A third-degree polynomial function with real coefficients that have zeros at -20 and -4i can be written in the form:

f(x) = a(x + 20)(x + 4i)(x - 4i)

where a is a constant.

Expanding the expression and using the fact that i² = -1:

f(x) = a(x + 20)((x² + 4² × i²)

f(x) = a(x + 20)(x² - 16)   ....(i)

To find the value of a, we can use the fact that f(5) = 1,025:

So f(5) = a(5 + 20)(5² - 16) = 1,025

a(25)(25-16) = 1,025

a(25)(9) = 1,025

a(225) = 1,025

a = 1,025 / 225

a = 4.55

Substitute the value of a = 4.55 in equation (i), and we get

f(x) = 4.55(x + 20)(x² - 16)

Therefore, the third-degree polynomial function is f(x) = 4.55(x + 20)(x² - 16).

Learn more about the polynomial here:

brainly.com/question/11536910

#SPJ1

The acceleration of the rocket is 11.1 m/s^2.

We know that the acceleration can be obtained from the net force that is  acting on the rocket. Given that force is a vector quantity the direction of the forces that are acting is very important in the problem.

We know that;

Net force = Thrust force - Frictional force

If the net force is given by ma then;

2100a = 2.4×10^4 - 650

a = 2.4×10^4 - 650 /2100

a = 11.1 m/s^2

Thus, we can see that the magnitude of the acceleration is 11.1 m/s^2.

Learn more about acceleration:https://brainly.com/question/12550364

#spj1

Answer:

11

Step-by-step explanation:

6^2+9^2=c^2

36+81=c^2

117=c^2

[tex]\sqrt{117\\[/tex]

11

The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is,  - 4.19.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ f (x) = -1.8x² + 7x - 11

Now, We can differentiate with respect to x as;

⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0

⇒ f ' (x) = - 3.6x + 7

Put f ' (x) = 0

⇒ - 3.6x + 7 = 0

⇒ 3.6x = 7

⇒ x = 1.94

Now, Again differentiate with respect to x as;

⇒ f ' (x) = - 3.6x + 7

⇒ f '' (x) = - 3.6 × 1 + 0

⇒ f '' (x) = - 3.6 < 0

Hence, Substitute x = 1.94 in function to get maximum value,

⇒ f (x) = -1.8x² + 7x - 11

⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11

⇒f (x) = - 6.77 + 13.58 - 11

⇒ f (x) = - 4.19

Thus, The maximum value = - 4.19

Learn more about the function visit:

https://brainly.com/question/28793267

#SPJ1

The new current if the voltage is increased to 9 volts is given as follows:

0.18A = 180 mA.

Ohm's First Law states that a circuit's voltage is obtained as the multiplication of the resistance and of the current, as follows:

V = RI.

In which:

When 8 volts are applied to a circuit, 160 milliamperes (mA) = 0.16 A of current flow through the circuit, hence the resistance is obtained as follows:

8 = 0.16R

R = 8/0.16

R = 50 ohms.

Then the new current if the voltage is increased to 9 volts is given as follows:

9 = 50I

I = 9/50

I = 0.18A = 180 mA.

More can be learned about Ohm's First Law at https://brainly.com/question/231741

#SPJ1

The solution of the functions  [tex]f(x) = \frac{3}{4}x + 2\frac{1}{4}[/tex] and [tex]g(x) = (\frac{1}{2})^x + 1[/tex]

is (1.286, 1.41).

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Are two functions [tex]f(x) = \frac{3}{4}x + 2\frac{1}{4}[/tex] and [tex]g(x) = (\frac{1}{2})^x + 1[/tex].

We know the solution to f(x) and g(x) is where the two functions intersect.

The graph of the functions intersects at (1.286, 1.41) and hence it is the solution.

learn more about functions here :

https://brainly.com/question/12431044

#SPJ1

In  2000, the population of bacteria reached 5 million, and it is projected to have 7.5 million in 2025. the value of a is 1.49.

A particular class of mathematical model used to explore population dynamics is called a population model.

P(x)  = C a ^ ( X - 2000)

C = 5m = 5(10⁶)

p( X ) = 5(10⁶) a ^ ( X - 2000)

7. 5 * 5(10^6) = 10 ^6 a^ 25

7. 5 = a ^ 5

 log 7.5 = 5 log a

  a =10 ^( log 7.5 / 5 )= 1.49

 P ( x ) =  ( 1.49m ) ^  ( X- 2000)

Models enable a better comprehension of the operation of intricate relationships and processes. Understanding how numbers change over time or in connection to one another may be made more manageable through the modelling of dynamic interactions in nature. Using population modelling as a technique allows for the detection of several trends.

Learn more about Model of population;

https://brainly.com/question/4531582

#SPJ4

In  2000, the population of bacteria reached 5 million, and it is projected to have 7.5 million in 2025. the value of a is 1.49.

A particular class of mathematical model used to explore population dynamics is called a population model.

P(x)  = C a ^ ( X - 2000)

C = 5m = 5(10⁶)

p( X ) = 5(10⁶) a ^ ( X - 2000)

7. 5 * 5(10^6) = 10 ^6 a^ 25

7. 5 = a ^ 5

log 7.5 = 5 log a

 a =10 ^( log 7.5 / 5 )= 1.49

P ( x ) =  ( 1.49m ) ^  ( X- 2000)

Models enable a better comprehension of the operation of intricate relationships and processes. Understanding how numbers change over time or in connection to one another may be made more manageable through the modelling of dynamic interactions in nature. Using population modelling as a technique allows for the detection of several trends.

To learn more about population of bacteria visit

https://brainly.com/question/6562651?

#SPJ4

We rule up the team members, say by Social Security number. We now ask each in turn her/his job explanation and political affiliation and data the information.

For any person, the information can be recorded as an instruct pair (x ,y) where x is one of B or W, and y is one of R, D, or I. So, there are for any person 6 possible records. The team conclusion is a sequence of such records, of length 15. Thus, for our team there are 6^15 possible results.

How many of these results have at least one blue-collar worker? How many have no blue-collar worker? Then x=W, and y can still take on any of 3 values, for a total of 3^15 possibilities. Thus, the number of possible summaries with at least one B is 6^15−3^15.

To know more about Probability:

https://brainly.com/question/30034780

#SPJ4

Answer:

Step-by-step explanation:

The square root of a negative real number can be represented as the imaginary unit, "i", multiplied by the square root of the absolute value of the negative number. In this case, the square root of -180 is:

√(-180) = i * √(180)

The standard form of a complex number is "a + bi", where "a" and "b" are real numbers and "i" is the imaginary unit. In this case, a = 0 and b = √(180), so the complex number can be written as:

0 + i * √(180) = i * √(180)

Therefore, the complex number √-180 in standard form is: i * √(180).

The volume of a cube with sides of length 2(1/4) inches is 11.4 inches³.

It is a polygon having six faces.

The volume of a cube is a side³

We have,

V = s³

s = 2(1/4) inches

s = 9/4 inches

Now,

V = s³

V = (9/4)³

V = 729/64

V = 11.4 inches³

Thus,

The volume of the cube is 11.4 inches³.

Learn more about cubes here:

https://brainly.com/question/11168779

#SPJ1

The exact length of the sides of the quadrilateral are as follows:

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, A quadrilateral ABCD with vertices A(4, 5), B(-3,3), C(-6,-13) and D(6,-2).

From the general formula of the distance between two coordinates in 2D plane.

Distance = √((x - x')² + (y-y')²)

For AB,

Distance = √((4  + 3)² + (5-3)²)

Distance = √49 + 4

Distance = √53

For BC,

Distance = √((-6 +3 )² + (-13-3)²)

Distance = √9 + 256

Distance = √264

Distance = 2√66

And the same process is to be continued For the CD and DA

While

CD = √265

DA = √53

Therefore, The exact length of the sides of the quadrilateral are as follows:

Learn more about coordinates here:

https://brainly.com/question/20282507

#SPJ1

It is not possible to determine whether the range of data set ii is smaller than the range of data set i.

The statement "Data set ii has a smaller range than data set i" cannot be justified based on the boxplots. This is because the range of a data set is the difference between the largest and smallest values in the set, and this information is not represented on a boxplot. To calculate the range of a data set, we use the formula Range = Max - Min, where Max is the largest value in the set and Min is the smallest value in the set. Since the boxplot does not show the actual values in the data set, it is impossible to calculate the range of the data set. Therefore, it is not possible to determine whether the range of data set ii is smaller than the range of data set i.

Learn more about smallest values here:

https://brainly.com/question/29627394

#SPJ4

Complete question: Which of the following statements about these two data sets cannot be justified based on the boxplots?

The candle burns at the rate of 0.5 inches per hour.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

The proportional relationship between the number of inches a candle has burned away, b, at any time in hours, t.

The expression can be represented by the equation

b = 0.5t.

The equation shows a proportional relationship.

That means,

b/t = 0.5.

Therefore, the rate is 0.5 inches per hour.

To learn more about the proportional relationship;

brainly.com/question/28777033

#SPJ1

The solution to the system of equations is  x= -12/7  and y= 9/7.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

5x + 2y = -6.............(1)

2x - 2y = -6............(2)

Solving equation (1) and (2) we get

5x+ 2x = -12

7x = -12

x= -12/7

and, 2(-12/7) -2y= -6

-2y = -6 + 24/7

y= 9/7.

Hence, the values are x= -12/7  and y= 9/7.

Learn more about Equation here:

https://brainly.com/question/29657992

#SPJ1

Best deal for the round pizza is,

''Two 12-inch diameter round pizzas for $17.50.''

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Pizza Shack offers the following pizza deals.

• A 16-inch diameter round pizza for $16

• Two 12-inch diameter round pizzas for $17.50

• A 15-inch square pizza for $17

Now, For first deal;

• A 16-inch diameter round pizza for $16

Hence, The cost of 1 inch diameter round pizza = $16/16

                                                                         = $1

For second deal;

• Two 12-inch diameter round pizzas for $17.50

Hence, Cost of 1 round pizza for 1 inch diameter = $17.50 / 2×12

                                                                          = $0.73

For third deal;

• A 15-inch square pizza for $17

Hence, The cost of 1 inch diameter round pizza = $17/15

                                                                         = $1.13

Thus, The best deal is,

Two 12-inch diameter round pizzas for $17.50

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ1

The angular acceleration of the cart would be (50/m) rad/s².

The relation between the linear and angular velocity is -

v = rω

Given is a cart with a force of 500N and moves along a circular track with a radius of 10 meters

We can write the tangential force as -

F{t} = 500

m a{t} = 500

m dv{t}/dt = 500

m d/dt (rω) = 500

mr dω/dt = 500

dω/dt = 500/10m

dω/dt = 50/m

α = 50/m

Therefore, the angular acceleration of the cart would be (50/m) rad/s².

To solve more questions on circular motion, visit the link below -

https://brainly.com/question/13091583

#SPJ1

{Question in english -

A horse pulls a cart with a force of 500N and moves along a circular track with a radius of 10 meters.}

The value of Y when X = 4 in the regression line that has the slope of 2,5 is a) 26

The equation of a straight line with slope m and y-intercept b is given by  :

y = mx + b.

Where

1. y is the dependent variable (i.e., the value of y depends on x)

2. x is the independent variable

3. m is the slope of the line, representing the rate of change of y with respect to x

4. b is the y-intercept, the point where the line intersects the y-axis when x = 0.

This equation can be used to describe the relationship between two variables, and it can be used to make predictions about the value of y for a given value of x, or to find the value of x for a given value of y.

From the question we have the following information :

1. Slope ( or m ) is 2.5

2. The intercept ( y-intercept or b ) is 16

So, using the values given (slope = 2.5, y-intercept = 16), we have:

y = mx + b

y = 2.5x + 16

When X is 4, substituting X with 4 in the equation gives us:

y = 2.5 * 4 + 16 = 26

So the value of Y when X is 4 is 26. Answer: a) 26.

Learn more about equation of a straight line with slope here

https://brainly.com/question/24143133

#SPJ4

Angle ECD will therefore be complementary to this and equal 15°

Angle DAQ will be supplementary to this as BAC = 23, which is 90 - 23 = 67.

Additionally, QDA = 90 - DAQ = 23

And because DP = PC, the angle DCP in the triangle DPC equals the angle PDC.

However, since transverse AC parallelizes DC and AB, angle BAC = angle DCP = 23.

PDC also equals 23.

So....

QDA plus PDC is 23 + 23 = 46°.

Keep in mind that the square's side equals the side of the equilateral triangle.

Thus, draw EC

EB = CB in the triangle ECB, and angle CBE is equal to 30°.

However, because EB = CB, ECB, and CEB's opposing angles will be equal.

Both will be equal to = (180 - 30) / 2 = 150 / 2 = 75°.

Thus, angle ECB = 75°.

Angle ECD will therefore be complementary to this and equal 15°.

Know more about rectangle

https://brainly.com/question/25292087

#SPJ4

Least common denominator is 100.

Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing.

Given fractions are,

20 7/10 = 207/10

20 3/4 = 83/4

18 9/10 = 189/10

20 18/25 = 518/25

Common Denominator is 10 × 4 × 10 × 25

                                       = (5 × 2) × (2 × 2) × (5 × 2) × (5 × 5)

Common factor among three numbers are 5 , 2.

Uncommon factors are 5 , 2                                        

Least common denominator = 5 × 2 × 5 × 2 = 100

Hence, 100 is least common denominator of the given fractions.

Learn more about fraction here:

https://brainly.com/question/1301963

#SPJ1