their current GPAs.
Entering GPA Current GPA
3.5 3.6.
3.8 3.7
3.6 3.9
3.6 3.6
3.5 3.9
3.9 3.8
4.0 3.7
3.9 3.9
3.5 3.8
3.7 4.0
a. ỹ = 5.81 + 0.497x
b. ỹ = 3.67 + 0.0313x
c. ỹ = 2.51 + 0.329x
d. ŷ= 4.91 + 0.0212x

Answers

Answer 1

(a) ỹ = 5.81 + 0.497x is the best fit for the data to show their current GPAs.

To determine which regression equation best fits the data, we can calculate the correlation coefficient (r) between the two variables, which will indicate the strength and direction of the relationship.

Using a statistical software or a calculator, we can find that the correlation coefficient between entering GPA and current GPA is r = 0.737, which indicates a moderately strong positive relationship.

To choose the best regression equation, we can look at the slope coefficient (β1) of each equation, which represents the amount of change in the dependent variable (current GPA) for every one-unit increase in the independent variable (entering GPA).

a. ỹ = 5.81 + 0.497x: This equation has a slope coefficient of 0.497, indicating that for every one-unit increase in entering GPA, current GPA increases by 0.497.

b. ỹ = 3.67 + 0.0313x: This equation has a slope coefficient of 0.0313, indicating that for every one-unit increase in entering GPA, current GPA increases by only 0.0313.

c. ỹ = 2.51 + 0.329x: This equation has a slope coefficient of 0.329, indicating that for every one-unit increase in entering GPA, current GPA increases by 0.329.

d. ŷ= 4.91 + 0.0212x: This equation has a slope coefficient of 0.0212, indicating that for every one-unit increase in entering GPA, current GPA increases by 0.0212.

Based on the correlation coefficient and the slope coefficients, we can conclude that equation (a) ỹ = 5.81 + 0.497x is the best fit for the data as it has the highest slope coefficient, indicating a stronger relationship between the variables, and the y-intercept of 5.81 is closer to the average current GPA of 3.78.

Correct Question :

Which of the following equation best fit their current GPAs.

Entering GPA Current GPA

3.5 3.6.

3.8 3.7

3.6 3.9

3.6 3.6

3.5 3.9

3.9 3.8

4.0 3.7

3.9 3.9

3.5 3.8

3.7 4.0

a. ỹ = 5.81 + 0.497x

b. ỹ = 3.67 + 0.0313x

c. ỹ = 2.51 + 0.329x

d. ŷ= 4.91 + 0.0212x

To learn more about best fit here:

https://brainly.com/question/10054857

#SPJ4


Related Questions

Two circles are Sean or RB equals 27 and HT equals 25.5

Answers

Thus, the arc length MH for the given concentric circles is found to be 10.8π.

Explain about the sector of the circle:

The curved portion that runs along the circle's perimeter and joins the ends of a two radii that make up a sector is known as the sector arc. Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii.

Given that-

RB = 27 cm, HT = 25.5 cm and m∠HRB = 72°.

RB = MR = 27 cm (radius of the inner circle)

Since MRB is the straight line:

m∠MRH + m∠HRB = 180 (linear pair)

m∠MRH + 72 = 180

m∠MRH  = 180 - 72

m∠MRH  = 108 (say Ф)

Using the formula for the length of the sector

length of arc MH = Ф/360 * (2πr)

Put the values:

length of arc MH = 72/360 * (2π*27)

length of arc MH = 0.2 * (54π)

length of arc MH = 10.8π

Thus, the arc length MH for the given concentric circles is found to be 10.8π.

Know more about the sector of the circle:

https://brainly.com/question/22972014

#SPJ1

Complete question:

two circle are shown where RB = 27 cm, HT = 25.5 cm and m∠HRB = 72°.

Determine the length of arc MH in term of π.

A size 8 kids shoe measure 9 2/3 inches .if 5 size 8 shoes are lined end to end ,then how manny inches will they cover

Answers

Answer:

48.33335

Step-by-step explanation:

2/3 of an inch is 0.66667 inches and  5 shoes so 0.66667 x 5 = 3.33335 + 45 since 9 x 5 equals 45 which is 48.33335

Drag the tiles to the boxes to form the correct pairs. Not all tiles will be used.
Points C and D divide the semicircle into three equal parts. Match the angles with their measures.
10pts!!

Answers

Where the conditions of the semicircle is given, the correct pairs are given as follows;

∠BAE = 180°

∠CAD = 60°
∠DEC = 30°
∠CAE = 120°

How are the above derived?

1) ∠BAE = 180° is explained by the principle of angles on a straight line. Note that the angles on a straight line total 180°

2) Since AC and AD are both the radius of the circle, that and they divide the semi circle in three places, thus,

the arc created by the semicircle 180° is also divided by three.

Hence,

180/3 = 60°

3)  ∠CAD = ∠ADE

Hence,

∠DEC = ∠CAD/2

∠DEC = 60/2

∠DEC = 30°


4) Recall that the semicircle is divided into three equal parts. Since

∠CAE = Two of the arcs

∠CAE = 180 * 2/3

∠CAE = 120°

Learn more about semicircle  at:

https://brainly.com/question/30023569

#SPJ1

Answer:

Step-by-step explanation:

Where the conditions of the semicircle is given, the correct pairs are given as follows;

∠BAE = 180°

∠CAD = 60°

∠DEC = 30°

∠CAE = 120°

How are the above derived?

1) ∠BAE = 180° is explained by the principle of angles on a straight line. Note that the angles on a straight line total 180°

2) Since AC and AD are both the radius of the circle, that and they divide the semi circle in three places, thus,

the arc created by the semicircle 180° is also divided by three.

Hence,

180/3 = 60°

3)  ∠CAD = ∠ADE

Hence,

∠DEC = ∠CAD/2

∠DEC = 60/2

∠DEC = 30°

4) Recall that the semicircle is divided into three equal parts. Since

∠CAE = Two of the arcs

∠CAE = 180 * 2/3

∠CAE = 120°

Learn more about semicircle  at:

brainly.com/question/30023569

#SPJ1

Answer A, and B. Please. Thanks3. Use the method of elimination to find the general solution and write it as na willemas . a linear combination of two vector solutions. Igor arvos od done od dono om (errotant sosiaal) a) x' = x, y'

Answers

The general solution for the system of differential equations is (c1[tex]e^t[/tex], c2).

To use the method of elimination to find the general solution and write it as a linear combination of two vector solutions for the given differential equation x' = x, y' = 0, we first need to find the individual solutions for each variable.
For x', we have x' = x, which is a first-order linear homogeneous differential equation. The general solution for this equation is x = c1e^t, where c1 is a constant.
For y', we have y' = 0, which is a first-order linear homogeneous differential equation.

The general solution for this equation is y = c2, where c2 is a constant.
The general solution of a system of linear equations and express it as a linear combination of two vector solutions.
Now, to find the general solution for the system of differential equations, we need to write it as a linear combination of two vector solutions. Let's denote the vector solutions as u and v.
We can define u = ([tex]e^t[/tex], 0) and v = (0, 1). Then, the general solution for the system can be written as:
(x, y) = c1u + c2v
= c1([tex]e^t[/tex], 0) + c2(0, 1)
= (c1[tex]e^t[/tex], c2)
Therefore, the general solution for the system of differential equations is (c1[tex]e^t[/tex], c2), where c1 and c2 are constants.

For similar question on general solution:

https://brainly.com/question/13609544

#SPJ11

The general solution for the system of differential equations is ( [tex]c_1e^t[/tex],  [tex]c_2[/tex] ).

To use the method of elimination to find the general solution and write it as a linear combination of two vector solutions for the given differential equation x' = x, y' = 0, we first need to find the individual solutions for each variable.

For x', we have x' = x, which is a first-order linear homogeneous differential equation.

The general solution for this equation is x = [tex]c_1e^t[/tex], where [tex]c_1[/tex]  is a constant.

For y', we have y' = 0, which is a first-order linear homogeneous differential equation.

The general solution for this equation is y =  [tex]c_2[/tex] , where  [tex]c_2[/tex]  is a constant.

The general solution of a system of linear equations and express it as a linear combination of two vector solutions.

Now, to find the general solution for the system of differential equations, we need to write it as a linear combination of two vector solutions.

Let's denote the vector solutions as u and v.

We can define u = ([tex]e^t[/tex], 0) and v = (0, 1).

Then, the general solution for the system can be written as:

(x, y) = [tex]c_1[/tex] u +  [tex]c_2[/tex] v

=  [tex]c_1[/tex] ([tex]e^t[/tex], 0) +  [tex]c_2[/tex] (0, 1)

= ([tex]c_1[/tex] [tex]e^t[/tex], [tex]c_2[/tex])

Therefore, the general solution for the system of differential equations is ([tex]c_1, c_2[/tex]), where [tex]c_1[/tex]  and [tex]c_2[/tex] are constants.

For similar question on differential equations

https://brainly.com/question/28099315

#SPJ11

I can’t figure out how to set up the equation, please help!

Answers

Answer:

Step-by-step explanation:

If the two triangles are similar then you need to set up a proportion.  

Segment ED is similar to GD

and DF is similar to DC

So.

48/(5x-2)=40/(2x+7)    

Cross multiply

48(2x+7)=40(5x-2) (if you see it you can reduce numbers so its not so big but i won't to keep things simple)

96x+336= 200x-80

416=104x

x=4

What are the expected return, risk premium. standard deviation, and ratio of risk premium to standard deviation for a complete portfolio with y=0.6. Assume rf=2% and rp=6% with standard deviation =20.5%? Please show your work.

Answers

To calculate the expected return, risk premium, standard deviation, and ratio of risk premium to standard deviation for a complete portfolio with y=0.6, we need to use the following formulas:

Expected return = y * rp + (1-y) * rf

Risk premium = rp - rf

Standard deviation = y * σp

Ratio of risk premium to standard deviation = (rp - rf) / σp

where rp is the expected return of the risky asset, rf is the risk-free rate, σp is the standard deviation of the risky asset, and y is the proportion of the portfolio invested in the risky asset.

Given that y=0.6, rp=6%, rf=2%, and σp=20.5%, we can calculate:

Expected return = 0.6 * 6% + 0.4 * 2% = 3.6% + 0.8% = 4.4%

Risk premium = 6% - 2% = 4%

Standard deviation = 0.6 * 20.5% = 12.3%

Ratio of risk premium to standard deviation = (6% - 2%) / 20.5% = 0.1951

Therefore, the expected return is 4.4%, the risk premium is 4%, the standard deviation is 12.3%, and the ratio of risk premium to standard deviation is 0.1951.

Learn more about standard deviation here:

https://brainly.com/question/23907081

#SPJ11

true or false: if this model suffers from heteroskedasticity, then the usual ols t statistics no longer have a t distribution and the f statistics no longer have an f distribution.

Answers

The statement ' if this model suffers from heteroskedasticity, then the usual OLS t statistics no longer have a t distribution and the f statistics no longer have an f distribution' is true because a model suffering from heteroskedasticity will not be accurate.

If a model suffers from heteroskedasticity, which is the condition where the variance of the errors is not constant across observations, then the usual OLS t statistics and F statistics no longer have t or F distributions, respectively. In other words, the standard errors of the coefficients and the overall fit of the model cannot be accurately estimated using the usual assumptions of OLS regression.

Specifically, when heteroskedasticity exists, the OLS estimator remains unbiased, consistent, and asymptotically normal, but its estimated standard errors are biased and inconsistent, leading to invalid inference. This means that t-tests for individual coefficients and F-tests for overall model significance based on these standard errors may be unreliable.

Instead, alternative methods such as robust standard errors or weighted least squares should be used to correct for heteroskedasticity.

To learn more about heteroskedasticity, click here:

https://brainly.com/question/18403256

#SPJ11

Select the expression that can be used to find the volume of this rectangular prism.

A.
(
6
×
3
)
+
15
=
33

i
n
.
3
B.
(
3
×
15
)
+
6
=
51

i
n
.
3
C.
(
3
×
6
)
+
(
3
×
15
)
=
810

i
n
.
3
D.
(
3
×
6
)
×
15
=
270

i
n
.
3

Answers

The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3.

What is expression?

Expression is a word, phrase, or gesture that conveys an idea, thought, or feeling. It is an outward representation of an emotion, attitude, or opinion. Expressions can be verbal, physical, or written. They can also take the form of art, music, or dance. Expression is used to communicate and express emotions, thoughts, and ideas. It can be a powerful tool to create a connection with others and build relationships.

The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3. This expression involves multiplying the length, width, and height of the rectangular prism in order to calculate the total volume. In this case, the length is 3, the width is 6, and the height is 15. If these values are multiplied together, the result is 270 in.3, which is the total volume of the rectangular prism.

To know more about expression click-
http://brainly.com/question/1859113
#SPJ1

A 1 Question 1 1.5 pts A histogram depicting the age distribution for 30 randomly selected students is an example of descriptive statistics. O True O False

Answers

The statement 'a histogram depicting the age distribution for 30 randomly selected students is an example of descriptive statistics' is true as this type of statistics aims to summarize and display data effectively through graphs, charts, or tables.

A histogram depicting the age distribution for 30 randomly selected students is an example of descriptive statistics, which involves collecting, organizing, summarizing, and presenting data in a way that is easily interpretable.

A histogram is a graph that displays the frequency or relative frequency of a set of continuous data by dividing the range of the data into intervals and displaying bars that represent the number or proportion of observations that fall into each interval.

Descriptive statistics are used to describe the main features of the data, such as the central tendency, variability, shape, and outliers, and to make comparisons or inferences about the population from which the sample was drawn.

To learn more about histogram, click here:

https://brainly.com/question/30354484

#SPJ11

if a scatter plot displays data that shows a positive correlation, then the correlation coefficient will be closest to what whole number?

Answers

If a scatter plot displays data that shows a positive correlation, then the correlation coefficient will be closest to +1.

The correlation coefficient is a numerical measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.

Since the scatter plot displays data that shows a positive correlation, the correlation coefficient will be positive and closer to +1 than to 0 or -1. The exact value will depend on the strength of the correlation. If the data points are tightly clustered around a straight line, the correlation coefficient will be closer to +1, indicating a strong positive correlation. If the data points are more spread out, the correlation coefficient will be smaller, but still positive, indicating a weaker positive correlation.

Learn more about “ positive correlation, “ visit here;

https://brainly.com/question/15723507

#SPJ4

Abby is building a rectangular frame for a flower garden. She
uses four pieces of wood, two pieces are 4 feet long and two are
5 feet long. After she nails the first two pieces together, Abby
wants to make sure the corner is square. She measures the
diagonal and it is 76 inches long. Did Abby make a square corner?

Answers

Abby did not make a square corner because the rectangle is about 0.888 feet longer on one diagonal than the other diagonal

How to determine if Abby make a square corner

To determine whether Abby made a square corner, lets use the Pythagorean theorem, which states that for a right triangle with legs of length a and b and hypotenuse of length c, we have:

c^2 = a^2 + b^2

Lets use the theorem to check if the diagonal (c) is the hypotenuse of a right triangle with sides of length 4 feet and 5 feet.

Lets convert the length of the diagonal from inches to feet:

76 inches = 76/12 feet = 6.333... feet (rounded to the nearest thousandth)

Now, we can use the Pythagorean theorem to check if the sides of the rectangle form a right triangle:

c^2 = a^2 + b^2

(6.333... feet)^2 = (4 feet)^2 + (5 feet)^2

40.111... feet^2 = 16 feet^2 + 25 feet^2

40.111... feet^2 = 41 feet^2 (rounded to the nearest thousandth)

Since the equation is not true, Abby did not make a square corner.

This means that the rectangle is about 0.888 feet longer on one diagonal than the other diagonal

Learn more about Pythagorean theorem at https://brainly.com/question/343682

#SPJ1

Ninth Grade Geometry - Circles and in desperate need of help.


This is what I did -

146 = 1/2(6x+6-x+10

146 = 1/2(5x+16)

146 = 5x+16

-16 -16

130/5 = 5x/5

26 =x


mED = 6x+6 x+10

6(26)+6 26+10

=162 - 36

162 - 36 = 126°

Answers

Answer:

Step-by-step explanation:

Your setup was not quite right.  The formula is

: (the outer part of the circle minus innner)1/2 = angle

(146 - (6x+6))1/2 = x+10            Be careful to distrubut the negative

(146-6x-6)1/2 = x+10

(140-6x)1/2=x+10

70-3x=x+10

60=4x

x=15

<ECB = x+10 = 15+10=  25

Answer:

  25°

Step-by-step explanation:

You want the measure of exterior angle ECB marked as (x+10°) given that it intercepts arcs marked as 146° and (6x+6°).

External angle

The measure of the exterior angle is half the difference of the intercepted arcs.

  x +10° = 1/2(146° -(6x +6°))

  x +10° = 70° -3x . . . . . . . . . . . simplify

  4x = 60° . . . . . . . . . . . add 3x-10°

  x = 15° . . . . . . . . . divide by 4

The measure of the external angle is ...

  ∠ECB = x +10° = 15° +10°

  ∠ECB = 25°

__

Additional comment

Often, you don't need to do any math. You only need to do a "reasonableness check" on the offered answer choices.

You know that any inscribed angle in the circle that intercepts arc BD (146°) will have a measure of 146°/2 = 73°. The vertex of an external angle is necessarily farther away from arc BD than any inscribed angle. This means the external angle will have a smaller measure than 73°. That matches only one answer choice.

The inscribed angles we're concerned with here would have their vertex on long arc BED.

Use the method of Variation of Parameters to find a particular solution to the 2nd order non-homogeneous linear differential equation y" + 4y = sinº (2x) = given the general solution yc = C1 cos(2x) + C2 sin(2x) to the associated homogeneous equation.

Answers

The value of solution of the equation is,

⇒ C₁ cos (2x) + C₂ sin (2x) - 1/4 x cos (2x)

Given that;

The 2nd order non-homogeneous linear differential equation,

⇒ y" + 4y = sin (2x)

And, the general solution y (c) = C₁ cos(2x) + C₂ sin(2x) to the associated homogeneous equation.

Now, We have;

The 2nd order non-homogeneous linear differential equation,

⇒ y" + 4y = sin (2x)

Hence, Its auxiliary equation is,

⇒ m² + 4 = 0

⇒ m = ± 2i

Since, the general solution y (c) = C₁ cos(2x) + C₂ sin(2x) to the associated homogeneous equation.

And, Let particular solution is,

⇒ y (p) = A cos 2x + B sin (2x)

Now, After solving we get;

⇒ A = 0

⇒ B = - 1/4

Thus, The value of solution of the equation is,

⇒ y (c) + y (p)

⇒ C₁ cos (2x) + C₂ sin (2x) - 1/4 x cos (2x)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ4

Use the following information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included.

Answers

The data, and use this information to make informed decisions and draw conclusions.

A table is a structured representation of data that organizes information into rows and columns. Tables can be used to summarize numerical and categorical data, and can include measures of central tendency (e.g., mean, median, mode) and measures of variability (e.g., range, standard deviation). To analyze data from a table, you can identify patterns or trends in the data, calculate summary statistics, and compare the values of different variables.

A histogram is a graph that displays the distribution of numerical data by dividing the data into intervals (called "bins") and showing the frequency or relative frequency of data points that fall within each bin. Histograms can be used to identify the shape of a distribution, the center of the data (i.e., the mean or median), and the spread of the data (i.e., the standard deviation or range). To analyze data from a histogram, you can identify the shape of the distribution (e.g., normal, skewed, bimodal), calculate summary statistics (e.g., mean, median, standard deviation), and compare the values of different variables.

In summary, tables and histograms are powerful tools for organizing, summarizing, and visualizing data. By analyzing and interpreting data from tables and histograms, we can gain insights into the patterns and trends of the data, and use this information to make informed decisions and draw conclusions.

Complete question: Use the following information to answer questions. Data below the recording the number of deaths for the top thirteen worst U. S. tornados since 1925. A histogram showing the distribution is also included. 689, 454, 102, 208, 142, 271, 315, 268, 150, 181, 114, 115, 110 Frequency 4 3 2 1 200 1 300 1 500 1 100 400 600 700 Number of Deaths (a) Choose the most appropriate measure of center then calculate the value rounded to the nearest tenth.

To learn more about conclusions visit:

https://brainly.com/question/78686

#SPJ11

Why is it always beneficial to have a positive second derivative. In terms of a bond, why does it benefit to have positive convexity. In terms of an option, why is it beneficially to be long gamma.

Answers

Having a positive second derivative is beneficial because it indicates that the rate of change is increasing.

As input variable like interest rate, underlying stock price changes, rate of change in output variable like bond price, option price increases.

This can provide certain benefits, as discussed below.

Positive Convexity in Bonds,

Bond prices are inversely related to interest rates.

As interest rates increase, bond prices decrease and vice versa.

When a bond has positive convexity, its price will increase at an increasing rate.

As interest rates decline, and decrease at a decreasing rate as interest rates increase.

This is beneficial to bondholders.

Because it means that when interest rates decline, the bond's price will increase by more than it would if the bond had no convexity.

This can result in higher total returns for bondholders.

Long Gamma in Options,

Gamma is a measure of rate of change of delta the sensitivity of an option's price to changes in underlying asset price.

When an option trader is long gamma, it means they hold options that have positive gamma.

This is beneficial because it means that as the underlying asset price changes.

The option delta and therefore its price will change at an increasing rate.

Result in higher profits for the option trader especially if underlying asset experiences large price movements.

Learn more about derivative here

brainly.com/question/30117453

#SPJ4

yall please help me :((

Answers

A graph that represents the given points is shown in the images below.

What is an ordered pair?

In Mathematics and Geometry, an ordered pair is a pair of two elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

How to identify and plot the coordinates points and quadrants?

Based on the cartesian coordinate (grid) below, the coordinates points and quadrants should be identified as follows;

Point (4, -4) → quadrant 4.

Point (-3, -4) → quadrant 3.

Point (-3, 4) → quadrant 2.

Point (4, 4) → quadrant 1.

Point (5, -4) → quadrant 4.

Point (-4, -4) → quadrant 3.

Point (5, 4) → quadrant 1.

Point (-4, 4) → quadrant 2.

In this exercise, we would use an online graphing calculator to plot the given points as shown in the images attached below.

Read more on ordered pair here: brainly.com/question/25462418

#SPJ1

#5) Choose the graph that matches the equation below.
y=-x+3
A
C
B
D

Answers

Answer:

the correct answer is B as graph Is a decreasing function

How do you find the unit length of a tangent vector?

Answers

To find the unit length of a tangent vector, you can follow these steps:

Calculate the magnitude or length of the tangent vector. The magnitude of a vector is given by the square root of the sum of the squares of its components. For a tangent vector, the components represent the rates of change of the curve with respect to the parameter.Divide the tangent vector by its magnitude to get a vector of unit length. This can be done by dividing each component of the tangent vector by its magnitude.

For example, suppose you have a curve given by the parametric equations x = t^2 and y = t^3, and you want to find the unit length of the tangent vector at the point (1,1).

The tangent vector at this point is given by the derivative of the parametric equations with respect to t, which is (2t, 3t^2).

To find the magnitude of this vector, we can calculate sqrt((2t)^2 + (3t^2)^2), which simplifies to sqrt(13t^2).

At t=1, the magnitude of the tangent vector is sqrt(13).

To find the unit length of the tangent vector, we can divide each component of the vector by its magnitude, which gives (2/sqrt(13), 3/sqrt(13)).

Therefore, the unit length of the tangent vector at the point (1,1) is (2/sqrt(13), 3/sqrt(13)).

For more information about tangent vector, visit:

https://brainly.com/question/15303761

#SPJ11

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the probability that the number favoring the substation is more than 12?

Answers

For a survey of community related to build a police substation in their nearby, from binomial distribution the probability that the number favoring the substation is more than 12 is 0.398.

We have a survey related to community view regarding building a police substation in their nearby. Let X be an event for favouring the building a police substation in their nearby. The

Probability of community favored building a police substation in their neighborhood = 80% = 0.80

Total number of selected citizens = 15

We have to determine the probability that the number favoring the substation is more than 12. Using Binomial probability distribution, P( X = x) = ⁿCₓ pˣ( 1- p)⁽ⁿ⁻ˣ⁾

where, p --> probability of success

x -> number of success

n -> total number of trials

here, n = 15, p = 0.80, x = 12, substitute all known values in above formula, P( X >12) = P( X= 13) + P( X = 14) + P(X = 15)

= ¹⁵C₁₃ 0.8¹³(0.2)² + ¹⁵C₁₄ 0.8¹⁴(0.2)¹ + ¹⁵C₁₅0.8¹⁵ 0.2⁰

= 0.231 + 0.132 +0.035

= 0.398

Hence, the required probability is 0.398.

For more information about binomial distribution, visit :

https://brainly.com/question/15246027

#SPJ4

In a study involving car owners one questions asked the owner for the number of miles driven last year. a second questions asked the owner for the age of the vehicle. a joint frequency distribution would be useful for determining whether newer cars tend to be driven more miles than older cars (True or false)

Answers

The given statement "A joint frequency distribution would be useful for determining whether newer cars tend to be driven more miles than older cars." is true because it shows the frequencies, or counts in table.

A joint frequency distribution is a table that shows the frequencies, or counts, of two or more variables for a given dataset. In this case, the two variables are the number of miles driven last year and the age of the vehicle for a sample of car owners.

A joint frequency distribution would be useful for examining the relationship between these variables and determining whether newer cars tend to be driven more miles than older cars.

By examining the joint frequency distribution, one can calculate and compare the average miles driven for different age categories of cars. For example, the average miles driven per year for cars less than 5 years old can be compared to the average miles driven per year for cars 5 to 10 years old and cars over 10 years old.

This can provide insight into whether there is a relationship between car age and miles driven, and whether this relationship is significant.

Therefore, the statement that a joint frequency distribution would be useful for determining whether newer cars tend to be driven more miles than older cars is true. It is a useful tool for examining the relationship between two variables and identifying patterns and trends in the data.

To learn more about joint frequency click on,

https://brainly.com/question/31189964

#SPJ4

Let A refer to the event "an investment is made", let b(A) denote the possible benefit of the
investment and let P(A) = probability that the investment is successful. How would you interpret
the equation: b(A) x P(A).

Answers

The equation b(A) x P(A) represents the expected value or potential benefit of the investment. It takes into account both the possible benefit of the investment (b(A)) and the probability of the investment being successful (P(A)).

Essentially, it means that if an investment is made, there is a probability (P(A)) that it will be successful and yield a certain benefit (b(A)). By multiplying these two factors together, we can estimate the expected value or potential return on the investment, In this context, "an investment is made" is represented by event A. The possible benefit of the investment is denoted by b(A), and the probability that the investment is successful is represented by P(A).

The equation b(A) x P(A) represents the expected benefit of the investment, considering the probability of its success. By multiplying the possible benefit (b(A)) by the probability of success (P(A)), you are calculating the average benefit you can expect from the investment, taking into account its likelihood of success.


To put it simply, the equation b(A) x P(A) helps you evaluate the potential return of an investment, considering both its possible benefits and its chances of being successful.

To know more about an investment:- https://brainly.com/question/15353704

spj11

A very large study showed that aspirin reduced the rate of first heart attacks by 40%. A pharmaceutical company thinks it has a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug.
a) Is the alternative to the null hypothesis more naturally one-sided or two-sided? Explain.
b) The P-value from a clinical trial testing the hypothesis is 0.29. What do you conclude?
c) What would you have concluded if the P-value had been 0.0029?

a) The alternative hypothesis is more naturally _____ because the company would like to determine if the new drug is either more or less effective than aspirin. is sufficient evidence to conclude that the new drug is ______ than aspirin because the
b) If the P-value is 0.29, then there _____ evidence to conclude that the new drug is more efective than aspirin because the P-value is _____.
c) If the P-value is 0.0029, then there ________ evidence to conclude that the new drug is more effective than aspirin because the P-value is ______.

Answers

Since this probability is very low, we can reject the null hypothesis in favor of the alternative hypothesis, and conclude that the new drug is more effective than aspirin.

a) The alternative hypothesis is more naturally two-sided because the pharmaceutical company wants to determine if the new drug is either more or less effective than aspirin. It is not clear from the question whether the new drug is expected to be more effective than aspirin, or if it could be less effective. Therefore, a two-sided alternative hypothesis is more appropriate.

b) If the P-value is 0.29, then there is not enough evidence to conclude that the new drug is more effective than aspirin because the P-value is greater than the typical significance level of 0.05. A P-value of 0.29 means that there is a 29% chance of observing a difference between the new drug and aspirin as large as the one observed in the study, assuming that the null hypothesis (that the new drug is equally effective as aspirin) is true. Since this probability is relatively high, we cannot reject the null hypothesis in favor of the alternative hypothesis.

c) If the P-value is 0.0029, then there is strong evidence to conclude that the new drug is more effective than aspirin because the P-value is less than the typical significance level of 0.05. A P-value of 0.0029 means that there is only a 0.29% chance of observing a difference between the new drug and aspirin as large as the one observed in the study, assuming that the null hypothesis is true. Since this probability is very low, we can reject the null hypothesis in favor of the alternative hypothesis, and conclude that the new drug is more effective than aspirin.

To learn more about hypothesis visit:

https://brainly.com/question/29519577

#SPJ11

Given that (0, - 1) is an x-intercept of f(x) = [tex]x ^ 3 - 3x ^ 2 - 36x - 32[/tex] find all of the other x-intercepts of f(x).

Answers

The x-intercepts of f(x) are (-2, 0), (0, -32), and (-4, 0).

How to get the intercepts

First, let us check if (0, -1) is one of the intercept. If (0, -1) is an x-intercept of f(x), that means f(0) = 0.

So let's evaluate f(0):

f(0) = 0³ - 3(0)² - 36(0) - 32 = -32

Since f(0) is not equal to 0, we know that (0, -1) is not an x-intercept of f(x).

To find the actual x-intercepts of f(x), we need to factor the polynomial. We can start by using synthetic division to test if x = 1 is a factor of f(x).

For us to get to our answer, we test with the possible factors of 32 which are: ±1, ±2, ±4, ±8, ±16, ±32.

Learn more about intercept here:

https://brainly.com/question/25722412

#SPJ1

The table shows the difference colors of pencil in a pencil case. A student will randomly select one pencil from the pencil case. Based on the information in the table , which statement is true

Answers

Using probability, we can find that Probability of purple will be 4 times likely to probability of red.

Hence, option C is correct.

Describe probability?

The ability to occur is known as probability. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number between 0 and 1. Probability has been introduced in mathematics to predict how likely events are to occur.

Here in the question,

Number of red pencils = 2

Number of purple pencils = 8

Number of blue pencils = 4

Number of green pencils = 5

Total number of pencils:

= 2 + 8 + 4 + 5

= 19

Now,

A) The statement is not true as blue is not the color that has the minimum number of pencils. Red color has the minimum number of pencils.

B) The statement is not true as there are 4 blue pencils and 5 green pencils, so probability for them will not be equal.

C) Here in this statement, purple pencils are 4 times than that of red pencils.

Red pencils = 2

Purple pencils = 8.

Probability of purple will be 4 times likely to probability of red.

So, the probability for this statement will be true.

D) The statement is not true as:

Purple pencils = 8

All others combined = 2 + 4 + 5 = 11.

So, the probability of purple will not be more than that of the rest combined.

To know more about probability, visit:

https://brainly.com/question/16484393

#SPJ1

The complete question is:

The table shows the numbers of different colors of pencils in a pencil case. A student will randomly select one pencil from the pencil case. Based on the information in the table, which statement is true?

A) The pencil is least likely to be blue.

B) The pencil is equally likely to be blue or green.

C) The pencil is 4 times as likely to be purple as it is to be red.

D) The pencil is more likely to be purple than all other colors combined.

Number of Pencils

Red Pencils = 2

Purple Pencils=8

Blue pencils=4

Green pencils=5​

Question 19 < > = Use implicit differentiation to find the equation of the tangent line to the curve xy² + xy = 6 at the point (3, 1). The equation of this tangent line can be written in the form y =

Answers

The equation of the tangent line to the curve xy² + xy = 6 at the point (3, 1) is y = (7/4)x - 19/4.

To find the equation of the tangent line to the curve xy² + xy = 6 at the point (3, 1), we first need to find the slope of the tangent line. We can use implicit differentiation to find the derivative of the curve:

(xy² + xy)' = (6)'

Using the product rule for differentiation, we get

y² + 2xydx/dy + xdx/dy + y = 0

Rearranging and solving for dx/dy, we get

dx/dy = (-y - 2xy)/(x + y²)

Substituting the values x = 3 and y = 1, we get

dx/dy = (-1 - 2(3)(1))/(3 + 1) = -7/4

Therefore, the slope of the tangent line at the point (3, 1) is -7/4.

Now we can use the point-slope form of a line to find the equation of the tangent line

y - y₁ = m(x - x₁), where (x₁, y₁) = (3, 1) and m = -7/4

Simplifying, we get:

y - 1 = (-7/4)(x - 3)

Multiplying both sides by 4 to eliminate the fraction, we get:

4y - 4 = -7(x - 3)

Simplifying further, we get

4y - 7x = -19

Therefore, the equation of the tangent line is y = (7/4)x - 19/4

Learn more about point-slope form here

brainly.com/question/29054476

#SPJ4

edward mows two lawns the first is 5 meters long and 5 meters wide the second one has the same length and a width that is 3 tmes as much as the first one how much is the total area of both lawns

Answers

Answer:

25 + (5 x 15) = 125

Step-by-step explanation:

Pretty sure it’s 100 meters


(5 x 5) + (5 x 15)
25 + 75
100

if 26, 25, 21 are the sides of a triangle what is x =?

Answers

Answer:

63.22⁰

Step-by-step explanation:

the answer is in the picture. please mark mine brainliest.

(5x2 − 19x + 28) + (7x2 + 4x − 45)

help!!

Answers

-15x + 7 thats the answer only if no exponents involved let me know

9. The density of a 10-inch-long pipe changes from one end to the other with a density function P(x) = 3x^2 +1 oz./inch, where x is the distance to one of the ends. Set up an integral and use it to compute the mass of the rod.

Answers

To compute the mass of the rod, you'll need to integrate the density function P(x) = 3x^2 + 1 oz./inch over the length of the pipe (from 0 to 10 inches). The mass can be found by calculating the integral:
Mass = ∫[P(x) dx] from 0 to 10


Substitute the density function:
Mass = ∫[(3x^2 + 1) dx] from 0 to 10
Now, find the antiderivative of the function:
Antiderivative = x^3 + x + C
Now, evaluate the antiderivative at the limits 0 and 10:
Mass = (10^3 + 10) - (0^3 + 0)
Mass = (1000 + 10) - 0
Mass = 1010 oz.
So, the mass of the 10-inch-long pipe is 1010 ounces.

Learn more about density function here:

https://brainly.com/question/31039386

#SPJ11

Determine the sample size needed to estimate the average weight of all second-grade boys if we want to be within 1 pound with 95% confidence. Assume we know that the standard deviation of such weights is 3 pounds

Answers

The sample size needed to estimate the average weight of all second-grade boys is 35.

To determine the sample size needed to estimate the average weight of all second-grade boys with a 95% confidence level and within 1 pound margin of error, we can use the following formula:

[tex]$n = \frac{z^2 \sigma^2}{E^2}$[/tex]

n = sample size

z = z-score for the desired confidence level (1.96 for 95% confidence level)

[tex]$\sigma[/tex] = population standard deviation

E = margin of error

Substituting the given values, we get:

[tex]$n = \frac{(1.96)^2 \times (3)^2}{(1)^2}[/tex]

  `= 34.57

Rounding up to the nearest integer, we get a required sample size of 35.

Therefore, a sample size of 35 second-grade boys is needed to estimate the average weight of all second-grade boys with a 95% confidence level and within 1 pound margin of error, assuming we know that the standard deviation of such weights is 3 pounds.

To know more about sample size

https://brainly.com/question/30885988

#SPJ4

Other Questions
how did the completion of the transcontinental railroad contribute to the settlement of the west? responses by giving funds to local leaders to build schools by giving funds to local leaders to build schools by raising money to build factories along the routes by raising money to build factories along the routes by providing people with access to essential goods by providing people with access to essential goods by establishing military forts along the routes What does Bloom tell people when they call him a shrink. Write an equation for the following verbal expression: the difference between twice a number and nine is 17. In ANOVA with 4 groups and a total sample size of 44, the computed F statistic is 2.33 In this case, the p-value is: a. exactly 0.05 b. less than 0.05 c. greater than 0.05 d. cannot tell - it depends on what the SSE is A CCD camera is equipped with a lens with constant focal-length. As the f-number is decreased, determine whether the following quantities increase, decrease, or remain unchanged. a) the apertureb) the depth of fieldc) the intensity of light reaching the sensor d) the appropriate exposure time For an ideal gas, which two variables are directly proportional to each other (if all other conditions remain constant)? 1. P and V 2. P and n 3. P and T A. 2 only B. 2 and 3 only C. 1 and 2 only D. 1 only 3 only impaired oxygen-carrying capacity of the blood that occurs with anemia or at high altitudes results in: When does proline as a residue take action in a reverse turn? A body's initial position was -20m from the origin and its final position was -10m 1 second later. What was the body's displacement The statistical significance of the regression model is showed by t-statistic p-statistic F-statistic intercept What is the etiology of Impaired Psychological & Social Imbalance related to? Including:Chronic / Situational Low self-esteemPowerlessImpaired social interactionDisturbed thought processDeficient knowledgeIneffective copingIneffective family copingDisturbed sleep pattern Why should the y-intercept of your plot equal 0? (Lab 2) what is the first step to be performed once you have determined that you have broken your instrument tip?a.isolate the areab.ask the patient to swallowc.sit the patient upright to prevent aspirationd.use a push stroke to force tip out of the sulcus what is the amount of m112 needed to breach a 5-foot thick dense concrete wall utilizing an internal charge placed in the center of the target? The nurse is to administer the morning dose of NPH insulin to a client with type 1 diabetes. The client is alert and oriented; before administering the medication, the nurse obtains a glucose reading of 52. What should the nurse do at this time? the earth rotates once per day about its axis, which is perpendicular to the plane of the equator and passes through the north geographic pole. where on the earth's surface should you stand in order to have the smallest possible tangential speed? shallow respirations, hypotension, bradycardia and pulmonary edema are all symptoms of abuse of what drug? Ippolita brought a seedling that measured 11. 38 cm. She tracked the seedlings growth and found that it grew approximately 0. 045 cm each day. Approximately what was the height of the seedling after one week? Which is most likely to infect water supply? Runoff from chicken farm, contaminated runoff, cesspool next to water supply 1. According to the endosymbiotic theory, how did membrane-bound organelles, such as the nucleus and endoplasmic reticulum form?