A Statistics Primer A researcher is interested in handedness in ants. (Here, handedness refers to the propensity of individuals to turn more often in one direction than another.) He hypothesizes that if ants show handedness they should be more likely to turn into the right or left arms of a T-maze. He plans to place 20 ants into a maze and use a binomial test to evaluate this hypothesis. When the 20 ants were placed into the maze he observed that 16 of the ants walked into the right arm and that three ants walked into the left arm (one ant managed to crawl over the edge of the maze before it went down either of the arms). (1 point) 5. What is the probability that exactly 16 of the ants enter the right arm when the null hypothesis is true? (1 point) 6. What outcomes are equally extraordinary or more extraordinary than the outcome observed under conditions in which the null hypothesis is true? (Example of a more extraordinary outcome: The outcome in which all 19 ants turn into the right arm and no ants turn into the left arm (19R, OL) is more extraordinary than the outcome he observed.] (1 point) 7. What are the probabilities associated with the outcomes identified in Problem 5 under conditions in which the null hypothesis is true? (Probability for example given in Problem 6: 1 (1 point) 8. What is the probability that an outcome as extraordinary or more extraordinary than the outcome observed would occur when the null hypothesis is true? Be sure to include the observed outcome in this calculation! (This is the P value for the binomial test.) (1 point) 9. Does the observed outcome indicate that the null hypothesis should be rejected at a rejection criterion of 0.05? What do you conclude?

Answer:

Step-by-step explanation:

what two numbers can you multiply that will equal to 30 when you multiply but 13 when you add them?

10+3=13     10*3=30  

so we can use 10 and 3

since the first symbol (x^2+13x) is positive than the bigger number you got earlier (10) will be positive

(x+10)

since the second symbol (13x+30) is positive than our next symbol will be positive as well

(x+3)

combine them so now they are (x+10)(x+3)

Angelita needs to sell at least 32 rugs to make money on her rugs.

The demand function for Angelita's rugs is p=150x-7000, which represents the linear relationship between the price per rug and the number of rugs sold. The cost function for the rugs is p=80x+2400, which is calculated by taking the same percentage of her average monthly costs to run the store as the percentage of display space needed by the product in question, which is 120 square feet of the total 1200. The revenue function for the rugs is p=150x-7000+220x, and the domain of this function is all real numbers. The maximum revenue is achieved when 40 rugs are sold, at $8800. The profit function for the rugs is p=150x-7000+220x-80x-2400, and the domain of this function is all real numbers. The maximum profit is achieved when 37 rugs are sold, at $4940. The break-even point is 32 rugs, which is the point where the cost and revenue functions intersect. This means that Angelita needs to sell at least 32 rugs to make money on her rugs.

Learn more about maximum profit here:

https://brainly.com/question/18270864

#SPJ4

Answer:

5

Step-by-step explanation:

This is a classic example of a system of equations with two variables. We can set up two equations to represent the given information:

x = number of ducks

y = number of sheep

heads: x + y = 15

legs: 2x + 4y = 38

To solve for the number of ducks, we can use substitution. We can solve one of the equations for one of the variables and substitute it into the other equation.

For example, solving the first equation for y: y = 15 - x. Then substitute it into the second equation:

2x + 4(15 - x) = 38

Solving this equation will give you the value of x, which is the number of ducks.

x = 5

So, there are 5 ducks in the meadow.

Answer:

ofc 15 heads 15 ducks bro comman sense no logic in there

The integral is evaluated and the value of the integral is found to be 3/2.

Given that,

The integral is ∫∫(5+10y) dy dx

To find : To evaluate the iterated integral,

= ∫(5y + 10y²/2) dx

= ∫ (5y + 5y²) dx

Substituting the limits x and x² in the variable y

= ∫ (5x + 5x² - (5x² + 5x⁴)) dx

= ∫(5x + 5x² - 5x² - 5x⁴) dx

= ∫(5x - 5x⁴) dx

= (5x²/2 - 5x⁵/5)

= (5/2 - 1)

= 3/2

Hence, The integral is evaluated and the value of the integral is found to be 3/2.

To know more about integral click here:

brainly.com/question/18125359

#SPJ4

Withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

The actions of withdrawing $ from your checking account and depositing it into a savings account will affect the measures of money supply, M1 and M2, as follows:

M1: M1 is a measure of the narrowest definition of the money supply, which includes all currency (including coins), checking accounts, and travelers' checks. Withdrawing money from your checking account will reduce the amount of money in M1. However, depositing the funds into a savings account will not have any impact on M1 since savings accounts are not included in this measure of the money supply.

M2: M2 is a measure of the broader definition of the money supply, which includes M1 and all-time deposits, savings accounts, and money market securities with a value of less than $100,000. Depositing money into a savings account will increase the amount of money in M2, as savings accounts are included in this measure of the money supply. However, withdrawing money from a checking account will not have any impact on M2 as the decrease in M1 will be offset by the increase in savings accounts.

Therefore, In conclusion, withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

To learn more about measurement,

Visit; brainly.com/question/12020266

#SPJ4

Question Correction: Suppose you withdraw $6,000 from your checking account and use the funds to invest in a savings account at the bank. How will these actions affect M1 and M2?

A. M1 wil decrease and M2 wil not change

B. M1 and M2 will increase

C. M1 and M2 will not change.

D. M1 wil decrease and M2 will increase

In a 10-player round-robin tennis tournament, each player must play 45 games, and a total of 90 games will be played in the tournament.

A round-robin tournament is a type of competition in which every participant plays against every other participant. In a 10-player tournament, the number of games needed can be calculated using the formula for combination.

The density of a tournament can be defined as the number of games each player must participate in to play against every other player.

To calculate the density of a 10-player round-robin tournament, we use the formula

=> n(n-1)/2,

where n is the number of players.

In this case, n = 10. So, the density of the tournament is

=> 10(10-1)/2 = 45.

This means that each player must play 45 games in total, and each game involves 2 players.

So, there will be a total of

=> 45*2 = 90

games played in the tournament.

To summarize, The density of the tournament, 45 games per player, is calculated using the formula n(n-1)/2.

To know more about total here.

https://brainly.com/question/14286201

#SPJ4

In order from x - y = 3 ... to y = 4 - 5x, the number of solutions of each system of equations is given as follows:

There are three possible number of solutions for each system of equations, and the cases are presented as follows:

We look at these coefficients, and then obtain the number of solutions for each system in this problem.

More can be learned about a system of equations at brainly.com/question/30374328

#SPJ1

The competition took 2 minutes.

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

Given that, the Turtle and Achilles compete. They start at the same time from the same place. Achilles runs at a speed of 13 mph while the Turtle moves at a speed of 1 mph. When Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him.

Let t be the time taken in competition and the distance covered by Achilles be x miles.

We have been given that when Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him. This means that the distance covered by turtle will be: x - 2/5

Since we know that, speed = distance / time

So, we can set two equations for time taken by Achilles and turtle as:

t = x / 13

x = 13t......(i)

t = (x-2/5)/1....(ii)

Substituting this value in equation (2) we will get,

t = 13t - 2/5

5t = 65t - 2

60t = 2

t = 2/60

t = 1/30

So, the competition took 1/30 hour, let us convert our given time in minutes.

1/30 × 60 minutes

= 2 minutes

Hence, the competition took 2 minutes.

Learn more about speed, click;

https://brainly.com/question/28224010

#SPJ1

The same coordinate axes, with the x-axis denoting the first coordinate, the y-axis denoting the second coordinate, and the z-axis denoting the third coordinate, may be used to plot the points s1, 5, 3d, s0, 2, 23d, s23, 0, 2d, and s2, 22, 21d.

First, plot the coordinate axes using the point s1, 5, and 3D. This point's x, y, and z coordinates are 1, 5, and 3, respectively.

Step 2: Draw a coordinate axes plot of the position s0, 2, 23d. This point has the x, y, and z coordinates of 0, 2, and 23, respectively.

Step 3: Draw a coordinate axes plot of the point s23, 0, 2d. This point's x, y, and z coordinates are 23, 0, and 2, respectively.

Step 4: Draw a coordinate axes plot of the position s2, 22, 21d. This point's x, y, and z coordinates are 2, 22, and 21 respectively.

The same coordinate axes, with the x-axis denoting the first coordinate, the y-axis denoting the second coordinate, and the z-axis denoting the third coordinate, may be used to plot the points s1, 5, 3d, s0, 2, 23d, s23, 0, 2d, and s2, 22, 21d. Plotting these points begins with the point s1, 5, 3d, which has the x, y, and z coordinates of 1, 5, and 3. Plot this point on the coordinate axes with the x, y, and z coordinates as 1, 5, and 3 respectively. The junction of the x, y, and z axes should be at this location. Plot the point s0, 2, 23d, which has coordinates of 0 on the x-axis, 2 on the y-axis, and 23 on the z-axis. The z-coordinate of this point should be 23 units above the x-y plane, and it should be located where the x- and y-axis meet. Plot the points s23, 0, 2d, and s2, 22, 21d to finish. These points should be located at 0 and 22 units above the x-z plane, respectively, and on the x and z axis. Plotting all the points should result in a three-dimensional figure.

Learn more about coordinate here

brainly.com/question/27749090

#SPJ4

Answer:

  9. Cylinder

  10. 14 in

  11. 20π in³

  12. circle, ellipse, rectangle, truncated ellipse

Step-by-step explanation:

You want the solid obtained by revolving a rectangle around one edge, the perimeter of the rectangle, the volume of the solid, and the names of at least 2 cross sections of the solid.

Every point on the outside edge of the solid will be 2 inches from the center axis. That is, the cross section perpendicular to the axis of revolution will be a circle. The solid is a cylinder.

The perimeter of a rectangle is given by the formula ...

  P = 2(L +W)

  P = 2(2 in + 5 in) = 2(7 in) = 14 in

The perimeter is 14 inches.

The radius of the cylinder is 2 inches, and its height is 5 inches. The volume is given by ...

  V = πr²h

  V = π(2 in)²(5 in) = 20π in³

The volume is 20π cubic inches, about 62.8 cubic inches.

The four attachments show possible cross sections of the cylinder. They include a circle, ellipse, rectangle, and truncated ellipse. The truncated ellipse may be cut off on one or both ends.

Answer:f

Step-by-step explanation:

its not that hard

The function is concave up for  x < 1 and concave down for x > 1 because the second derivative is positive for x < 1 and negative for x > 1. As a result, the critical point at x  < 1 is a relative maximum.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is common to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The derivative of the function f(x) can be found by taking the derivative of the expression e^(-x) (x^2 + 2x) using the product rule:

f'(x) = -e^(-x) (x^2 + 2x) + e^(-x) (2x + 2) = 2e^(-x) - 2xe^(-x) (x + 1)

Setting f'(x) equal to zero and solving for x gives us the critical points:

0 = 2e^(-x) - 2xe^(-x).(x + 1)

2xe^(-x).(x + 1) = 2e^(-x)

x(x + 1) = e^x

x^2 + x - e^x = 0

Next, we determine the concavity of the function at the critical points by analyzing the second derivative of the function:

f''(x) = 2e^(-x) + 2xe^(-x) + 2xe^(-x).(x + 1) - 2e^(-x).(x + 1)

= 2e^(-x).(1 - x)

Since the second derivative is positive for x < 1 and negative for x > 1, the function is concave up for x < 1 and concave down for x > 1. Thus, the critical point at x < 1 corresponds to a relative maximum.

To know more about function,

https://brainly.com/question/28193995

#SPJ4

Changing a figure's location without spinning, reflecting, or changing its size is known as a translation in geometry.So g(x) = ln[1/8(x - 3)] + 1.

When you group "3" with the "right-left" variable, which is "x," you will have 3 units to the right.

However, "x" is the opposite of what it seems to be, therefore in order to shift right, you must subtract 3 from "x," making ln(x) into ln (x - 3).

Simply add 1 to the function to advance it up one unit, making ln(x-3) become ln(x-3) + 1.

In order to multiply the "horizontal variable" (also known as "x") by a factor of 8, you must divide by 8 (or multiply by 1/8), because "x" is the opposite of what it seems to be.

Ln(x - 3) + 1 so becomes Ln[1/8(x - 3)] + 1.

so that g(x) = ln[1/8(x - 3)]

+ 1.

To learn more about Translate the figure refer

https://brainly.com/question/29078702

#SPJ1

one may determine how much fence is necessary for a playground with a 256 square yard area is P = 1024 / x.

What is quadrilateral?

Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

P = 4x

Area = x²

Px = 4x²

x² = Px/4

Area = Px/4

The fencing will be equal to the perimeter, with an area 256 sq yd

256 = Px/4

P = 1024 / x

Thus, using a straightforward equation, one may determine how much fence is necessary for a playground with a 256 square yard area is P = 1024 / x.

Learn more about Quadrilaterals, by the following link.

brainly.com/question/23935806

#SPJ1

Answer:

c = 72/0.45

c = 160

So the value of c =160

well, let's call "c" the 100%, and we know that 45% of that is 72, hmmm so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} c & 100\\ 72& 45 \end{array} \implies \cfrac{c}{72}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{ c }{ 72 } ~~=~~ \cfrac{ 20 }{ 9 }\implies 9c=1440\implies c=\cfrac{1440}{9}\implies c=160[/tex]

The function h(x) represents the cost of the jeans if you first use the coupon and then apply the store discount.

The function h(x) can be computed using the composition of functions f(x) and g(x). The function j(x) represents the cost of the jeans if you first apply the store discount and then use the coupon.

The function g(x) can be computed using the composition of functions g(x) and f(x).

If you use the composition h(x), you will pay $27 for the jeans. If you use the composition j(x), you will pay $30 for the jeans.

Therefore, the composition h(x) will give you a better discount since it is cheaper.

Learn more about a function on https://brainly.com/question/12431044

#SPJ1

The function that represents how much you would pay if you use the store discount first and then mall coupon is:

j(x) = 0.75*x - 5

Wewant to write a function that represents how much you would pay if you use the store discount and then tha mall coupon.

We know that:

So if first we apply the discount, then we need to do the composition:

f(g(x)) = g(x) - 5

Replacing g(x) there we will get:

f(g(x)) = g(x) - 5 = 0.75*x - 5

j(x) = 0.75*x - 5

Learn more about composition of functions:

https://brainly.com/question/10687170

#SPJ1

The numerical form of the statement is 4n + 7 = 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement the sum of 4 times a number and 7 is equal to 2.

Let, The number be 'n'.

The numerical form of the statement will be,

4n + 7 = 2.

4n = 2 - 7.

4n = - 5.

n = - 5/4.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

The value of the function when evaluated is 3

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

g(x) = 2x ^ 2 - 3x + 5

Express properly

So, we have the following representation

g(x) = 2x^2 - 3x + 5

Substitute the known values in the above equation, so, we have the following representation

g(-2) = 2(-2)^2 - 3(-2) + 5

Evaluate the like terms

g(-2) = -8 + 6 + 5

So, we have

g(-2) =

Hence, the function value is 3

Read more about function at

https://brainly.com/question/28532394

#SPJ1

Answer:

What equation

Step-by-step explanation:

Volume of the cement required to pave the driveway is = 125/9 cubic yards.

A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid may become a cube by varying the lengths of the edges or the angles between the faces.

Features of a Cuboid :

A cube is a specific instance of a cuboid in which the length, width, and height are all equal. Accordingly, a cuboid is a cube.

Length of the Driveway = 150 ft = 50 yards

Width of the driveway = 10 ft = 10/3 yards

Thickness of the cement pavement = 3 inches = 3/36 = 1/12 yards

Volume of the cement required is = length*breadth*width = 50*(10/3)*1/12 = 125/9 cubic yards

To learn more about Volume refer to :

https://brainly.com/question/29194158

#SPJ4

Answer:

The answer is C

Step-by-step explanation:

This is because the graph shifts to the right as the value correlated with x is 6, meaning the new zeros of the graph would be at (0,0) and (6,0)

The minimal degree of the Taylor Polynomial required to calculate to 4 decimal places depends on the smoothness of the function and the error term in the Taylor Series is 0.0001

Taylor Polynomial is a mathematical tool used to approximate a function near a point using a polynomial. The degree of the polynomial determines how accurate the approximation is.

To calculate a Taylor Polynomial to 4 decimal places, we need to use a minimal degree that provides us with the desired accuracy.

The minimal degree depends on the smoothness of the function we are trying to approximate. The smoother the function, the lower the degree we need.

However, if the function has many twists and turns, we may need a higher degree to get the desired accuracy.

To calculate a Taylor Polynomial to 4 decimal places, we need to consider the error term in the Taylor Series.

The error term represents the difference between the actual value of the function and its approximation.

If the error term is less than 0.0001, we can be confident that our approximation is accurate to 4 decimal places.

To know more about decimal here.

https://brainly.com/question/29878290

#SPJ4

The Probability that a randomly selected student who performed in the spring play, but did not perform in the spring concert is chosen is 26/53.

Now let A be the event of the student performing in Spring play

Let B be the event of students performing i the spring concert

Now according to what we know,

n(A) = 68

n(B) = 54

n(A ∩ B) = 16

Now total no. of students will be n(A U B) = 68 + 54 - 16

= 106

We need to find the number of people who performed in the spring play and not in the concert

Hence we need to find the Probability

P(A ∩ not B)

Now we can say that (A ∩ not B) will clearly be

A - (A ∩ B) Hence we get it to be

68 - 16 = 52

Hence, P(A ∩ notB) = 52/106

= 26/53

To learn more about Probability visit

https://brainly.com/question/29251004

#SPJ4

The investor is doing a two-stage sampling or a two-phase sampling. This type of sampling involves two steps: first, a simple random sampling is used to create a set of groups, and then individuals are selected from within the selected groups for analysis.

In this case, the investor created 10 groups through simple random sampling and then selected and analyzed all the individuals in two groups. Random sampling is a statistical sampling technique where a sample is selected from a larger population so that each member of the population has an equal chance of being selected. This means that the sample should be selected randomly and not based on systematic or predetermined criteria.

The goal of random sampling is to produce a sample representative of the population, allowing for more accurate inferences about the population as a whole. Random sampling helps to eliminate bias in the sample selection process, improving the accuracy and validity of the results obtained from the sample.

To learn more about sampling, visit here

https://brainly.com/question/14937422

#SPJ4

a) The number of poker hands with exactly 2 aces and 3 kings is 24.

b) The probability that the first king is dealt out on the 13th card is approximately 0.0045, or approximately 0.45%.

a) To find the number of poker hands with exactly 2 aces and 3 kings, we have to choose which 2 aces out of the 4 available and which 3 kings out of the 4 available to include in our hand. We can do this in C(4,2) * C(4,3) ways, where C(n, k) is the number of combinations of n things taken k at a time.

Therefore, the number of poker hands with exactly 2 aces and 3 kings is C(4,2) * C(4,3) = 6 * 4 = 24.

b) The probability that the first king is dealt on the 13th card is the number of combinations of 12 cards that do not include any kings divided by the total number of combinations of the first 12 cards. This can be calculated as (48 choose 12) / (52 choose 12), where C(n, k) is the number of combinations of n things taken k at a time.

The probability is (48 choose 12) / (52 choose 12) = (48! / (12! * (48-12)!) ) / (52! / (12! * (52-12)!)) = (48 * 47 * 46 * 45 * 44 * 43 * 42 * 41 * 40 * 39 * 38 * 37) / (52 * 51 * 50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41) = approximately 0.0045, or approximately 0.45%.

Learn more about combinatorics and probability here: https://brainly.com/question/3901018

#SPJ4

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

-5x-3(-3) = -7

Apply distributive property:

(-5x)*-3 + (-3)*-3

15x + 9 = -7

      -9    -9

15x = -15

Divide both sides by 15:

15x/15 = x

-15/15 = -1

[tex]x=-1[/tex]

Hope this helped!

Explanation:

Each term has an x attached to it. We add the numbers in front

4x+7x+x = 4x+7x+1x = (4+7+1)x = 12x

Think of it like saying

4 boxes + 7 boxes + 1 box = 12 boxes

Replace each "boxes" with the letter "x".

Answer:

27.6 is a rational number

Step-by-step explanation:

A rational number is any number that can be expressed as a fraction. Since 27.6 Since 27.6 can be expressed as 276/10 or 138/3, 27.6 is a rational number.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

Basket A contains 8 balls, basket B contains 8 + 6 = 14 balls, and basket C contains 17 - (8 + 6) = 3 balls.

Let's call the number of balls in basket A "x".

Since there are 6 more balls in basket B than in basket A, we can write the equation for the number of balls in basket B as x + 6.

And since the total number of balls in baskets B and C is 17, we can write the equation for the number of balls in basket C as 17 - (x + 6) = 17 - x - 6.

So the total number of balls in baskets A, B and C is x + (x + 6) + (17 - x - 6) = x + x + 6 + 17 - x - 6 = 22.

Therefore, we can solve for x:

2x + 6 = 22

2x = 16

x = 8

So basket A contains 8 balls, basket B contains 8 + 6 = 14 balls, and basket C contains 17 - (8 + 6) = 3 balls.

Regarding the carpet, a room measuring 5 m x 7 m is 35 m². If each box of carpet covers 10 m², then 35 m² will need 35/10 = 3.5 boxes of carpet. This means that there will be 3.5 boxes * 10 m²/box = 35 m² of carpet. So there will be no carpet left over.

Answer:

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

We have:

Use the difference of the first two equations to find A:

Then find B, using third equation:

Finally find C, using second equation:

Area of the room is:

If each box covers 10 m² we need to buy 4 boxes:

Carpet left over:

The ESE (estimated standard error) in the bottom of the independent-measure t statistic measures the variability in the sample data used to calculate the t statistic and provides information on the precision of the t statistic.

The t statistic is used to compare the difference between two means from independent groups to determine if the difference is significant or not.

The ESE reflects the degree of uncertainty in the difference between the two sample means and is calculated as the standard deviation of the sampling distribution of the difference between the two sample means. The ESE is an estimate of the standard deviation of the population difference and is used to calculate the t statistic.

The ESE is an important measure because it provides information on the precision of the t statistic, which is used to make inferences about the population difference. If the ESE is large, it means that the sample difference is less precise and the t statistic is less significant. If the ESE is small, it means that the sample difference is more precise and the t statistic is more significant.

To know more about estimated standard error click here:

https://brainly.com/question/15063024#

#SPJ11