What is the image of the point (-3,8) after a rotation of 180 counterclockwise about the origin

Answer:

I think the answer is 8d + 4.

Step-by-step explanation:

Combine the like terms, 6d + 2d = 8d. 6 - 2 = 4.

The residual for the amount of monthly interest paid on a loan after 30 months is $0.13.

To find the residual, we need to compare the actual value of monthly interest paid after 30 months with the predicted value based on the regression equation.

The regression equation is:

monthly interest = 968 - 3.34x

To find the predicted value for 30 months, we substitute x = 30 into the equation:

monthly interest = 968 - 3.34(30) = 865.8

So the predicted value for monthly interest after 30 months is $865.8.

The residual is the discrepancy between the actual and expected values:

residual = actual value - predicted value

residual = $865.93 - $865.8 = $0.13

Therefore, the residual for the amount of monthly interest paid on a loan after 30 months is $0.13.

To learn more about the regression equation visit:

brainly.com/question/1564293

#SPJ4

1/70 is the probability of having slips numbered 1, 2, 3, and 4 drawn in order from the box.

To calculate the probability of drawing slips numbered 1, 2, 3, and 4 in order from a box containing slips numbered 1 through 8, we need to first find out the total number of possible outcomes when drawing four slips without replacement from the box.

The number of ways to draw 4 slips from a set of 8 slips without replacement is given by the combination formula:

= 8!/4!(8-4)! = 70

This means there are 70 possible outcomes when drawing four slips from the box.

To calculate the probability of drawing slips 1, 2, 3, and 4 in that order, we need to consider that there is only one way to draw the slips in that specific order, out of the 70 possible outcomes.

Therefore, the probability of drawing slips 1, 2, 3, and 4 in order is:

P(1,2,3,4 in order) =  number of favorable outcomes/total number of possible outcomes = 1/70

So the probability of drawing slips numbered 1, 2, 3, and 4 in order from the box is 1/70.

To learn more about probability refer here:

https://brainly.com/question/30034780

#SPJ11

(a)The equation x - 7 = 2x - 14 + 1 has 7 as a solution (when v = 2) and an extraneous solution of -8.

(b) To have a real number solution, the value of bx + c should be nonzero.

(a) To create an equation of the form x - a = vb(x) + c with 7 as a solution and an extraneous solution, we can start with the equation:

x - 7 = v * (x - 7) + 1

Simplifying this equation, we have:

x - 7 = vx - 7v + 1

Rearranging the terms, we get:

x - vx = 7v - 6

Now, let's assume v = 2. Substituting this value, the equation becomes:

x - 2x = 14 - 6

Simplifying further, we have:

-x = 8

Multiplying both sides by -1, we get:

x = -8

(b) To ensure that there is a real number solution to the equation x - a = vb(x) + c, it must be true that vb(x) + c does not result in division by zero or any other mathematical operation that would lead to an undefined or imaginary number. This implies that bx + c should not be equal to zero, as dividing by zero is undefined.

Therefore, to have a real number solution, the value of bx + c should be nonzero.

To know more about real number , refer here:

https://brainly.com/question/17019115

#SPJ11

The overall limit is undefined as the the second limit is undefined

The given limit is of the indeterminate form 0/0 and hence we can apply l'Hôpital's Rule to evaluate it.

Applying l'Hôpital's Rule, we get:

lim sin(3x) / (3x) = lim [cos(3x) * 3] / 3 = cos(3x)

Now, we need to evaluate lim (3x)/(1 - cos(x)) as x approaches 0.

Again, this limit is of the indeterminate form 0/0, so we can apply l'Hôpital's Rule once again:

lim (3x)/(1 - cos(x)) = lim (3)/(sin(x)) = 3/0 (which is undefined)

Since the second limit is undefined, the overall limit is also undefined.

For more questions like Limit click the link below:

https://brainly.com/question/12207539

#SPJ11

The given values for uo and u3 are uo = 1 and u3 = 21. We can use the recurrence relation Un+2 = 2 * Un+1+1* Un to find the remaining terms:

U1 = U3 - 2U2 - 1*U0
U1 = 21 - 2U2 - 1*1
U1 = 20 - 2U2

U2 = U1 - 2U0 + 1*U0
U2 = 20 - 2U0 + 1*1
U2 = 19 - 2U0

Therefore, the first four terms are: 1, 19, -17, -53

So, the answer is: 1, 19, -17, -53.

Learn more about recurrence relation: https://brainly.com/question/4082048

#SPJ11

The required answer is x = 14

To solve this problem, we can use algebraic equations. Let's start by representing the number of points that Aisha has with the variable "x".

According to the problem, we know that Carter has 7.5 more points than Aisha, so we can write:
Carter = x + 7.5
An algebraic equation or polynomial equation is an equation in which both sides are polynomials (see also system of polynomial equations). These are further classified by degree: linear equation for degree one. quadratic equation for degree two.

We also know that Jamila has 4.5 more points than Carter, which means:

Jamila = (x + 7.5) + 4.5

a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. In mathematical logic, a variable is either a symbol representing an unspecified term of the theory (a meta-variable), or a basic object of the theory that is manipulated without referring to its possible intuitive interpretation.
Finally, we know that Jamila has 26 points:

Jamila = 26

Now we can solve for x:

(x + 7.5) + 4.5 = 26

x + 12 = 26

x = 14

Therefore, Aisha has 14 points.

To show the work:

Aisha = x

Carter = x + 7.5

Jamila = (x + 7.5) + 4.5

Jamila = 26

(x + 7.5) + 4.5 = 26

x + 12 = 26

x = 14

To know more about algebraic equations. Click on the link.

https://brainly.com/question/953809

#SPJ11

The equation of the tangent line to the curve at (1,4) is: y = 8x - 4

To verify whether the point (1,4) is on the curve [tex]\sqrt{xy}= x^2y - 2,[/tex]

We can substitute x=1 and y=4 into the equation and see if it is satisfied:

√(14) = 1^24 - 2

2 = 2

Since the equation is true, (1,4) is on the curve.

To find the tangent line to the curve at the point (1,4),

We need to find the derivative of the equation with respect to x and evaluate it at x=1:

[tex]\sqrt{xy} = x^2y - 2[/tex]

Differentiating with respect to x:

[tex](1/2)(x^{(-1/2))}(y) + (1/2)(y^{(-1/2))}(x) = 2xy[/tex]

Simplifying and evaluating at x=1, y=4:

[tex]2 + (1/2)(4^{(-1/2))(1)} = 8[/tex]

The slope of the tangent line is 8.

Using point-slope form, the equation of the tangent line to the curve at (1,4) is:

y - 4 = 8(x - 1)

y = 8x - 4

For more such questions on point-slope form

https://brainly.com/question/6497976

#SPJ11

Answer:

Area = w(l)  l = 5 + w

Step-by-step explanation:

Zombie Epsilon would require 52.5 days of doses, Zombie Zeta would need 163.3 days, and Zombie Eta would require 636e days to be cured.

To develop a theoretical antidote, you would need to consider the virus strand, concentration (mag/ml), and the equation to calculate the number of doses needed.

For Zombie Epsilon, Zeta, and Eta, the amounts of virus are 150, 230, and 636 mag/ml, respectively. To create an effective antidote, you would need to identify the specific virus strands for each zombie type (e.g., strand 3.5 for Epsilon, 7.1 for Zeta, and "e" for Eta).

Using the provided information, the equation should be used to determine the number of days (doses needed) for each zombie type. As an example, let's assume the equation is as follows: Days = (Amount of Virus * Strand) / 10.

For Zombie Epsilon: Days = (150 * 3.5) / 10 = 52.5 days
For Zombie Zeta: Days = (230 * 7.1) / 10 = 163.3 days
For Zombie Eta: Days = (636 * e) / 10 = 636e days (where e is a constant value)

In this theoretical scenario, Zombie Epsilon would require 52.5 days of doses, Zombie Zeta would need 163.3 days, and Zombie Eta would require 636e days to be cured.

Please note that this is a fictional scenario and not based on real-life medical information.

To learn more about equation, refer below:

https://brainly.com/question/29657983

#SPJ11

Answer:

B

Step-by-step explanation:

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Given we can see that the line intersects with the Y-Intercept at (0,3), we can use process of elimination and erase answer choices A and D.

Now we are left with answr choices B and C, lets see where the line intersects with the X axis.

Helpful Tip:

If the line intersects with the X-Axis in between whole numbers, like for example this line intersects between 1 and 2, the slope will always be a fraction, which in this case the only fraction that we have left in answer choice B, which leads us to our answer.

The missing angles ;

22.6°

53.1°

28.1°

A right triangle is a type of triangle that has one of its angles measuring 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti.

We have that;

[tex]Sin \alpha = 5/13\\ \alpha = Sin-1(5/13)\\ \alpha = 22.6[/tex]

[tex]Tan  \alpha = 16/12\\\alpha = Tan-1 (16/12)\\= 53.1[/tex]

[tex]Sin \alpha = 8/17\\\alpha = Sin-1(8/17)\\\alpha = 28.1[/tex]

Right triangles have many practical applications, such as in trigonometry, engineering, and architecture.

Learn more about triangle:https://brainly.com/question/2773823

#SPJ1

If you cut a 6-inch long sausage roll that is 1/2 inch thick, you can make 12 pieces.

To understand how to arrive at this answer, we need to use some basic math.

First, we need to determine the volume of the sausage roll. We can do this by multiplying the length, width, and height of the roll. In this case, the length is 6 inches, the width is 1/2 inch, and the height is also 1/2 inch. So:

Volume = Length x Width x Height

Volume = 6 x 1/2 x 1/2

Volume = 1.5 cubic inches

Next, we need to determine the volume of each individual piece. To do this, we divide the total volume of the sausage roll by the number of pieces we want to make. In this case, we want to make two equal pieces, so we divide the total volume by 2:

Volume per piece = Total volume / Number of pieces

Volume per piece = 1.5 / 2

Volume per piece = 0.75 cubic inches

Finally, we can determine the dimensions of each individual piece by using the volume per piece and the thickness of the sausage roll. We can calculate the length of each piece by dividing the volume per piece by the thickness:

Length per piece = Volume per piece / Thickness

Length per piece = 0.75 / 0.5

Length per piece = 1.5 inches

So each piece will be 1.5 inches long. To determine how many pieces we can make, we divide the total length of the sausage roll by the length of each piece:

Number of pieces = Total length / Length per piece

Number of pieces = 6 / 1.5

Number of pieces = 4

However, since we are cutting the sausage roll in half, we can make 2 sets of 4 pieces, for a total of 8 pieces.

Alternatively, if we want to make only one cut, we can make two 3-inch long pieces from each half, for a total of 12 pieces.

Learn more about sausage

brainly.com/question/12415483

#SPJ11

The equation of the plane is -x(tan(r/4)) + z(sin(r/4)) = 1.

Let the equation of the plane be Ax + By + Cz = D. Since the plane contains the y-axis, we know that x = 0 when y = 0. Therefore, the equation becomes:

0A + 0B + Cz = D

=> Cz = D

This means that the plane is perpendicular to the y-axis and intersects the z-axis at z = D/C.

Now, we need to find the values of A, B, and C. Since the plane makes an angle of r/4 with the positive x-axis, we can use the direction cosines to find these values. The direction cosines of a vector are the cosines of the angles it makes with the x, y, and z axes.

Let the direction cosines of the vector perpendicular to the plane be (l, m, n). Then, we have:

cos(r/4) = l/√(l^2 + m^2 + n^2)

=> l = cos(r/4) / √2

cos(π/2) = m/√(l^2 + m^2 + n^2)

=> m = 0

cos(π/2) = n/√(l^2 + m^2 + n^2)

=> n = sin(r/4) / √2

Therefore, the vector perpendicular to the plane is:

(l, m, n) = (cos(r/4) / √2, 0, sin(r/4) / √2)

Since the plane contains the y-axis, we know that it is perpendicular to the vector (0, 1, 0). Therefore, the dot product of the two vectors is zero:

0A + B + 0C = 0

=> B = 0

Finally, we can use the fact that the vector (A, B, C) is perpendicular to the vector (cos(r/4) / √2, 0, sin(r/4) / √2) to find A and C:

A(cos(r/4) / √2) + 0 + C(sin(r/4) / √2) = 0

=> A = -C(tan(r/4) / √2)

Therefore, the equation of the plane is:

-C(tan(r/4) / √2)x + 0y + C(sin(r/4) / √2)z = D

Multiplying through by √2/C and setting D = √2, we get:

-x(tan(r/4)) + z(sin(r/4)) = 1

To know more about plane, here

brainly.com/question/14907256

#SPJ4

Connie's team lost 4 out of 16 games this season. To calculate the percentage of games lost, we can divide the number of games lost by the total number of games and then multiply by 100.

In this case, 4 divided by 16 is equal to 0.25, or 25% as a percentage. Therefore, Connie's team lost 25% of their games this season.

We first note that the total number of games played is 16. Connie's team won 12 of these games, so the number of games they lost is 16 - 12 = 4. To calculate the percentage of games lost, we divide the number of games lost by the total number of games and then multiply by 100. This gives:

(4 / 16) * 100 = 25%

Therefore, Connie's team lost 25% of their games this season.

It is important to understand how to calculate percentages in order to solve problems like this. In this case, we used the formula:

percentage = (part / whole) * 100

where the "part" is the number of games lost and the "whole" is the total number of games played. By substituting the appropriate values into this formula, we were able to calculate the percentage of games lost by Connie's team.

To know more about  games lost refer here:

https://brainly.com/question/29967991#

#SPJ11

Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.

To determine the number of planks required, we need to calculate the total amount of wood needed for all 18 students' treasure boxes.

Each treasure box has two identical rectangular sides.

Each side is cut from a wooden plank that is 5/9 feet long and 1 foot wide.

Therefore, the area of each side is [tex](5/9) \times 1 = 5/9[/tex] square feet.

Since there are two identical sides for each treasure box, the total area of wood needed for one treasure box is [tex](5/9) \times 2 = 10/9[/tex] square feet.

To find the total wood needed for 18 students' treasure boxes, we multiply the area per treasure box by the number of treasure boxes:

Total wood needed [tex]= (10/9) \times 18 = 20[/tex] square feet.

So, Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.

For similar question on rectangular sides.

https://brainly.com/question/29001951

#SPJ11

Question: What is the number of planks required for Mr. Penny's 18 students to each construct one treasure box if the rectangular sides of the treasure box will be cut from wooden planks that are 5/9 feet long and 1 foot wide?

The dot plot that most accurately displays Miss Little's class data is illustrated below.

To create a dot plot, we first need to determine the range of the data, which is the difference between the highest and lowest values. In this case, the range is from 8 to 16. We then draw a number line that spans the range, and mark each data point along the line with a dot.

Let's take a look at the first data set: 13, 14, 9, 12, 16, 11, and 10. The range is from 9 to 16, so we draw a number line from 9 to 16. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 13, one dot above 14, two dots above 9, one dot above 12, one dot above 16, one dot above 11, and one dot above 10.

We repeat this process for the second data set: 9, 8, 10, 10, 11, 15, and 10. The range is from 8 to 15, so we draw a number line from 8 to 15. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 9, one dot above 8, three dots above 10, one dot above 11, one dot above 15, and zero dots above 14.

To know more about dot plot here

https://brainly.com/question/22742650

#SPJ4

Complete Question:

Miss. Little wants to know how many pairs of shoes each of her students owns. She decides to ask each of her students to write the number of pairs of shoes that he or she owns. This data is displayed in the provided chart. Plot the dot plot that most accurately displays Miss Little's class data.

13 14 9 12 16 11 10

9 8 10 10 11 15 10

1) If you get 2 and 5, the multiplication is 10, which is not a multiple of 6. so, you would win.

2) If you get 4 and 2, the multiplication is 8, which is not a multiple of 6. so, you would win.

3) If you get 1 and 6, the multiplication is 6, which is a multiple of 6. so, I would win.

The question asks about probability  which player would win if the numbers rolled are 2 and 5. To answer this, we calculate the product of 2 and 5, which is 10. Since 10 is not a multiple of 6, the person who did not roll the dice (i.e., "you") would win.

The question asks which player would win if the numbers rolled are 4 and 2. We calculate the product of 4 and 2, which is 8. Since 8 is not a multiple of 6, "you" would win again.

The question asks which player would win if the numbers rolled are 1 and 6. We calculate the product of 1 and 6, which is 6. Since 6 is a multiple of 6, the person who rolled the dice (i.e., "me") would win.The game described in the question involves rolling two dice and calculating the multiplication of the two numbers rolled. The outcome of the game depends on whether the product is a multiple of 6 or not.

The solution also provides a general explanation of how to calculate the probability of rolling a multiple of 6 with two dice. To do this, we count the number of ways to roll each multiple of 6 (there are two ways to roll a 6, one way to roll a 12, and no ways to roll an 18) and divide by the total number of possible outcomes (which is 36, since there are 6 possible outcomes for each die and 6*6=36 possible combinations of two dice). This gives us a probability of 1/12, or approximately 0.0833, for rolling a multiple of 6. We can then calculate the probability of not rolling a multiple of 6 by subtracting this probability from 1, which gives us 11/12, or approximately 0.9167.

Learn more about probability

brainly.com/question/11234923

#SPJ11

There are 9 tables with 4 chairs in the restaurant.

Let's establish the variables:

Let x be the number of tables with 4 chairs

Let y be the number of tables with 5 chairs

Let z be the number of tables with 6 chairs

We know that there are a total of 19 tables, therefore:

x + y + z = 19 (equation 1)

We also know that the total number of people that can be accommodated in tables with 4 or 5 chairs is 64, therefore:

4x + 5y = 64 (equation 2)

We want to find the value of x, so we need to eliminate y from the equations above. We can do this by multiplying equation 2 by 4, and then subtracting it from equation 1:

x + y + z - 16x - 20y = 19 - 256

Simplifying:

-15x - 19y = -237

Dividing both sides by -19:

x = 9

Therefore, there are 9 tables with 4 chairs.

Learn more about multiplying equation

https://brainly.com/question/2272951

#SPJ4

Translated Question: Clear the selection Question 2: In a restaurant for 94 people there are 19 tables that can seat 4.5 or 6 people. If we know that the total number of tables with 4 or 5 chairs can accommodate 64 people, how many tables have 4 chairs?

Answer:

Her dad is 36 years old and brother is 12

Step-by-step explanation:

Since Alesha's brother is one year older you need to add 11+1 to get her brothers age, which is 12.
To get Alesha's dad's age you need to multiply 12x3, which is 36.

So, Alesha's dad is 36 and her brother is 12

Answer: [tex]\frac{x^2}{2}[/tex]

Step-by-step explanation:

If two of the tiles form a square together, then one of them must be half of a square. this means that the square is split diagonally.

If you've ever done trigonometry, you'll know this is a 45-45-90 special right triangle. The side lengths are in the ratio of x, x, and xsqrt(2).

so we know the area of one of these tiles will be [tex]\frac{x^2}{2}[/tex], where x is the side length of the square formed.

This procedure is not appropriate because (A) the two sample proportions were not computed from independent samples.

Independent samples are those chosen at random such that their observations do not depend on the values of other observations. Many statistical analyses are predicated on the assumption of independent samples. Others are intended to evaluate non-independent samples.

Assume that quality inspectors want to compare two laboratories to see if their blood tests produce identical results. Both labs receive blood samples drawn from the same ten children for analysis.

The test results are not independent because both labs analyzed blood samples from the same ten youngsters. The inspectors would need to perform a paired t-test, which is based on the assumption that samples are dependent, to compare the average blood test results from the two labs.

To know more about independent samples:

https://brainly.com/question/12054496

#SPJ4

Correct question:

A polling organization asks a random sample of 1,000 registered voters which of two candidates they plan to vote for in an upcoming election. Candidate A is preferred by 400 respondents, Candidate B is preferred by 500 respondents, and 100 respondents are undecided. George uses a large sample confidence interval for two proportions to estimate the difference in the population proportions favoring the two candidates. This procedure is not appropriate because

(A) the two sample proportions were not computed from independent samples

(B) the sample size was too small

(C) the third category, undecided, makes the procedure invalid

(D) the sample proportions are different: therefore the variances are probably different as well

(E) George should have taken the difference interval for a single proportion instead 500-400 1,000 and then used a large sample confidence

The expression for the area of the triangle is given as follows:

A = 6x² - 7x - 3.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the expression for the area of the triangle is given as follows:

A = 0.5(4x - 6)(3x + 1)

A = 0.5(12x² - 14x - 6)

A = 6x² - 7x - 3.

More can be learned about the area of a triangle at brainly.com/question/21735282

#SPJ1

The surface area of the triangular prism is

The surface area of the triangular prism is

= area of the two side rectangles + area of the base rectangles + area of the 2 triangles

= 2 * 36 * 30 + 36 * 36 + 2 * 1/2 * 36 * 24

= 2160 + 1296 + 1296

= 5752 square millimeters

Learn more about triangular prism at

https://brainly.com/question/29663752

#SPJ1

Dominick has earned $6,465.55 - $4,420.00 = $2,045.55 more interest than Ryan after 10 years.

To solve this problem, we can use the formulas for compound interest and simple interest.

Compound interest formula:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

Where:

A = the amount after time t

P = the principal

r = the annual interest rate

n = the number of times the interest is compounded per year

t = time in years

Simple interest formula:

I = Prt

Where:

I = the interest earned

P = the principal

r = the annual interest rate

t = time in years

Using the compound interest formula for Dominick's account:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

A = 6500(1 + 0.068/365)^(365*10)

A ≈ $12,965.55

Using the simple interest formula for Ryan's account:

I = Prt

I = 65000.06810

I = $4,420.00

Dominick's account has earned: $12,965.55 - $6,500 = $6,465.55 in interest.

Ryan's account has earned: $4,420.00 in interest.

Therefore, Dominick has earned $6,465.55 - $4,420.00 = $2,045.55 more interest than Ryan after 10 years.

Learn more about Earned  interest

brainly.com/question/31112017

#SPJ11

The weight of the goods on the ship decreased by 50 percent.

To find the percentage decrease in the weight of goods on the ship, we need to calculate the difference between the initial weight and the final weight, divide it by the initial weight, and then multiply by 100 to get the percentage decrease.

The initial weight of the goods on the ship was 60,010 tons and the final weight after unloading was 30,005 tons.

The difference between the initial weight and the final weight is 60,010 - 30,005 = 30,005 tons.

To find the percentage decrease, we divide the difference by the initial weight:

30,005 / 60,010 = 0.5

Multiplying by 100 gives us the percentage:

0.5 x 100 = 50%

Therefore, the weight of goods on the ship has decreased by 50 percent.

In conclusion, the percentage decrease in the weight of goods on the ship is 50 percent. This means that the ship has unloaded half of its initial weight and now carries only half of the weight it carried when it left the port last week. This calculation can be helpful for the shipping company to determine the efficiency of their transportation and to plan for future shipments.

Learn more about percentage here: https://brainly.com/question/24877689

#SPJ11

[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex] when simplified gives 0

Indices are small number that tells us how many times a term has been multiplied by itself. Indices are also the power or exponent which is raised to a number or a variable.

How to determine this

[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex]

When all of then are perfect square

[tex]\sqrt[4]{81}[/tex]= 3 * 3 *3 *3

[tex]\sqrt[3]{216}[/tex] = 6 * 6 * 6

[tex]\sqrt[2]{32}[/tex] = 2 * 2 * 2 * 2 * 2

[tex]\sqrt{225}[/tex] = 15 * 15

Therefore,

3 - 8(6) + 15(2) + 15

3 - 48 + 30 + 15

By collecting like terms

3 + 30 + 15 - 48

48 - 48

= 0

Read more about Indices

https://brainly.com/question/8412270

#SPJ1

Our calculated t-value (-2.54) is beyond this critical value, we can reject the null hypothesis and conclude that there is a significant difference between the mean number of miles run per week by group runners and individual runners.

To test if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons, we can use a two-sample t-test.

Let's assume that the population standard deviation for the individual runners is also 4.2 miles per week.

We can set up the hypotheses as follows:

Null hypothesis: The mean number of miles run per week by group runners and individual runners is the same.

Alternative hypothesis: The mean number of miles run per week by group runners and individual runners is different.

Mathematically, we can write:

H0: μ1 = μ2

Ha: μ1 ≠ μ2

where μ1 is the population mean for group runners and μ2 is the population mean for individual runners.

We are given the sample mean for the group runners, which is 49.0 miles per week. We do not know the sample mean for the individual runners. Let's assume that we collect a random sample of 32 individual runners and find that their sample mean is 52.0 miles per week.

We can calculate the test statistic as follows:

t = (X1 - X2) / sqrt((s1^2/n1) + (s2^2/n2))

where X1 and X2 are the sample means for group runners and individual runners, s1 and s2 are the population standard deviations for group runners and individual runners, and n1 and n2 are the sample sizes for group runners and individual runners.

Plugging in the values, we get:

t = (49.0 - 52.0) / sqrt((4.2^2/32) + (4.2^2/32))

t = -3.0 / 1.182

t = -2.54

Using a t-distribution table with 62 degrees of freedom (32 + 32 - 2), we can find that the critical value for a two-tailed test with a significance level of 0.05 is approximately ±2.0. Since our calculated t-value (-2.54) is beyond this critical value, we can reject the null hypothesis and conclude that there is a significant difference between the mean number of miles run per week by group runners and individual runners.

To learn more about null hypothesis visit: https://brainly.com/question/28920252

#SPJ11