HIKING Morgan stopped to rest after hiking 1.8 kilometers. Her mother rested after 2.1 kilometers. Who hiked farther?

The perimeter of square ABCD is 28 units.

The perimeter of a square is the sum of all its sides. In this case, we need to find the perimeter of square ABCD.

The question provides two possible answers: 28 units and 37 units. However, we can only choose one correct answer. To determine the correct answer, let's think step by step.

A square has all four sides equal in length. Therefore, if we know the length of one side, we can find the perimeter.

If the perimeter of the square is 28 units, that would mean each side is 28/4 = 7 units long. However, if the perimeter is 37 units, that would mean each side is 37/4 = 9.25 units long.

Since a side length of 9.25 units is not a whole number, it is unlikely to be the correct answer. Hence, the perimeter of square ABCD is most likely 28 units.

In conclusion, the perimeter of square ABCD is 28 units.

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A piece of wire 28 inches long is bent into the shape of a rectangle having width x and length y. The length y of the rectangle can be represented as a function of its width x using the formula y(x) = 14 - x.

To express y as a function of x, we first need to consider the properties of a rectangle and the given information.

Student question: A piece of wire 28 inches long is bent into the shape of a rectangle having width x and length y.

From the given information, we know that the wire is used to form the perimeter of the rectangle. The perimeter of a rectangle can be calculated using the formula:

Perimeter = 2 * (Width + Length)

In this case, we are given the width as x and the length as y. The perimeter is 28 inches. So, we can write the equation as:

28 = 2 * (x + y)

Now, our goal is to express y as a function of x. To do this, we need to solve the equation for y. We can start by dividing both sides of the equation by 2:

14 = x + y

Next, we need to isolate y. We can do this by subtracting x from both sides of the equation:

14 - x = y

Now we have expressed y as a function of x:

y(x) = 14 - x

In conclusion, the length y of the rectangle can be represented as a function of its width x using the formula y(x) = 14 - x. This equation is derived from the given information that the wire is 28 inches long and is bent to form a rectangle with width x and length y.

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the mean of that set is 31

Answer:

31

Step-by-step explanation:

Add all the numbers:

29 + 26 + 35 + 34 =  124

Divide by 4 (because there are 4 total numbers):

124/4 = 31

Answer:

4

Step-by-step explanation:

The solid produced by rotating the figure around the given axis is a cone.

Step-by-step explanation:

A solid is a 3-dimensional structure obtained by rotating the 2-dimensional figure at a given axis.

The line or axis at which the given figure is rotated is known as the axis of revolution.

Given:

A right-angle triangle

To find :

Solid produced by rotating the given figure.

Solution:

When we rotate the given figure as shown in the image, we will obtain a solid known as a cone.

The solid produced by rotating the figure around the given axis is a cone.

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Answer: 4. 27x + 18            8. 4x - 5

Step-by-step explanation: should be right

Answer: (-5/2, 0) or (-2.5,0)

Step-by-step explanation:

In the image below, I set y=0 to solve for the x-intercept, isolating the variable x to get my answer. I checked my work by graphing the function on Desmos to see if I got the right answer, as seen below! Hope this helps :)

Answer:

16

Step-by-step explanation:

Step 1: Write out expression

a²

a = -4

Step 2: Substitute

(-4)²

Step 3: Evaluate

16

There are 303600 ways to choose 4 members of the club to serve on an executive committee.

A permutation is the act of putting things or numbers in a certain order. Combinations are a method of picking things or numbers from a set of objects or collections without regard for their order.

No. of members = 25

We are supposed to find the no. of ways to choose a president, vice-president, secretary, and treasurer of the club

No. of posts = 4

The order matters here since each member will get different posts .

So, we will use permutation over here

formula - n P r = n! / (n-r)!

n = 25

r = 4

using calculator

25 P 4 = 303600
Hence there are 303600 ways to choose 4 members of the club to serve on an executive committee.

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The total change in temperature, in degrees Fahrenheit, for the package of food is 50°F

The initial temperature of the package of food as given in the question is -15°F

At noon, the temperature of the package of food was changed to 35° F

We need to find out the total change in temperature which is

Temperature of food package at noon - The initial temperature of the package of food

By substituting the values given in question we get

                       = 35° - (-15° F)

Which is a simple integer problem

                      = 35 - (-15)

                     = 35 + 15

                     =   50 F

Hence, the total change in temperature, in degrees Fahrenheit, for the package of food is 50° F

An integer is the range 0, a wonderful natural number or a poor integer with a minus signal. The poor numbers are the additive inverses of the corresponding advantageous numbers. in the language of arithmetic,

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Therefore, after answering the given query, we can state that With simple interest  a 5% rise per year, Beth's income in 14 years will be $69,394.38.

By dividing the base by the interest income, the time between payments, and many other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula for use in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating payment is as a portion of the principle amount. For example, if he takes $100 from a buddy and undertakes to pay back the loan at 5% interest, he only will pay his share of the 100% curiosity. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must collect interest when you give it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.

The following is the compound interest formula:

A is equal to P(1 + r/n)(n*t), where A is the total sum.

P is equal to the starting principal.

the annual compound interest rate at the annual compound interest rate at the annual compound interest rate at the rate at the rate (as a decimal)

n represents how many times the interest is compounded annually.

t = the duration in years

The beginning wage (P) in this scenario is $37,000, the interest rate (r) is 5%, the number of times compounded (n) is 1 (since we're assuming the raise occurs once a year), and the number of years (t) is 14. This allows us to enter these values into the formula:

A =\($37,000(1 + 0.05/1)^(1*14)\)

A = $37,000(1.05)^14*A =  $69,394.38

With a 5% rise per year, Beth's income in 14 years will be $69,394.38.

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Answer:

Step-by-step explanation:

Answer is p/320

The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

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

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

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Answer: 4.5

Step-by-step explanation:

It comes from after you divide 27 ÷ 6

Answer:

4.5 ounces

Step-by-step explanation:

Okay, to find out how much rice is in each container, you need to divide the 27 ounces into 6 equal groups.

This can be calculated using division.

27 ÷ 6 = ?

27 ÷ 6 = 4.5

Therefore, there are 4.5 ounces in each container.

Answer:

B 18√3

Step-by-step explanation: 1. Calculate the base and height of the triangle.

2. Multiply the base and height of the triangle.

3. Divide the result by 2.

4. Multiply the result by the square root of 3.

5. The answer is 18√3.

Based on typical expectations for the relationship between trunk circumference and tree height, the slope is most likely to be closer to 1.

The slope of the regression model represents the change in the dependent variable (height of the pine tree) for every one-unit increase in the independent variable (circumference of the trunk).

In this scenario, the slope is most likely to be closer to 1. This is because we expect a reasonably linear relationship between the circumference of the trunk and the height of the pine tree. Generally, as the trunk's circumference increases, we anticipate a proportional increase in the height of the tree.

If the slope were closer to 0, it would suggest little to no relationship between the circumference of the trunk and the height of the tree. However, in reality, there is usually a positive correlation between these variables.

If the slope were closer to 0.1 or 100, it would indicate a more extreme relationship where a small change in trunk circumference results in a significantly larger or smaller change in tree height. While this is possible in some cases, it is less likely to be the norm.

Therefore, based on typical expectations for the relationship between trunk circumference and tree height, the slope is most likely to be closer to 1.

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The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

Given,

A triangle ABC with vertices A(2,3) , B(4,-5), and C(-1,2)

To find the coordinates of the vertices of each figure after a reflection over the given axis.

Now, According to the question:

We should know that:

You should know that you can predict changes in coordinates after translations without a graph or anything like that.

(x, y) reflected over the x axis = (x, -y)

(x, y) reflected over the y axis = (-x, y)

(x, y) rotated 90 degrees around the origin = (y, -x)

(x, y) rotated 180 degrees around the origin = (-x, -y)

(x, y) rotated 270 degrees around the origin = (-x, y)

So here's our set of points.

A(2,3) , B(4,-5), and C(-1,2)

Here's those points reflected over the x axis.

A' (2, -3) B' (4, 5) and C' (-1, -2)

Hence, The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

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Answer:

Step-by-step explanation:

There are 26 letters in the alphabet and 10 digits that you can use (0,1,2,3,4,5,6,7,8,9)

As a result, we can find the number of combinations by doing the following:

26 x 26 x 10 x 10 x 10

since the first two symbols are alphabets and the last three are digits. After doing the math you get

26 x 26 x 10 x 10 x 10 = 676000 => You can make a total of 676,000 PIN codes

With a greater mean value , we can conclude that the sixth period class test was better than the second period .

Second period class:

Mean = (55+70+6*75+6*80+2*85+3*90+95)/20

Mean = 1590/20 = 79.5

Sixth period class:

Mean = (65+3*75+5*80+6*85+3*90+2*95)/20

Mean = 1660/20 = 83

Therefore, From the mean values , we can infer that students performed better in test for the sixth period class than the second .

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Answer:

9.5

Step-by-step explanation:

the numbers go up by 1.5

so, 7.5 + 1.5 = 9

According to the statement, the new flavour received 3 votes for every vote received by the original flavour. Denoting:

• x = # of votes of the original flavour,

• n = # of votes of the new flavour.

We can write the following equation for the number of votes:

Now, according to the statement, the number of votes of the new flavour is n = 723, replacing this number in the equation above and solving for x, we get:

Answer

The original flavour received 241 votes.

For function g(x) = -x + 10x the values of g(a + h) = 9a + 9h, g(-a) = -9a, g(√a) = 9√a, a + g(a) = 10a, and 1/g(a) = 1/9a.

To find the values of g(a + h), g(-a), g(√a), a + g(a), and 1/g(a) for the function g(x) = -x + 10x, we substitute the given values into the function.

g(a + h):

g(a + h) = -(a + h) + 10(a + h)

= -a - h + 10a + 10h

= 9a + 9h

g(-a):

g(-a) = -(-a) + 10(-a)

= a - 10a

= -9a

g(√a):

g(√a) = -√a + 10√a

= 9√a

a + g(a):

a + g(a) = a + (-a + 10a)

= 10a

1/g(a):

1/g(a) = 1/(-a + 10a)

= 1/(9a)

= 1/9a

Therefore, the values are:

g(a + h) = 9a + 9h

g(-a) = -9a

g(√a) = 9√a

a + g(a) = 10a

1/g(a) = 1/9a

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The question is -

Let g be the function defined by g(x) = -x + 10x. Find g(a + h), g(-a), g(√a), a+g(a), and 1/g(a).

Answer:

A and C are functions.

The domain is x and the range is y

Step-by-step explanation:

Each x - value can have only one y -value

Function= unique x-values

Y can be the same answer but the X has to be different

The given series with partial sums sn = (n² - 1) / (3n²) has a sum of 1/3. The convergence of the partial sums to 1/3 as n approaches infinity confirms this result.

To calculate the sum of the series where the partial sums are given as

sn = (n² - 1) / (3n²), we can analyze the expression and determine its behavior as n approaches infinity.

Looking at the expression, we can simplify it as sn = (1 - 1/n²) / 3. As n approaches infinity, the term 1/n² becomes negligible, and we are left with sn = 1 / 3. This means that the partial sums converge to a fixed value of 1/3 as n becomes larger.

Since the partial sums converge to 1/3, we can conclude that the sum of the series is also equal to 1/3. This is because the sum of an infinite series is defined as the limit of its partial sums as n approaches infinity. In this case, the partial sums approach 1/3, indicating that the series converges to 1/3.

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Answer: im pretty sure its 14 divided by 79 soo 0.17?

if not im sorry

use your brain tho:)

hope this helps you

Answer:

I think it is A

Step-by-step explanation:

While a common rule of thumb is to have a minimum sample size of 100 for continuous data to be statistically significant, the actual appropriate sample size may vary depending on the specific study design and research question. Option(D)

In statistics, the term "statistical significance" refers to whether an observed effect or relationship in the data is likely to be real and not just due to random chance. To determine statistical significance, we often perform hypothesis testing.

The sample size is a crucial factor in hypothesis testing. A larger sample size generally provides more reliable and precise estimates of population parameters and increases the statistical power of the test. With a larger sample size, even smaller effects or differences between groups can become statistically significant.

While there is no hard and fast rule for the minimum sample size to achieve statistical significance, a common guideline is to aim for at least 30 samples. This guideline is often used in the context of the Central Limit Theorem, which states that the sampling distribution of the sample mean becomes approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In practice, the appropriate sample size depends on various factors, including the nature of the data, the effect size being studied, the desired level of confidence, and the statistical test used. Researchers often conduct sample size calculations based on these factors before conducting their studies to ensure they have an adequate sample size to achieve meaningful results and detect significant effects if they exist.

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The change in the price of the company's stock from the beginning of the 6-week period to the end of it is a decrease of $7.50.

The change in the price of the company's stock from the beginning of the 6-week period to the end of it is calculated by multiplying the number of weekdays in 6 weeks by the daily decrease in stock price.

First, we need to determine the number of weekdays in 6 weeks. There are 5 weekdays in a week, so we multiply 5 by 6 to get 30 weekdays.

Next, we multiply the number of weekdays (30) by the daily decrease in stock price ($0.25) to find the total decrease in stock price over the 6-week period.

30 weekdays * $0.25 decrease per day = $7.50

Therefore, the change in the price of the company's stock from the beginning of the 6-week period to the end of it is a decrease of $7.50.

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The null space N(A) for the given matrix A is the zero vector:

N(A) = {(0, 0, 0)}

To find the null space N(A) for the given matrix A, we need to find the solutions to the equation Ax = 0, where x is a vector in the null space.

Given matrix A:

A = [13 22 31]

To find the null space, we need to solve the equation Ax = 0:

13x + 22y + 31z = 0

We can rewrite this equation as a system of linear equations:

13x + 22y + 31z = 0

To solve this system, we can use row reduction or Gaussian elimination. Let's use Gaussian elimination:

Step 1: Perform row operations to put the matrix A in row-echelon form:

R₂ = R₂ - (22/13) * R₁

R₃ = R₃ - (31/13) * R₁

The resulting matrix is:

[13 22 31]

[0 -2.15 -4.15]

[0 -3.54 -6.54]

Step 2: Continue row operations to put the matrix in reduced row-echelon form:

R₂ = -1/2.15 * R₂

R₃ = -1/3.54 * R₃

The resulting matrix is:

[13 22 31]

[0 1 1.93]

[0 1 1.85]

Step 3: Perform additional row operations to obtain the reduced row-echelon form:

R₃ = R₃ - R₂

The resulting matrix is:

[13 22 31]

[0 1 1.93]

[0 0 -0.08]

Step 4: Now, we can write the system of equations corresponding to the reduced row-echelon form:

13x + 22y + 31z = 0

y + 1.93z = 0

-0.08z = 0

From the last equation, we can see that z = 0. Substituting z = 0 into the second equation, we get y = 0. Finally, substituting z = 0 and y = 0 into the first equation, we get x = 0.

Therefore, the null space N(A) for the given matrix A is the zero vector:

N(A) = {(0, 0, 0)}

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The null space (N(A)) for the matrix A = [1 3 2; 2 3 1] is given by the vector [z, -z, z], where z is a real number.

To find the null space (N(A)) of a matrix A, we need to solve the equation Ax = 0, where x is a vector.

Given the matrix A:

A = [ 1 3 2 ; 2 3 1 ]

We need to find the values of x that satisfy the equation Ax = 0.

Writing out the equation, we have:

1x + 3y + 2z = 0

2x + 3y + z = 0

To solve this system of equations, we can row reduce the augmented matrix [A|0]:

[ 1 3 2 | 0 ]

[ 2 3 1 | 0 ]

Performing row operations, we can obtain the row echelon form:

[ 1 3 2 | 0 ]

[ 0 -3 -3 | 0 ]

To simplify further, we can divide the second row by -3:

[ 1 3 2 | 0 ]

[ 0 1 1 | 0 ]

Now, we can eliminate the entries above and below the pivot in the first column:

[ 1 0 -1 | 0 ]

[ 0 1 1 | 0 ]

The row echelon form reveals that x - z = 0 and y + z = 0.

Simplifying these equations, we have:

x = z

y = -z

Thus, the null space N(A) can be represented by the vector [ x, y, z ] = [ z, -z, z ], where z is a real number.

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Answer:

Steps to simplifying fractions

   Find the GCD (or HCF) of numerator and denominator. GCD of 224 and 100 is 4.

   224 ÷ 4100 ÷ 4.

   Reduced fraction: 5625. Therefore, 224/100 simplified to lowest terms is 56/25.

Step-by-step explanation:

The value of the sample statistic is used to estimate the value of the population parameter.

The sample statistic is the value that is calculated from the sample data, which is used to make inferences about the population parameter. Sample statistics are used to estimate population parameters. A sample statistic is an estimate of a population parameter that is obtained from a sample, whereas a population statistic is a value that is computed from a population.

Therefore, the correct answer is a. sample statistic.

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