In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. consider the following data set.
8, 16, 14, 8, 16

a) use the defining formula, the computation formula, or a calculator to compute s. (enter your answer to four decimal places.)

b) add 8 to each data value to get the new data set 16, 24, 22, 16, 24. compute s. (enter your answer to four decimal places.)

c) compare the results of parts (a) and (b). in general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

adding the same constant c to each data value results in the standard deviation remaining the same.

adding the same constant c to each data value results in the standard deviation increasing by c units.

adding the same constant c to each data value results in the standard deviation decreasing by c units.

there is no distinct pattern when the same constant is added to each data value in a set.

For the demand of apartments in terms of rent: The equation of the line giving the demand x in terms of the rent p is x = -0.0263p + $62.5764.

For the value of the taffy-pulling machine during its useful life: The equation of the line giving the value V of the taffy-pulling machine during the 5 years it will be in use is V = -$177t + $885.

For the first scenario:

We are given two data points: when the rent is $98 per month, all 60 units are occupied, and when the rent is $630 per month, the average number of occupied units drops to 46.

Let's assign the rent as p and the demand (number of occupied units) as x. We are told that the relationship between the monthly rent p and the demand x is linear.

We can find the equation of the line using the slope-intercept form:

y = mx + b

where y represents the demand x, m represents the slope, and b represents the y-intercept.

Using the given data points, we can calculate the slope:

Slope (m) = (change in y) / (change in x)

Slope (m) = (46 - 60) / ($630 - $98)

= -14 / $532

= -0.0263 (rounded to four decimal places)

Now, we can use one of the data points (let's use p = $98, x = 60) to find the y-intercept:

60 = -0.0263($98) + b

Solving for b:

60 = -$2.5764 + b

b = 60 + $2.5764

b = $62.5764 (rounded to four decimal places)

Therefore, the equation of the line giving the demand x in terms of the rent p is:

x = -0.0263p + $62.5764

For the second scenario:

We are given that the taffy-pulling machine is purchased for $885 and has a useful life of 5 years. The depreciation of the machine is assumed to be linear.

Let's assign the value of the machine as V and the number of years since purchase as t. We want to find the linear equation that gives the value of the taffy-pulling machine during the 5 years it will be in use.

Since the useful life of the machine is 5 years, the initial value is $885, and the final value is $0 (since it will have to be replaced after 5 years), we can use the slope-intercept form to find the equation:

y = mx + b

where y represents the value V, m represents the slope, t represents the number of years since purchase, and b represents the initial value.

Using the given data points, we can calculate the slope:

Slope (m) = (change in y) / (change in x)

Slope (m) = ($0 - $885) / (5 - 0)

= -$177

Now, we can use one of the data points (let's use t = 0, V = $885) to find the initial value:

$885 = -$177(0) + b

Solving for b:

$885 = b

Therefore, the equation of the line giving the value V of the taffy-pulling machine during the 5 years it will be in use is:

V = -$177t + $885

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The function g(x) that satisfies the given conditions is \(g(x) = -256 - x^4 + 3x.\)It has a derivative of \(g'(x) = -512 - x^3\) and its maximum value is 3.

To find the function g(x) that satisfies the given conditions, we start by integrating the derivative \(g'(x) = -512 - x^3.\) The integral of -512 gives -512x, and the integral of \(-x^3\) gives\(-(1/4)x^4\). Adding these terms together, we have the general antiderivative of g(x) as \(-512x - (1/4)x^4 + C\), where C is a constant of integration.

Next, we apply the condition that the maximum value of g(x) is 3. To find this maximum value, we take the derivative of g(x) and set it equal to 0, since the maximum occurs at a critical point. Taking the derivative of g(x) = \(-512x - (1/4)x^4 + C\), we get g'(x) = \(-512 - x^3\).

Setting g'(x) = \(-512 - x^3 = 0\), we solve for x to find the critical point. By solving this equation, we find x = -8. Substituting this value back into g(x), we have g(-8) =\(-256 - (-8)^4 + 3(-8) = 3\). Thus, the function g(x) = \(-256 - x^4 + 3x\) satisfies the given conditions, with a derivative of g'(x) = -\(512 - x^3\) and a maximum value of 3.

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The given statement is True because If the sample mean is close to the population parameter, it suggests representative sampling regarding the variable of interest, although other factors should be considered too.

When the sample mean closely approximates the population parameter, it indicates that the sample is capturing the central tendency of the population. The mean is a measure of central tendency that reflects the average value of the variable of interest in the population.

If the sample mean is similar to the population mean, it suggests that the sample is a good representation of the population in terms of that particular variable.

However, it is important to note that representativeness is a relative concept. A sample may be considered representative in one sense but not necessarily in all aspects. Other factors, such as the sampling method, sample size, and sampling bias, also influence the representativeness of a sample.

In summary, when the obtained mean of the observations in a research study is close to the population parameter, it provides evidence that the sample is representative of the target population to some degree, indicating that the sample captures the central tendency of the population for the variable under investigation.

However, representativeness should be assessed in consideration of other factors as well.

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The equation that can be formed from the given set of numbers

1) (3 + 4) * 6 + 7 = 24

2) 3 + 4 * (6 + 7) = 24

3) 3 + 4 + 6 + 7 = 20, so (3 + 4 + 6 + 7) * 1 = 24

4) 3 * 4 * 6 * 7 = 168, so 168 / 7 = 24

Mathematical Operations :

The mathematical “operation” refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.

Mathematical Equations :

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

BODMAS

According to the BODMAS rule, mathematical equations containing numerous operators must be resolved in the order of BODMAS, starting from the left.

Keep in mind that the order in which you perform the operations will affect the result. Parentheses are used to indicate the order in which operations should be performed.

In the first example above, the operation inside the parentheses (3 + 4) is done first, and then that result is multiplied by 6 and added to 7.

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Answer:

14;8

Step-by-step explanation:

a、700*(1+3%)^n>1850*(1-4%)^n ,n is the minimum :14；

b、1000+50n>1850*(1-4%)^n,n is the minimum :8

a. After approximately 24.89 years, the wildebeest population will be greater than the zebra population.

b. After approximately 57.77 years, the antelope population will be greater than the zebra population.

To find the exact answers for the time when the wildebeest population surpasses the zebra population and when the antelope population surpasses the zebra population, we need to solve the equations:

a) For the wildebeest and zebra populations:

\(700 * (1.03)^t = 1850 * (0.96)^t\)

To solve this equation, we can isolate the exponential terms and solve for t:

\((1.03)^t / (0.96)^t = 1850 / 700\)

Now, take the natural logarithm (ln) of both sides:

\(ln[(1.03)^t / (0.96)^t] = ln(1850 / 700)\)

Using the properties of logarithms, we can simplify the equation:

\(t * ln(1.03) - t * ln(0.96) = ln(1850 / 700)\)

Factor out t:

\(t * [ln(1.03) - ln(0.96)] = ln(1850 / 700)\)

Now, solve for t:

\(t = ln(1850 / 700) / [ln(1.03) - ln(0.96)]\)

we get: \(t \approx 24.89 years\)

So, after approximately 24.89 years, the wildebeest population will be greater than the zebra population.

b) For the antelope and zebra populations:

\(1000 + 50t = 1850 * (0.96)^t\)

We can solve this equation similarly:

\(1000 + 50t = 1850 / (0.96)^t\\\\t * 50 = ln(1850 / 1000) / ln(0.96)\\\\t = ln(1850 / 1000) / ln(0.96) / 50\)

we get: \(t \approx 57.77 years\)

So, after approximately 57.77 years, the antelope population will be greater than the zebra population.

Keep in mind that these are approximate values, and the actual year may need to be rounded to the nearest whole number, as populations cannot be fractional. Therefore, the final answers are: a) After 25 years, the wildebeest population will be greater than the zebra population.

b) After 58 years, the antelope population will be greater than the zebra population.

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Answer:

Yes it is proportional (Equation: y=3.5x)

Step-by-step explanation:

Notice that there is a constant change in y and a constant change in x. But by how much? Given the last point (13,45.5) we can see that 13-12=1 and 45.5-42=3.5 so that means as x increases by 1, y always increases by 3.5, making the relationship proportional. You can also write the equation y=3.5x to show this

The seasonal total prior to the recent storm was 76.42 inches.

To calculate the seasonal total prior to the recent storm, we need to subtract the rainfall from the recent storm (50 inches) from the updated seasonal total (26.42 inches).

Let's assume that the seasonal total prior to the recent storm is represented by "x" inches.

So, we can set up the equation:

x - 50 = 26.42

To solve for x, we can add 50 to both sides of the equation:

x - 50 + 50 = 26.42 + 50

This simplifies to:

x = 76.42

Therefore, the seasonal total prior to the recent storm was 76.42 inches.

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Answer:

12x^2-5x-2

Step-by-step explanation:

Answer:

I put down my steps in the comment section. If you still don't understand just comment to me.

Step-by-step explanation:

Answer: I answered 6-11

Step-by-step explanation:

When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

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Answer:

C

Step-by-step explanation:

So to do this problem, first find the area of the figure before you apply the scale factor, and then multiply that by 49. The reason you multiply it by 49 and not 7 is because you're multiplying both the length and the width of the figure by 7, so you have 7 * 7 = 49.

The area of the figure to start is 10 (you can find this by simply counting the blocks).

Then, 10 * 49 = C. 490 units squared.

hope that makes sense!

The function can they use to determine if the error is repeated throughout the dataset is " COUNTA ".

The given condition needs the following function;

Data Integration Error:

Data from a single source, obtained and entered in the same way across time is unusual to be present in a database of significant size and age. A database frequently comprises data that has been gathered over time from various sources using various ways. As an illustration, consider how the meaning of "affected" is evolving or changing as the crisis progresses and the number of people affected is tracked over time. In addition, many databases evolve in practice by joining together different pre-existing databases. Almost always, the databases involved in this merging effort include discrepancies involving various data units, measurement intervals, formats, etc. Any process that combines data from various sources has the potential to make mistakes. When two or more databases are combined, errors will be found where there are discrepancies between the databases as well as new errors will be produced (i.e. duplicate records). A few potential origins and types of errors in a big assessment are shown in Table 1 below, at three fundamental levels: after completing the survey, when adding information to the database, and when conducting the analysis.

So, we use " COUNTA "

The function can they use to determine if the error is repeated throughout the dataset is " COUNTA ".

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Answer:

2187

Step-by-step explanation:

Multiply 3 seven times in your calcultor to check this answer or look it up on google

Answer:

60

Step-by-step explanation:

LCM of 12 and 15

First Method: Listing the multiples

First, write the common multiples of all three numbers.

Common Multiples of 12: 12,24,36,48,60,72,….

Common Multiples of 15: 15, 30, 45, 60, 75,…

Hence, the Least common multiple of 12 and 15 is 60.

Second method: By prime factorisation

Let us write the prime factors of the two numbers individually.

12 = 2 x 2 x 3

15= 3 x 5

Multiply each factor the maximum number of times it occurs in either number

= 2 X 2 X 3 X 5

= 60

LCM of 12 and 15= 60

Answer

LCM of 12 and 15= 60

Hope this helps :)

Answer:

60

Step-by-step explanation:

we have to use prime factorisation method to obtain the answer.

12 and 15 have LCM 60.

The mean of all exam scores in the class is found as 71.

For the given question;

The z-score is found by;

z = (x - μ)/σ

x =  sample mean

μ =  mean score

σ =  standard deviation

Now, from this,

x = zσ + μ

For p = 80th percentile= 0.8, see z value from z score table.

z = 0.85

x = 85 points

85 = 0.85σ +  μ  .....eq 1

For p = 30% = 0.3, see z value from z score table.

z = -0.3802

x = 65

65 = -0.3802σ +  μ  .....eq 2

Solving eq 1 and 2.

σ = 16.25

Put in eq 1

μ = 71.19

μ = 71

Thus, the mean of all exam scores in the class is found as 71.

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The correct answer is D. All of the above. When the spread of scores around the arithmetic mean gets smaller, it means that the data points are closer to the mean.

This has several implications:
A. The coefficient of variation (CV) gets smaller: The coefficient of variation is the ratio of the standard deviation to the mean. When the standard deviation decreases (due to smaller spread of scores), the CV also decreases.
B. The interquartile range (IQR) gets smaller: The IQR represents the range between the first quartile and the third quartile. When the spread of scores decreases, the values at the first and third quartiles are closer together, resulting in a smaller IQR.
C. The standard deviation gets smaller: The standard deviation measures the average distance of data points from the mean. As the spread of scores decreases, the data points are closer to the mean, resulting in a smaller standard deviation.
In summary, when the spread of scores around the arithmetic mean gets smaller, the coefficient of variation, interquartile range, and standard deviation all decrease.

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Answer:

\(22cm {}^{2} \)

Step-by-step explanation:

\(the \: area \: = \: \frac{1}{2} \times (bh) = \frac{1}{2} (4 \times 11) \\ = \frac{1}{2} (44) = 22 {cm}^{2} \)

Step-by-step explanation:

steps are in the picture.

Volume is a three-dimensional scalar quantity. The depth of the YMCA lap pool is 2 meters.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given that the following details about the YMCA lap pool:

Since the pool is in the space of a right rectangular prism, therefore, the volume of the prism will be the product of length, width and depth. Therefore, the volume of the pool can be written as,

The volume of the pool = Length × width × depth

1472m³ = 36.8m × 20 m × depth of the pool

Depth of the pool = (1472m³ ) / (36.8m × 20m)

                              = 2 meter

Hence, the depth of the YMCA lap pool is 2 meters.

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Step-by-step explanation:

40.

f(x)=x^2-6x-16

=x^2-8x+2x-16

=x(x-8)+2(x-8)

=(x-8)(x+2)

for root

f(x)=0

(x-8)(x+3)=0

x=8 or -3

41.

=x^3-x

=x(x^2-1)

=x(x+1)(x-1)

for root

x(x+1)(x-1)=0

x=0,1,-1

42.

=x^3-x^2-3x+3

=x^2(x-1)-3(x-1)

=(x-1)(x^2-3)

for root

(x-1)(x^2-3)=0

x=1,-√3,√3

Sonia will spend $1600 on airfare , $ 1200 on accommodations and $ 800 on food .

Multiplication is the polar opposite of division. If three groups of four add up to 12, then division of 12 into three groups of equal size yields four in each group.The basic objective of splitting is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.

Given that: She has allocated $3600 (in canadian dollars) to spend on airfare, accommodations, and food in a ratio of 4:3:2.

She has allocated $3600 (in canadian dollars) to spend on airfare, accommodations, and food in a ratio of 4:3:2.

let the sonia spend x

4x + 3x +2x = $3600

9x = $3600

x=$400

On airfare sonia will spend 4 × $400 = $1600

On accommodations sonia will spend 3 × $400 =$1200

On food sonia will spend 2 × $400 = $800

Sonia will spend $1600 on airfare , $ 1200 on accommodations and $ 800 on food .

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Answer:

B

Step-by-step explanation:

The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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Answer:

26

Step-by-step explanation:

The probability that the number pyramid will land on three and the spinner will stop on blue is 1/24.

To determine the probability that the number pyramid will land on three and the spinner will stop on blue, we need to know the total number of possible outcomes for both events and the number of favorable outcomes for the desired outcome.

Let's assume that the number pyramid has six sides numbered from one to six, and the spinner has four sections colored blue, red, green, and yellow. If both the number pyramid and spinner are fair and unbiased, each outcome is equally likely.

Number pyramid outcomes: There are six possible outcomes, namely numbers one to six.

Spinner outcomes: There are four possible outcomes, namely blue, red, green, and yellow.

To find the probability of both events happening together, we need to multiply the probabilities of each event occurring individually, assuming they are independent events (i.e., the outcome of one event does not affect the outcome of the other).

Probability of landing on three: Since the number pyramid has six sides, and we want to land on three, there is only one favorable outcome (three) out of the six possible outcomes. Therefore, the probability of landing on three is 1/6.

Probability of stopping on blue: Since the spinner has four sections, and we want it to stop on blue, there is only one favorable outcome (blue) out of the four possible outcomes. Therefore, the probability of stopping on blue is 1/4.

To find the probability of both events occurring, we multiply these probabilities:

Probability of landing on three and stopping on blue = (1/6) * (1/4) = 1/24

Therefore, the probability that the number pyramid will land on three and the spinner will stop on blue is 1/24.

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Answer:

She needs to eat 5 ounces of cheese and 1 ounce of yogurt

Step-by-step explanation:

Rachel should have 15 ounces of  yogurt and 14 ounces of cheese.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: An ounce of cottage cheese contains 3 grams of protein and 12 milligrams of calcium. An ounce of yogurt contains 1 gram of protein and 44 milligrams of calcium. let Rachel have x ounces of cheese and y ounces of yogurt. Then we have the following equations

3x+y=57

0.012x+0.044y=0.84

Solving these two equations we get y=15.3 or 15 ounces (approx)

and x= 13.9 or 14 ounces(approx) respectively.

Hence, Rachel should have 15 ounces of  yogurt and 14 ounces of cheese.

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