what property is this


5+(a+8)= (5+a)+8

Answer:Therefore, the domain is restricted to non-negative values of x so that the function values will be defined. The variable x is often referred to as the independent variable, while the variable y is referred to as the dependent variable

Step-by-step explanation:

The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

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We have 3⁴ = 81, so we can factorize this as a difference of squares twice:

\(x^8 - \dfrac1{81} = \left(x^2\right)^4 - \left(\dfrac13\right)^4 \\\\ x^8 - \dfrac1{81} = \left(\left(x^2\right)^2 - \left(\dfrac13\right)^2\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)\)

Depending on the precise definition of "completely" in this context, you can go a bit further and factorize \(x^2-\frac13\) as yet another difference of squares:

\(x^2 - \dfrac13 = x^2 - \left(\dfrac1{\sqrt3}\right)^2 = \left(x-\dfrac1{\sqrt3}\right)\left(x+\dfrac1{\sqrt3}\right)\)

And if you're working over the field of complex numbers, you can go even further. For instance,

\(x^4 + \dfrac19 = \left(x^2\right)^2 - \left(i\dfrac13\right)^2 = \left(x^2 - i\dfrac13\right) \left(x^2 + i\dfrac13\right)\)

But I think you'd be fine stopping at the first result,

\(x^8 - \dfrac1{81} = \boxed{\left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)}\)

Yolanda is buying school supplies. She buys n packages of pencils at 1.40 per package and m pads of paper at 1.20 each. The expression 1.4 represents the cost of one package of pencils while the expression 1.2 represents the cost of one pad of paper.

The given expressions represent the cost of one package of pencils and one pad of paper. Hence,1.4 represents the cost of one package of pencils.1.2 represents the cost of one pad of paper.Yolanda buys n packages of pencils.

Therefore, the total cost of pencils will be n × 1.4

Similarly, Yolanda buys m pads of paper.

Therefore, the total cost of pads will be m × 1.2

Therefore, the total cost of buying n packages of pencils at 1.40 per package and m pads of paper at 1.20 each will be,1.4n + 1.2m

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Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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Answer:

def*de

Step-by-step explanation:

To function effectively, a subtotal row must contain at least one aggregate function, which performs calculations on a group of values and produces a single, concise result that conveys the relevant information.

A subtotal row is an essential tool for data analysis in spreadsheets, allowing for easy organization and summarization of large datasets.

A subtotal row is a crucial element in organizing and analyzing data within spreadsheets, as it allows users to break down information into manageable sections. To achieve this, a subtotal row must contain at least one aggregate function. Aggregate functions perform calculations on a group of values, generating a single result that summarizes the data.
Examples of common aggregate functions include SUM, AVERAGE, COUNT, MIN, and MAX. These functions facilitate various mathematical operations, such as summing up values, finding the average, counting the number of instances, identifying the smallest value, and determining the largest value, respectively.
In practice, when creating a subtotal row in a spreadsheet, users typically sort the data by the desired category first. Then, they apply the appropriate aggregate function(s) to generate the desired summary statistics for each subset of data. This enables users to quickly gain insights into the data trends and make informed decisions based on the summarized information.

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1. This task would likely be framed as a supervised learning problem

2. This task would also be framed as a supervised learning problem.

3. This task would typically be framed as an unsupervised learning problem.

4. This task would likely be framed as a regression problem since the goal is to estimate the repair time,

5. This task can be considered as an unsupervised learning problem.

Deciding whether to issue a loan to an applicant based on demographic and financial data (with reference to a database of similar data on prior customers):

This task would likely be framed as a supervised learning problem. The goal is to predict whether to approve or reject a loan application based on the given data. Hence, it can be considered a classification problem.

In an online bookstore, making recommendations to customers concerning additional items to buy based on the buying patterns in prior transactions:

This task would also be framed as a supervised learning problem. The goal is to recommend additional items to customers based on their buying patterns. It can be approached as a recommendation system using collaborative filtering techniques, which involve predicting customer preferences. This can be considered a classification problem.

Identifying segments of similar customers:

This task would typically be framed as an unsupervised learning problem. The objective is to identify groups or clusters of similar customers based on their attributes or behaviors. Unsupervised learning algorithms such as clustering can be used to accomplish this task.

Estimating the repair time required for an aircraft based on a trouble ticket:

This task would likely be framed as a regression problem since the goal is to estimate the repair time, which is a continuous variable. Supervised learning techniques such as regression algorithms can be employed to predict the repair time based on the provided input features.

Automated sorting of mail by zip code scanning:

This task can be considered as an unsupervised learning problem. The aim is to sort mail based on zip codes, which involves grouping similar items together. Unsupervised learning algorithms like clustering can be utilized to identify patterns and group the mail accordingly.

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Answer:

7

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just don’t want to waste my time in case you don’t want me to :)

Answer:

the answer is 18! 72÷4=18

In the given problem, random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below:21 226 22 725 21
Given that,The null hypothesis H0: All the population means are equal. The alternative hypothesis H1: At least one population mean is different from the others .

To find the hypothesis test, we will use the one-way ANOVA test. We calculate the grand mean (X-bar) and the sum of squares between and within to obtain the F-test statistic. Let's find out the sample size (n), the total number of samples (N), the degree of freedom within (dfw), and the degree of freedom between (dfb).
Sample size (n) = 4 Number of samples (N) = n × 4 = 16 Degree of freedom between (dfb) = n - 1 = 4 - 1 = 3 Degree of freedom within (dfw) = N - n = 16 - 4 = 12 Total sum of squares (SST) = ∑(X - X-bar)2
From the given data, we have X-bar = (21 + 22 + 26 + 25) / 4 = 23.5
So, SST = (21 - 23.5)2 + (22 - 23.5)2 + (26 - 23.5)2 + (25 - 23.5)2 = 31.5 + 2.5 + 4.5 + 1.5 = 40.0The sum of squares between (SSB) is calculated as:SSB = n ∑(X-bar - X)2
For the given data,SSB = 4[(23.5 - 21)2 + (23.5 - 22)2 + (23.5 - 26)2 + (23.5 - 25)2] = 4[5.25 + 2.25 + 7.25 + 3.25] = 72.0 The sum of squares within (SSW) is calculated as:SSW = SST - SSB = 40.0 - 72.0 = -32.0
The mean square between (MSB) and mean square within (MSW) are calculated as:MSB = SSB / dfb = 72 / 3 = 24.0MSW = SSW / dfw = -32 / 12 = -2.6667
The F-statistic is then calculated as:F = MSB / MSW = 24 / (-2.6667) = -9.0
Since we are testing whether at least one population mean is different, we will use the F-test statistic to test the null hypothesis. If the p-value is less than the significance level, we will reject the null hypothesis. However, the calculated F-statistic is negative, and we only consider the positive F-values. Therefore, we take the absolute value of the F-statistic as:F = |-9.0| = 9.0The p-value corresponding to the F-statistic is less than 0.01. Since it is less than the significance level (α = 0.05), we reject the null hypothesis. Therefore, we can conclude that at least one of the population means is different from the others.

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A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Answer:

Segment Addition Postulate

The segment addition postulate in geometry is applicable on a line segment containing three collinear points. The segment addition postulate states that if there are two given points on a line segment A and C, then point B lies on the same line segment somewhere between A and C only if the sum of AB and BC is equal to AC.

Segment Addition Postulate Definition

The segment addition postulate states that if a line segment has two endpoints, A and C, a third point B lies somewhere on the line segment AC if and only if this equation AB + BC = AC is satisfied. Look at the image given below to have a better understanding of this postulate.

Answer:

$345.60

Step-by-step explanation:

From the above question,

P = Principal = $200

R = Interest rate = 20%

T = Time in years = 3 years

n = Number of times interest is compounded = Annually = 1

First, convert R as a percent to r as a decimal

r = R/100

r = 20/100

r = 0.2 rate per year,

Then solve the equation for A

The formula =

A = P(1 + r/n)^nt

A = 200.00(1 + 0.2/1)^(1×3)

A = 200.00(1 + 0.2)^(3)

A = $345.60

Therefore, the total amount that Molly will have in her account at the end of 3 years is $345.60

Answer:

option c

Step-by-step explanation:

The zeros of 3x+1

3x=-1

x=-⅓

plug in -⅓ into the trinomial. if it gives an answer of 0 then it's a factor

3(-⅓)²+16(-⅓)+5

=0

Answer:

\(A = \frac{Cr}{2}\)

Step-by-step explanation:

Given

\(A = \frac{C}{4}\)

Required

Describe another way to get area from circumference

Circumference C is calculated using:

\(C = 2\pi r\)

Area, A is calculated using:

\(A = \pi r^2\)

Using: \(C = 2\pi r\)

Divide both sides by 2

\(\frac{C}{2} = \frac{2\pi r}{2}\)

\(\frac{C}{2} = \pi r\)

Multiply both sides by r

\(r*\frac{C}{2} = \pi r*r\)

\(r*\frac{C}{2} = \pi r^2\)

\(\frac{Cr}{2} = \pi r^2\)

The expression on the right-hand side is the area.

So, substitute \(\pi r^2\) for A

\(\frac{Cr}{2} = A\)

Reorder

\(A = \frac{Cr}{2}\)

Answer:

9?

Step-by-step explanation:

The correct choice for the given options would be: OA. The point(s) at which the tangent line is horizontal is (approximately) (√(7/3), 3√(7/3)), (-√(7/3), 3√(7/3))

To find the point on the curve y = 8x² + 3x where the slope of the tangent line is equal to 197, we need to find the derivative of the curve and set it equal to 197.

Find the derivative of y = 8x² + 3x:

y' = d/dx (8x² + 3x)

= 16x + 3

Set the derivative equal to 197 and solve for x:

16x + 3 = 197

16x = 194

x = 194/16

x = 12.125

Substitute the value of x back into the original equation to find the corresponding y-value:

y = 8(12.125)² + 3(12.125)

y ≈ 1183.56

Therefore, the point on the curve y = 8x² + 3x where the slope of the tangent line is equal to 197 is approximately (12.125, 1183.56).

To find the point at which the slope of a tangent line is 19 for the function (not specified), we would need the equation of the function to proceed with the calculation.

For the function y = x³ - 7x + 3, to find the points on the graph where the tangent line is horizontal, we need to find the values of x where the derivative of the function is equal to 0.

Find the derivative of y = x³ - 7x + 3:

y' = d/dx (x³ - 7x + 3)

= 3x² - 7

Set the derivative equal to 0 and solve for x:

3x² - 7 = 0

3x² = 7

x² = 7/3

x = ±√(7/3)

Substitute the values of x back into the original equation to find the corresponding y-values:

For x = √(7/3):

y = (√(7/3))³ - 7(√(7/3)) + 3

= 7√(7/3) - 7(√(7/3)) + 3

= 3√(7/3)

For x = -√(7/3):

y = (-√(7/3))³ - 7(-√(7/3)) + 3

= -7√(7/3) + 7(√(7/3)) + 3

= 3√(7/3)

Therefore, the points on the graph where the tangent line is horizontal are approximately (±√(7/3), 3√(7/3)).

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The solution of the quadrilateral is given as A' = -5 , 10

2 1/2 is a mixed fraction that is

2 + 1/2

= 4 + 1 / 2

= 5 / 2

we have to multiply this by the vertex that would give us a solution in the option for Vertex A

-2 * 5 / 2 , 4 * 5 / 2

= -10 / 2 , 20 / 2

= -5, 10

The solution of the quadrilateral would be A' = -5 , 10

option A is correct

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Step-by-step explanation:

72 times 108 = 7776 sq inches

to convert inches to yds divide by 36

7776/ 36 = 216 sq yds

Answer: 6 yards^2

Step-by-step explanation:

first lets find the area of the space in inches and then convert the total to square yards :)

area = length * width

A = 108 * 72 = 7776 inches^2

now lets convert it

there are 1296 inches in a yard, so we divide 7776 by 1296 to find the number of square yards

7776 / 1296 = 6

so the area of the space is 6 yards^2

\(\text{Hello! :)}\)

\(\large\boxed{(3x + 4)(x + 8)}\)

\(\text{Factor the polynomial:}\\3x^{2} +28x +32\\\\\text{Find two numbers that multiply into 32 and sum up to 28.}\\\text{Take into account the leading coefficient of 3:}\\\\\text{The numbers 4 and 8 work; arrange them so that they sum up to 28:}\\\\(3x + 4)(x + 8)\)

The probability least 1 zodiac sign match astrological signs is just the product of (12/12)(11/12 … (8/12).

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated.

The probability that in a group of five friends, at least two share the same astrological sign

= 1 - the probability that all five friends have different astrological signs

= 1 - (12/12)(11/12)(10/12)(9/12)(8/12)

= 1 - 12P5/125

= 1 - 0.381944

= 0.618056

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Answer:

theres five digits

If a lab class conducts a 1000 trial scattering probability experiment. nine marbles were used on a 47.20 cm wide board. The number of hits recorded were 615, the diameter of the marbles is approximately 4.1 cm.

Assuming that the experiment was conducted with the same conditions (e.g. speed, direction) for each trial, we can estimate the diameter of the marbles using the scattering probability and the size of the target area.

The scattering probability is the ratio of the number of hits to the total number of trials. In this case, the scattering probability is:

P = 615/1000 = 0.615

This means that, on average, 61.5% of the marbles that were aimed at the board hit one of the target marbles.

The target area is the area of the board divided by the number of targets. The area of the board is the product of its width and height, which we don't know. However, we can assume that the height of the board is much larger than the diameter of the marbles, so that the height does not significantly affect the scattering probability.

Therefore, we can estimate the target area by dividing the width of the board by the number of targets:

A = 47.20 cm / 9 = 5.2444 cm^2

The target area is the area of one target marble, assuming they are all the same size. The area of a circle is given by:

A = π (d/2)^2

where d is the diameter of the circle.

Solving for d, we get:

d = √(4A/π) = √(4 × 5.2444 cm^2 / π) ≈ 4.1 cm

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Answer:

Anything.

Step-by-step explanation:

The reason why I say " anything " is because the fraction, \(\frac{1}{1}\) is bascially representing the number 1, nothing else so you can put whatever you want, tens, hundreds, thousands, millions, and so on.

So whatever number you want to put it will always equal, \(\frac{1}{1}\), But just remember to always put the number that you choose on top or the numerator such as the following:

\(\frac{4}{1}\).

Thus, you answer is, anything.

Answer:

There should be a little keyhole behind the steering wheel put your key in it and turn it to the right

Answer:

To find the mean: Multiply midpoints by frequencies, add the subtotals and divide by the total of the frequencies.

Step-by-step explanation:

Put the results in numerical order (in a frequency table this will already be done)

Count the total amount of results and add one.

Divide this by 2 to find the the position of the middle result.

Find the middle result in the numerically ordered list or frequency table.