Why do we study distance formula?

This polynomial, 4x² is the GCF and (x + 2)(x - 1)(x + 3) are the remaining factors.

What is polynomial?

A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.

A polynomial with a GCF of 4x² means that 4x² is a factor common to all terms in the polynomial. One example of such a polynomial is:

4x² (x + 2)(x - 1)(x + 3) = 4x⁵ + 24x²- 36x³ - 72x²

In this polynomial, 4x² is the GCF and (x + 2)(x - 1)(x + 3) are the remaining factors.

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d) The best interpretation of the standard deviation is that "On average, the number of breakdowns per day varies from the mean by about 0.23"

The standard deviation is a measure of how much the data in a set varies or deviates from the mean. In this case, the standard deviation of 0.23 for the number of equipment breakdowns means that on average, the number of breakdowns per day varies by 0.23 from the mean.

This means that the majority of the data falls within 0.23 above or below the mean. The standard deviation is a way to quantify the spread of the data, which can help in understanding the distribution of the data set.

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Distance formula in the Physics is given by the product of ( speed × time ).

As given in the question,

Speed of any object is given by

= ( Total distance travelled ) /( total time taken )

From the distance formula can be derived as :

Distance Formula is given by :

= Product of Speed and time

= Speed × Time taken

Distance covered by any moving object is defined as the product of the speed of the object to the total time taken by object to cover the required distance.

Therefore, the distance formula in the Physics is defined as the product of speed and time.

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Answer:

312

Step-by-step explanation:

120x0.4=48

48x3=144

120x0.7=84

84x2=168

168+144=312

When did not take the reciprocal of the divisor.

Convert Celsius to Fahrenheit ?

Celsius to Fahrenheit conversion will be like one celsius is equal 32 Fahrenheit.

Given,

The temperature fell from 0 Degrees Fahrenheit to 15 and one-half Degrees Fahrenheit below 0 in 5 and three-fourths hours. Wen tried to find the change in temperature per hour.

When she checked the answer by estimating, it did not make sense. What error did When make, Wen incorrectly converted a mixed number to an improper fraction. Wen added the numerators and denominators instead of multiplying. Wen did not take the reciprocal of the divisor

Hence , When did not take the reciprocal of the divisor.

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Algebraic solutions that appear while we solve rational equations but do not fulfil the original equations are known as extraneous solutions. In other words, whereas unnecessary solutions appear to be ones, they are not.

Equations with variables in the denominators of rational expressions are referred to as rational equations.

In order to answer the rational equation we have to follow the rules:

(1) Rewrite the equation till the variable is removed from the denominators of the rational expressions.

(2) Rearrange the equation and then solve the linear or quadratic one that results.

In order to look for extraneous solutions we have to follow rule:

(1) Resolve the rational equation.

(2) Replace the original equation with the solution(s). If a solution does not fulfil the initial equation, it is superfluous.

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The value of x for the right triangle is 15 units.

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle (90°). Triangle ABC is a right triangle in the illustration, consisting of the base, altitude, and hypotenuse. Here, the hypotenuse is BC, the altitude is AC, and the base is AB.

Given a right triangle,

QRS and RT is perpendicular on SQ,

ST = 9 units, TQ = 16 units,

RS = x,

let RQ = z and QT = y, SQ = 25 units

from figure, we have 3 right triangles,

RST, QTR and QRS,

using the Pythagorean theorem to find x,

in ΔRST

x² = 9² + y²......... (1)

in ΔQTR

z² = y² + 16² ..........(2)

in ΔQRS

25² = x² + z²

substituting values from equations 1 and 2

25² = y² + 9² + y² + 16²

2y² = 625 - 81 - 256

y² = 288/2

y = √144

y = 12 units

substitute the value of y in equation 1

x² = y² + 9²

x² = 12² + 9²

x² = 144 + 81

x = √225

x = 15 units

Hence the value of x is 15 units.

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A proportion is a statement of equality between two ratios. To determine whether two ratios form a proportion, you can use the cross-multiplication method.

This method involves multiplying the numerator of the first ratio by the denominator of the second ratio, then comparing it to the result of multiplying the denominator of the first ratio by the numerator of the second ratio. If the two results are equal, the two ratios form a proportion.

For example, let's look at the pair of ratios 7/9 and 28/36. To determine if they form a proportion, we can cross-multiply:

7/9 * 36 = 252 and 28/36 * 9 = 252

Since 252 = 252, the two ratios form a proportion. Similarly, we can use the cross-multiplication method to check the other pairs and confirm that all of them form a proportion.

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Answer:

8x-6

12x-9-4x+3

Step-by-step explanation:

12x-4x-9+3

=8x-6

Answer:

[tex] \sf \: 8x - 6 [/tex]

Step-by-step explanation:

Given expression,

→ 12x - 9 - 4x + 3

Let's simplify the expression,

→ 12x - 9 - 4x + 3

→ (12x - 4x) + (-9 + 3)

→ (8x) + (-6)

→ 8x - 6

Hence, the answer is 8x - 6.

The product formula for log X is logb (xy) = logb x + logb y.

A logarithm is just another way of writing exponents. When we cannot solve a problem using the exponents, then we use logarithms. There are different logarithm formulas that are derived by using the laws of exponents.

There are two types of logarithms, common logarithm (which is written as "log" and its base is 10 if not mentioned) and natural logarithm (which is written as "ln" and its base is always "e"). The below logarithm formulas are shown for common logarithms. However, they are all applicable for natural logarithms as well. Here are the most commonly used log formulas.

1) logb 1 = 0

2) logb b = 1

3) logb (xy) = logb x + logb y

4) logb (x / y) = logb x - logb y

5) logb ax = x logb a

6) logb a = (logc a) / (logc b)

The problems that cannot be solved using the exponents' properties can be solved using logs. The log formulas are used to either compress a group of logarithms into a single logarithm or vice versa. The natural logarithm formulas are as same as that of logarithmic formulas except "log with some base" is replaced with "ln".

Thus, the product formula for log X is logb (xy) = logb x + logb y.

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The clothing store is having a going out of business sale where every purchase is 35% off the original purchase price. The price of any purchase after the discount can be determined using the following expressions:

What is a mathematical expression?

What does a mathematical expression mean? Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

p - (0.35 * p)

p * (1 - 0.35)

p * 0.65

p / (1 + 0.35)

All the above expressions are equivalent and will give the same price of any purchase after the 35% discount.

p - (0.35 * p) is the expression for subtracting 35% of the original price from the original price.

p * (1 - 0.35) is the expression for multiplying the original price by (1- 0.35) which represents 65% of the original price.

p * 0.65 is the expression for multiplying the original price by 0.65, which represents 65% of the original price.

p / (1 + 0.35) is the expression for dividing the original price by (1 + 0.35) which represents 65% of the original price.

In all the above expressions, the original price is represented by p.

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The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

Due to the fact that mass is the quantity of matter contained in an item and does not change with gravity, mass is always the same. As long as the amount of matter in an object doesn't change, its mass will remain constant. In contrast, an object's weight refers to the force of gravity acting on it.

No matter where you are in the cosmos, you have the same mass since mass is a measurement of how much matter is in an object. But because weight measures the force between an object and the body it is resting on, it fluctuates (whether that body is the Earth, the Moon, Mars, et cetera).

Given : A mass of student 40 kg

length is represented by l

Position of the pivot point from the board = l/3

The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

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a) Relative Frequency of class D is equals to 0.2..

b) Frequency of class D is equals to the 40.

c) Frequency distribution of classes is third column of above table.

d) The percent frequency distribution for classes is fourth column of above table in figure.

A relative frequency distribution is one important type of frequency distribution. Relative frequency calculated by the number of times an event occurs divided by the total number of events occurring in a scenario. We have, a table consists relative frequency for three classes A,B and C and we have to calculate the relative frequency for class D. Total sum of all relative frequencies for values = 1

a) So, relative frequency for class D = 1 - relative frequencies for A,B and C

= 1 - 0.24 - 0.16 - 0.4

= 1 - 0. 8 = 0.2

b) Sample size, n = 200 i.e.,

Possible frequency value = 200 .

Frequency of class D = 200× 0.2 = 40

c)

Relative frequency = frequency/ total frquency

=> Frequency of a value = relative frequency × n = 0.24 × 200 = 48

Frequency of class B = 0.16 × 200 = 32

Frequency of class C = 0.4 × 200 = 80

Frequency of class D = 0.2 × 200 = 40

Frequency distribution table present above.

d) Now, the percent frequency distribution .

percent frequency= relative frequency × 100

So, percent frequency of class A

= 0.24 × 100 = 24%

Percent frequency of class B = 0.16 × 100

= 16%

Percent frequency of class C = 0.4 × 100

= 40%

Percent frequency of class D = 0.2 ×100

= 20%

Thus, all required values are present in above table in figure.

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Complete question:

A partial relative frequency distribution is given. class relative frequency

A 0.24

B 0.16

C 0.40

D ?

a) what is the relative frequency of class D?

.2 correct: your answer is correct.

(b) the total sample size is 200. what is the frequency of class D?

40 correct: your answer is correct.

(c) show the frequency distribution.

class frequency a 48 correct: your answer is correct. b 32 correct: your answer is correct. c 80 correct: your answer is correct. d 40 correct: your answer is correct. total 200 correct: your answer is correct.

(d) show the percent frequency distribution. class percent frequency a .24 incorrect: your answer is incorrect. b .16 incorrect: your answer is incorrect. c .4 incorrect: your answer is incorrect. d .2 incorrect: your answer is incorrect. total 1 incorrect: your answer is incorrect.

The sampling method used in the problem is simple random sampling.

Based on the information given, the pollster used a sampling method called "simple random sampling."

Simple random sampling is a statistical sampling method in which every member of a population has an equal and independent chance of being selected as part of the sample. This is done by using a random number generator or a random selection process, such as using a table of random numbers, to select the sample(in this case, residential addresses) from the population(all the residential addresses in Sandy Springs). The sample size is determined in advance and the selection of individual units is purely by chance. The goal of simple random sampling is to ensure that the sample is representative of the population, so that inferences and conclusions about the population can be made based on the sample data.

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Answer: $460

Step-by-step explanation:

plug in hours to equation

30(6)+25(4)+21(9)= 460 dollars

The angle subtended by the arc rounded off to the nearest 10th is 3.6 radians.

We have been given that the length of the arc subtended by the angle at the center is 26.2 units.

The radius of the said circle is 7.3 units.

Now the relation between the length of the arc, the angle subtended by it on the center of the circle, and the radius of the circle is given by

l = rθ

where,

l s the length of the arc in radians

r is the radius of the circle in radians

θ is the angle subtended by the arc

Here l = 26.2 units

r = 7.3 units

Hence we get

θ = l/r

θ = 26.2/7.3

= 3.589 radians

= 3.6 radians

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For a given non-zero vector v in r3 there is a unique unit vector parallel to it the correct answer is 'True'.

How about a value vector which is a non-zero vector, this one? What connection does this have to a unit vector?

I'm given the following justification: "Remember that two vectors a and b are parallel if

If and only if two vectors A and B are scalar multiples of one another, they are said to be parallel. k is a constant that does not equal zero. The cross-product of the two vectors can be determined.

Let u

be a non-unit vector. Set n=u/|u|

Then n is a unit vector and u is parallel to n since u=|u|n.

a⃗ =λb⃗

for a certain scalar λ

Keep in mind that|  λa⃗ |=|λ||a⃗ |

Therefore, given a vector a is λ, the value will result in a vector λ =λa⃗ with magnitude 1.

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The transformation from function f(x) to g(x) is a vertical shift of 4 units up.

The transformation from f(x) to g(x) is a vertical shift of 4 units up. This can be seen by comparing

f(x) = |x| to g(x) = |x| + 4

. In other words, the graph of g(x) is 4 units higher than that of f(x), and the x-intercepts of the two functions are 4 units apart.

The transformation from f(x) to g(x) is a vertical shift of 4 units up. This can be seen by comparing the equations of the two functions. The parent function, f(x), is defined as f(x) = |x|, and the transformed function, g(x), is defined as g(x) = |x| + 4. By adding 4 to the parent function, the graph of the transformed function is shifted up 4 units, which is the same as saying it is shifted 4 units in the positive y-direction. This can be seen in the graphs of the two functions, where the x-intercepts of the two functions are 4 units apart. The transformation from f(x) to g(x) is a vertical shift of 4 units up, and it is the same as the transformation of

y = f(x) to y = f(x) + 4.

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The answers are a) 25 coaches, b) 24 coaches c) 26 people.

A division is a process of splitting a specific amount into equal parts.

Given that, there are 2546 people waiting for a train, each coach of the train holds 105 people.  

To find the number of coaches needed for 2546 people we will divide total by 105,

Therefore, 2546 / 105 = [tex]24\frac{26}{105}[/tex]

That mean, there are needed 25 coaches for 2546 people.

And, there will be 24 coaches which are completely filled and the last 25th coach, will have 26 people

Hence, the answers are a) 25 coaches, b) 24 coaches c) 26 people.

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There is a 1.78 probability that John packed your dinner if you found there is no salt in your purchased dinner.

We know that John packs 45% of the dinners, Mary packs 25% of the dinners, and Sue packs the remaining dinners.

We also know that if John packs the dinner, 4% of the time the salt packet is omitted. If Mary packs the dinner, 2% of the time the salt packet is omitted. Lastly, 3% of the dinners do not include salt if Sue does the packing.

Let's call the event of not having a salt packet A, and the event of John packing the dinner B. We are looking for P(B|A), the probability of John packing the dinner, given that there is no salt packet.

Using Bayes' theorem: P(B|A) = P(A|B) * P(B) / P(A)

In this case,

P(A) is the probability of there not being a salt packet, which is (4+2+3)% = 9%.

P(B) is the probability of John packing the dinner, which is 45%.

P(A|B) is the probability of not having a salt packet, given that John packed the dinner, which is 4%.

P(B|A) = P(A|B) * P(B) / P(A) = (4/100) * (45/100) / (9/100) = 1/5 = 0.2

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Divide the numerator by the denominator to create a mixed number from an incorrect fraction. The mixed number is created after the division in such a way that the achieved quotient becomes the whole number, the leftover becomes the new numerator, and the denominator stays the same.

A mixed number is one that combines both a proper fraction and a full number. Mixed fractions are another name for mixed numbers.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. "Top-heavy" fractions are sometimes used to describe improper fractions.

Follow these procedures to convert a mixed number to an incorrect fraction:

1. Divide the entire number by the numerator.

2. Increase the numerator by that sum.

3. Add that total to the denominator from the previous step.

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The measure of the variability in the response variable that is not explained by the regression model is known as the residual sum of squares (RSS).

The residual sum of squares (RSS) is a measure of the variability in the response variable that is not explained by the regression model. It is calculated by summing the squared differences between the predicted values (from the regression model) and the observed values of the response variable. RSS is often used to measure the goodness of fit of a regression model and to compare different models. A lower RSS indicates a better fit. RSS can also be used to identify influential observations and outliers that may have a large impact on the regression results.

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Horizontal shift is negative when the graph is shifted to the left. This means that the x-value of the graph is decreased, resulting in a negative shift.

The horizontal shift of a graph is the amount the graph is shifted to the left or right, measured in units along the x-axis. When the graph is shifted to the left, the x-values of the graph decrease, resulting in a negative shift. Conversely, when the graph is shifted to the right, the x-values of the graph increase, resulting in a positive shift. The horizontal shift of a graph can be calculated by subtracting the x-value of the new graph from the x-value of the original graph. If the result is a negative number, the graph has undergone a negative shift; if the result is a positive number, the graph has undergone a positive shift. The magnitude of the shift is equal to the absolute value of the difference between the x-values of the two graphs.

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Right triangle ABC with altitude BD down to hypotenuse AC if AC = 25 and BC = 15, then the length of DC is 9.

What is the Pythagorean theorem?

Pythagoras theorem is: In a right angle triangle, the sum of squares of sides is equal to the square of the hypotenuse.

We can use the geometric properties of right triangles and the Pythagorean theorem to solve this problem.

Let's label the length of DC as x. We know that BD is an altitude of the right triangle ABC, which means that it is perpendicular to AC. Therefore, we can use the similar triangles formed by the right triangles ABD and CBD to find the length of x.

In triangle ABD, we have:

BD/AB = AB/AC

Simplifying, we get:

BD/15 = 15/25

Multiplying both sides by 15, we get:

BD = 9

Now, in triangle BCD, we have:

BD/BC = BC/DC

Substituting BD = 9 and BC = 15, we get:

9/15 = 15/x

Multiplying both sides by x, we get:

x = (15 * 9)/15 = 9

Therefore, the length of DC is 9.

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The correct answer is: O x(x² + 5) - 6(x + 5)

To determine the factors of the polynomial x³ + 5x² - 6x - 30 by grouping, we can factor out the greatest common factor (GCF) of the first two and the last two terms. In this case, the GCF of the first two terms is x and the GCF of the last two terms is -6. If we factor out x from the first two terms and -6 from the last two terms, we get:

x(x² + 5) - 6(x + 5)

Now we can see that x(x + 5) and -6(x + 5) are binomials that have the same factor (x + 5) in common. This allows us to factor out the common factor x + 5 and get:

(x + 5)(x² - 6)

This is one way of factoring x³ + 5x² - 6x - 30 by grouping.

It's important to note that the polynomial x³ + 5x² - 6x - 30 also has other factorizations.

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The mystery number is satisfying the above mentioned conditons is 283.

The mystery number is a three-digit number made up of the digits 2, 8, and 3. The 3 and the 8 are not next to each other in the number and the 2 comes before the 3. From the given information, we know that the only possible arrangement of the digits is 283. Therefore, the mystery number is 283. It's important to note that there could be other possibilities if more information was provided about the mystery number. But given the information provided, 283 is the only possible answer.

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Chart and Graph Types:

(1) Statistical Diagrams (bar graph, pie graph, line graph, etc.)

(2) Exponential graphs

(3) Logarithmic graphs

(4) Graphs using trigonometry.

(5) Frequency Distribution Graph

(6) Pictograph

(1) Statistical Diagrams: The graphical depiction of statistical data in a visual format is known as a statistical graph or chart.

(2) Exponential graphs: Exponential graphs are used to illustrate exponential functions by displaying the points on graph paper using a table of values.

(3) Logarithmic graphs: It is necessary to create a table of values before drawing the points on graph paper in order to plot logarithmic graphs.

(4) Graphs using trigonometry: The six trigonometric functions are represented as trigonometric graphs, which contain the sine, cosine, tangent, cotangent, cosec, and sec functions.

(5) Frequency Distribution Graph: The frequency of the results in a certain sample is displayed on a frequency distribution graph.

(6) Pictograph: The categories are not listed in numerical order in pictographs. On a graph paper, their photographs are positioned in the appropriate squares. You may quickly determine the maximum and minimum value for that category by using a number of photographs.

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Answer:2)5

Step-by-step explanation:

Look and do it eith the thing

The earning of Luke if he mowed lawn for 9.5 hours is, $133.75

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

Luke earns $12.50 per hour mowing lawns

He also earned a $5.00 tip from three customers

Earning if he mowed for 9.5 hours = ?

Suppose, he works for x hours

Total earning = From mowing + Tip

                      = 12.50×X + 15

Y =  12.50X + 15

If he mowed for 9.5 hours,

Y = 12.50 × 9.5 + 15

Y = 133.75

Hence, The earning of 9.5 hours is $133.75

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Andrea produced 5 pillows. She made the decision to create two additional pillows but realised she would require an additional 4. 5 yards of cloth. 2 yards of fabric were utilised by her.

We must multiply 5 by 4 in order to find the answer.

[tex]$$\begin{aligned}& 5=5 / 1 \\& 4 =4 / 1 \\& 5 \times 2=10 \\& 1 \times 5 =5 \\& =10 / 5\end{aligned}$$[/tex]

Simplifying 10/5 ⇒ 10 / 5= 2

Using 2 yards of material, Andrea

Once more, when adding whole numbers and fractions, determine the sum of the whole numbers first, and then add the remainder as a fraction to the answer. Placing a decimal number above its place value will allow you to convert it to a fraction. For instance, we multiply 6 by 10 to get the comparable fraction of 6/10 since in 0.6, the number six is in the tenths place. Condense the portion if necessary. Sal Khan is the author.

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