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When multiplying two powers with the same base, the exponent is added.

According to the exponent "product rule," you can add the exponents when multiplying two powers with the same base. This illustration will show you how it functions. Exponent addition is only a shortcut!

According to this rule, the exponents are added when multiplying two powers by the same base. According to the "power rule," we only need to multiply the exponents to increase a power to a power.

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For the three random tosses, there are only 4 potential values out of 8 possible combinations.

The sample space for W is thus:

HHH, W = 3-0 = 3

HHT, W= 2-1=1

HTH, W= 2-1=1

THH, W=2-1 =1

HTT, W= 1-2=-1

THT, W= 1-2=-1

TTH, W=1-2=-1

TTT, W=0-3 = -3

In this instance, W is defined as the random variable that captures the difference between the number of heads and tails in three coin flips.

W = the number of heads minus the number of coins.

We have 3 coin tosses, which gives us 2*2*2=8 outcomes. The outcomes and accompanying values for W can be listed as follows:

HHH, W = 3-0 = 3

HHT, W= 2-1=1

HTH, W= 2-1=1

THH, W=2-1 =1

HTT, W= 1-2=-1

THT, W= 1-2=-1

TTH, W=1-2=-1

TTT, W= 0-3 = -3

Describe probability.

 Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Which four forms of probability are there?

There are four primary forms of probability, which is the area of mathematics that concerns with the possibility of a randomized incident occurring: classical, empirical, random, and essential

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This statement can be represented mathematically as: 2(x - 7) ≤ -29. The solution to the inequality is x ≤ -8 means x is less than or equal to -8.

Here, x is the number we are trying to find and "2(x - 7)" represents "twice the difference of a number and seven."

To solve for x, we can start by expanding the expression inside the parentheses:

2(x - 7) = 2x - 14

Now, we can substitute the expression for 2(x - 7) into the inequality:

2x - 14 ≤ -29

Next, we can isolate x by adding 14 to both sides of the inequality:

2x ≤ -15

Finally, we can divide both sides by 2 to obtain:

x ≤ -8

So, the solution to the inequality is "x is less than or equal to -8". This means that any number that is less than or equal to -8 satisfies the inequality.

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Answer:

b) 31.25

Step-by-step explanation:

Since it is an isosceles triangle, the two missing angles are equal.

The sum of the angle measures in a triangle is 180 degrees.

Angle D and E are both x

So we set up an equation:

180 = 117.5 + x  + x

180 = 117.5 +2x

62.5 = 2x

x = 31.25

According to the given statements regarding matrix and vectors, we found that statements a, b, and c are true. Others are false.

a. True. Certain elementary row operations on a matrix, such as row swaps, row scalings, and row additions, can affect the linear dependence relationships among the columns of the matrix.

b. True. The columns of an invertible matrix form a linearly independent set, which is also a basis for the vector space of the matrix.

c. True. A basis is a spanning set (a set of vectors that can generate any other vector in the space) that is as large as possible, meaning that it has the minimum number of vectors required to generate all other vectors in the space.

d. False. A single vector by itself is linearly independent, meaning that it cannot be expressed as a linear combination of other vectors.

e. False. If W is a subspace of a vector space V, then a basis for W is a set of vectors that can generate any other vector in W, but not necessarily all vectors in V.

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Complete Question:

Show T/F.

a. in some cases, the linear dependence relations amoung the columns of a matrix can be affected by certain elementary row operations on the matrix.

b. the columns of an invertible matrix form a basis for .

c. a basis is a spanning set that is as large as possible.

d. a single vector by itself is linearly dependent.

e. if , then is a basis for .

Answer:

The number of times a variable appears in a date set is called a constant.

Answer:

think its B

Step-by-step explanation:

im doing the test

Answer:

Step-by-step explanation:

its b

Calculating a relationship between college admission scores and freshman gpa requires the  Correlational statistics type of statistics. Correlational statistics are used to measure the strength of the relationship between two variables.

This type of statistic is used when attempting to determine the relationship between college admission scores and freshman GPA. By measuring the correlation between the two variables, it can be determined if there is a correlation between college admission scores and freshman GPA. Correlational statistics can measure the direction, strength, and significance of the relationship between two variables.

This type of statistics can provide information such as the degree to which two variables move together and the extent to which one variable changes as the other variable changes. Correlational statistics can also provide information on how much of the variability in one variable is explained by the other variable. Correlational statistics can be used to determine if there is a correlation between the two variables and, if so, the strength of that correlation.

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The polynomial is written as -x + 3y - 1/7

The values are -1, 3 and - 1/7

Algebraic expressions are defined as expressions that are composed of terms, factors, constants, coefficients and variables,

These algebraic expressions are also composed of arithmetic operations, such as;

From the information given, we have the polynomial as;

-1/7-x+3y

Now, let us rearrange it in the form of the general formula, ax + by + c, we get;

-x + 3y - 1/7

Then, the values are;

a = -1

b = 3

x = -1/7

Hence, the values are -1, 3 and  -1/7

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The triangles GHJ and IHJ are congruent based on side-angle-side congruency.

The triangles UVW and XYZ are congruent based on side-side-side congruency.

A triangle is a polygon that has three angles and three sides. Types of triangles are scalene, equilateral, isosceles, right angled.

Two triangles are said to be congruent if all the three sides and angles of one triangle is congruent to that of another triangle. Therefore their corresponding sides and angles are equal.

1) The triangles GHJ and IHJ are congruent based on side-angle-side congruency.

2) The triangles UVW and XYZ are congruent based on side-side-side congruency.

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When 3 is the input, the output is 30 and When 10 is the input, the output is 150.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

We need to find the output When 3 is the input and 10 is the input.

When 3 is the input, the output is 30. When 10 is the input, the output is 150 Based on the plots, both bulbs have y increasing as x increases.

Therefore, first bulb and second bulb are both increasing.

Hence,  When 3 is the input, the output is 30 and When 10 is the input, the output is 150.

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Answer: D

Step-by-step explanation:

Answer:

Y=2x+2

Step-by-step explanation:

The equation of a line with gradient "m" and passing through the point (x1, y1) can be found using the point-slope form of a line:

y - y1 = m (x - x1)

For a gradient of 2 and a point of (1, 4), we can substitute the values into the equation:

y - 4 = 2 (x - 1)

Expanding the right-hand side, we get:

y - 4 = 2x - 2

Adding 4 to both sides:

y = 2x + 2

So, the equation of the line with a gradient of 2 and passing through the point (1, 4) is y = 2x + 2.

Answer:

y=2x+2

This answer should work on mathswatch

Answer:

2d=90

d=45

Explanation: Complementary angles add up to 90 degrees. If the two angles are congruent, it means that both angles have the same measurements.

Answer:

One person represents 360 degrees / (204 + 84 + 36 + 204 + 12) = 360 degrees / 540 = 4/6 = 2/3 degrees.

The correct response is c. scatter plot. An essential sort of data visualization that demonstrates the correlations between variables is the scatter plot.

In a scatter plot, dots are used to show the values for two different numerical variables (also known as a scatter chart or scatter graph). The position of each dot on the horizontal and vertical axes indicates the values for each data point. Frequency distributions are used to show how variables are linked to each other. The scatterplot shows how two numerical variables that were evaluated for the same individuals correlate with one another. On the horizontal axis, one variable's values are displayed, and on the vertical axis, the values of the other variable. On the graph, each data point represents a unique person. The correlation between the two variables, or the strength of the association, increases with the approach of a straight line to which the data points can be plotted.

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what plot will show it to you?

The expression (c - 4)³ in the expanded form will be c³ - 12c² + 48c - 64.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given as,

⇒ (c - 4)³

Expand the expression, then we have

⇒ (c - 4)³

⇒ (c - 4)(c - 4)(c - 4)

⇒ (c² - 4c - 4c + 16)(c - 4)

⇒ (c² - 8c + 16)(c - 4)

⇒ c³ - 4c² - 8c² + 32c + 16c - 64

⇒ c³ - 12c² + 48c - 64

The expression (c - 4)³ in the expanded form will be c³ - 12c² + 48c - 64.

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Answer:

#9       (x, y) = (6, 32)

#10      The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same and is $32

Step-by-step explanation:

The graph legend is missing so by looking at the graph alone we are unable to determine which color line corresponds to which kind of kite(Kites-R-Fun or Windy Kites)

However the associated table will help us determine this

The linear equation for a line is expressed as

y = mx + c

where m = slope of the line and b = y-intercept which is the y-value for the point where the line crosses the y-axis(at x = 0)

Slope m = rise/run = Δy/Δx = (y2 - y1)/(x2 - x1) for any two points (x1, y1) and (x2, y2) on the line

Let's take the two  x values as x1=0 and x2=1 and use the table

For Kites-R Fun

x1 = 0 ==> y1 = 8. This is also the y-intercept, b

We see that the red line corresponds to x = 0, y = 8

x2 = 1 ==> y2 = 12

y2 - y1 = rise = Δy =12 - 8 = 4

x2 -   x1 = Δx = 1 - 0 =1

Slope m = 4/1 = 4

Equation of Kites-R Fun is 4x + 8

For Windy Kites

x1 = 0 ==> y1 = 20

y-intercept = 20 or b = 20

x2 = 1 ==> y2 = 22

Rise = Δy =22 - 20 = 2

Run = Δx = 1 - 0 = 1

Slope = m, b = 20

Equation of blue line is

y = 2x + 20

The two equations are:

y = 4x + 8

y = 2x + 20

Equating right sides:

4x + 8 = 2x + 20

Move 2x to the left side and 8 to the right side:

4x + 2x + 8 - 8 = 2x - 2x + 20 -8

2x = 12

x = 6

For x = 6 the costs are the same

Plugging x = 6into equation y = 4x + 8:

y = 4(6) + 8 = 24 + 8 = 32

So the solution set is

(6, 32)

Looking at the graph we see the two lines intersect at this point

(Heck, we could have avoided all this work and just looked at the graph but I don't expect that was what they intended. You can add this as a side note)

On the second part

For Kites-R-US, each kite costs $4

The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same.

As per unitary method the recipe makes 20.5 servings of lemonade.

The unitary method is a method used to find the number of servings in a recipe by dividing the total amount of ingredients by the serving size.

Let's say a serving size of lemonade is 1 cup. To find the number of servings, we need to divide the total amount of lemonade by the serving size.

In this case, the total amount of lemonade is

=> 2 cups of lemon juice + 16 cups of water + 2.5 cups of agave nectar

=> 20.5 cups.

So, the number of servings can be found by dividing 20.5 cups by 1 cup per serving, which equals 20.5.

In conclusion, the unitary method is a simple way to find the number of servings in a recipe by dividing the total amount of ingredients by the serving size

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Inferential statistics employs probability to produce population forecasts based on a sample of data. Inferential statistics is a branch of statistics that makes conclusions or predictions about a population using sample data.

In inferential statistics, probability is used to calculate the likelihood of a specific event or result based on sample data. For example, the sample data may be used to compute the likelihood that a given mean value is larger than a given value or that a certain fraction of the population has a given viewpoint. Furthermore, probability is utilized to calculate the amount of confidence associated with the inferences drawn from the sample data. Confidence levels are presented as percentages and show how certain the sample estimate is of the underlying population parameter. Thus, probability is important in inferential statistics because it allows us to generate population predictions based on sample data and determines confidence levels.

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The two x-values that the supplied vectors are orthogonal to are 0 and 10 respectively.

A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector.

The term can also refer to a quantity's mathematical or geometrical representation.

Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

A movement from one point to another is described by a vector. A vector quantity has a magnitude and a direction (size).

There is just magnitude for scalar quantities.

An arrow-labeled line segment can serve as a visual representation of a vector.

So, we have:

xi+2xj and xi - 5j

As is common knowledge, when two vectors are orthogonal, their dot product equals zero, which means:

(xi + 2xj)*(xi-5j) = 0

x*x+2x*-5 = 0

x²-10x = 0

x(x-10) = 0

x = 0 or x - 10 = 0

x = 0 or x = 10

Therefore, the two x-values that the supplied vectors are orthogonal to are 0 and 10 respectively.

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The value of the variable x in the isosceles trapezoid is 14.

An isosceles trapezium is a trapezium with equally sized non-parallel sides. In other words, the legs are equal in length and the bases are parallel.

Calculation of the value of the variable:

Since the measure of one angle should be 38 degrees

And, there is the equation 2x + 10 degrees

So for determining the value of x here we have to equate the equation

Since Angles are equal in an isosceles trapezoid

So,

2x + 10 = 38

2x = 38 - 10

2x = 28

x = 14

Therefore, The value of the variable in the isosceles trapezoid is 14.

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There are 14,400 ways to select 5 working days in January without working on more than one Sunday.

Let the 5 working days be denoted by x1, x2, x3, x4, x5

Since there are 5 Sundays in the month of January, we need to select 5 days out of 26 days, such that none of them are Sundays. Therefore, the total number of ways to select 5 days out of 26 days without selecting any Sunday is 26C5.

This can be represented mathematically as:

26C5 = 26! / (5! x (26-5)!)

= 26! / (5! x 21!)

= 26 x 25 x 24 x 23 x 22 / (5 x 4 x 3 x 2 x 1)

= 14,400

Therefore, there are 14,400 ways to select 5 working days in January without working on more than one Sunday.

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The length of SR is 3.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

ST is parallel to PQ.

The length of PQ is the same as the length of SR.

PR = 10 and ST = 3

Now,

ST = 3 and ST is parallel to PQ.

This means,

PQ = 3 and the length of PQ is the same as the length of SR.

So,

SR = 3

Thus,

SR is 3.

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The  value of x is 94.5.

We are given that a basketball player averages 13.5 points per game.

x=Number of points scored in 7 games

We have to find the value of x

In order to find the points scored in 7 games we will multiply 7 by 13.5.

Number of games=7

Number of point scored in one game=13.5

Number of points scored in 7 games=

Number of points scored in 7 games=94.5

Hence, value of x=94.5

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The approximately 99.38% of the data falls between the values 120 and 280.

To find the percentage of data that falls between the values 120 and 280, we need to find the standard scores (z-scores) that correspond to these values and use a standard normal table to find the proportion of data within this range.

First, we'll find the z-score for 120:

z = (120 - 200) / 40 = -2.5

Similarly, the z-score for 280 is:

z = (280 - 200) / 40 = 2.5

Now we can use a standard normal table to find the proportion of data between -2.5 and 2.5 standard deviations from the mean. This proportion is approximately 0.9938 or 99.38%.

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The degree of the polynomial is 12 and the leading coefficient is -1

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

4w^11 - w^12

The degree of a polynomial is the highest power of the polynomial

In this case, we have

Degreee = 12

The leading coefficient is the coefficient of the degree term

So, we have

leading coefficient = -1

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A random variable cannot be negative.

This statement is false.

A random variable can be either positive, negative, or zero.

A random variable is a mathematical representation of a number or object that is affected by random occurrences. It is a function or mapping between probable outcomes in a sample space to a measurable space, frequently to real values.

A random variable is a rule that assigns a number value to each outcome in a sample space, or it may be defined as an unknown variable or a function that assigns numerical values to each outcome of an experiment.

Random variables are classed as discrete or continuous. The key distinction between the two groups is the range of potential values for each variable.

The range of a random variable depends on the underlying probability distribution and the specific scenario being modelled.

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We must first obtain the number in order to obtain the fraction. You can find the number by using an algebraic expression. The fraction is [tex]\frac{12}{30}[/tex].

A fraction is a piece of the entire. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction contains a fraction. In mathematics, there are three different types of fractions. Proper fractions, wrong fractions, and mixed fractions are the three types that exist. Fractions are defined by their numerator and denominator terms. In the context of these two words, we describe its types.

Given fraction [tex]\frac{2}{5}[/tex]

Let numerator is [tex]n[/tex]

The denominator is [tex](n+18)[/tex] and the numerator is [tex]18[/tex] less, the fraction is [tex]\frac{n}{n+18}[/tex]

To determine the answer, write the algebraic expression in the form of the question.

[tex]\frac{n}{n+18}=\frac{2}{5}\\n=12[/tex]

Calculate the fraction.

[tex]\frac{n}{n+18}=\frac{12}{12+18}\\\frac{n}{n+18}=\frac{12}{30}[/tex]

As a result, the fraction is [tex]\frac{12}{30}[/tex]

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