Solve the system of linear equations:

x + y - 3z = 9
y + z - 3x = 5
z + x - 3y = 1
Find x y and z

Answer:25

Step-by-step explanation:

Example and or statements in statistics are logic statements used in statistics to describe the probability of events occurring together (and) or separately (or)."

The "and" statement is used to describe the probability of two or more events occurring together (to calculate the joint probability of multiple events).

For example, the probability of rolling a 4 on a fair die and flipping a head on a fair coin is,

P(rolling a 4 AND flipping a head) = P(4) x P(head)

                                                        =(1/6) x (1/2) = 1/12    = P(A)

The "or" statement is used to describe the probability of one or more events occurring (to calculate the probability of at least one event).

For example, the probability of rolling a 4 on a fair die or flipping a head on a fair coin is,

P(rolling a 4 OR flipping a head) = P(4) + P(head) - P(A)

                                                     = (1/6) + (1/2) - (1/12)    = 7/12

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A solution to this inequality 2(x - 6) < 1/2(12x - 8) include the following: x > -2.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would multiply both sides of the inequality by 2 as follows;

2(x - 6) < 1/2(12x - 8)

4(x - 6) < (12x - 8)

4x - 24 < 12x - 8

By collecting like-terms and rearranging the expression, we have:

8 - 24 < 12x - 4x

-16 < 8x

x > -2

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This means that his new bearing is 323° clockwise from true north, or simply 0°, which is equivalent to facing due north.

A bearing is a direction measured in degrees relative to a fixed reference point, usually true north. In this case, the man's initial bearing of 307° means that he is moving in a direction that is 307 degrees clockwise from true north.

After he turns 90° to his right, he will be facing in a new direction that is perpendicular to his original direction of travel. Turning 90° to the right means he is now facing due north (since 307° + 90° = 397°, which is equivalent to 37° clockwise from true north).

However, bearings are typically measured as angles clockwise from true north, so we need to convert the angle of 37° counterclockwise from true north into a bearing that is measured clockwise from true north.

To do this, we subtract 37° from 360° to get 323°.

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Answer:

Step-by-step explanation:

For y=7x, if y = 2, you have to do the same for x.

Example; 7x = y, 7(2) = (2), 14 = 2, 14,2

(please comment if I did anything wrong)

After converting from Celsius to Fahrenheit , we will get 54 Celsius is equivalent to 129.2 Fahrenheit.

To convert Celsius to Fahrenheit, you can use the following formula:

°F = (°C x 9/5) + 32

In this case, to convert 54 Celsius to Fahrenheit, we can substitute 54 for °C in the formula:

°F = (54 x 9/5) + 32

Simplifying this expression, we can first perform the multiplication and division:

°F = (97.2) + 32

Then we can add 97.2 and 32 to get the final answer:

°F = 129.2

It's worth noting that the Celsius and Fahrenheit scales are both used to measure temperature, but they have different starting points and different degrees of scale. Celsius is based on the freezing and boiling points of water, where 0 degrees Celsius is the freezing point and 100 degrees Celsius is the boiling point at sea level.

Fahrenheit, on the other hand, is based on a system of degrees devised by Gabriel Fahrenheit, with 32 degrees being the freezing point and 212 degrees being the boiling point at sea level.

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The coordinates of V' after reflection(Dilation) across y=-x will be (3,1).

In mathematics, what is dilation?

Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit and there are only four basic types of transformations. They are as follows:

Some characteristics stay constant during dilation are:

Now,

Before reflection

Coordinates of V are (−3, −1).

and reflection of V is across y=-x, which will make values for x and y opposite or change the sign of coordinates.

then coordinates of V' are (3,1)

hence,

           The coordinates of V' after reflection(Dilation) across y=-x will be (3,1).

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If data is skewed right, it means that the data is concentrated towards the left side of the histogram, with a tail stretching towards the right.

If data is skewed right, it implies that the data focuses are not evenly dispersed around the mean, and there is a long tail of higher qualities reaching out to one side of the distribution. This intends that there are more qualities on the left side of the distribution and fewer qualities on the right side. The right-skewed dissemination is likewise called an emphatically skewed dispersion in light of the fact that the tail of higher qualities is situated on the positive side of the x-axis. In a right-skewed conveyance, the mean is typically more prominent than the middle, and the mode is not exactly the middle, it isn't equitably dispersed to show that the information.

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The store must sell 30 bicycles each month to break even.

To break even, the total revenue from selling bicycles must be equal to the total cost of operating the store. Let's calculate the revenue and cost of the store for selling x bicycles in a month.

Revenue from selling x bicycles = selling price per bike × number of bikes sold

= $195x

Cost of operating the store = fixed cost + variable cost

= $4200 + (cost per bike × number of bikes sold)

= $4200 + ($55x)

To break even, the revenue must equal the cost. So we can set up the linear equation equation:

$195x = $4200 + $55x

Solving for x, we get:

$140x = $4200

x = $4200 / $140

x = 30

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2. 8.472 * 10^5 in standard form is

3. The scientific notation of 0.000067 is 6.7 * 10^-5

4. The division gives 4.455 * 10^3

Scientific notation is a way of expressing very large or very small numbers in a compact and convenient way.

In scientific notation, a number is written as a coefficient multiplied by a power of 10.

The coefficient is a number between 1 and 10 (or between -1 and -10 for negative numbers), and the power of 10 indicates the size of the number.

Calculator can be used to get numbers to scientific notation and in standard form

The required division can be performed using calculator to get 4.455 * 10^3

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The conversion of 185 centimetres in feet is equals to the 6.06 feet. Thus, conversion factor from centimetres to feet is 6.06/185 = 0.032.

A conversion factor is a number used to convert one set of units into another set of units by multiplication or division. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So,185 meters

= 185 × 3.28 feet

= 606.8 feet --(1)

But we need to convert 185 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 185 meters = 18500 centimeters --(2). Now from equations (1) and (2),

18500 centimeters = 606.8 feet,

Divide both parts by 100,

=> 185 centimetres = (606.8/100 ) feet

= 6.06 feet

Hence required value is 6.06 ft.

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Answer:

2/3/5/8/9/21 I hope it is able to help you

The simplified expression is [tex]4.0 \times 10^{32}[/tex]

A mathematical statement without an equals sign that contains variables, constants, and mathematical operations is known as an algebraic expression. Algebra and other branches of mathematics both employ algebraic expressions to represent mathematical connections.

Simple algebraic expressions include x + 2, which consists of the addition operation, the constant (2), and the variable x. Several variables, constants, and operations can be found in more complicated algebraic formulas, like 2x2 + 3xy - 4.

Whereas constants are fixed values that never change, variables in algebraic expressions indicate unknowable values that can vary or change. Variables and constants are combined using mathematical operations including addition, subtraction, multiplication, and division.

In several academic disciplines, such as physics, chemistry, economics, and engineering, algebraic expressions are employed to solve issues. Moreover, they are used to manipulate and simplify mathematical formulas and equations as well as to mimic actual life circumstances.

By combining like terms, or terms with the same variable raised to the same power, algebraic expressions can be made simpler. For instance, the like words 3x and 2x in the equation 3x + 2x + 5 can be combined to create 5x, resulting in the abbreviated expression 5x + 5.

[tex]2\times 2 \times 10 = 20\times 2[/tex]

Next, we can use the rule that when we multiply two numbers with the same base, we add their exponents. Therefore:

[tex]10^{58} \times 10^{-27} = 10^{(58-27)} = 10^{31}[/tex]

Putting it all together:

[tex](2\times 2 \times 10) \times (10^{58} \times 10^{-27}) = 20\times 2 \times 10^{31} = 40\times 10^{31} = 4.0 x 10^32[/tex]

Therefore, the simplified expression is [tex]4.0 \times 10^{32}[/tex]

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The AP Statistics formula sheet is illustrated below.

An Advanced Placement (AP) Statistics class, you may be wondering if there is a formula sheet available to help you study and prepare for exams.

The formula sheet includes formulas and equations that are commonly used in statistics, such as measures of central tendency, standard deviation, probability, hypothesis testing, and regression analysis. These formulas are essential for understanding statistical concepts and solving problems in real-world applications.

It's important to note that while the formula sheet is available during the AP exam, it does not include every formula that you will need to know. You will still need to have a solid understanding of statistical concepts and be able to apply them to new situations.

In addition to the formula sheet, it's also helpful to practice working with data sets, analyzing graphs and charts, and interpreting results.

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Answer:

Length = 16 feet, width = 12 feet

Step-by-step explanation:

Scale is 2 cm = 4 feet

Therefore 1 cm = 4/2 = 2 feet

8 cm length = 8 x 2 = 16 feet

6 cm width = 6 x 2 = 12 feet

So the room size is Length = 16 feet, width = 12 feet

Answer: In the scale drawing, each 2 cm represents 4 feet. So, 1 cm represents 2 feet (since 2 cm is twice 1 cm). Therefore, the length of the room in feet is:

8 cm x (2 feet/1 cm) = 16 feet

Similarly, the width of the room in feet is:

6 cm x (2 feet/1 cm) = 12 feet

So, the actual dimensions of the room are length = 16 feet and width = 12 feet.

Answer: Length = 16 feet, width = 12 feet

Step-by-step explanation:

Option C. No, because the 100 adults were selected without replacement, the selections are dependent.

The binomial probability formula assumes that the trials are independent, meaning that the probability of success or failure for each trial remains the same regardless of the outcomes of previous trials. However, in this case, the 100 adults were selected without replacement, so the probability of being left-handed for each selection depends on the outcomes of previous selections. Therefore, the binomial probability formula cannot be used to find the probability in this situation. Instead, the hypergeometric distribution can be used to account for the dependence between selections.

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Complete question:

It is assumed that approximately 15% of adults in the U.S. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Why or why not?

A. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.

B. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.

C. No, because the 100 adults were selected without replacement, the selections are dependent.

D. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.

Answer:

B=11x2x2

Step-by-step explanation:

Prime factors of 44
44 ÷ 2 = 22
22 ÷ 2 = 11

11 ÷ 11 = 1

Prime factorization of 44 : 11 x 2 x 2

Factorization Tree

       44    

 /  \    

     2    22  

     /  \  

 2   11

Angle B is an acute angle in a right triangle, it must be less than 90 degrees. Therefore, a reasonable approximation for angle B ≈ 76 degrees.

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behavior of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

Let's use the trigonometric ratio for the sine of angle B, which is the ratio of the opposite leg to the hypotenuse:

sin(B) = opposite leg / hypotenuse

We are given that the ratio of the opposite leg to the hypotenuse is 0.96:

opposite leg / hypotenuse = 0.96

So, we can substitute 0.96 for opposite leg / hypotenuse:

sin(B) = 0.96

Now we can use the inverse sine function to find the value of angle B:

B = sin^(-1)(0.96)

Using a calculator, we get:

B ≈ 75.96 degrees

Since angle B is an acute angle in a right triangle, it must be less than 90 degrees. Therefore, a reasonable approximation for angle B is:

B ≈ 76 degrees

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Approximately 27% of the jerseys did not sell.

What is Percentage?

Percentage is a way of expressing a number as a fraction of 100. It is used to describe ratios, proportions, and changes in quantities in terms of a fraction of the whole.

Solution:

The school ordered 225 jerseys and sold 165, so the number of jerseys that did not sell is:

225 - 165 = 60

To find the percentage of jerseys that did not sell, we need to divide the number of unsold jerseys by the total number of jerseys ordered and then multiply by 100:

60 / 225 x 100% = 26.67%

Rounding this to the nearest percent gives: 27%

Therefore, approximately 27% of the jerseys did not sell.

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The distance traveled in the first 5.2 seconds when the speed dropped from the rest as v(t) = 9.8t is equal to 132.496 meters.

'v' is the speed of the object in meter per second

't' is the time in seconds.

Speed dropped from rest 'v(t) = 9.8t '

Distance traveled in the first 5.2 seconds is equal to

= [tex]\int_{0}^{5.2}[/tex]9.8t dt

= ( 9.8 / 2 )t² [tex]|_{0}^{5.2}[/tex]

Substitute the lower and upper limit to get the required distance we have,

= 4.9 [ ( 5.2)² - 0² ]

= 4.9 × 27.04

= 132.496 meters

Therefore, the distance traveled for the given first 5.2 seconds is equal to 132.496 meters.

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The above question is incomplete, the complete question is:

Free fall the speed v of an object dropped from rest is given by v(t)=9.8t where v is meters per second and time 't' is in seconds.

(a) Express the distance traveled in the first 5.2 seconds as an integral.

Answer:

Domain: {-3, 5, 0, -1, -2, 1}

Range: {-6, -4, -2, 1, 3}

The relation is a function.

Step-by-step explanation:

The domain of this relation is the set of all x-values from the ordered pairs, which are:

Domain: {-3, 5, 0, -1, -2, 1}

The range of the relation is the set of all y-values from the ordered pairs, which are:

Range: {-6, -4, -2, 1, 3}

To determine if the relation is a function, we need to check if there are any repeated x-values with different y-values. If there are no such cases, then the relation is a function.

Looking at the domain and range, we can see that each x-value has only one corresponding y-value, so there are no repeated x-values with different y-values. Therefore, the relation is a function...

Answer: [tex]r=\Large\boxed{\pm 2\sqrt{21} }[/tex]

Step-by-step explanation:

Given equation

[tex]8r^2+8=680[/tex]

Subtract 8 on both sides

[tex]8r^2+8-8=680-8[/tex]

[tex]8r^2=672[/tex]

Divide 8 on both sides

[tex]8r^2\div8=672\div 8[/tex]

[tex]r^2=84[/tex]

Take square roots on both sides

[tex]r=\pm \sqrt{84}[/tex]

[tex]r=\Large\boxed{\pm 2\sqrt{21} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Linear transformation of a matrix is discussed below.

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Given is to discuss the linear transformation of a matrix.

Therefore, linear transformation of a matrix is discussed above.

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Answer:

Below

Step-by-step explanation:

First ball 1        then second ball makes  2 3 4

First ball2         then second makes a        3 4 5

First ball 3       then second makes a             4 5 or 6

  you can see that '4' is the most likely

The probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

To solve this problem, we can use the normal distribution and the standard normal distribution table (also known as the z-table).

Let X be the salary of a first-year teacher. We are given that X is approximately normally distributed with a mean (average) of mu = $27,989 and a standard deviation of sigma = $3250. We want to find the probability that a randomly selected first-year teacher makes certain salaries.

A. Between $20,000 and $30,000 a year

To find the probability that a first-year teacher makes between $20,000 and $30,000 a year, we need to standardize the interval using the z-score formula:

z1 = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45

z2 = (30000 - mu) / sigma = (30000 - 27989) / 3250 = 0.63

Using a standard normal distribution table or calculator, we can find that the probability of a random variable being between z1 and z2 is approximately 0.8461.

Therefore, the probability that a randomly selected first-year teacher makes between $20,000 and $30,000 a year is approximately 0.8461.

B. Less than $20,000 a year

To find the probability that a first-year teacher makes less than $20,000 a year, we need to standardize this value using the z-score formula:

z = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45

Using a standard normal distribution table or calculator, we can find that the probability of a random variable being less than z is approximately 0.0071.

Therefore, the probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.

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Answer: 2 inches of rain

Step-by-step explanation:

Since Monday has rainfall of 0.50 inches and Tuesday 0.25, we can use this information to solve the final question. Since it rained on Monday the amount of it in three days, we can multiply 0.5 by 3 and get 1.5. For Tuesday it was 2 days so we can multiply 0.25 by 2 and get 0.5. Add them up and you get 2. Put the unit in inches.

Answer:

B. 360

Step-by-step explanation:

A rule of polygons (octagon included) is that the sum of the exterior angles always equals 360 degrees.

It take 20 years for Eva's initial deposit to double?.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

Eva deposits $2,000 in a savings account with an interest rate of 5% compounded continuously.

Here, Principal amount = $2000

Amount = $4000

Interest rate = 5%

Now, We know that;

⇒ Interest = PRT

Substitute all the values, we get;

⇒ 2000 = 2000 × 0.05 × T

⇒ T = 1/0.05

⇒ T = 100/5

⇒ T = 20 years

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A correlation coefficient based on the observational study cannot be used to support a claim of cause and effect. The correct answer is D: never.

Correlation does not imply causation, and while a strong correlation between two variables may suggest that there is a relationship between them, it does not prove that one variable causes the other. Observational studies are particularly susceptible to confounding variables, which can make it difficult or impossible to determine whether a relationship between two variables is causal or not.

To establish causality between two variables, a randomized controlled experiment is required. In a randomized controlled experiment, the experimenter can manipulate the independent variable and observe the effect on the dependent variable, while controlling for other variables that might affect the outcome. By randomly assigning subjects to different treatment groups, the experimenter can ensure that any differences in the outcome between groups are due to the treatment, rather than some other factor.

Therefore, while a correlation coefficient can be a useful tool for describing the relationship between two variables, it cannot be used to establish causality.

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The linear equation for salary will be S=$35000+$2000n where n=no. of years.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.

Now,

Given that Initial salary=$35000

Increment of $2000 every year

Then after n years salary will be

S=35000+2000n

where n=no. of years

hence,

          The linear equation for salary will be S=$35000+$2000n.

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