name the property the statement illustrates​

The statement "If the system of a linear equation has the unique solution, then the system is inconsistent." is False since a single solution is an indication that the equations intersect at a specific point, making it consistent.

A system of linear equations is a set of two or more linear equations that contain two or more variables. A solution to the system of linear equations is a set of values for the variables that satisfies all the equations in the system.

The system of linear equations having a single solution is a consistent system since a single solution is an indication that the equations intersect at a specific point. This contradicts the notion that the system is inconsistent. An inconsistent system is one that has no solutions.

Thus, if a system of linear equations has a unique solution, it must be consistent.

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a) The probability of selecting two different colors is obtained as 9/10.

b) The probability of not selecting a yellow marble is obtained as 3/20.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

a) To find the probability of selecting two different colors, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

So the probability of selecting two different colors can be found by calculating the probability of selecting two marbles of the same color and subtracting that from 1.

The probability of selecting two marbles of the same color from the first bag is (2/5) x (1/4) = 1/10, since there are 2 red marbles out of 5 total marbles in the bag, and the probability of selecting a second red marble is 1/4.

The probability of selecting two marbles of the same color from the second bag is 0, since there is only one marble of each color.

So the probability of selecting two different colors is -

1 - (1/10 + 0) = 9/10

Therefore, the probability value is 9/10.

b) To find the probability of not selecting a yellow marble, we can again use the complement rule.

The probability of not selecting a yellow marble is equal to 1 minus the probability of selecting a yellow marble from either bag.

The probability of selecting a yellow marble from the first bag is 1/5, since there is one yellow marble out of 5 total marbles in the bag.

The probability of selecting a yellow marble from the second bag is also 1/4, since there is one yellow marble out of 4 total marbles in the bag.

So the probability of not selecting a yellow marble is -

1 - (1/5 + 1/4) = 3/20

Therefore, the probability value is 3/20.

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The figure represented here is a square pyramid.

With a square base and fοur triangular sides that are cοnnected at a vertex, a square pyramid is a three-dimensiοnal geοmetric οbject. It has a pentahedrοn shape with five faces.

Fοur triangles are jοined at each vertex tο a square fοundatiοn tο fοrm a square pyramid. It has a square fοundatiοn, and triangles with a shared vertex make up its side faces.

We can get the squared pyramidal figure by fοlding the triangles οf equal size frοm all the sides.

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Answer: See attached for the graph. There is an undefined slope and no y-intercept.

Step-by-step explanation:

      See attached for a graph. Since this is only greater than, (>) we will use a dashed line. Then we will shade everything greater than -4.

      The slope of this graph is undefined because this line is straight up and down. If we try to write it as an equation, you end up dividing by zero (which ends up undefined)

      Lastly, there is no y-intercept. Since this line does not cross the y-axis, there is no point of intersection.

In answering the question above, the solution is Zany thus has 1,533.75 expressions pounds more apples than Peter does.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

There are 412 bags of apples in all, with 10 apples in each bag, at Zany. Zany thus has a total of:

412 bags multiplied by 10 bags is 4,120 apples.

24,720 ounces is equal to 4,120 apples at 6 ounces each.

16,080 pounds divided by 24,720 ounces is 1,545 pounds.

Peter has a total of three bags of apples, or:

30 apples are equal to 3 bags times 10 bags

Each of Peter's apples weighs 6 ounces, making his total apple weight:

30 apples divided by 6 ounces each equal 180 ounces.

160 ounces / 16 ounces per pound equals 11.25 pounds.

After deducting Peter's weight from Zany's weight, we can determine how many pounds more apples Zany possesses than Peter:

11 pounds less than 1,545 pounds is 1,533.75 pounds.

Zany thus has 1,533.75 pounds more apples than Peter does.

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The expected value of the number of tests taken is 1.92 an the variance of the number of tests taken is 1.5852 and the standard deviation is 1.259.

The expected value, variance, and standard deviation can be calculated using the following formulas:
Expected value (E) = ΣxP(x)
Variance (Var) = Σ(x - E)² P(x)
Standard deviation (SD) = √Var

a. To find the expected value of the number of tests taken, we can use the formula E = ΣxP(x), where x is the number of tests taken and P(x) is the probability of taking x tests.
E = (1)(22/50) + (2)(15/50) + (3)(8/50) + (4)(5/50)
E = 0.44 + 0.6 + 0.48 + 0.4
E = 1.92


b. To find the variance and standard deviation, we can use the formulas Var = Σ(x - E)² P(x) and SD = √Var.
Var = (1 - 1.92)²(22/50) + (2 - 1.92)² (15/50) + (3 - 1.92)² (8/50) + (4 - 1.92)^2 (5/50)
Var = 0.8464 + 0.0104 + 0.2928 + 0.4356
Var = 1.5852
SD = √1.5852
SD = 1.259

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Therefore , the solution of the given problem of unitary comes out to be child can purchase 39 roller coaster excursions with 273 ride tickets as a result.

To finish the job using the unitary technique, the expression from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

The boy can purchase the following amount of roller coaster rides:

39 trips using 273 ride tickets at 7 tickets each (rounded down to the nearest whole number)

The child can purchase 39 roller coaster excursions with 273 ride tickets as a result.

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a) The probability that a person spent more than $28 is of: 0.2033 = 20.33%.

b) The probability that a person spent between $9 and $21 is given as follows: 0.3608 = 36.08%.

c) The middle 95% of the amounts falls between $11.24 and $34.76.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the problem are given as follows:

[tex]\mu = 23, \sigma = 6[/tex]

The probability of a person spending more than $28 is one subtracted by the p-value of Z when X = 28, hence:

Z = (28 - 23)/6

Z = 0.83

Z = 0.83 has a p-value of 0.7967

1 - 0.7967 = 0.2033.

The probability of a person spending between $9 and $21 is given by the p-value of Z when X = 21 subtracted by the p-value of Z when X = 9, hence:

Z = (21 - 23)/6

Z = -0.33

Z = -0.33 has a p-value of 0.3707

Z = (9 - 23)/6

Z = -2.33

Z = -2.33 has a p-value of 0.0099.

0.3703 - 0.0099 = 0.3608 = 36.08%.

The middle 95% of amounts is between the 2.5th percentile(Z = -1.96) and the 97.5th percentile, Z = 1.96, hence:

-1.96 = (X - 23)/6

X - 23 = -1.96 x 6

X = 11.24.

1.96 = (X - 23)/6

X - 23 = 1.96 x 6

X = 34.76.

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Answer:

A megabyte is 1,000,000 bytes

A gigabyte is 1,000,000,000 bytes

A terabyte is 1,000,000,000,000 bytes

A kilobyte is 1,000 bytes

A byte has 8 bits

1. True. The CPI is not just one index, but includes a large number of groups, subgroups and selected items, such as a food index, a medical care index and an entertainment index.

2. True. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another.

The Consumer Price Index (CPI) is actually a collection of indices that measure the changes in prices of a wide range of goods and services.

The CPI includes several different groups, subgroups, and selected items, such as a food index, a medical care index, and an entertainment index.

Each of these indices is used to track the changes in prices of specific goods and services within that category.

An index number is a statistical measure that is used to compare the changes in prices, quantities, values, or other items of interest from one time period to another.

Index numbers are typically expressed as a percentage, with a base value of 100 representing the initial time period. Any changes in the index number from one time period to another reflect the percentage change in the item of interest over that time period.

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Answer:

1 < x < 15

Step-by-step explanation:

To find the range of values for the third side, you must subtract and add the other known sides. The lower limit for the range of the third side will be 8 - 7, which equals 1. The upper limit for the range of the third side will be 8 + 7, which equals 15

Answer:

1<x<15

Step-by-step explanation:

Triangle inequalities state that the sum of two sides of any triangle must be less than the other. This is true for all three sides of the triangle.

In this case, we know two sides. Let us set a variable for the third, as x.

So the sum of 8 and 7 has to be bigger than x:

8+7>x

15>x

8 and x have to be greater than 7:

8 +x >7

x>-1

And 7 and x have to be greater than 8:

7 + x>8

x>1

Looking at the inequalities between x, we must choose the most inclusive ones. x>-1, but 1 is within that, so we can go with x>1. x<15 is a statement that cannot change because it is the only end value given. Therefore, the answer is 1<x<15

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The equatiοn οf the least squares regressiοn line which mοst clοsely matches the data set is y = 3.5 x + 43.8

Tο sοlve fοr the data set, lets lοοk at the table,

X            1190         1992          1994         1996           1998

Y             45             51               57            61               75

Let the equatiοn that shοws the abοve data be

y = b + a x ---------(1)

Where, a = Σy Σx² - Σx Σxy

And, b = (Σxy - Σx Σy) / n Σx² -(Σx)²

By the abοve table,

Σx=20

Σxy = 1296

Σx² = 120

Σy=289

By substituting these values in the abοve value οf a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equatiοn (1)

We get, the equatiοn that shοws the given data is,

y = 3.5 x + 43.8

Therefοre, οptiοn 3 is cοrrect.

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The set is linearly independent.

Yes, the given set is linearly independent. To prove this, we can use the determinant method. To calculate the determinant, arrange the columns of the array in a 3x3 matrix. This gives us the following matrix:

$$\begin{bmatrix}1 & -1 & -2\\-1 & 0 & 1\\0 & 1 & -1\end{bmatrix}$$

The determinant of this matrix is 1, which is not equal to 0. This shows that the given set is linearly independent.

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This is the appropriate set notation for the set J, which includes all integers between -5 and -3.

The set J can be rewritten by listing its elements in the appropriate set notation. Since the set J contains all integers between -5 and -3, we can list the elements as follows:

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

J = {-5, -4}

In set notation, this can be written as:

J = {x | x is an integer and -5 <= x < -3}

Therefore, the set J can be rewritten as:

J = {-5, -4}

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The ordered pairs for the linear equation, y=3x-13 is (0,-13), (1,-10), and (2,-7).

To complete the table of ordered pairs for the linear equation y=3x-13, we need to substitute different values of x into the equation and solve for y. This will give us the ordered pairs (x,y) for the equation.

Step 1: Choose a value for x. Let's start with x=0.

Step 2: Substitute the value of x into the equation and solve for y.
y=3(0)-13
y=-13

Step 3: Write the ordered pair (x,y) for this solution. In this case, the ordered pair is (0,-13).

Step 4: Repeat steps 1-3 for different values of x. Let's try x=1 and x=2.

For x=1:
y=3(1)-13
y=-10
The ordered pair is (1,-10).

For x=2:
y=3(2)-13
y=-7
The ordered pair is (2,-7).

Step 5: Complete the table with the ordered pairs that we found.

   x        y
   0      -13

   1       -10
 
   2        -7
 

So, the table of ordered pairs for the linear equation y=3x-13 is:
(0,-13), (1,-10), and (2,-7).

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The simplified expression is (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).

The given expression is ((-4m4n-4)3) / ((mn)2).

To simplify the expression ((-4[tex]m^{(4)}[/tex] ) (([tex]n^{(-4)[/tex])[tex])^{(3))}[/tex]/ ((mn[tex])^{(2)}[/tex]), we will use the power rules of exponents.

First, we will apply the power rule to the numerator:

((-4)[tex])^{3}[/tex])([tex]m^{(4*3)}[/tex])([tex]n^{(4*3)}[/tex]) = (-64)([tex]m^{(12)}[/tex])([tex]n^{(12)}[/tex])

Next, we will apply the power rule to the denominator:

([tex]m^{(2)}[/tex])([tex]n^{(2)[/tex]) = [tex]m^{(2)}[/tex][tex]n^{(2)[/tex]

Now we can simplify the expression by canceling out the common terms in the numerator and denominator:

((-64)([tex]m^{12}[/tex])([tex]n^{12}[/tex])/([tex]m^{(2)}[/tex][tex]n^{(2)}[/tex])

= (-64)([tex]m^{12-2}[/tex])([tex]n^{12-2}[/tex])

= (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex])

Finally, we can write the final expression in simplified form:

(-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).

Therefore, the simplified expression is (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).

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From the given information provided, A is crest, B is wavelength, C is  trough, D is amplitude, E is equilibrium line in the transverse wave.

Amplitude: The maximum displacement of wave from its equilibrium position. In other words, it is the height of the wave measured from the midpoint (or equilibrium position) to the crest or trough.

Wavelength: The distance between two consecutive crests or troughs of a wave. It is usually denoted by Greek letter lambda (λ) and measured in meters.

Crest: The highest point or peak of a wave. It is the point on the wave with maximum positive displacement from the equilibrium position.

Trough: The lowest point of a wave. It is the point on the wave with maximum negative displacement from the equilibrium position.

Equilibrium: The position where there is no net force acting on an object. In the context of waves, the equilibrium position is the position where there is no displacement of the medium through which the wave is travelling.

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We have shown that ∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)-∫_((a,b])▒〖F(x)dG(x)〗〗 as required.

The given statement is that F and G are two cumulative distribution functions on the real line, and they have no common points of discontinuity in the interval (a, b). We need to show that ∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)-∫_((a,b])▒〖F(x)dG(x)〗〗

First, we can use the fact that F and G are cumulative distribution functions to write the integral of G(x)dF(x) as the difference of the product of F and G at the endpoints of the interval:

∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)〗

Similarly, we can write the integral of F(x)dG(x) as the difference of the product of F and G at the endpoints of the interval:

∫_((a,b])▒〖F(x)dG(x)=F(b)G(b)-F(a)G(a)〗

Subtracting the second equation from the first gives us:

∫_((a,b])▒〖G(x)dF(x)-∫_((a,b])▒〖F(x)dG(x)=F(b)G(b)-F(a)G(a)-F(b)G(b)+F(a)G(a)〗

Simplifying the right-hand side of the equation gives us:

∫_((a,b])▒〖G(x)dF(x)-∫_((a,b])▒〖F(x)dG(x)=0〗

Therefore, we have shown that ∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)-∫_((a,b])▒〖F(x)dG(x)〗〗 as required.

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The inequality for the statement "5 is greater than or equal to a" is 5 ≥ a.

To write an inequality for the statement "5 is greater than or equal to a," we can use the greater than or equal to symbol (≥) to represent the relationship between 5 and a. The inequality would be written as:
5 ≥ a
This inequality can also be written as a ≤ 5, which means that a is less than or equal to 5. Both of these inequalities represent the same relationship between 5 and a, and either one can be used to represent the statement "5 is greater than or equal to a."

In Mathematics, the relationship between two values that are not equal is defined by inequalities.

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Answer:

right one is correct explanation

Answer: y = -2x + 2 3/7

Step-by-step explanation:

The slope-intercept form is y = mx + b

Start:

14x + 7y = 17

Subtract 14 from each side to get y alone:

7y = -14x + 17

Divide by 7 on each side:

y = -2x + 2 3/7

Hope this helps!

Answer:

$2.48

Step-by-step explanation:

50 coins in all

16% of 50 is 8. (50 x 0.16 = 8)

That means we have 14 Nickels

34% of 50 is 17. (50 x 0.34 = 17)

Multiplying each number by their value (i.e. 14 x 5 for Nickels)

We get 248. We can assume we don't have 248 dollars, and more likely have $2.48 instead.

Answer: A

Step-by-step explanation:

A best represents the graph

Answer:

mine either hahahahahaha

a. The average velocity between 1s and 5s is -30 m/s.
b. The average velocity between 5s and 9s is -70 m/s
c. The velocity at -5 is -50 m/s.

A. The average velocity between 1 s and 5 s can be calculated by finding the displacement divided by the time interval. The displacement is the difference between the final and initial positions, which can be found by plugging in the values of t into the equation s(t) = 500 - 5t^2.
So, s(1) = 500 - 5(1)^2 = 495 m and s(5) = 500 - 5(5)^2 = 375 m.

The displacement is 375 - 495 = -120 m. The time interval is 5 - 1 = 4 s.

Therefore, the average velocity is -120 m / 4 s = -30 m/s.

B. The average velocity between 5 s and 9 s can be calculated in the same way. s(5) = 375 m and s(9) = 500 - 5(9)^2 = 95 m.

The displacement is 95 - 375 = -280 m. The time interval is 9 - 5 = 4 s.

Therefore, the average velocity is -280 m / 4 s = -70 m/s.

C. The velocity at t = 5 can be found by taking the derivative of the position function s(t) = 500 - 5t^2.

The derivative is s'(t) = -10t. Plugging in t = 5 gives s'(5) = -10(5) = -50 m/s.

So the velocity at t = 5 is -50 m/s.

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Using basic arithmetic operations, we concluded that a) Bryony wrote more words in total than Arthur.

b) Bryony wrote 220 more words than Arthur.

The four basic mathematical operations are addition, subtraction, multiplication, and division.

a) In order to establish who wrote more words overall, we must total the words that each participant wrote. By dividing the typical words per minute by the total number of minutes each person worked, we may determine this:

Arthur: 65 minutes × 16 words/minute = 1040 words

Bryony: 90 minutes × 14 words/minute = 1260 words

Therefore, Bryony wrote more words in total than Arthur.

b) To find out how many more words Bryony wrote than Arthur, we can subtract Arthur's total from Bryony's total:

1260 words - 1040 words = 220 words

Hence, Bryony wrote 220 more words than Arthur.

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The two integer values of a for which the quadratic equation x² + ax + 8a = 0 have integer solutions are

A quadratic equation is an polynomial in which the highest power of the variable is 2.

Since we have the equation x² + ax + 8a = 0, we desire to find how many integer values of a that will make the equation have integer solution.

To do that, we use the discriminant of a quadratic equation

D = b² - 4ac where

Now, for a quadratic equation to have real solutions D ≥ 0

So, b² - 4ac ≥ 0

Now from the equation we have that

So, substituting the values of the variables into D, we have that

D = b² - 4ac

a² - 4(1)(8a) ≥ 0

a² - 32a ≥ 0

For integer values of a

a² - 32a = 0

a(a - 32) = 0

a = 0 or a - 32 = 0

a = 0 or a = 32

So, we have two integer values of a which are

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Answer:

5 2/3

Step-by-step explanation:

all you need is to add because the fraction is the same.

Answer:

36

Step-by-step explanation:

do x to the second power then multiply 4 to get your answer

Hence, the sum of the fixed expenses ($75 + $25 = $100) and the expressions variable charges ($15 per person) would equal the total cost for catering.

Mathematically speaking, you can multiply, divide, add, or subtract. This is how an expression is constructed: Math operation, expression, and numerical value Functions, parameters, and numbers make up a mathematical expression. It is feasible to use opposing words and phrases. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical operation between them. As an instance, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.

Finding the slope of the line will allow you to compute the rate of change for Smokey Joe's catering. The slope in this instance is $15, which indicates that the price will rise by $15 for each extra person served. The variable cost that Smokey Joe's incurs every person served is represented by this rate of change.

If Smokey Joe's charges a $25 delivery fee, this will be an extra set expense that they will pay no matter how many customers they serve. Hence, the sum of the fixed expenses ($75 + $25 = $100) and the variable charges ($15 per person) would equal the total cost for catering.

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