6|x|≥72

If all real numbers are solutions, click on "All reals".
If there is no solution, click on "No solution".
IV

The size of the augmented matrix for this system will be 2x3. Option B is the correct answer.

Augmented matrix is a mathematical tool developed in matrix theory to solve linear equations that combine two matrices or vectors to make a new matrix type.

For solving linear equations, the coefficients of the linear equations are written in a matrix form with a column beside it containing its constant values, which makes it an augmented matrix.

one example of an augmented matrix is,

x+y=1

x-y=2

can be represented as

= [tex]\left[\begin{array}{ccc}42&61&|393\\59&78&|529\\\end{array}\right][/tex]

In the given question the linear equations contain two variables, hence the number of rows in the augmented matrix will be 2.

Since it is an augmented matrix it will contain 3 columns with 2 columns of the coefficient matrix and 1 column of the constant matrix.

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The alternative hypothesis for this problem is that the population variance is significantly more than 0.003, represented as [tex]H1: S2 > 0.003.[/tex]

To test this hypothesis, we can use a chi-square test of variance. This test is calculated as [tex]X2 = (n-1) * (s2/σ2)\\[/tex], where n is the sample size, s2 is the sample variance, and σ2 is the hypothesized population variance.

In this case, the sample size is 26, so n = 26. The sample variance is 0.06, so s2 = 0.06. The hypothesized population variance is 0.003, so σ2 = 0.003. Plugging these values into the formula above gives us [tex]X2 = (26-1) * (0.06/0.003) = 75.[/tex]

Since this value is greater than the critical value of the chi-square distribution at α = 0.05, the null hypothesis can be rejected and it can be concluded that the population variance is significantly more than 0.003.

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The circumstances in which the median is the preferred measure of central tendency is given as follows:

There are three measures of central tendency of a data-set, which are defined as follows:

The median represents the middle value of the distribution, hence it should be used in these following cases:

They should be used in this case as the median is less affected by outliers compared to the mean.

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The 100 percent of the asked number is 5x/4

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given that, 80% of a number is x, we need to find 100% of the number,

Let the number be y,

Therefore,

80% of y = x

y = 5x/4

Therefore, the number is 5x/4

100% of 5x/4 = 5x/4

Hence, the 100 percent of the asked number is 5x/4

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In the diagram, the area of the square c is 2009

The area of the square is solved using the formula

length x length

The lenght is caluclalted using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required dimensions

x² = 35² + 28²

x² = 1225 + 784

x² =  2009

x = √2009

x = 44.82

Area of the square is x² =  2009

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The option which is most appropriate for describing the number line below is option C. [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex]

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

Given a number line, where it is divided into twelfths, with each twelfth labeled.

So the labeled numbers are [tex]\frac{1}{12}[/tex], [tex]\frac{2}{12}[/tex], ..............[tex]\frac{10}{12}[/tex], [tex]\frac{11}{12}[/tex], [tex]\frac{12}{12}[/tex].

A dashed arrow is shown starting at ten-twelfths and ending at, as well as pointing to, seven-twelfths.

Arrow starts at [tex]\frac{10}{12}[/tex] and ends at [tex]\frac{7}{12}[/tex].

There is a distance of [tex]\frac{10}{12}[/tex] - [tex]\frac{7}{12}[/tex] = [tex]\frac{3}{12}[/tex].

So the first form of expression is [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] in order to get [tex]\frac{7}{12}[/tex].

Then the dashed arrow starts from [tex]\frac{7}{12}[/tex] and ends at [tex]\frac{3}{12}[/tex].

There is a distance of [tex]\frac{7}{12}[/tex] - [tex]\frac{3}{12}[/tex] = [tex]\frac{4}{12}[/tex].

So the second form is [tex]\frac{7}{12}[/tex] - [tex]\frac{4}{12}[/tex] in order to get [tex]\frac{3}{12}[/tex].  

So the complete description of the number line is,

[tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex]

Hence the correct option is [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex].

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Round each number to the nearest whole

Compare the estimated sum to the actual sum

Look at the tenths place to round to the nearest whole number

The estimated answer is close to the actual answer

Two or more expressions with an Equal sign is called as Equation.

The key phrases used are:

Round each number to the nearest whole

Compare the estimated sum to the actual sum

Look at the tenths place to round to the nearest whole number

The estimated answer is close to the actual answer

These phrases are all related to the process of approximating a sum by rounding the addends to the nearest whole number and comparing the resulting estimate to the exact sum.

Hence, Round each number to the nearest whole

Compare the estimated sum to the actual sum

Look at the tenths place to round to the nearest whole number

The estimated answer is close to the actual answer

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The height of the plane to the nearest meter is, 1023. So option A  is correct

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

To find the height of the plane, we can use the following formula:

height = horizontal distance x tanα

Plugging in the given values, we have:

height = 4,812 × tan(12°)

          = 4,812 × 0.21213

          = 1,015.7 meters

Rounding to the nearest meter, the height of the plane is 1,016 meters.

So the answer is 1,016 meters

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The solution to the proportion  4/(x+1) = 3/(x+2) is x = -5 and

The solution to the proportion  x/(x+3) = (x-2)/x is x = 2.

A quadratic polynomial is a polynomial of degree 2, which means that the highest power of the variable in the polynomial is 2. A quadratic polynomial can be expressed in the general form:

a[tex]x^2[/tex] + bx + c

where a, b, and c are constants, and x is the variable.

In this form, coefficient a is the leading coefficient, and it determines the concavity of the quadratic function. If a is positive, the function is concave up, meaning that it opens upward and has a minimum value. If a is negative, the function is concave down, meaning that it opens downward and has a maximum value.

The quadratic polynomial is named as such because it is a polynomial of degree 2, and the term "quad" means "square." The quadratic function is commonly seen in geometry, algebra, and physics, and it has many applications in real-life problems, such as finding the maximum or minimum values of a function, determining the trajectory of a projectile, and modeling certain natural phenomena.

Quadratic polynomials can be solved by various methods, including factoring, completing the square, and using the quadratic formula.

To solve the proportion 4/(x+1) = 3/(x+2), we can cross-multiply to get:

4(x+2) = 3(x+1)

Expanding the brackets gives:

4x + 8 = 3x + 3

Subtracting 3x from both sides gives:

x + 8 = 3

Subtracting 8 from both sides gives:

x = -5

To solve the proportion x/(x+3) = (x-2)/x, we can cross-multiply to get:

[tex]x^2[/tex] - 2x = (x+3)(x-2)

Expanding the brackets gives:

[tex]x^2[/tex]- 2x = [tex]x^2[/tex] + x - 6

Subtracting[tex]x^2[/tex] from both sides gives:

-2x = x - 6

Subtracting x from both sides gives:

-3x = -6

Dividing both sides by -3 gives:

x = 2

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The probability of exactly 90 defective washers is approximately 0.021, and the probability of at least 2 defective items is approximately 0.985.

A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. The probability of exactly 90 defective washers being chosen and the probability of at least 2 defective items being found can be calculated using the hypergeometric distribution formula.

A. The probability of exactly 90 defective washers being chosen can be calculated using the hypergeometric distribution. The probability mass function of the hypergeometric distribution is given by:

P(X = 90) = (400 choose 90) * (1100 choose 110) / (1500 choose 200)

Substituting the given values, we get:

P(X = 90) ≈ 0.021

B. The probability of at least 2 defective items can be calculated as 1 minus the probability of 0 or 1 defective item. The probability of 0 defective items is given by:

P(X = 0) = (1100 choose 200) / (1500 choose 200)

The probability of 1 defective item is given by:

P(X = 1) = (400 choose 1) * (1100 choose 199) / (1500 choose 200)

Substituting these values, we get:

P(X >= 2) = 1 - P(X = 0) - P(X = 1) ≈ 0.985.

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The complete question is:

A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. Two hundred washers are chosen at random (without replacement) and classified as defective or non-defective_ a) What is the probability that exactly 90 defective washers are found? (Do NOT compute out:) b) What is the probability that at least 2 defective items are found?

The transformed function is g ( x ) = ( -1/2 ) | x - 1 | + 2

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented a f ( x )

Now , the value of f ( x ) = | x |

Let the function be plotted on the graph and

when the function is transformed by a reflection on y axis , we get

h ( x ) = - | x |

Let the function be shifted left by 1 unit , we get

h' ( x ) = - | x - 1 |

Now , when the function is transformed by a vertical stretch of ( 1/2 ) units , we get

j ( x ) = - ( 1/2 ) | x - 1 |

Now , when the function is shifted vertically up by 2 units , we get

g ( x ) = ( -1/2 ) | x - 1 | + 2

Hence , the transformed function is g ( x ) = ( -1/2 ) | x - 1 | + 2 and it is plotted

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Answer: 97.5% ( look at the image for the solution )

Step-by-step explanation:

Answer: also too tiny

Step-by-step explanation:

show a closer picture

The probability of being dealt a flush is 0.001980,  probability of being dealt a one pair is 0.422569,  probability of being dealt two pairs is 0.04753.

a) First select a suit: 4 choices

then, we can have to select 5 cards out of 13:  C(13, 5)

required probability: 4*C(13, 5)/C(52, 5)

= 0.001980

b)- We have to select two cards to make a pair: C(4, 2) choices (we have to select 2 from 4 because a suit can't have 2 cards    of  same number, so we are selecting 2 suits from 4),

then select a number for the pair: 13 choices,

now for remaining three cards: each card can be of same suit but number must be different, i.e. 4³*C(12, 3)

required probability: 13*C(4, 2) * C(12, 3) *4³ / C(52, 5)

= 0.422569

c)- First, we have to select two numbers for two pairs: C(13, 2) ,

Select suits for both pairs: C(4, 2) * C(4, 2) ,

For the remaining one card: 11 choices for the number and 4 choices for the suit,

required probability: C(13, 2)*C(4, 2)*C(4, 2)*11*4/C(52, 5)

= 0.04753

Probability means possibility. It's a branch of mathematics that deals with the circumstance of a arbitrary event. The value is expressed from zero to one. Probability has been introduced in Maths to prognosticate how likely events are to be. The meaning of probability is principally the extent to which commodity is likely to be.

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Complete question:

If it is assumed that all (52 5) poker hands are equally likely, what is the probability of being dealt (a) a flush? (A hand is said to be a flush if all 5 cards are of the same suit.)

(b) one pair? (This occurs when the cards have denominations a, a, b, c, d, wherea, b, c, and d are all distinct.)

(c) two pairs? (This occurs when the cards have denominations a, a, b, b, c, wherea, b, andc are all distinct.)

Answer:

37.7 mm

Step-by-step explanation:

Buying 36 bottles for $4 is cheaper than buying 3 bottles for 24.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Target sells 24 bottles for 3$,

Therefore, The unit price of a bottle is $(3/24) = $0.125.

Target also sells 36 bottles for $4,

Therefore, The unit price of a bottle is,

= $(4/36) = $0.11.

So, Buying 36 bottles for $4 is cheaper.

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The expected value of cream-filled donuts the store City Donuts is selling should be 2.

We are aware of In the realm of probability theory, the expected value, commonly referred to as the expected average, is a generalization of the weighted average.

Given, City Donuts recently sold 14 donuts, of which 4 were cream-filled donuts.

So, The probability of cream-filled donuts is = 4/14 = 2/7.

Therefore, The expected number of cream-filled donuts is,

= (2/7)×7.

= 2.

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The answers to each part is given below.

Given is that Greenville Fine Jewelry charges $12 per charm, plus $14 for the bracelet. Hanson Jewelers, in contrast, charges $11 per charm and $21 for the bracelet.

For the Greenville Fine Jewelry, we can write -

A{x} = 14 + 12x

For the Hanson Jewelers, we can write -

B(x) = 21 + 11x

To add a certain number of charms to her bracelet, the cost will not be same.

Therefore, the answers to each part is given above.

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There are 6, 8, 10 are yellow pencils.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single one.

Unitary method is a technique so that we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. This is the method that we use for most of the calculations in math.

We are given that if there are 5, 7, 9, 11, or 13 blue ones.

Then the rest could be the yellow pencils.

Which are as follows;

6, 8, 10

These could be the yellow pencils are there, if there are 5, 7, 9, 11, or 13 blue ones

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The complete question is;

There are total number of 8 pencils. How many yellow pencils are there if there are 5, 7, 9, 11, or 13 blue ones

The required minimal sample size would be 26. This is because in order to estimate the mean score with a margin of error of 10 and a confidence level of 90%, the sample size must be large enough for the Central Limit Theorem to apply.  Therefore, in this case, the sample size would be (1.96*100)/10 = 19.6, which is approximately 26.

1. Calculate the sample size, n: n = (1.96*σ)/m

2. Plug in the values: n = (1.96*100)/10

3. Calculate: n = 19.6

4. Round up: n = 26

The required minimal sample size of 26 is necessary in order to estimate the mean SAT score for a population of students with a 90% confidence interval and a margin of error of 10. This is because, in order for the Central Limit Theorem to apply, the sample size must be large enough. The formula for the sample size is (1.96*σ)/m, where σ is the population standard deviation and m is the margin of error. Plugging in the values, we get (1.96*100)/10, which is approximately 19.6. Therefore, the required minimal sample size is 26. This sample size is necessary in order to make sure that the estimates have a high degree of accuracy and reliability.

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Answer: thanks for 14 points

Step-by-step explanation:lol

If a certain affects virus 0.2% of the population:

a. The probability that a person has the virus given that they have tested positive is  1.7%.

b. The probability that a person does not have the virus given that they test negative is 99.8%.

a) Using Bayes' theorem, we can find the probability that a person has the virus given that they have tested positive:

P(Infected | Positive Test) = P(Positive Test | Infected) * P(Infected) / P(Positive Test)

where P(Positive Test) is the probability of a positive test result, regardless of whether the person is infected or not. This can be calculated as:

P(Positive Test) = P(Positive Test | Infected) * P(Infected) + P(Positive Test | Not Infected) * P(Not Infected)

= 0.88 * 0.002 + 0.1 * 0.998

= 0.10064

Now we can plug in the given values:

P(Infected | Positive Test) = 0.88 * 0.002 / 0.10064 ≈ 0.0174

So the probability that a person has the virus given that they have tested positive is approximately 1.7%.

b) Similarly, we can use Bayes' theorem to find the probability that a person does not have the virus given that they test negative:

P(Not Infected | Negative Test) = P(Negative Test | Not Infected) * P(Not Infected) / P(Negative Test)

where P(Negative Test) is the probability of a negative test result, regardless of whether the person is infected or not. This can be calculated as:

P(Negative Test) = P(Negative Test | Infected) * P(Infected) + P(Negative Test | Not Infected) * P(Not Infected)

= 0.12 * 0.002 + 0.998 * 0.998

= 0.99796

Now we can plug in the given values:

P(Not Infected | Negative Test) = 0.998 * 0.99796 / 0.998 = 0.99796

So the probability that a person does not have the virus given that they test negative is approximately 99.8%.

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Answer:

the number is 14.

Step-by-step explanation:

Let's start by using algebra to solve the problem.

We can translate the given information into an equation:

5x + 2 = 72

where x is the unknown number.

To solve for x, we need to isolate it on one side of the equation. We can do this by first subtracting 2 from both sides:

5x = 70

Then, we can divide both sides by 5:

x = 14

Therefore, the number is 14.

The similar doll's quilt has a width of (1/4) yards.

Two or more than two shapes are said to be similar if they have equal corresponding measures of angles and the ratio of corresponding sides should be the same.

Given, The daughter's quilt has a length of 2 yards and a width of 1 yard

and the other similar quilt ahs a length of (1/2) yards.

Now, (1/2)/(2) = 1/4.

Therefore, The width of a similar quilt is (1/4)×1 = 1/4 yards.

Q. A woman sews similar quilts for her daughter's doll. If the daughter's quilt has a length of 2 yards and a width of 1 yard, and the doll's quilt has a length of 1/2 yard, what is the width of the doll's quilt?

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The sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.

Population sampling is the process of selecting a representative sample from a larger population for the purpose of making statistical inferences about the population.

a. The sampling distribution for samples of 25 customer receipts for a supermarket for a year would likely be approximately normally distributed. This assumes that the receipts are randomly selected from the entire population of receipts and that the population distribution of receipts is roughly normal.

The central limit theorem suggests that for a sufficiently large sample size (usually at least 30), the sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.

b. The sampling distribution for samples of 25 insurance payouts in a particular geographical area in a year would likely be positively skewed, assuming that most payouts are relatively small and a few are very large. The central limit theorem may still apply, but the distribution of the sample means would not be exactly normal.

c. The sampling distribution for samples of 25 call centre logs of inbound calls tracking handling time for a credit card company during the year would likely be approximately normally distributed. This assumes that the call centre logs are randomly selected from the entire population of logs and that the population distribution of handling times is roughly normal.

The central limit theorem suggests that for a sufficiently large sample size (usually at least 30), the sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.

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The coordinates of R′ for the dilation centered at P with scale factor 0.5 is (2, 2.5).

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

Given:

Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.

The coordinate of the R' after the dilation is (-1,-0.5)

Given:

The points of PQRS are Q(-3,2), R(1,2), P(-3,-3), S(1,-3).

The given points are dilated. This dilation can be measured by subtracting the point P from each point . Thus the point of Q is,

Q' = Q- P

Q' = (-3 -(-3), 2- (-3))

Q' = (0, 5)

Similarly for R' = R- P

R' = (1 -(-3), 2- (-3))

R' = (4, 5)

and, after dilation by scale factor 0.5 then

R" = 0.5 x (4, 5)

R" = (2, 2.5)

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The probabilities of winning are 1/6 and 2/9

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

Devices = Number cube and spinner

Using the above as a guide, we have the following sample space:

S = {(1, Red), (2, Red), (3, Red), (4, Red), (5, Red), (6, Red), (1, Yellow), (2, Yellow), (3, Yellow), (4, Yellow), (5, Yellow), (6, Yellow), , (1, Blue), (2, Blue), (3, Blue), (4, Blue), (5, Blue), (6, Blue)}

For Zeke, we have: Factor of 2 and Red

From the sample space, we have

P(Zeke) = 3/18

P(Zeke) = 1/6

For Erin, we have: 5 or 6 and Yellow or Blue

From the sample space, we have

P(Erin) = 4/18

P(Erin) = 2/9

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The given relationship is a function, as of the given condition it consists of 3 sub-functions,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,

Let's assume that, 3-time intervals

1 . 0 to 5

2. 5 to 7  

3. 7 to 10

So for intervals, we have 3 different equation of functions which represents the distance traveled by Camilla in time t.

Thus,  the given relationship is a function, as of the given condition it consists of 3 sub-functions.

When she increased her pace, she principally made up for lost time standing at the position. assuming that she made it in the same quantum of time if she did not stop, you can assume that she didn't waste presently time because she picked up the pace.

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