The sum of two numbers is twenty-five. Using x to represent the smaller of the two numbers, translate "the difference between four more than the larger number and twice the smaller number" into a variable expression. Then simplify.

The z-score for the given values is - 0280, -1.08, 0.49, 0.147 respectively.

The z-score of a data point defines this precise distance in terms of standard deviations above or below the mean.

This formula is used to determine a z-score:

mean standard deviation for each data point

Means of the data points with a standard deviation of z

Below is the same equation in symbol form:

z= x−μ / σ

Here are some noteworthy z-score details:

When the z-score is high, the data point is.

A negative z-score indicates that a data point is below average.

If the z-score is close to 0.00, the data point is thought to be around average.

For the given data set,

14 9 19 18 5 8

Mean of the data =sum of observations / no. of observations =  73/6 = 12.16

Mean of the data is 12.16

Standard deviation = √∑(x - μ)² / n-1

= ​5.70

a) The z- score of 12 is

z=  x−μ / σ

z = 12 - 12.16 / 5.70

z = - 0280

b) x = 6,

z = 6 - 12.16/5.70

z = -1.08

c) x = 15

z = 15 - 12.16/5.70

z = 0.49

d) x = 13

z = 13 - 12.16 / 5.70

z = 0.147

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Answer:

Mean = 243.625

Median = 275.5

Mode = 284

Each value is exact without any rounding.

=================================================

Original data set:

$155 $267 $284 $194 $299 $284 $287 $179

Let's remove the dollar signs, and separate each item with a comma:

155,267,284,194,299,284,287,179

Then sort the values from lowest to highest.

155,179,194,267,284,284,287,299

---------------------

To find the mean, we add up the values and divide by n = 8 since there are 8 items in the list.

(155+179+194+267+284+284+287+299)/8 = 243.625 is the mean

----------------------

Refer to the sorted data set.

The median is the middle-most value. Because the sample size n = 8 is even, we'll have two values tied for the middle.

n/2 = 8/2 = 4

The items in slot 4 and 5 are tied for the middle.

The values in slot 4 and 5 are 267 and 284 in that exact order.

Compute the midpoint: (267+284)/2 = 275.5 is the median

----------------------

The mode is the most frequent value. Look through the sorted data set to see that 284 shows up twice. This is the most frequent compared to the other values (that show up only once).

Therefore, the mode is 284

Side note: It's possible to have multiple modes. It's also possible to not have any modes at all.

The equation of the line that is parallel to x + y = 4 and passes through (2, 3) is expressed as: y = -x + 5.

Two lines are parallel if and only if their slopes are equal. The equation of the line x + y = 4 is in slope-intercept form (y = mx + b), where m is the slope. The slope of this line is m = -1, as the coefficient of x is -1.

An equation of a line that is parallel to the line x + y = 4 and passes through the point (2, 3) can be written in the form y = mx + b, where m = -1.

Substituting the point (2,3) and the slope -1 into the point-slope form of a line gives:

y - 3 = -1(x - 2)

Expanding the right hand side gives:

y - 3 = -x + 2

And rearranging the equation gives the final form of the equation of the line:

y = -x + 5

So, the equation of the line that passes through the point (2, 3) and is parallel to the line x + y = 4 is y = -x + 5.

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Applying the linear pair definition, m<KGH = 60°.

In geometry, a linear pair is a pair of adjacent angles that are supplementary, meaning that their measures add up to 180 degrees. The two angles must be adjacent, meaning that they share a common side or vertex, and they must be linear, meaning that they are formed by two intersecting lines.

Therefore:

m<FGK + m<KGH = 180

Substitute

120 + m<KGH = 180

m<KGH = 180 - 120

m<KGH = 60°

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If two friends shop for fresh fruit. Jaxson buys a watermelon for $8.25 and 3 pounds of cherries. The expression to represent how much more Jaxson spent is :5.1 +p.

P = price of the cherries per pound

Price of cherries bought by Jaxson= $3p

Total amount spent by Jaxson =  $8.25 + $ 3p

Price of cherries bought by Tim = $2p

Total amount spent by Tim = $3.15 + $ 2p

Now let find how much more Jaxson spent.

8.25 + 3p - 3.15 + 2p

5.1 + 3p - 2p

Combine like terms

5.1 +1p

Multiply by 1

5.1 + p

Therefore the expression to represent how much more Jaxson spent is :5.1 +p.

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Hey there!

If you are solving for x, then your final solutions are [tex]x=\sqrt{-y},-\sqrt{-y}[/tex].

Hope this helps!

Answer:

a)  Domain:  (-∞, 10)

b)  k⁻¹(8) = 6

c)  CBD

d)  Range:  (-∞, 7)

e)  k⁻¹(0) = 4

f)  x = -5

Step-by-step explanation:

The domain of the inverse of a function is the same as the range of the original function.  

Therefore, the domain of the inverse function is:

The inverse of a function is its reflection in the line y = x.

Therefore, given that function k(6) = 8 then:

The inverse of a function is its reflection in the line y = x.

We cannot find k⁻¹(-9) since we have not been given the value of x when k(x) = -9.

The range of the inverse of a function is the same as the domain of the original function.  

Therefore, the range of the inverse function is:

The inverse of a function is its reflection in the line y = x.

Therefore, given that function k(4) = 0 then:

The zero of the inverse function is the y-intercept of the original function.  Therefore, given that k(0) = -5 then:

Therefore, x = -5 is a zero of k⁻¹(x).

The measure of the angle represented by the expression (7x+12) is 61°.

The measure of the angle represented by the expression (7x+12) is determined as follows:

The same-side interior angles are supplementary and their sum is 180°.

7x + 12 and 17x are same-side interior angles and are, therefore, supplementary.

7x + 12 + 17x = 180°

solving for x by summing similar terms:

24x + 12 = 180

24x = 168

Dividing both sides by 24

x = 7

Therefore,

7x + 12 = 7 * 7 + 12

7x + 12 = 61°

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The temperature of city A is 4°C.

The temperature of city B is 4°C.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4= 6 is an equation.

We have,

5x = 8 + 3y  ______(1)

x − 2y = −4 _______(2)

Where x is the temperature of city A and y is the temperature of city B.

Now,

From (2),

x = -4 + 2y

Substitution in (1).

5 (-4 + 2y) = 8 + 3y

-20 + 10y = 8 + 3y

-20 - 8 = 3y - 10y

-28 = -7y

y = 4

Now,

x = -4 + 2y

x= -4 + 2 x 4

x = -4 + 8

x = 4

Thus,

The temperature of both city A and city B is 4°C.

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The first diagram of the triangle DEF correctly represents the transformation.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The preimage of the triangle is ABC and the image is DEF.

Therefore, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F>

A 90° rotation counterclockwise will rotate the vertex C one-quarter left of a complete circle.

Therefore, The first triangle represents the correct transformation.

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The probability  that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child  is 12/25 , 1/ 6  respectively.

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes  and number of total outcomes.

Given in the table ,

Probability that a randomly chosen person is a child

= 48 / 100

= 12/25

Probability that a randomly chosen person prefers running and is a child

= 6/48

= 1/8

Probability that a person prefers running given that the person is a child

= 6/48

=1/8

Therefore, The probability  that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child  is 12/25 , 1/ 6  respectively.

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Answer:

A

Step-by-step explanation:

Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].

The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].

When 62.5 pairs of jeans are sold, the price is $112.50.

Based on the information, the store should discount $112.50 from the price to maximize its revenue.

To calculate the amount of discount that the store must make to maximize its profits we must perform the following mathematical operation:

First we have to analyze the available data which are:

According to the above information, the problem could be answered with the following mathematical formula:

(175 - x)(40 + 0.8x)

x = 175

x = -50

x = 62.50.

According to the above, the correct answer is $112.50 (option A).

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The measure of other two angles in the given quadrilateral are 10° and 25°.

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

Given that, two angles of a quadrilateral measure 130° and 195°.

The other two angles are in a ratio of 2:5.

So, the other two angles are 2x and 5x

Now, 130°+195°+2x+5x=360°

325°+7x=360°

7x=360°-325°

7x=35°

x=5

So, 2x=10° and 5x=25°

Therefore, the measure of other two angles in the given quadrilateral are 10° and 25°.

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Based on the steps for solving the equation, a true statement include the following: A. there are infinitely many solutions to the equation.

In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal:

3x - 9x + 1 = 2(-3x + 1) - 1

-6x + 1 = -6x + 2 - 1

-6x + 1 = -6x + 1

When x = 1, we have:

-6(1) + 1 = -6(1) + 1

-5 = -5.

When x = 2, we have:

-6(2) + 1 = -6(2) + 1

-11 = -11.

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The value of tan 30 degrees is √3 / 3

We are to solve this problem using SOH CAH TOA

We are to find the tangent of Y

Tan (Y)  = opposite / adjacent

the value of y is 30 degrees

In this question, we can name opposite and adjacent as a and b respectively. No value is given for both

To get the value of a , we have to use sine

sin (y) = opposite / hypotenuse

sin 30 = opposite / 4

4 * 0.5 = opposite

opposite = 2

Cosine Y = opposite / hypotenuse

cos 30 = adjacent / 4

4 * 0.8660 = adjacent

3.464 or 2√3 = adjacent

Then tan 30 = opp / adj

tan 30 = 2 / 3.464

tan 30 = 0.5773

or tan 30 = √3 / 3

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The answer is x4 – 6x2 – 27 = 0 and this is a quadratic equation in the polynomials .

This is a quartic equation because the highest degree is 4

In the second option, we have 3x⁴ = 2x, this is also another quartic equation.

In the third equation, we have 2(x + 5)⁴ + 2x² + 5 = 0, this is a quartic equation because the highest degree is 4

In the fourth equation, 6(2x + 4)² = (2x + 4) + 2

This is a quadratic equation because the highest degree is 2

In the fifth equation, we have 6x⁴ = -x² + 5 which is also another quartic equation

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x2 (a 0) for an equation to be a quadratic equation. The x2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are typically expressed as integral values rather than fractions or decimals.

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Span(u,v) is the set of all linear combinations of u and v, including scalar multiples of both. It does not include the origin.

Span(u,v) is the set of all linear combinations of u and v, meaning any combination of u and v multiplied by scalars. This includes scalar multiples of both u and v, but does not include the origin. To calculate Span(u,v), first write u and v as vectors u = (u1,u2,...,un) and v = (v1,v2,...,vn). Then, any linear combination of u and v can be written as c1u + c2v, where c1 and c2 are scalars, and the set of all such linear combinations is Span(u,v). For example, if u = (1,2) and v = (3,4), then Span(u,v) = {(1,2), (3,4), (4,6), (5,8), (7,10), ...}. In other words, Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v.

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The numeric value of the greatest sum that can be obtained by Greg is given as follows:

1173.

When two n digit numbers are added, the numbers in the equivalent positions are added with each other, that is, starting from the end of the number to the begining.

For example, 21 + 32:

Hence the sum is of 54.

Hence the greatest sum would be obtained as follows:

Hence the sum would be given as follows:

642 + 531 = 1173.

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Because the ratios between each set of numbers are equal, and the graph passes through the point, the linear relationship is proportionate (0,0).

Proportional connections are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportional relationship. The "constant of proportionality" is the name given to this variable.

The origin, points (2,14.5), (4,29), and (6,43.5) are provided (0,0).

We are aware that the ratios are equivalent in a proportional connection, i.e.

So,

⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25

The linear relationship is a proportionate relationship since the ratios are equal.

The given situation's graph has been drawn, and it is evident that the graph passes through its origin, or "zero," which is (0,0)

Since the ratios between each set of data are equal, the linear relationship can only be a proportional relationship because the graph passes through the point (0,0).

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Answer: 1,200. None of the above.

Step-by-step explanation:

200 revolutions per minute times 60 feet. 1,200

Answer:

(pr²)

given,

p=3 r=3

(3 X 3²)

(3 X 9)

27

The graph that represents an exponential decay function is the second graph.

For you to determine which of the graphs represents an exponential decay, we will need to check the curve that passes through or lies on the x-axis.

we can draw a graph by putting the value of x and we are getting the value of y in this way we get the coordinates of a point

From both figures, we can see that the curve of the second graph almost lies on the x-axis as it curves downwards. This makes it an exponential decay function.

Hence the graph that represents an exponential decay function is the second graph.

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complete question is

Which description matches the function represented by this graph?

A. exponential growth

B. linear growth

C. linear decay

D. exponential decay

Answer:

B or 2

Step-by-step explanation:

The answer above is correct.

The frequency table is added below

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

7 9 6 8 7 6 8 6 9 5 7 7

6 8 9 8 8 6 4 8

When represented on a frequency table, we have

Class limits Class boundaries Frequency

2.5 - 3.5            3.0 - 4.0         0

3.5 - 4.5            4.0 - 5.0              1

4.5 - 5.5             5.0 - 6.0            1

5.5 - 6.5             6.0 - 7.0       5

6.5 - 7.5              7.0 - 8.0          4

7.5 - 8.5              8.0 - 9.0           6

8.5 - 9.5             9.0 - 10.0            3

Total        20

The class boundary is calculated as

class boundary = Class limits ± 0.5

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Approximation of decimals is a mathematical technique for finding or measuring approximations and minimizing the number of decimal places.

A fractional representation of a real number that comes close to representing it. Any real number a can be represented by an endless number of decimal fractions.

The number of decimal places in a decimal number is the number of digits following the decimal point. A mathematical method for locating or measuring approximations and reducing the number of decimal places is known as approximation of decimals.

Any comparison that is close but not accurate to another entity is called an approximation. By rounding, one can get a good idea of a number. By rounding the values in a computation before performing the operations, a calculation can be approximated.

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Length of malcom's story is 418lines, the operation used to solve this problem is; lines of zac story+ extra lines of malcom story.

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

Given;

Number of lines in zac story=273

Number of lines in malcom story= 273+145

Now.

Total number of lines in malcom story

=273+145

=418

Therefore, the answer after simplification will be 418

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The equation of the exponential function is y = 0.2⋅2^x

The steps for this process are as follows:

Step 1: Set up the equation.

The equation of an exponential function has the form y = a⋅b^x

where a and b are constants and b is greater than 0 and not equal to 1.

Step 2: Find the constants.

We can use the given points to find the constants in the equation. For example, when x = 0, y = 0.2.

So we can set 0.2 = a⋅b^0.

This means that a = 0.2 and b^0 = 1,

so b = 1.

Step 3: Write the equation.

Substituting a = 0.2 and b = 1 into the equation gives us y = 0.2⋅2^x.

This is the equation of the exponential function represented by the table.

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