If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?

Pythagoras property geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Example :

\( \red{ \star} \: h^2 = b^2 + p^2\)

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

It is a rhombus kind of quadrilateral.

What is quadrilateral?

A quadrilateral has four sides, is two-dimensional (flat), closed (the lines join up), and has straight sides.

A rhombus is a four-sided quadrilateral with all of the features of a parallelogram.

A rhombus has three more characteristics: consecutive sides that are congruent; diagonals that bisect pairs of opposite angles; and diagonals that are perpendicular to one another.

Moving clockwise, beginning at point A in the top left corner of a hypothetical rhombus ABCD, you can see that side AB is congruent to side BC and side CD is congruent to side DA.

Additionally, you can see that diagonals AC and DB are perpendicular to one another and that the rhombus' diagonals split pairs of opposing angles.

Hence, It is a rhombus kind of quadrilateral.

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Answer: There is a two-digit number . whose units digit is . six less than the tens digit. Four times the tens digit . plus five times the units digit equal

51. x - 6 = y

. 4x + 5y = 51.

4x - 4y = 24.

9y = 27. y = 3, x = 9.

The number is 93.

Step-by-step explanation: pls mark brainliest

Answer:

The probability of spinning a 5 or less is 1/8 or, you can say ⅛

Really Hope I helped! ♡♡♤♤♧♧

The probability of spinning a natural number and a number less than 5 would be 2/3.

The probability exists the branch of mathematics involving numerical descriptions of how likely an event is to happen, or how likely it exists that a proposition is true. The probability of an event exists in a number between 0 and 1, where, roughly speaking, 0 demonstrates the impossibility of the event and 1 demonstrates certainty.

No of total outcomes =6

No of favorable outcomes=4 {1,2,3,4}

Therefore,  Probability of getting a number less than 5 is= 4/6 = 2/3.

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Answer:

see below

Step-by-step explanation:

a) set the two equations equal to each other and isolate the variable

3x+8 = 7x-24

3x+32=7x

32=4x

x=8

b) Plug in the value of x we got into the equation

7(8)-24 = 56

56-24=32

c) Angle k and h are both 72 (add 20 and 502 together) so h+k=144

J and m are going to have the same measurement so we can set up and equation, we also know all angles must add up to 360

144+2x=360

2x=216

x=108

HMK=108

Answer:

3

Step-by-step explanation:

the and is no 3 hope l could help

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

Ashley read 27 books and her brother read 6 books.

Step-by-step explanation:

Let the number of books her brother read be x.

No. of books her brother reads = x

No. of books Ashley reads = 4x + 3

No. of books her brother reads + No. of books Ashley reads = 33

x + 4x + 3 = 33

Evaluate.

5x + 3 = 33

Isolate 5x.

5x = 33-3

    = 30

Find x.

x = 30 ÷ 5

x = 6

Amount of books her brother reads = 6

Amount of books Ashley reads = 4(6) + 3

                                                    = 24 + 3

                                                    = 27

There is also a marginal distribution of Y .The marginal p.m.f. is symbolized fY and is calculated by summing over all the possible values of X : fY(y)def=P(Y=y)=∑xf(x,y).

Now, According to the question:

If X and Y are discrete random variables and f (x,y) is the value of

their joint probability distribution at (x,y), the functions given by:

g(x) = Σy f (x,y) and h(y) = Σx f (x,y) are the marginal distributions of X and Y , respectively (Σ = summation notation).

A marginal distribution is a distribution of values for one variable that ignores a more extensive set of related variables in a dataset.

A marginal distribution is the percentages out of totals, and conditional distribution is the percentages out of some column. UPD: Marginal distribution is the probability distribution of the sums of rows or columns expressed as percentages out of grand total.

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According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

p=1 foot

b=1 foot

\(h^{2} = p ^{2} + b ^{2}\)

\(h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\\)

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9514 1404 393

Answer:

  1. f^-1(x) = 4/(x+2) -2

  2. f^-1(x) = (-(x+3)/2)^(1/5)

Step-by-step explanation:

1. As with all "inverse function" problems, solve for y:

  x = f(y)

  x +2 = 4/(y +2) . . . . add 2

  y +2 = 4/(x +2) . . . . . multiply by (y+2)/(x+2)

  y = 4/(x+2) -2 . . . . . subtract 2

We see that this function is its own inverse. The attached graph shows it is symmetrical about the line y=x.

  f^-1(x) = 4/(x+2) -2

__

2. x = f(y)

  x +3 = -2y^5 . . . . add 3

  -(x +3)/2 = y^5 . . . . . divide by 2

  (-(x +3)/2)^(1/5) = y . . . . take the 5th root

  f^-1(x) = (-(x +3)/2)^(1/5)

In typeset form, that is ...

  \(\displaystyle f^{-1}(x)=\sqrt[5]{\frac{-(x+3)}{2}}\\\\\text{or}\\\\f^{-1}(x)=-\frac{1}{2}\sqrt[5]{16x +48}\)

This last version is with the denominator "rationalized" and the contents of the radical "simplified." It may be a preferred form.

_____

The graphs show the function and inverse are symmetrical about the line y=x, as they should be.

Answer:

  (a)  1024 ways

  (b)  243 ways

Step-by-step explanation:

When answers are independent, the total number of ways all questions can be answered is the product of the number of ways each question can be answered.

__

The first question can have one answer 4 ways. The second question can be answered 4 ways for each of the ways the first question was answered. That is, the two questions can be answered 4×4 = 16 ways. Similarly, each additional question multiplies the number of ways the questions can be answered by 4.

The 5 questions can be answered 4×4×4×4×4 = 4^5 = 1024 ways.

__

There are 3 ways to answer the first question incorrectly. Each additional question can be answered incorrectly 3 ways for each of the ways previous questions were answered. The total number of ways all questions can be answered incorrectly is ...

  3^5 = 243

A student can answer all questions wrong in 243 different ways.

Please Mark my answer brilliant

Answer:

1

Step-by-step explanation:

We need to points

(-1,0) and (0,1)

The slope is found by

m= (y2-y1)/(x2-x1)

m = (1-0)/(0- -1)

   = (1-0)/(0+1)

   = 1/1

The slope is 1

Answer:

1

Step-by-step explanation:

The slope is rise/run and can be found by counting how many units up and over you must go from one point on the line to another.

Therefore the answer is

1

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

Answer:

Step-by-step explanation:

The length of material needed for the border is the perimeter of the backyard play area

How to calculate the length of material needed

The area of the play area is given as:

The area of a trapezoid is calculated using:

Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.

The given parameter is not enough to solve the length of material needed.

So, we make use of the following assumed values.

Assume that the parallel sides are: 25 feet and 31 feet long, respectively.

While the other sides are 10.2 feet and 8.2 feet

The length of material needed would be the sum of the above lengths.

So, we have:

Using the assumed values, the length of material needed for the border is 74.4 feet

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

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The Distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.

The distance between two points in a coordinate plane. The distance formula is based on the Pythagorean theorem and calculates the straight-line distance between two points.

The coordinates of the first point as (x1, y1) = (4, -2) and the coordinates of the second point as (x2, y2) = (7, -9).

The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values:

d = sqrt((7 - 4)^2 + (-9 - (-2))^2)

d = sqrt((3)^2 + (-7)^2)

d = sqrt(9 + 49)

d = sqrt(58)

Hence, the distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.

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An example of time-ordered typical sample statistics is shown in the Control chart. It is used to process the Mean bar.

A control chart is a statistical tool for monitoring the effectiveness of a process over time. It has the form of a graph with two additional lines representing the upper control limit and lower control limit. The central line in the graph represents the mean or average of the data.

Control charts are a type of graph used in production control to assess the effectiveness of exceptional production procedures under challenging circumstances. Control charts are actually the tools used in control strategies. These curves were produced using historical data.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator does a nice job of graphing these equations.

__

The very steep slope suggests the graph will need somewhat different vertical and horizontal scales in order to show anything useful.

Answer:

A1 7% = $400 & A2 8% = $16,600

Step-by-step explanation:

A1 * 7% + A2 * 8% = 1356

A1 + A2 = 17000

A1 = 17000 - A2

(17000 - A2) * 0.07 + A2 * 0.08 = 1356

1190 - 0.07 A2 + 0.08 A2 = 1356

1190 + 0.01 A2 = 1356

0.01 A2 = 166

A2 = 16600

A1 = 17000 - A2

A1 = 17000 - 16600

A1 = 400

Answer:

Step-by-step explanation:

Yesenia's solution is as followed.

                   Step                                  Justification

1). -4(3x - 1) = 12 - 4x                     1). Original equation

2). 3x - 1 = -3 + x                          2). Distributive property

3). 3x + 2 = x                                3). Addition Property of equality

4). 2 = -2x                                     4). Subtraction property of equality

5). -1 = x                                        5). Division property of equality