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We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -

[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]

Given is the inequality -

3 (m + n)! ≥ m! + n!

We have -

3 (m + n)!

3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}

3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)

3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)

Now, for (m! + n!) --

(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

It can be seen that -

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥

m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

Hence, it can be seen that -

3 (m + n)! ≥ m! + n!

Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.

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Answer:

Since the apparent height h of the tower varies inversely with Corin's distance d from the tower, we know that h and d are inversely proportional. This means that the product of h and d is constant. We can write this relationship as:

hd = k

where k is a constant.

We can find the value of k by substituting the known values of h and d:

9 inches * 800 feet = k

Solving for k, we find that k = 7200 inches * feet.

Since h and d are inversely proportional, we can write the inverse relationship as:

d = k / h

Substituting the value of k that we found earlier, we have:

d = 7200 inches * feet / h

To find the apparent height of the tower if Corin is standing 2000 feet away, we can substitute 2000 for d in the equation above:

h = 7200 inches * feet / 2000 feet = 3.6 inches

Therefore, the apparent height of the tower would be 3.6 inches if Corin is standing 2000 feet away.

Step-by-step explanation:

I'm assuming x and y intercepts which would be (2.5,0) and (0,10)

Answer:

Step-by-step explanation:

34x60

60 minutes in a hour

34x60=204

204+204= 408

408 copies in 2 hours

Answer:

4080

Step-by-step explanation:

First you would multiply 34 by 120. After you multiply those numbers you should get 4080 as your answer.

Answer:

20.25

Step-by-step explanation:

6.75 times by 3 is 20.25

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

Slope "m"

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~

( 4 , - 7 )

m = [tex]-\frac{1}{2}[/tex]

y - ( - 7 ) = [tex]-\frac{1}{2}[/tex] ( x - 4 )

y + 7 = [tex]-\frac{1}{2}[/tex] ( x - 4 )

Answer:

From left to right picture,

Scale factor = 2/3

x = 24

y = 12

z = 21

Step-by-step explanation:

Look at the two figures and identify the sides where both lengths are known.

That is the top right-hand side.

Scale factor is hence 18/27 = 2/3

Next, find x, y and z:

Bottom left-hand side:   16/x = 2/3

                                            x = 3/2 x 16

                                             x = 24

Bottom right-hand side:    y/18 = 2/3

                                            y = 18 x 2/3

                                             y = 12

Top left-hand side:       14/z = 2/3

                                           z = 3/2 x 14

                                            z = 21

the equation in the form of slope interpretation is y = 1/3x -4.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation has the conventional form y = mx + c.

Given data in a table such as it makes a linear equation slope-intercept form of the given equation is y = mx +c

Where m is the slope

c is constant

The slope for the given data

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 + 6 )/ (-3 + 6)

m = 1/3

Hence, the equation would be

y = 1/3x + c

for constant we would satisfy the equation with other coordinates of the line.

Substituting ( 0, -4) in the above equation

-4 = 0 + c

c = -4

thus, the equation of the line is  y = 1/3x  -4

therefore, the linear equation of the given data is y = 1/3x -4.

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Work Shown:

75+54m

75+54*10

75+540

615

The value of hydronium ion concentration in the vinegar is 3.162×10^-3 (optionD)

pH is defined as the negative log of the hydrogen ion concentration. The range of pH extends from zero to 14. A pH value of 7 is neutral, because pure water has a pH value of exactly 7.

pH can also be defined as the measure of acidity and alkalinity of a substance.

pH = –log(H+)

Therefore (H+) = 10^-(pH)

For a pH of 2.5, the hydronium ion concentration

= 10^-2.5

(H+) = 0.003162 = 3.162×10^-3

Therefore hydronium ion concentration of the vinegar is 3.162×10^-3

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22/7×14×14×12

the answer is 7392

Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.

We suppose a general triangle, for which:

The lengths and the sine of the angles are proportionally related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The segments in this problem are given as follows:

Hence it can be affirmed that:

BC > AB.

As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.

As for segment AC, we need the measure of angle B, hence nothing can be affirmed.

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Answer:

A 0.9102

Step-by-step explanation:

A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.

The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.

A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.

A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.

Hence, the correlation coefficient is A, 0.9102

The value of x and y in equations 17x - y = 40 and 2x + 4y = 50 are x = 3 and y = 11.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

17x - y = 40  ⇒ (1)

2x + 4y = 50 ⇒ (2)

(1)* 4

68x - 4y = 160

Adding equation (1) and (2)

68x - 4y = 160

2x + 4y = 50

⇒ 70 x = 210

        x = 3

Substituting the value of x in equation (1)

17*3 - y = 40

51 - y = 40

-y = 40 - 51

-y = -11

y = 11

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We will solve the expression:

(3 + 5)*5 - 20*(2 + 5)

Step by step, and we will get the solution -100.

Here we want to solve the following expression:

(3 + 5)*5 - 20*(2 + 5)

The first thing that you need to solve when working in these type of problems, are the operations inside the parenthesis, then we will get:

(3 + 5)*5 - 20*(2 + 5) = (8)*5 - 20*(7)

Now we need to solve the two products, we will get:

(8)*5 - 20*(7) = 40 - 140 = -100

Thus, the solution of that expression is -100.

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Answer:

Step-by-step explanation:

One side of a square field is 92m. Find the cost of raising lawn on the field at the rate of 1.50 per sq.m

Square area = l²

Square area = 92²

Square area = 8466 m²

Cost = Area × rate of 1.50 per sq.m

Cost = 8466 × 1.50

Cost = 12696

she will be able to knit 13 scarfs

Given ,

To Find : Scarfs Mr John will be able to make if he has 30.42 yards of yarn

2.34 yards of yarn = 1 scarf

30.42 yards of yarn = [tex]\frac{30.42}{2.34}[/tex]

                                 = 13 scarfs

Hence , the number of scarfs Mr John will make with 30.42 yards of yarn is 13

The line that passes through these two points is y=x-2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here function whose graph contains the points (9, 7) and (4, −8)

Thus using the two point formula for a line we get the equation as              y-7=(x-9)

y=x-2

Hence, The line that passes through these two points is y=x-2

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Step-by-step explanation:

{x : x < 100}

means all numbers smaller than 100. but that includes all negative numbers. so, NO.

{y|y > -0.1}

while this includes all positive numbers, it also includes all numbers between -0.1 and 0. e.g. -0.001

so, NO

{x|x in N}

N is the set of all natural numbers. that is the set of all positive integers.

so, YES

{y : 0 < y < 1}

that is all numbers between 0 and 1. that's are only positive numbers between 0 and 1.

so, YES

{x|x in Z}

Z is the set of all integer numbers (including the negative ones). so, NO

{y : 3 <= y < 22}

ask numbers between 3 and 22, including 3. there are only positive numbers, as there cannot be suddenly a negative number between 2 positive numbers.

so, YES.

Answer:

$2

Step-by-step explanation:

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Step-by-step explanation:

Let x = number of ounces of 63% solution.

Let y = number of ounces of 33% solution.

The total solution to be made is 100 oz.

x + y = 100

x ounces of 63% solution is 0.63x ounces of acid.

y ounces of 33% solution is 0.33y ounces of acid.

100 ounces of 39% solution is 39 ounces of acid

0.63x + 0.33y = 39

The system of equations is

x + y = 100

0.63x + 0.33y = 39

Multiply the both sides of the first equation by -0.33. Then add it to the second equation.

         -0.33x - 0.33y = -33

    +    0.63x + 0.33y = 39

   ---------------------------------

             0.3x             = 6

x = 6/0.3

x = 20

x + y = 100

20 + y = 100

y = 80

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

The equation that correctly solves the formula of r is r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

The concept here is the concept of subject of the formula.

The variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own. For instance, the subject of the formula for the area of a rectangle is A = b h (area = base height).

The formula given was A=4πr^2h, then we can r the subject of the formula as

r^2 = A /4π

Then r = [tex]\sqrt{\frac{ A }{4\pi } }[/tex]

Therefore, option B iscorrect.

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missing options:

A) r = 4πA B) r = A 4π C) r = A 4π D) r = A 4π

A percentage of Bashir's commute that would be shorter than 32 minutes, to the nearest 10th is 50%.

Mathematically, the z-score of a given sample size or data set can be calculated by using this formula:

Z-score, z = (x - μ)/σ

Where:

Substituting the parameters into the z-score formula, we have;

Z-score, z = (32 - 32)/3

Z-score, z = 0/3

Z-score, z = 0

Since a commute of 32 minutes on a test has a z-score of 0, the percentage of Bahir's commute that would be shorter than 32 minutes can be calculated as follows:

P(x > 32) = P(z > 0)

P(z > 0) = 0.5

P(z > 0) = 50%.

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Answer:

24 minutes

Step-by-step explanation:

100% = 60 minutes is 100%

So that means that 40% = 24 minutes.

Answer:

1) Let D be the number of dimes and Q be the number of quarters. We can set up the following system of equations to represent the given information:

D + Q = 65

0.1D + 0.25Q = 10.70

The first equation represents the total number of coins Victoria has, and the second equation represents the total value of those coins in dollars. Solving this system of equations will give us the number of dimes and quarters Victoria has.

2) Let M be the number of hours Max spends mowing lawns and T be the number of hours he spends tutoring. We can set up the following system of equations to represent the given information:

M + T = 14

12M + 15T = 192

The first equation represents the total number of hours Max worked over the weekend, and the second equation represents the total amount of money he made during that time. Solving this system of equations will give us the number of hours Max spent on each job.

The geometry object known as a line extends on both sides and is defined as an object with zero width. Any line without curves is said to be straight.

An object with zero width that extends on all sides is referred to as a line in geometry. Simply put, a straight line is an uncurved line. As a result, a straight line is one without any curves that stretches to infinity on both sides.

A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length.

y=mx+c

Definition. Y=mx+c is the formula for a straight line. m is the gradient and c is the height, commonly known as the y-intercept, at where the line crosses the y-axis in the equation y = m x + c.

[tex](b) $\because$ perpendicular makes an angle of $60^{\circ}$ with the line $x+y=0$.$\therefore$ the perpendicular makes an angle of $15^{\circ}$ or $75^{\circ}$ with $x$-axis.[/tex]

[tex]Hence, the equation of line will be $x \cos 75^{\circ}+y \sin 75^{\circ}=4$or $x \cos 15^{\circ}+y \sin 15^{\circ}=4$$(\sqrt{3}-1) x+(\sqrt{3}+1) y=8 \sqrt{2}$or $\quad(\sqrt{3}+1) x+(\sqrt{3}-1) y=8 \sqrt{2}$[/tex]

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Answer: 48 cm

Step-by-step explanation:

12 + 12 + 12 + 12 = 48

(1). ΔIJH ≅ ΔKHJ, by SSS criterion,

and (2) we need,  ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove  ΔTNS ≅ ΔUHS, by HL criterion.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

We have the triangle:

ΔIJH ≅ ΔKHJ.

To prove the congruent by SSS:

We have to show that three sides of the triangle are congruent to three sides of  the other triangle.

Here,

IJ ≅ KH.

IH ≅ JH, Given.

And both triangles share the same side JH.

So,

JH ≅ JH

So, ΔIJH ≅ ΔKHJ, by SSS criterion.

ΔTNS ≅ ΔUHS.

To prove the congruent by HL:

We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.

So, we need;

ΔTNS and ΔUHS are right-triangles.

S is the mid-point.

So,

SN ≅ SH.

ST ≅ US

So, ΔTNS ≅ ΔUHS, by HL criterion.

Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;

ΔTNS and ΔUHS are right-triangles and S is the mid-point.

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