If the sum of 12 numbers is 480 then what is their mean? (a) 20 (b)40 (c) 30 (d)24​

The circumference of one tire is 75.36 inches.

We are given the diameter of tire of bicycle. The formula of circumference is as follows -  

Circumference = 2× π × r, where r is representative of radius of circle.  As we are given the diameter, we will use the formula of circumference with diameter. The formula to be used is as follows -

Circumference = π × d, where d is representative of diameter of circle.

Keep the values in formula to find the value of circumference of one tire. We will be taking the value of π as 3.14.

Circumference = 3.14 × 24

Performing multiplication to find the circumference of one tire.

Circumference = 75.36 inches

Hence, the circumference of one tire of bicycle is 75.36 inches.

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The simplified form of expression is  (2y + 3).

Rewriting the provided mathematical expression first -

5/(y + 3) + 15/(y - 3)

Shifting the second expression on other side of equation -

5/(y + 3) = - 15/(y - 3)

Performing cross multiplication

5 (y - 3) = -15 (y + 3)

5y - 15 = -15y - 45

Rearranging the equation

5y - (-15y) = -45 - (-15)

Performing addition and subtraction

5y + 15y = -45 + 15

20y = -30

Dividing both sides of equation by 10

2y = - 3

Rearranging the equation -

2y + 3

Hence, the simplified form of expression is (2y + 3).

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Two angles that form a linear pair are supplementary:  Always TRUE

Therefore, the statement "two angles that form a linear pair are supplementary" is Always TRUE.

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The angle ∠JKN  is 79°

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. A bisector divides an angle into two equal angles.

∠JKN = (8x - 13)°                     (given)

∠NKL = (6x +11)°                      (given)

∠JKN = ∠NKL                         ( As KN bisects ∠JKL )

8x - 3 = 6x + 11                        ( substituting equations from question )

8x - 6x = 11 + 3                        ( bringing like terms on same side)

2x = 23                                    

x = 23/2

x = 11.5

Now, put value of x in the given equation: ∠JKN = (8x - 13). we get

∠JKN = (8x - 13)

∠JKN = (8*11.5 - 13)

∠JKN  = (92 - 13)

∠JKN  = 79°

Therefore, We can conclude that the angle ∠JKN  is 79°.

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Based on the loan amount of $15,000 and the fair credit score, the amount of interest to be paid on the loan at the end of the first month is $80.

The interest on a credit score that is fair is 6.40%.

That means the annual interest on the loan is:

= 15,000 x 6.40%

= $960

The interest in the first month is:

= Annual interest / number of months in year

= 960 / 12 months

= $80

In conclusion, the interest in the first month is $80.

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The number of ounces gained by the Kitten before it went home with its new owner is; 3 1/8 ounces.

It follows from the task content that the it is required that the weight gained by the kitten in ounces is to be determined.

Since the kitten weighed 5 1/2 ounces on the day it was sold and weighed; 3 3/8 ounces at birth, the number of ounces gained is;

= 5 1/2 - 3 3/8

= 11/2 - 27/8

= (44 - 27)/8

= 17/8

= 2 1/8 ounces.

Ultimately, the weight gained by the kitten, in ounces following evaluation from the task content is; 2 1/8 ounces.

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D = M/12 + N/4 represents the relationship between Elena's distance in miles, D, and her biking speed.

Speed = distance/ time

Here, we are given that Elena bikes 20 minutes each day for exercise. She bikes at a constant speed of M miles per hour for the first 5 minutes, then at N miles per hour for the last 15 minutes.

Therefore, distance covered by her in the first 5 minutes = speed x time

time = 5 minutes = 5/60 hours

= 1/12 hours

Thus, distance = M(1/12)

= M/12

Now, similarly, distance covered by her in the last 15 minutes = N(15/60)

=N/4

Thus, the total distance in miles, D, covered by her in the last 15 minutes = N(15/60)

= N/4

Thus, the total distance in miles, D, covered by her is D = M/12 + N/4

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According to the given statement

The sum of a number x and 7, divided by 15 , is at most is -52

Ax+b = 0, where a and b are two integers, and x is a variable, is an example of a linear equation with one variable. This equation has just one solution. In the linear equation 2x+3=8, for instance, there is just one variable.

The fundamental equation used to express and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown visually. A mathematical statement is simply represented by a linear equation. Unknown quantities can be represented by any variable or symbol, but often, the unknown quantity in a linear equation with one variable is represented by the variable "x." There are a few straightforward procedures for solving linear equations. 

According to the given value;

= (x+7)/3=15

⇒x+7=-45

=>x=-45-7

   x= -52

Therefore your answer is = -52

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The recursive formula for the given sequence: 1,5,14,30, . . . is a(n) = a(n-1) + n². It can also be expressed as a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -a(n-4), with a(1) = 1.

A recursive formula of a sequence tells us how to find the nth term, a(n), from the preceding terms, a(n-1), a(n-2), ....

The sequence is:

    1,5,14,30, . . . .

Here:

a(1) = 1, a(2) = 5, a(3) = 14, and a(4) = 30.

Let us write:

a(1) = 1

a(2) = 1 + 4 = a(1) + 2²

a(3) = 5 + 9 = 5 + 3² = a(2) + 3²

a(4) = 14 + 16 = 14 + 4² = = a(3) + 4²

So we can conclude the recursive formula is:

a(n) = a(n-1) + n²

However, we can find another recursive formula.

We have:

a(n) = a(n-1) + n²   ........ (1)

For n -1 this becomes:

a(n-1) =  a(n-2) + (n-1)²

a(n-1) = a(n-2) + n² - 2n + 1 ........ (2)

Subtract (1) - (2):

a(n) - a(n-1) = a(n-1) + n²  - a(n-2) - n² + 2n - 1

a(n) - a(n-1) = a(n-1) -a(n-2) + 2n - 1

⇒ a(n) = 2a(n-1) -a(n-2) + 2n - 1  ...(3)

Equation (3) applies for any n, therefore for n -1, eq.(30 becomes:

a(n-1) = 2a(n-2) -a(n-3) + 2(n-1) - 1   ....(4)

Subtract Eq.(3) - Eq.(4).

a(n) - a(n-1) =  2a(n-1) -a(n-2) + 2n - 1 - (2a(n-2) -a(n-3) + 2n - 3)

a(n) - a(n-1) = 2a(n-1) - 3a(n-2) + a(n-3) + 2

⇒ a(n) = 3a(n-1) - 3a(n-2) + a(n-3) + 2   ....(5)

Substitute for n-1 again into Eq.(5):

a(n-1) = 3a(n-2) - 3a(n-3) + a(n-4) + 2 .....  (6)

Subtract Eq.(6) - Eq.(5)

a(n) - a(n-1) =  3a(n-1) -3a(n-2) +a(n-3) +2 -3a(n-2) +3a(n-3) -a(n-4) -2

a(n) - a(n-1) =  3a(n-1) -6a(n-2) +4a(n-3) -a(n-4)

⇒ a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -a(n-4)

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7th term of the series = 27.5

Here the series is in arithmetic sequence

Now we have to find the common difference between the series,

common difference (d) = 15- 12.5 = 17.5 - 15 = 2.5

To find the nth term of an arithmetic series we have a formula,

[tex]t_{n}[/tex] = a + (n-1) d

So by this we can find the 7th term of the series

[tex]t_{7}[/tex] = 12.5 + (7-1) 2.5

  = 12.5 + 6 × 2.5

  = 12.5 + 15

 = 27.5

So the 7th term of the series is 27.5

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Answer:

118

Step-by-step explanation:

[tex]10^{2} + 2(6-3)^{2}[/tex]   To start off, we work in the Parenthesis; 6-3 = 3

[tex]10^{2} + 2(3)^{2}[/tex]  Now, we must do the exponents; 10^2 = 100; 3^2 = 9

[tex]100 + 2(9)[/tex]   Next, we have to distribute the 2 to the 9; 2 x 9 = 18

[tex]100 + 18[/tex]  Lastly, we have to add 100 and 18; 100 + 18 = 118

So! Our final answer is 118!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

118

Step-by-step explanation:

m)  [tex]10^{2} + 2(6-3)^{2} = 10^{2} + 2(3)^{2} = 10^{2} + 2(9)= 100 + 18 = 118[/tex]

The area of the parallelogram = 7 × 6 = 42 units².

The area of a parallelogram = base × height.

Given the following:

The length base of the given parallelogram = 7 units

The height of the parallelogram, is the rise of the side = 6 units.

Using the area formula for a parallelogram, we have:

The area of the parallelogram = 7 × 6

The area of the parallelogram = 42 units²

Therefore, the area of the parallelogram = 7 × 6 = 42 units².

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According to the given statement,

The distance between the two points of Traingle A and B is 7.85 m

The area created between two of a triangle's side lengths is known as the angle. Both internal and external angles are present in a triangle. In a triangle, there are three interior angles. When the sides of a triangle are stretched to infinity, exterior angles are created.

Between a triangle's shorter side and its extended side, external angles are created. There is an inside angle next to each outer angle. Angles that share a vertex and side are said to be adjacent.

According to the given value;

Angle B = 60° , Angle A = 50°

In ∆ BCD

tan60° = 30/BC

√3 = 30/BC

BC = 30/√3

BC = 10√3

In ∆ ACD

tan50° = 30/AC

tan50° = 30/(BC+AB)

BC + AB = 30/tan50°

10/√3 + AB = 30/tan50°

AB = 30/tan50° - 10√3

AB = 25.173 - 10√3

AB = 7.85 m

Hence, distance between the two points A and B is 7.85 m.

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The position and label of the given right angle triangle ΔX Y Z whose hypotenuse will be 3.16 b have been plotted.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

Given the right-angle triangle ΔX Y Z

XY = b(base) and XZ = 3b(perpendicular).

By Pythagoras theorem,

Hyp² = Base² + Perp²

Hyp² = b² + (3b)²

Hyp² = 10b²

Hyp = 3.16b

Hence "The position and label of the given right angle triangle ΔX Y Z whose hypotenuse will be 3.16 b have been plotted".

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Answer: MP is 29 units

Step-by-step explanation:

MP=MN+NP

5y+9=17+3y

5y+9-3y=17+3y-3y

2y+9=17

2y+9-9=17-9

2y=8

Divide both parts of the equation by 2:

y=4

Thus:

5*4+9=

20+9=

29 units

There are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.

The permutation is defined as considered an ordered combination.

The general formula for this is:

P(n, r) = n! (n-r)!

Ten runners are racing

There are ten runners who can win first place, hence there are ten ways.

Any of the remaining 9 runners may get up to the second position in nine different ways.

Any of the remaining 8 runners may get up to the third position in eight different ways

Any of the remaining 7 runners may get up to the fourth position in seven different ways

So total number of ways = 10 × 9 × 8 × 7 = 5040

Another way 4 Out of 10 need to select where order matters

= ¹⁰P₄

= 10!/6!

= 10 × 9 × 8 × 7

= 5040

Hence, there are 5040 different ways can the runners finish first, second, third, and fourth place if ten runners are racing.

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The solutions of the quadratic equations are listed below:

In this problem we find quadratic equations of the form a · x² + b · x + c = 0, whose roots can be found analytically by using the quadratic formula:

x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c), a ≠ 0

Now we proceed to solve each quadratic equation:

1) 2 · x² + 7 · x + 6 = 0

x = - 7 / (2 · 2) ± [1 / (2 · 2)] · √(7² - 4 · 2 · 6)

x₁ = - 1.5, x₂ = - 2

2) 5 · b² - 11 · b - 12 = 0

b = 11 / (2 · 5) ± [1 / (2 · 5)] · √[(- 11)² - 4 · 5 · (- 12)]

b₁ = 3, b₂ = - 0.8

3) m² - 7 · m + 2 = 0

m = 7 / (2 · 1) ± [1 / (2 · 1)] · √[(- 7)² - 4 · 1 · 2]

m₁ ≈ 6.702, m₂ ≈ 0.298

4) 2 · h² - 5 · h - 11 = 0

h = 5 / (2 · 2) ± [1 / (2 · 2)] · √[(- 5)² - 4 · 2 · (- 11)]

h₁ ≈ 3.908, h₂ ≈ - 1.408

5) 3 · x² + 2 · x - 8 = 0

x = - 2 / (2 · 3) ± [1 / (2 · 3)] · √[2² - 4 · 3 · (- 8)]

x₁ ≈ 1.333, x₂ = - 2

6) n² - 15 · n + 8 = 0

n = 15 / (2 · 1) ± [1 / (2 · 1)] · √[(- 15)² - 4 · 1 · 8]

n₁ ≈ 14.446, n₂ ≈ 0.554

7) 4 · a² + 9 · a + 1 = 0

a = - 9 / (2 · 4) ± [1 / (2 · 4)] · √(9² - 4 · 4 · 1)

a₁ ≈ - 0.117, a₂ ≈ - 2.133

8) 5 · k² - 2 · k - 18 = 0

k = 2 / (2 · 5) ± [1 / (2 · 5)] · √[(- 2)² - 4 · 5 · (- 18)]

k₁ ≈ 2.108, k₂ ≈ - 1.708

9) 8 · t² + 6 · t - 35 = 0

t = - 6 / (2 · 8) ± [1 / (2 · 8)] · √[6² - 4 · 8 · (- 35)]

t₁ = 1.75, t₂ = - 2.5

10) 3 · y² - 2 · y + 7 = 0

y = 2 / (2 · 3) ± [1 / (2 · 3)] · √[(- 2)² - 4 · 3 · 7]

y₁ ≈ 0.333 + i 1.491, y₂ ≈ 0.333 - i 1.491

11) 2 · q² + q - 14 = 0

q = - 1 / (2 · 2) ± [1 / (2 · 2)] · √[1² - 4 · 2 · (- 14)]

q₁ ≈ 2.408, q₂ ≈ - 2.908

12) 0.5 · x² - 3 · x - 9.4 = 0

x = 3 / (2 · 0.5) ± [1 / (2 · 0.5)] · √[(- 3)² - 4 · 0.5 · (- 9.4)]

x₁ ≈ 8.273, x₂ = - 2.273

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Answer:

29

Step-by-step explanation:

ur in high school bro. Im in 7th grade. Get good bc is gonna get harder

Yes, there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be a = 5,184p.

It should be noted that the information is to simply know if there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be:

= Number of pixels / Screen size

= 31.104 / 6

= 5.184

Therefore, the equation representing the relationship will be a = 5,184p.

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Hence, the number of people are in the Smith family is [tex]23[/tex].

What is the division?

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.

Here given that,

A hotel charges $[tex]80[/tex] for a basic room for one person per night. It charges $[tex]15[/tex] for each additional person per night. The Smith family takes three rooms for three nights. The bill comes to $[tex]1035[/tex].

So,

Rent for the one day is

[tex]\frac{1035}{3}=345[/tex]

Number of people are in the Smith family is

[tex]\frac{345}{15}=23[/tex]

Hence, the number of people are in the Smith family is [tex]23[/tex].

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It should be noted that the expression for 72 + 40 will be 8(9 + 5).

The factors of 72 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

The factors of 40 include:

1, 2, 4, 5, 8, 10, 20 and 40

Therefore, it can be seen that the greatest common factor between the numbers is 8.

The expression for 72 + 40 will be 8(9 + 5).

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[tex]\displaystyle\\Answer:\ y=\frac{x}{3}-3[/tex]

Step-by-step explanation:

      [tex](0,-3)\ \ \ \ \ (6,-1)[/tex]

     [tex]\displaystyle\\ Equation\ of\ the\ line\\\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1} }[/tex]

 [tex]\displaystyle\\x_1=0\ \ \ \ x_2=6\ \ \ \ \ y_1=-3\ \ \ \ \ y_2=-1\\\\\frac{x-0}{6-0}=\frac{y-(-3)}{-1-(-3)}\\\\\frac{x}{6}=\frac{y+3}{-1+3} \\\\\frac{x}{6} =\frac{y+3}{2} \\\\Multiply\ both\ parts\ of \ the\ equation \ by \ 2:\\\\\frac{x}{3}=y+3\\\\\frac{x}{3}-3=y+3-3\\\\ \frac{x}{3} -3=y \\\\Thus,\\\\y=\frac{x}{3}-3[/tex]              

Answer:

3 and 4

Step-by-step explanation:

Since complementary angles add up to 90,

and 1 is a right angle while 3 and 4 are vertical angles

Answer:

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

Supplementary angles sum to 180°.

The solution to this equation is equal to 6.

Equations are expressions which are formed by constants, operators and variables. In this question we find a linear equation in implicit form, in which the variable t has to be solved:

- 9 · (t - 2) = 4 · (t - 15)                         Given

- 9 · t + 18 = 4 · t - 60                          Distributive property / (- a) · b = - a · b / (- a) · (- b) = a · b

78 = 13 · t                                             Compatibility with addition / Existence of additive inverse / Modulative and distributive properties

13 · t = 78                                              Symmetric property

t = 6                                                      Compatibility with multiplication / Existence of multiplicative inverse / Associative and modulative properties / Result

The solution to this equation is equal to 6.

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Answer:

[tex]t = 6[/tex]

Step-by-step explanation:

[tex] - 9(t - 2) = 4(t - 15)[/tex]

[tex] - 9t + 18 = 4t - 60[/tex]

[tex] - 9t - 4t = - 60 - 18[/tex]

[tex] \frac{ - 13t}{13} = \frac{ - 78}{ - 13} [/tex]

Cross out -13t/13

[tex]t = 6 \: final \: answer[/tex]

Answer:

Plug the following equation in your calculator and this will be your result

7.247 x 10^6

The value of the exponential equation in scientific notation A = 7.247 x 10⁶

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Let the first number be p = 7.26 x 10⁶

Let the second number be q = 1.3 x 10⁴

Now , the equation is A = p - q

A in the scientific notation is

Substituting the values in the equation , we get

A = 7.26 x 10⁶ - 1.3 x 10⁴

On simplifying the equation , we get

Taking the common factor as 10⁴ , we get

A = 10⁴ ( 7.26 x 10² - 1.3 )

A = 10⁴ ( 726 - 1.3 )

On further simplification , we get

A = 10⁴ ( 724.7 )

And , the value of A in scientific notation is A = 7.247 x 10⁶

Hence , the exponential equation is A = 7.247 x 10⁶

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Answer:

this is the solution for your question