what is the fifteenth term in the sequence 12, 24, 36, 48, 60,...? A72 B76 C96 D180

Answer:

x=8

Step-by-step explanation:

set both equations equal to each other

x^2-3x-10=-2x=2

combine like terms

x^2=1x+8

x+8

Hope this helps!

well when thinking of gravity you have to think of the size and mass of the object so,

The sun (largest and most mass)

Earth

Earth's moon

Discover satellite (cause it's tiny and light compared to the sun!)

Answer:

Step-by-step explanation:

\(\frac{3x^4}{(\frac{1}{x^2})^2} \\= 3x^8\)

Answer:

\(3x^{8}\)

Step-by-step explanation:

\((x^{-2})^{2}\) is equal to \(x^{-4}\). Whenever an x has a negative exponent, it means that you can put it to the other side, whether it be from denominator to numerator or numerator to denominator. In this case, because it is in the bottom it goes from denominator to numerator. You will end up with something like \(3x^{4} x^{4}\) but you can add the X's and end up with the answer.

In a group of 7 participants, each person shakes hands with 6 other participants, resulting in a total of 42 handshakes.  To determine the number of participants that will make 45 handshakes in total, we need to find a number that satisfies the given condition. Let's assume that the number of participants is 'n.'

In a group of 'n' participants, each person shakes hands with (n-1) other participants since they don't shake hands with themselves. Therefore, the number of handshakes in a group of 'n' participants can be calculated by the formula: n x (n-1).

We need to find the value of 'n' that satisfies the equation n x (n-1) = 45.

Expanding the equation, we get \(n^2 - n - 45 = 0.\)

By factoring or using the quadratic formula, we can solve this equation to find two possible values for 'n': n = -6 or n = 7.

Since the number of participants cannot be negative, we discard the negative solution and consider n = 7.

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Let s be the number of hours that Nick swam and r the number of hours that he ran, then we can set the following system of equations:

Solving the second equation for s, and substituting in the first equation we get:

Substituting r=5.5 in the second equation, and solving for s we get:

Therefore he swam for 3 hours and ran 5.5 hours.

Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

The gallons of a 80​% antifreeze solution must be mixed with 70 gallons of ​25% antifreeze to get a mixture that is ​70% ​antifreeze is  x=315

Use a weighted average........ let x = an unknown number of gallons of the 80​% solution.

then     {x(80​%) + 70 (25%)}/{x +70} =70% ​

{x*\(\frac{80}{100}\) + 70*\(\frac{25}{100}\)}/{x +70} =70% ​

{\(\frac{4x}{5}\) +17.50}/{x +70} =70% ​

\(\frac{4x+87.5}{5x+350}\) = \(\frac{70}{100}\)

40x+875 = 35x + 2450

40x-35x = 2450-875

5x = 1575

x=315

Keep in mind that the substance with the highest concentration is the solvent.

There are numerous varieties of solutions. A solute, for instance, could be a gas, a liquid, or a solid. Additionally, solvents can be solids, liquids, or gases.

The behavior of several types of solutions at the microscopic level is depicted in the following illustrations. You'll see that the solute particles are evenly spaced out among the solvent particles in each instance.

A solution is a homogeneous mixture of one or more solutes dissolved in a solvent. solvent: the substance during which a solute dissolves to produce a homogeneous mixture. solute: the substance that dissolves during a  solvent to produce a homogeneous mixture. The solute is the substance that is being dissolved, while the solvent is the dissolving medium. Solutions are often formed with many different types and forms of solutes and solvents.

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Answer:

15 degrees

Step-by-step explanation:

Answer:

The earth turns 15 degrees in one hour. Hope this helps!

Step-by-step explanation:

Answer:

The awnser is 3

Step-by-step explanation:

(3+1) = 4 x 6= 24+1 = 25

;)

Answer:

the answer of equation is C. x=3

Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, Where the base of these triangles are same

And also given that the two angles are the same.

Since,

Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).

Thus, the third angle is also equal

From AAS:

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,

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An inequality that describes a possible length in yards of the rectangular parking lot is L < 6.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Since the city wants the width of the parking lot to be 5 yards and the area of the rectangular parking lot to be more than 30 square yards, an inequality that models a possible lengths of the rectangular parking is giving by;

A > LW

30 > 5L

Dividing both sides of the inequality by 5, we have:

6 > L

L < 6

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Answer:

The first part is of permutations.

We are selecting 3 elements from three different elements {1,2,3}

Points given:

We permit overlapped elements for the sequence. Here "overlapped elements" indicates that repetition is allowed.

So when repetition is allowed and order matters, we use permutations.

Formula to compute permutation is:

Lets say n is the three elements {1,2,3}

We have to select 3 elements so r = 3

Total number of selections using permutations = \(n^{r}\) =  n × n × n

                                                                    = 3³ = 3 * 3 * 3

                                                                    = 27

This means if we have 3 different elements then we have have 3 choices each time for making a sequence.

Hence  If we make a sequence selecting three elements from three different elements  {1, 2, 3} and we permit overlapped elements for the sequence, then the total  number of sequences is 27.

Step-by-step explanation:

The second part indicates combinations.

This is because the statement of the question:  If we do not take into account the order.

When the order does not matter, we use combinations.

So when the order does not matter and repetition is allowed we use the following formula:

Total number of selections using combinations = (r + n - 1)! / r! (n - 1)!

                                                                                = (3 + 3 - 1) ! / 3! (3 - 1)!

                                                                                = (3 + 2) ! / 3! (2!)

                                                                                = 5! / 3! 2!

                                                                                = 5*4*3*2*1 / (3*2*1 ) (2*1)

                                                                                = 120 / 6 * 2

                                                                                = 120 / 12

                                                                                = 10

So these are the number of combinations of 3 elements taken 3 at a time with  repetition.

The total number that will be selected in the permutations is 27.

Based on the information given, the total number of permutations will be:

= n³

= 3 × 3 × 3

= 27

Also, the total number of selection using combination will be:

= (3 + 3 - 1)! / 3!(3 - 1)!

= 120 / (6 × 2)

= 120/12

= 10

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Answer:

36   and -1/8

Step-by-step explanation:

x^2 = 3^2 = 9 * 4 = 36

y^-3 = (-2)^-3 = -1/8

Answer:

-4.5.

Step-by-step explanation:

4x^2 y^-3

= 4x^2 / y^3

When x = 3 and y = -2

it is 4(3)^2 / (-2)^3

= 36 / -8

= -4.5.

Answer: 115 degrees

Step-by-step explanation:

Give me the brainliest plz!

Answer:

The 3rd answer.

Step-by-step explanation:

2(pi)10 is the equation.

Answer:

a= 0

b= \(-\frac{\sqrt{42} }{12}\)

Step-by-step explanation:

We can rewrite the expression to be:

\(\frac{i\sqrt{7} }{i^{2}\sqrt{24} }\)

We then can cancel out the i and we get

\(\frac{\sqrt{7} }{\sqrt{24} i}\)

Can be rewritten as

\(\frac{\sqrt{7} }{2\sqrt{6} i}\)

We then rationalize and get

\(-\frac{\sqrt{42} }{12} i\)

Answer:

5x+40

Step-by-step explanation:

You would distribute 5 to x+8 and that would add up to 5x+40.

Answer:

Step-by-step explanation:

5x+40

Answer:

Degrees of freedom for independence  in chi-square statistic

ν = ( r-1) (s-1) =6

Step-by-step explanation:

Explanation:-

Given data  chi-square test for independence is being used to evaluate the relationship between two variables

Given "A" is classified into 3 categories

Second 'B' is classified into 4 categories

In this chi-square test, we test if two attributes A and B under consideration are independent or not

We will assume that

Null Hypothesis : H₀: The two variables are independent

Degrees of freedom in chi-square test for independence

ν = ( r-1) (s-1)

Given data 'r' = 3  and  's' = 4

Degrees of freedom for independence

ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6

Test statistic

                       χ ²  =  ∑  \(\frac{(O-E)^{2} }{E}\)

This question is based on Chi-square test. Therefore, the chi-square statistic for this test would have df equal to \(X^{2} = \sum \dfrac{(O-E)^2}{E}\).

Given:

Chi-square test for independence is being used to evaluate the relationship between two variables . Given "A" is classified into 3 categories . Second 'B' is classified into 4 categories

According to the question,

In this chi-square test, we would be test if two attributes A and B under consideration are independent or not.

Let assumed that,  null Hypothesis : H₀: The two variables are independent

Now, degrees of freedom in chi-square test for independence is,

 ⇒ ν = ( r-1) (s-1)

It is given that, 'r' = 3  and  's' = 4.

Thus, degrees of freedom for independence is,

ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6

Therefore, test statistic be,

\(X^{2} = \sum \dfrac{(O-E)^2}{E}\)

Therefore, the chi-square statistic for this test would have df equal to \(X^{2} = \sum \dfrac{(O-E)^2}{E}\).

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The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.

The rate of change is $ 0.75 per attraction.

The table on the number of tickets and total cost is:

Number of tickets                 1                        5                 10               15

Total cost                          $ 10. 75             $ 13.75       $17.50        $ 21. 25

The number of tickets that Sam can buy when he has $ 37 is:

= (Amount to spend - Cost of admission ) / Cost per ticket

= ( 37 - 10 ) / 0.75

= 36 tickets

The rate of change is therefore the $ 0.75 charged per ticket per event.

The number of tickets for $ 10. 75 is:

= ( Total cost - Cost of admission ) / cost per ticket

= ( 10. 75 - 10 ) / 0.75

= 1 ticket

The cost of 5 tickets :

= ( Number of tickets x cost per ticket) + cost of admission

= (5 x 0. 75 ) + 10

= $ 13. 75

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The equivalent expression of 1/2 + 3c + 4/5 is \(\frac{13 + 15c}{10}\)

The expression is given as:

1/2 + 3c + 4/5

Take the LCM of the expression

\(\frac{5 + 15c + 8}{10}\)

Evaluate the like terms

\(\frac{13 + 15c}{10}\)

Hence, the equivalent expression of 1/2 + 3c + 4/5 is \(\frac{13 + 15c}{10}\)

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Answer:

150 in^2

Step-by-step explanation:

The surface area, in general, is A = 6s^2, where s is the length of one side of the cube.

If the edge length is 5 in, then the surface area of the cube is

A = 6(5 in)^2 = 6(25 in^2) = 150 in^2

The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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Answer:

Length: 25

Width: 9

Step-by-step explanation:

Answer:

The period is 12 months

Step-by-step explanation:

The temperature values (y-axis) repeat every 12 months (x-axis).

Step-by-step explanation:

\(f(x) = {x}^{2} + 2x - 10 \\ f( - 2) = { (- 2)}^{2} + 2( - 2) - 10 = \\ = 4 - 4 - 10 = - 10\)