find the right number that fits the sequence 54 , 48 , 18 , 24 , 6 , 12 , ?
how can I find the solution

The total value of Martin's account after 36 months is $7,682.50. $682.50 in interest was earned.

The three options given in the question are not the correct steps to solve the given quadratic equation.

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared (raised to the power of 2).

The three steps that Inga could use to solve the quadratic equation [tex]2x^2 + 12x - 3 = 0[/tex] are:

1.Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are constants: [tex]2x^2 + 12x - 3 = 0.[/tex]

2.Use the quadratic formula x = [-b ± sqrt([tex]b^2[/tex] - 4ac)]/2a, where a = 2, b = 12, and c = -3, to find the values of x:

x = [-12 ± [tex]\sqrt{(12^2 - 4(2)(-3))[/tex]]/(2*2)

x = [-12 ± [tex]\sqrt{(156)[/tex]]/4

x = (-3 ± [tex]\sqrt{(39)[/tex])/2

3.Simplify the roots if possible:

x = (-3 + [tex]\sqrt{(39)[/tex])/2 or x = (-3 - [tex]\sqrt{(39)[/tex])/2

Therefore, the three options given in the question are not the correct steps to solve the given quadratic equation.

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To find the middle term of the expansion of (2x/y^3)^12, we need to first determine the number of terms in the expansion.

Using the formula for the binomial theorem, we know that the number of terms in the expansion of (2x/y^3)^12 is 13.

Now, to find the middle term, we need to find the term that is in the middle of the expansion. Since there are 13 terms in the expansion, the middle term is the 7th term.

The general term of the expansion is given by:

T(r+1) = (12 C r) (2x)^r (y^-3)^(12-r)

So, the 7th term is:

T(8) = (12 C 7) (2x)^7 (y^-3)^(5)

Simplifying this expression, we get:

T(8) = (792) (128x^7 / y^15)

Therefore, the middle term of the expansion is 792(128x^7/y^15)

Answer:

P = 3

Step-by-step explanation:

[tex] {p}^{3} = 27[/tex]

[tex]p = \sqrt[3]{27} = 3[/tex]

Answer:

P = 3

Step-by-step explanation:

Write down the equation:

p^3 = 27

Then divide both sides by cubed:

p = 3

Answer:

65

Step-by-step explanation:

Identify the two numbers in the ordered pair, locate the x-axis and y-axis on the plane, move along the x-axis to the position corresponding to the first number, move vertically along the y-axis to the position corresponding to the second number, mark the point with a dot or small circle, and connect the dots to show patterns.

The procedures below must be followed in order to plot or graph an ordered pair of integers, usually known as a point, on a two-dimensional plane:

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To find a point that represents a solution for the equation x + 3y = 8, we need to find a point (x,y) that satisfies this equation. One way to do this is to choose a value for x, and then solve for y. For example, if we let x = 2, we have:

2 + 3y = 8

Subtracting 2 from both sides, we get:

3y = 6

Dividing both sides by 3, we get:

y = 2

So the point (2,2) is a solution for the equation x + 3y = 8. To check, we can substitute x = 2 and y = 2 into the equation:

2 + 3(2) = 8

8 = 8

This is true, so (2,2) is a solution for the equation.

Alternatively, we could choose a value for y and solve for x. For example, if we let y = 0, we have:

x + 3(0) = 8

x = 8

So the point (8,0) is also a solution for the equation x + 3y = 8.

The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space refers to the set of all possible outcomes or events that can occur in an experiment or random process. It is denoted by the symbol "S" and contains all the possible values, results, or states that can be observed or measured. In probability theory, the sample space is used to define the range of possible outcomes that can be observed or measured in a given experiment or event.

Probability is a measure of the likelihood or chance of an event occurring. It quantifies the likelihood of an event happening based on the ratio of the number of favorable outcomes to the total number of possible outcomes. It is expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

According to the given information:

When you roll a 12-sided dice, number of dots on the uppermost face is called as outcome. Now, whenever a dice is rolled we can get either 1, 2,3,4,5,6,7,8,9,10,11 or 12 dots on the uppermost face that is now outcome.

So experiment here is "Rolling a 12-faced dice" and list of possible outcomes is "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}".

Sample space by its definition is list of all the possible outcomes of an experiment.

S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

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Answer:

Exact Form: 1/216

Step-by-step explanation:

Answer:

Step-by-step explanation:

H(n)=91x(-1/7) n-1

do not know

Hope it helps the answer is the 2nd one have a great day

The required password for different conditions are 216 and 120.

(a) If a letter can be repeated, then we can use the multiplication principle to determine the number of possible passwords. For each of the three positions in the password, there are six choices of letters. Therefore, the total number of possible passwords is:

[tex]$6^3 = \boxed{216}$[/tex]

(b) If a letter cannot be repeated, then we can use the permutation formula to determine the number of possible passwords.

There are six choices for the first letter, five choices for the second letter (since one letter has already been used), and four choices for the third letter (since two letters have already been used). Therefore, the total number of possible passwords is:

[tex]$P(6,3) = 6 \times 5 \times 4 = \boxed{120}$[/tex]

Thus, required password for different conditions are 216 and 120.

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Without the exact Number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make

Step 1: Identify the number of leftover bread slices.
Unfortunately, the question doesn't provide the exact number of leftover bread slices. Let's assume Rosa and Clarice have "B" bread slices in total.

Step 2: Determine the number of sandwiches needed.
We know that they are making sandwiches for the custodian, librarian, and office staff. We need to know the number of people in each category to calculate the total number of sandwiches required. Since this information is not provided, let's assume there are "C" custodians, "L" librarians, and "O" office staff members.

Step 3: Calculate the number of sandwiches required.
Each sandwich typically requires 2 slices of bread. Therefore, the total number of sandwiches required can be calculated using the following formula:

Total Sandwiches = (C + L + O)

Step 4: Determine if there is enough bread.
We can now compare the total number of sandwiches required with the number of bread slices available. If there are enough bread slices (B >= 2 * Total Sandwiches), Rosa and Clarice can make sandwiches for everyone. Otherwise, they will not be able to make enough sandwiches for everyone.

In conclusion, without the exact number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make. To answer the question accurately, please provide the missing information.

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Answer:

A .278

Step-by-step explanation:

138 x 14÷28+209 = 1932 ÷28+209=69+209=278

Therefore, the distance from the coal tray is approximately 301.96 inches when the heat intensity is 0.685 and the width of the coal tray is 25 inches.

We can write the following using the formula in the question:

[tex]P = 100/(1 + d^2)[/tex]

where d represents the proportion of the food's distance from the coals to the tray's width.

Substituting d = z/25 results in:

[tex]P = 100/(1 + (z/25)^2)[/tex]

With y = 0.685, we can replace P with P = 0.685 and find z:

[tex]0.685 = 100/(1 + (z/25)^2)[/tex]

By dividing the two sides by [tex](1 + (z/25)^2)[/tex], we get at:

[tex]0.685 + 0.685(z/25)^2 = 100[/tex]

If we simplify, we get:

[tex](z/25)^2 = (100/0.685) - 1(z/25)^2 = 145.9854[/tex]

When we square the two sides, we obtain:

[tex]z/25 = 12.0783z = 25*12.0783z = -25*12.0783[/tex]

Given that z cannot be negative, we decide:

Z=25 * 12.0783 * 301.9575 inches

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Answer: w/explanation

To calculate your merit increase, we need to first determine your performance score on a scale of 0 to 100. We can convert your score of 3.4 to this scale by subtracting 2 and multiplying by 25:

performance score = (3.4 - 2) x 25 = 35

Now that we have your performance score, we can use the given merit increase formula to calculate your increase:

Merit increase = (performance score - 26) / 4

Merit increase = (35 - 26) / 4

Merit increase = 2.25%

Therefore, your merit increase is 2.25%.

Answer:

c

Step-by-step explanation:

To find the x-intercept, we set y to 0 and solve for x:

0 = x + 8

x = -8

Therefore, the x-intercept is -8.

To find the y-intercept, we set x to 0 and solve for y:

y = 0 + 8

y = 8

Therefore, the y-intercept is 8.

Hopes this helps

The associative law holds in all three composition tables.

No matter how they are arranged, integers can be multiplied and added together according to the associative property. We refer to the numbers in the parenthesis as grouping (). Let's imagine that you are adding three integers, 2, 5, and 6. It doesn't matter how we add the numbers together—using the formulas 2 + (5 + 6) or 2 + (5) + 6—the outcome will be the same. The multiplication equation is consistent: Equals to (2 x 5) x 6 is (2 x 5) x 6. The commutative characteristic is almost identical to this one when only two integers are used.

In the given composition tables the law of associativity is followed

a(bc) = (ab)c

from 13,

a(a) = bc

a = a

The associative law holds in all three composition tables

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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

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

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

The equatiοn fοr H, the number οf times Nοah’s beats in m minutes is H = k * m

Expressiοns that perfοrm the same functiοn regardless οf appearance are said tο be equivalent. If twο algebraic expressiοns are equivalent, then they have the same value when the same variable value is used.

Assuming yοu meant "Nοah's heart beats", the equatiοn fοr H, the number οf times Nοah's heart beats in m minutes can be given by:

H = k * m

where k is a cοnstant that represents the number οf heartbeats per minute.

The value οf k may vary depending οn the individual and their physical cοnditiοn.

Hence,  the equatiοn fοr H, the number οf times Nοah’s beats in m minutes

is H = k * m

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Complete Question;

A persons resting heart rate is typically between 60 and 100 beats per minute. Nοah looks at his watch, and counts 8 heartbeats in 10 seconds.

Is his heart rate typical? Explain how you know.

Write an equation for h, the number of times Noahs heart beats (at this rate) in m minutes.

The composition (f ∘ g)(–2) = 3.

What is Function ?

In mathematics, a function is a relation between two sets of values, where each value in the first set (called the domain) is associated with exactly one value in the second set (called the range). A function can be represented by a formula or an equation, which specifies how the input values are transformed into output values.

To find the composition (f ∘ g)(–2), we need to apply the function g to –2 first, and then apply the function f to the result. Here's how we can do it:

First, we need to find g(–2) by substituting –2 for x in the expression for g(x):

g(–2) = (–2)2 – 3

g(–2) = 4 – 3

g(–2) = 1

Now that we have found g(–2) = 1, we can substitute it for x in the expression for f(x) to find f(g(–2)):

f(g(–2)) = 2(1) + 1

f(g(–2)) = 3

Therefore, the composition (f ∘ g)(–2) = 3.

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Answer:

23°

Step-by-step explanation:

46 = 2x (Vertically opp. angles)

x = 46÷2

x = 23

Hope this helps!

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Answer:

x = 23°

Step-by-step explanation:

46 = 2x

46/2 = 2x/2

x = 23°

Answer:

(x, y) → (-x, y)

Step-by-step explanation:

The coordinates of the points that make up the function are equal to (x, y).

If we reflect the function over the y-axis, the sign of the y-value stays the same due to still being on the same side of the x-axis. The x-value sign will be the opposite of its current value due to being reflected over the y-axis.

This leads us to the algebraic expression:

(x, y) → (-x, y)

According to the popular legend, Archimedes discovered a principle of buoyancy while taking a bath.

what was his discovery ?

He realized that the volume of water displaced by his body was equal to the volume of his body. This insight led him to formulate the principle of buoyancy, which states that an object placed in a fluid experiences an upward force equal to the weight of the fluid it displaces.

Archimedes was reportedly so excited by this discovery that he ran through the streets of Syracuse shouting "Eureka!" (meaning "I have found it" in Greek). This principle has numerous practical applications, including in shipbuilding and the design of submarines and other underwater vehicles.

In geometric terms, the principle of buoyancy can be explained using the concept of displacement. When an object is submerged in a fluid, it displaces a certain volume of fluid, which is equal to the volume of the object. This volume of fluid has weight, and the fluid exerts an upward force on the object that is equal to the weight of the displaced fluid. This is what causes objects to float in water or other fluids, as long as their weight is less than the weight of the fluid they displace.

As for what Archimedes did next with his new discoveries, it's difficult to say for certain, as there are many stories and legends about his life. However, we do know that he was a prolific inventor and mathematician, and he likely continued to explore the implications of his principle of buoyancy and other discoveries. He may have also used this principle in his work as an engineer and designer, creating new machines and devices that were more efficient and effective thanks to his insights into fluid mechanics.

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The sum of the matrices A + B is  5      8

                                                        2.6   2

To add two matrices, they must have the same dimensions (the same number of rows and the same number of columns).

To add two matrices A and B, you can add the corresponding elements of the two matrices and place the result in the corresponding position of a new matrix C.

In mathematical notation, if A and B are two matrices of the same dimensions, then the sum C = A + B is defined by:

C[i,j] = A[i,j] + B[i,j]

Using the above as a guide, we have the following:

A + B =  5      8

             2.6   2

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Answer:

90°

Step-by-step explanation:

Since CD is a tangent to circle B and BA is the circle's radius, the tangent to the radius forms a right angle at the point of contact:

∠BAD = 90°

Answer:

[tex]\textsf{A.} \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

Given geometric sequence:

[tex]8,\;2,\;\dfrac{1}{2},\;\dfrac{1}{8},\;\dfrac{1}{32}[/tex]

The common ratio for a geometric sequence can be found by dividing a term by the previous term.

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{2}{8}=\dfrac{2 \div 2}{8 \div 2} =\dfrac{1}{4}[/tex]

Therefore, the common ratio for the given geometric sequence is 1/4.