Find the 5th term in the sequence described by 3n - 2. (1 point)
O 13
O 17
07
0-13

In a finite group, the inverse of an element 'a' can be expressed as a positive power of 'a', namely \(a^n^-^1\).

In a finite group, the inverse of an element is a positive power of that element means that for any element 'a' in the group, there exists a positive integer 'n' such that \(a^n = e\), where 'e' is the identity element of the group. In other words, the inverse of 'a' can be obtained by raising 'a' to a positive power 'n'.

This property holds for finite groups because every element in a finite group has a finite order. The order of an element 'a' is the smallest positive integer 'n' such that \(a^n = e.\) If the group is finite, then the order of each element must also be finite. Therefore, there exists a positive integer 'n' such that \(a^n = e\), which implies that \(a^(^-^1^) = a^(^n^-^1^).\)

So, in a finite group, the inverse of an element 'a' can be expressed as a positive power of 'a', namely \(a^(^n^-^1^).\)

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Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

Answer:

4 cups of fruit sorbet.

Step-by-step explanation:

There are 128 cups in 1 gallon. So, 1 gallon of fruit sorbet is equal to 128 cups.

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

The solution is, each person get 4 cups of fruit sorbet.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

Hugo is serving fruit sorbet at his party.

He has 1 gallon of fruit sorbet to serve to 32 friends .

now. we get,

There are 128 cups in 1 gallon.

So, 1 gallon of fruit sorbet is equal to 128 cups.

so, we have,

Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.

If each person receives the same amount,

then, each person will receive 4 cups of fruit sorbet.

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\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

(p ² q ⁵) ⁻⁴ (p ⁻⁴ q ⁵) ⁻²

= (p ⁻⁸ q ⁻¹⁰) (p ⁻⁸ q ⁻¹⁰)

= p ⁻¹⁶ q ⁻²⁰

Answer:

yes rhudurueufuurehhehduruejjdjdif

Answer:

11 miles

Step-by-step explanation:

3 centimeters is 1/3 of 9 centimeters so whatever you do to that you do the other number, so you divide 36 by 3 which is 11

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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The two items that together cost 34% of her budget have a summed cost of $170

From the question, we have the following parameters that can be used in our computation:

She has a budget of $500.

To calculate which two items together cost 34% of her budget, we use

Amount = 34% * Budget

substitute the known values in the above equation, so, we have the following representation

Amount = 34% * 500

Evaluate

Amount = 170

Hence, the two items would have a summed cost of $170

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Answer:

Step-by-step explanation:

1)

Congruency shortcuts:  

HL, SSS, SAS, ASA, and AAS

where S=side

A=angle

H=hypotenule

L=leg

HL is only for a right triangle

If you can prove sides and angles are congruent according to those 5 rules, you have proven the triangles are congruent

Similarity shortcuts:

AA, SAS, SSS

We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS)

2)

BG ≅ GD              >Given from image

IG ≅ GO               >Given from image

<BGI ≅ <DGO        >Vertical Angles

ΔBGI  ≅ ΔDGO        >SAS            

You have proven that the triangles are congruent because you used the shortcut by proving a side and angle and a side are congruent so SAS makes them congruent

The given expression ((−3⁴)⁻⁷)⁻³ using only positive exponents is equal to  (-3)⁻⁸⁴.

To write the expression ((−3⁴)⁻⁷)⁻³ using only positive exponents, we can apply the rule of exponentiation that states that a negative exponent can be converted to a positive exponent by moving the base to the denominator and changing the sign of the exponent.

In this case, we have a negative exponent raised to another negative exponent, so we need to apply this rule twice.

First, we can rewrite the expression as:

((-3⁴)⁻⁷)⁻³ = (-3⁴)⁷³

Next, we can apply the rule of negative exponent to obtain:

(-3⁴)⁷³ = (1/(-3⁴))⁻²¹

Finally, we can simplify the expression by moving the negative exponent to the numerator, changing the sign of the exponent and using the power rule of exponents to get:

(1/(-3⁴))⁻²¹ = (-3⁻⁴)²¹ = (-3)⁻⁸⁴

In conclusion, we can convert a negative exponent to a positive exponent by moving the base to the denominator and changing the sign of the exponent. We can use this rule multiple times to simplify expressions with negative exponents.

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SOLUTION:

Step 1:

In this question, we are given the following:

Finding the area of the shaded sector or segment:

Step 2:

The details of the solution are as follows:

Recall that the area of the circle =

CONCLUSION:

The area of the shaded sector or segment =

Step-by-step explanation:

35% of 19.99 is 6.99. so subtract 6.99 from 19.99

19.99-6.99= 13.00

Step-by-step explanation:

To calculate the correlation coefficient (r) given SSxx, SSxy, and other information, we need to use the following formula:

r = √(SSxy / SSxx)

Given SSxx = 950 and SSxy = 205.2, we can substitute these values into the formula:

r = √(205.2 / 950)

Calculating the value:

r = √(0.216)

r ≈ 0.465

The correlation coefficient (r) is approximately 0.465.

Interpretation: The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the value of r = 0.465 indicates a positive linear relationship between the variables, but it's not a strong relationship. The closer the value of r is to 1 or -1, the stronger the relationship. Since r = 0.465 is relatively close to zero, it suggests a weak positive linear association between the variables being an analyzed.

hope it help you

The Pearson's correlation coefficient (r) based on given data is approximately 0.44, implying a moderate positive correlation.

The formula for calculating Pearson's correlation coefficient (r) in this case is given as: r = SSxy / sqrt(SSxx * SSyy). However, we don't have the value for SSyy directly, but we can calculate it. We know that SSyy = Σy² -(Σy)² / n. Given that Σy² is 2028 and Σy is 120 and number of samples n is 12, we can calculate SSyy as: SSyy = 2028 - (120)² / 12 = 52. Now, substitute SSxx = 950, SSxy = 205.2 and SSyy = 52 in the formula to find r: r = 205.2 / sqrt(950 * 52), giving us an r-value of approximately 0.44. This value of r suggests a moderate positive correlation between the variables in the dataset.

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Answer:

C - 0.75, -0.5, -3, 1.5, 2

Step-by-step explanation:

Becayse 0.75 is the lowest, and 2 is the highest. If you put both up on a number line you would put -0.75 at the end and 2 at the end. Hope this helps :)

Therefore , the solution of the given problem of probability comes out to be AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

(a) The voting box contains a total of seven slips, four of which are for candidate A and three for candidate B. Thus, there are 35 events that can occur from 7 choose 4 (or 7 choose 3) options.

Each vote can be represented by a letter, with A standing for a vote for candidate A and B for candidate B, so that all outcomes can be listed. These are the potential results:

AAAA

AAAB

AABA

ABAA

BAAA

AABB

ABAB

BABA

BBAA

ABBB

BABB

BBAB

BBBA

(b)

For instance, the following results could occur if the slips were removed in the following order:

A (1 vote for contender A) (1 vote for candidate A)

AA (2 ballots for candidate A) (2 votes for candidate A)

AAB (2 ballots for candidate A, 1 vote for candidate B) (2 votes for candidate A, 1 vote for candidate B)

AAAB (3 ballots for candidate A, 1 vote for candidate B) (3 votes for candidate A, 1 vote for candidate B)

AAAAB (4 ballots for candidate A, 1 vote for candidate B) (4 votes for candidate A, 1 vote for candidate B)

AAAABB (4 ballots for candidate A, 2 votes for candidate B) (4 votes for candidate A, 2 votes for candidate B)

AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

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Answer:

You use decimal values. Like for the first one, multiply 100 by 0.01.

Step-by-step explanation:

The multiplication or division is 10^6/10^4

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b

Then, their multiplication can be interpreted as:

\(a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}\)

For example,

\(5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}\)

Given;

From 100 to 10^6;

100 * 10^4  = 10^6

From 100 to 90;

100/10*9=90

From 90 to 100

90/9*10=100

From 10^6 to 100

10^6/10^4=100

Therefore, by multiplication or division will be 10^6/10^4

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Answer:

x ≥ 11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

2x + 5 ≥ 27

Step 2: Solve for x

Here we see that any value x greater than or equal to 11 would work as a solution to the inequality.

Answer:

6 feet per minute.

Step-by-step explanation:

The turtle and snail are moving towards each other, so their speeds add up. Therefore, the combined speed at which they approach each other is:

5 feet/min (turtle's speed) + 1 feet/min (snail's speed) = 6 feet/min

Therefore, the turtle and snail are approaching each other at a speed of 6 feet per minute.

Answer:

6 feet per minute.

Answer:

Step-by-step explanation:

The total mass of the alloy is the sum of the masses of the two metals:

mass = density x volume = (8800 kg/m³ x 15 m³) + 850 kg = 132,000 kg + 850 kg = 132,850 kg

The total volume of the alloy is the sum of the volumes of the two metals:

volume = 15 m³ + 6.2 m³ = 21.2 m³

Therefore, the density of the alloy is:

density = mass / volume = 132,850 kg / 21.2 m³ ≈ 6266 kg/m³

Rounding to the nearest integer, the density of the alloy is 6266 kg/m³.

the answer is 3 3/20

3.15 = 63/20 = 3/20

Answer:

C. 3 3/20

Step-by-step explanation:

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.

the distance between the two planes is represented by the variable D, and time is represented by the variable t.

At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.

Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.

To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:

D^2 = (2000 km)^2 + (3600 km)^2

Simplifying the equation:

D^2 = 4000000 km^2 + 12960000 km^2

D^2 = 16960000 km^2

Taking the square root of both sides:

D = sqrt(16960000) km

D = 4120 km

Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time

dD/dt = 0

Since the distance between the planes is constant, the rate of change is zero.

Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

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Considering the given regression equation, the number of weeks that will pass before the value of the stock reaches $600 is of:

B. 8.3.

The value of the stock y after x weeks is given as follows:

log(y) = 0.3x + 0.296.

We have to solve for x when y = 600, hence:

log(600) = 0.3x + 0.296

0.3x = 2.7782 - 0.296

x = (2.7782 - 0.296)/0.3

x = 8.3 weeks.

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The total area of the garden is 52 ft².

First we need to calculate the area of the current garden and the area of the rectangular piece that will be added, and then add them together.

The current garden has an area of 20 square feet.

To find the area of the rectangular piece that will be added, we can use the formula for the area of a rectangle:

Area = length x width

The length of the rectangle is the distance between the points (-18, 13) and (-14, 13), which is 4 units. The width of the rectangle is the distance between the points (-18, 13) and (-18, 5), which is 8 units.

Therefore, the area of the rectangular piece that will be added is:

Area = 4 x 8 = 32 square feet

The total area of the garden is the sum of the areas of the current garden and the rectangular piece that will be added:

Total area = 20 + 32 = 52 square feet

Therefore, the total area of the garden is 52 ft².

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Answer:

x = 4

Step-by-step explanation:

You can solve for "x" by rearranging the equation and getting the "x" by itself on one side. Remember, whatever you do to one side of the equation, you must do to the other side.

-6 + x = -2                         <----- Original equation
+6         +6                        <----- Add 6 to both sides to isolate "x"

0 + x = 4                           <----- After the addition

x = 4                                 <----- Rewrite

Answer:

None of the above (x = 4) \( \sf {} \)

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ -6 + x = -2

Then the value of x will be,

→ -6 + x = -2

→ x = -2 + 6

→ [ x = 4 ]

Hence, the value of x is 4.

By applying the PEMDAS rule, the given expression "1 × (-4) - 8 × - 3/9" is equal to -20/8.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to evaluate this expression, we would apply the PEMDAS rule, where operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the operations of addition or subtraction would be performed from left to right.

Expression = 1 × (-4) - 8 × - 3/9

Expression = -4 - 8 × - 3/9

Expression = -4 - 8 × 1/3

Expression = -4 - 8/3

Expression = -4/1 - 8/3

Expression = (-12 - 8)/3

Expression = -20/8.

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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The slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

The given coordinate point is (-1, 5) and slope=-4.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Substitute (x, y)=(-1, 5) and m=-4 in standard form of the slope intercept form, we get

5=-4×(-1)+c

⇒ c=5-4

⇒ c=1

Substitute m=-4 and c=1 in y=mx+c, we get

y=-4x+1

Therefore, the slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

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Answer:

$191.25

Step-by-step explanation:

multiply 255 dollars by 25 percent, and then divide the answer by one hundred, then deduct that result from the original price.

(255 x 25)/100 = $63.75

255 - 63.75 = $191.25