Lauren and Shayla have ½ pound of Skittles. They want to share the Skittles between themselves and 2 friends.

How many pounds of Skittles will each of them receive?

The first 8 terms of the sequence are 12, 16, 22, 30, 40, 52, 66, 82 respectively.

(a) The first 8 terms of the sequence are as follows:

a1 = 1 + (1^2) + (2^3) + 2 = 12

a2 = 1 + (2^2) + (2^3) + 3 = 16

a3 = 1 + (3^2) + (2^3) + 4 = 22

a4 = 1 + (4^2) + (2^3) + 5 = 30

a5 = 1 + (5^2) + (2^3) + 6 = 40

a6 = 1 + (6^2) + (2^3) + 7 = 52

a7 = 1 + (7^2) + (2^3) + 8 = 66

a8 = 1 + (8^2) + (2^3) + 9 = 82

(b) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 4n for all n ≥ 3. Hence, a = 3.

(c) We will prove the statement "an > 4n for all integers n ≥ a" using strong induction.

Base case (n=3): a3 = 28 and 28 > 4 * 3 = 12, which is true.

Inductive step: Suppose an > 4n for all integers n = k (k ≥ 3). We need to show that a(k+1) > 4(k+1).

a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 4k + 3 = 4(k+1)

(d) Observing the values of a1, a2, a3, a4, and so on, we can see that an > 45 for all n ≥ 7. Hence, b = 7.

(e) We will prove the statement "an > 5n for all integers n ≥ b" using strong induction.

Base case (n=7): a7 = 120 and 120 > 7 * 5 = 35, which is true.

Inductive step: Suppose an > 5n for all integers n = k (k ≥ 7). We need to show that a(k+1) > 5(k+1).

a(k+1) = 1 + (k+1)^2 + (2^3) + (k+1) = 1 + (k^2 + 2k + 1) + (2^3) + (k+1) = an + 2k + 3 > 5k + 3 = 5(k+1)

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Answer:

4632/8=579

Step-by-step explanation:

MARK ME BRAINLISIST.

Answer: 579

Hope I'm right

A mathematical operation which is the same as dividing a number by 1,000 include the following: C. move the decimal 3 places to the left.

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

This ultimately implies that, a quotient in terms of numerical data simply refers to a division of a number (numerator) by another number (denominator).

In terms of determining the decimal place after a division of a number by 1000, we have the following:

Number = 1/1000

Number = 0.001 (3 places to the left.)

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The measure of PQ is approximately 57.8 units.

Now, According to the question:

A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

Quadrilateral JKLM is similar to quadrilateral NOPQ .

We have the sides are:

JK = 9, LM = 13.7, NO = 38,

and To find the measure of PQ.

Corresponding sides in similar figures are proportional in length:

PQ/LM = NO/JK

PQ/13.7 = 38/9

PQ = 13.7(38/9) = 2603/45 ≈ 57.8

Hence, The measure of PQ is approximately 57.8 units.

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Answer: A = shade the square above and below the third square (3 to the right). B = Make a straight line of 4 and put a square below the first square of the line, and above the second square. (Let me know if you need help.)

Step-by-step explanation:

Answer:

X = 37.8

Step-by-step explanation:

Since they stated angle BAC equals angle DEC, makes me believe these sides are just a factor of each other.

Because of that, we can make a proportion, then cross multiply and divide

Making that proportion, you get;

15. 18

---. =. ----

31.5. x

Cross multiply the (15)(x) = (31.5)(18), also known as

15x = 567

Last thing we do is divide both sides by 15 to get that X alone.

567/15 = 37.8

Concluding that x = 37.8

The correct option is C. ((6, 5), (3,2), (2, 4), (6, 3), (1, 0))

Reason: This relation has two y-values of 6 which violates the vertical line test and therefore is not a function.

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Jessica's speed is 4 mph and Janine's speed is 8 mph

Let us assume that x represents Jessica's speed.

Janine bikes 4 mph faster than her sister, Jessica.

So, Janine's speed would be (x + 4) mph

We know that the formula for the speed is: speed = distance/time

Here, Janine can ride 24 mi in 3 hr less time than Jessica can ride the same distance.

24/(x+4) = (24/x) - 3

24/(x+4) = (24 - 3x)/x

24x = (24 - 3x)(x + 4)

24x = 24x + 96 - 3x² - 12x

3x² + 12x - 96= 0

After solving above quadratic equation we get.

(x - 4) (x + 8) = 0

x = -8 speed is not possible.

So, x = 4 mph

And x + 4 = 8 mph

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Answer: 391.92ft²

Step-by-step explanation:

Answer: 391.92

Step-by-step explanation:

All you simply do in multiply the two numbers together.

Answer:

10 Slices

Step-by-step explanation:

6x5=30

30 slices in total

We are trying to find 2/3 of 30 slices so we multiply them.

(2x30)/3

=60/3

=20

20 slices were sold out of 30 total slices

This means that 10 slices are left

30-20=10

The quotient of the expression is 7x² + 8x +  1

From the question, we have the following expression that can be used in solving the quotient

(7x^3-13x^2-23x-5)/(x-3)

Express properly

So, we have

(7x³ - 13x² - 23x - 5)/(x-3)

Set the divisor to 0

x - 3 = 0

So, we have

x = 3

Using a synthetic setup, we have

3 | 7 - 13 - 23 - 5

The synthetic division is then carried out as follows

3 | 7 - 13 - 23 - 5

        21   24    3

    7   8     1    -2

So, we have

Quotient = 7   8   1

Remainder = 2

Introduce the variable

Quotient = 7x² + 8x +  1

Remainder = 2

Hence, the result is 7x² + 8x +  1 remainder 2

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The measure of one interior angle in the regular polygon is 180° degrees.

Polygon:

A polygon is a shape that is made of straight line segments that are connected to each other.

The polygons are named according to their properties and the number of sides they have which have a minimum of three sides.

A polygon cannot have curved sides they are all straight line segments and can measure each side equal to one other.

The formula to find the interior angles of a regular polygon is required.

The required formula is     [tex]\frac{(n-2)*180}{n}[/tex]

where n = Number of sides of the polygon.

given to measure one interior angle n=1

Substitute the n value in the above formula, and we get

[tex]A=\frac{(2-1)*180}{1}[/tex]

A=180°

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Answer:

0.02

Step-by-step explanation:

hope it helped

Answer:

0.0266666667 or 0.02

Step-by-step explanation:

Answer:

m < -1 5/8

Step-by-step explanation:

attached pic

The equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

The solution is obtained by using the arithmetic operations.

What are arithmetic operations?

In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given that the coldest temperature recorded in a city in Texas was −22.3°F and the coldest temperature recorded at Vostok Station in Antarctica was 4 times as cold.

This means that the coldest temperature recorded at Vostok Station in Antarctica was

4*(−22.3)°F = 89.2°F

Hence, the equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

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If a bicycle is of worth $500 and decreases in value by 7.8% per year , then the function to model this situation is P(n) = 500(0.922)ⁿ  and the value of bicycle after 5 years is  $333.14    .

The price of  bicycle is = $500 ;

the percent decrease in the value per year is = 7.8% = 0.078   ;

let number of years be = "n" years ;

So , the Price of bicycle after "n" years is written as :

⇒ P(n) = 500(1 - 0.078)ⁿ ;

⇒ P(n) = 500(0.922)ⁿ ;

to find the value of bike after 5 years , we substitute n = 5 ;

⇒ P(5) = 500(0.922)⁵  ;

⇒ P(5) = 500 × 0.66627

⇒ P(5) = 333.138334052816

⇒P(5) ≈  $333.14

Therefore , the value of bike after 5 years is $333.14   .

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Answer:

To find the value of k and the equation of the line, we can use the slope-intercept form of a line: y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope of the line (m) is given as -⅔. To find the y-intercept (b), we can substitute one of the given points and the value of m into the equation.

Let's use the point (3,k) :

y = mx + b

k = -⅔ * 3 + b

k = -2 + b

b = k + 2

Now we have the equation of the line in the slope-intercept form: y = -⅔x + (k + 2)

To find the value of k we can use the other point (-3, 2k) and substitute into the equation:

2k = -⅔(-3) + (k + 2)

2k = 2 + k + 2

k = -2

So the value of k is -2 and the equation of the line is y = -⅔x + (k + 2) = -⅔x - 2

This line is a straight line with the slope of -⅔ which passes through the points (3, k) and (-3, 2k) and its equation is y = -⅔x - 2

Answer:

6931.73

Step-by-step explanation:

π =3

cone base diameter = 6 so r=3

it's given height is 11

so use formula given V = π/3*3²*11 =99

sphere r =3

so use formula given V = 4/3*π*3³ = 4*81 = 324

total 99+324 =423 cubic INCHES!!!

1" = 2.54 cm

so you'll have to multiply 2.54³ to covert it to

cubic CMS = 6931.73 cubic CMS

Answer:

36 cm²

Step-by-step explanation:

Area=Length*Width

so... 9*4 = 36

36 cm²

The graph of the polynomial function is given by the following option:

Not C or D.

At z = -3, the function has a zero with an even multiplicity of 2, meaning that the graph of the function turns at z = -3, due to the even multiplicity.

At z = 2, the function has a zero with an odd multiplicity of 3, meaning that the graph of the function crosses the x-axis at z = 2, due to the odd multiplicity.

At z= -4, the function is negative, hence it becomes positive at z = 2 and goes towards infinity.

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Answer:

Step-by-step explanation:

Oohh yeah

The probability of an event happening in half an hour cannot be determined simply by multiplying or dividing the probability of the event happening in an hour by a factor of 2.

Probabilities are not linear in that way. The probability of an event happening in half an hour would depend on the specific details of the event and the underlying probability distribution.

The probability of an event happening in half an hour, given an 84% chance of it happening in an hour, cannot be determined without additional information. The probability of an event occurring in half an hour would depend on the specific circumstances of the event and how the 84% probability was determined.

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if there is an 84% chance of an event happening in an hour, then the probability that it happens in half an hour will be 84% = 0.84.

One cannot easily calculate the likelihood of an event occurring in half an hour by multiplying or dividing the chance of the event occurring in an hour by a factor of 2.

In that sense, probabilities are not linear. The likelihood of an event occurring in half an hour is determined by the event's specifics and the underlying probability distribution.

Without further information, the likelihood of an event occurring in half an hour given an 84% chance of occurring in an hour cannot be computed. The likelihood of an event occurring in half an hour is influenced on the event's unique circumstances and how the 84% probability was calculated.

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If a red balloon costs $0.80, then 9 red balloons costs would be $7.20.

What is an algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

To find out how much 9 red balloons cost, you need to multiply the cost of one red balloon by the number of red balloons.

So 9 red balloons cost $0.80 * 9 = $7.20

Hence, If a red balloon costs $0.80, then 9 red balloon costs would be $7.20.

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Answer:

Step-by-step explanation:

7

The use of x^2^k is a more efficient way to multiplying than starting with x and successively squaring.

according to question,

real number = x

positive integer = k

x^2^k

Starting with x and squaring to find x², x⁴, xⁿ

The efficient way of multiplying is

x^2^k

where, k = 1, 2, 3, 4,.....…

check:

when k = 1

x^2^1

= x²

when k = 2

x^2^2

= x⁴

when k = 3

x^2^3

= x^2*2*2

= x^8

Therefore,

x^2^k

is a more efficient way to multiplying.

Integer

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

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Answer:

  D(3.4, 20.8)

Step-by-step explanation:

Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.

The equation for the slope between two points is ...

  m = (y2 -y1)/(x2 -x1)

Using this formula and the given points, we can find D(x, y) to satisfy ...

  2 = (y -10)/(x +2)

  -3 = (y -7)/(x -8)

Putting each of these equations in general form, we have ...

  2(x +2) -(y -10) = 0

  2x -y +14 = 0

and

  -3(x -8) -(y -7) = 0

  3x +y -31 = 0

Adding the two equations eliminates the y-variable:

  (2x -y +14) +(3x +y -31) = 0

  5x -17 = 0 . . . . . . simplify

  x -3.4 = 0 . . . . . . divide by 5

  x = 3.4 . . . . . . . . . add 3.4

Substituting for x in the first equation gives ...

  2(3.4) -y +14 = 0

  y = 6.8 +14 = 20.8 . . . . add y

The point D has coordinates (3.4, 20.8).

__

Additional comment

The graph shows the equations of the lines written in point-slope form.

The volume of the cabinet where Samantha stores all her important documents would be given as = 7.2 ft

A cabinet is defined as an equipment usually located in offices or laboratory which is used for the storage of documents that are of high importance to an organisation.

The shape of the cabinet is the shape of a cube and the volume of a cube is the product of all the sides given

That is = 2⅙ × 1¼ × 2⅔ ( change to single fraction)

= 13/6 × 5/4 × 8/3

= 520/72

= 7.2 ft

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Answer:

group has raised $1680 in the first three months.

Step-by-step explanation:

The students group has raised $1680 in the first three months.

Due of this, The Helping Hands Student Club decided to fundraise $4,000 by the end of the academic year.

How much is a percentage?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

It accomplishes 42% of its goal after three months.

The money raised over the initial three months is

42% of 4000

= 42/100 × 4000

= 42×40

= $1680

Thus, the students' group has raised $1680 in the first three months.

The inequality involving absolute value is 2 < x < 4 and the graph is attached below.

The term called inequality in math is defined as when two real numbers or two algebraic expressions are represented with symbols like <, > or ≤, ≥.

Here we need to find the inequality involving absolute value for the graph. And here we also need to find the point that is the same distance from 2 as it is from 4.

Here we have consider that x be the number that the inequality is formed than it can be written as

=> 2 < x < 4

And the graph of the inequality is plotted and attached below.

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No, these given system specifications are not consistent.

They present a logical contradiction, also known as a paradox. The first claim claims that "Users cannot access the file system if the system software is changed," while the second claim claims that "Users can store new files if they can access the file system."

The third assertion, which reads, "If users cannot save new files, then the system software is not being upgraded," is in direct opposition to the first. All three of the aforementioned assertions cannot be true at the same time.

Hence, these given system specifications are not consistent.

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