help pls

1. Renae has been playing Tower of Hanoi and has noticed that the minimum number of moves it takes to defeat the game is related to the number of disks she must move. She has recorded her observations below. Write an equation that describes this pattern.

2. Use a proof by mathematical induction to show that your equation from question 1 applies to the minimum number of moves required to defeat the Tower of Hanoi game, based on the number of disks you must move. Think about the process of the game; and describe how your equation applies to it.

Answer: A) t + 2

Step-by-step explanation:

If t represents an odd integer, then it can be written as t = 2k + 1 for some integer k.

A) t + 2 = (2k + 1) + 2 = 2k + 3 = 2(k + 1) + 1, which is an odd integer.

B) 2t - 1 = 2(2k + 1) - 1 = 4k + 1, which is an odd integer.

C) 3t - 2 = 3(2k + 1) - 2 = 6k + 1, which is an odd integer.

D) 3t + 2 = 3(2k + 1) + 2 = 6k + 5 = 2(3k + 2) + 1, which is an odd integer.

E) 5t + 1 = 5(2k + 1) + 1 = 10k + 6 + 1 = 2(5k + 3) + 1, which is an odd integer.

Therefore, the only expression that represents an even integer is option A) t + 2.

Answer:

The center of the circle is at (0, 3), and the radius of the circle is 2.

So the equation of the circle is

[tex] {x}^{2} + {(y - 3)}^{2} = {2}^{2} [/tex]

[tex] {x}^{2} + {(y - 3)}^{2} = 4[/tex]

Answer:

9, 10, 3y, 5, 3y, 5

Step-by-step explanation:

First look at the second row

_(2y+3)+_(2y+3)

We know that if we multiply the first blank time 2y is should equal 6y^2, so the answer for the first one is 3y. The third blank times 3 should be 15, so the answer for the third one is 5. Therefore, 3y(2y+3)+5(2y+3).

Now if we distribute, we get the answer for the first part: 6y^2+9y+10y+15.

In the second line we got, 3y(2y+3)+5(2y+3), we can factor out the 2y+3 and end up with (2y+3)(2y+5).

Answer:

Step-by-step explanation:

312/520 equals 60%

other people 40%

Answer is in the photo attached. Hope this helped!

The number of orange skittles in the bag is 32.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

The ratio of purple skittles to orange skittles= 5:2

Total skittles= 112

Now,

Let's call the number of purple skittles in the bag "5x" and the number of orange skittles in the bag "2x", where x is a common factor.

We know that the total number of skittles in the bag is 112. So we can write:

5x + 2x = 112

Simplifying, we get:

7x = 112

Dividing both sides by 7, we get:

x = 16

Now we can find the number of orange skittles by substituting x = 16 into our expression for the number of orange skittles:

2x = 2(16) = 32

Therefore, by the given ratio answer will be 32 orange skittles in the bag.

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Answer: 30

180 - x = 180 - 2x + 30

x = 30

Answer:

The measure of the unknown angle is 30°.

Step-by-step explanation:

Let the measure of the unknown angle be x°.

Supplementary angles are two angles whose measures sum to 180°.

Complementary angles are two angles whose measures sum to 90°.

Therefore, the supplement of x° is (180 - x)°, and its complement is (90 - x)°.

Given that the supplement is 30° more than twice its complement:

(180 - x)° = 2(90 - x)° + 30°

To find the measure of the angle, solve the equation:

⇒ (180 - x)° = (180 - 2x)° + 30°

⇒ 180° - x° = 180° - 2x° + 30°

⇒ 180° - x° = 210° - 2x°

⇒ 180° - x° + 2x° = 210° - 2x° + 2x°

⇒ 180° + x° = 210°

⇒ 180° + x° - 180° = 210° - 180°

⇒ x° = 30°

Therefore, the measure of the unknown angle is 30°.

Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.

What is division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. Division is denoted by the symbol "÷" or "/", and it is usually expressed as a fraction or a quotient.

To solve this problem, we need to determine the amount of money represented by the shaded region. Here are the steps:

Assuming that each small square represents $0.01 and there are 143 shaded cells, the total amount of money represented by the shaded region is:

143 cells x $0.01/cell = $1.43

Now, we need to divide $1.43 evenly among Karla's three brothers to find the maximum number of pieces of candy each brother can buy.

$1.43 ÷ 3 = $0.476666...

Since we cannot buy fractional pieces of candy, we need to round down to the nearest whole number. Therefore, each of Karla's three brothers can buy a maximum of:

$0.47 ÷ $0.10/piece = 4 pieces of candy

So each of Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.

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Answer:

28/51

Step-by-step explanation:

First you add up all the values: 28 + 15 + 8 = 51. That is your denominator because the total is the denominator. Then you put 28 as your numerator because that's how many off all the people that only like pizza.

The answer of the given question based on the Compound interest the answer is option a) Rounding to 2 decimal places gives D ≈ 824.50, so the closest option provided is a) 825. Therefore, the number that goes in box D is approximately 824.50, rounded to 2 decimal places.

In compound interest, term "principal" refers to the initial amount of money that is invested or borrowed. The principal is  starting point for calculating interest that will be earned or paid over time.

When you invest money at compound interest rate, interest earned is added to  principal amount, and  resulting sum becomes new principal for next interest calculation.

Based on the information provided in the image, we can calculate the value in box D by multiplying the values in boxes B and C and then dividing by 100:

D = (B × C) ÷ 100

D = (850 × 97) ÷ 100

D = 824.5

Rounding to 2 decimal places gives D ≈ 824.50, so the closest option provided is a) 825. Therefore, the number that goes in box D is approximately 824.50, rounded to 2 decimal places.

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Total equity after adding the simple interest in the amount will be $825.

What is simple interest?

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any interest that may have accumulated in previous periods.

In simple interest, the amount of interest earned or owed is calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.

simple interest is found using

I = P * r * t

Where I is the amount of interest earned or owed, P is the principal amount, r is the annual interest rate as a decimal, and t is the              time period in years.

Now,

Assuming that the return rate of 10% is a simple annual interest rate, the total equity after one year can be calculated using the formula for simple interest:

Total equity = Principal + Interest

where the interest is calculated as:

Interest = Principal x Rate x Time

In this case, the principal is $750, the rate is 10%, and the time is one year.

Then,

Interest = $750 x 0.10 x 1 = $75

Therefore, the total equity after one year would be:

Total equity = $750 + $75 = $825

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Neil will be able to receive Olga's weather updates for a distance of 10 miles on the road.

Equation is a mathematical statement that expresses the equality of two expressions. It is usually written using symbols, such as '=', '<', '>', '+', and '-'. Equations can be used to describe, model, and solve real-world problems. They can also be used to predict the behavior of a system or to find unknown values.

To calculate the approximate number of miles Neil will be able to receive Olga's weather updates, a quadratic equation can be used. The equation is as follows:

A = (x - 15)²+ (y - 15)² <= 100

where A is the area of a circle with a radius of 10 miles, centered at the ranger station, and (x,y) is the position of Neil's car on the road. The equation represents the area that is within the range of Olga's walkie-talkie, which is the area where Neil's car can receive Olga's weather updates.

To solve for x and y, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2 - x1)² + (y2 - y1)². Since we know the starting and ending points of Neil's road, we can use this formula to solve for x and y:

x = Square root of [ (10 - 15)² + (20 - 15)² ] = 10
y = Square root of [ (10 - 15)² + (10 - 15)² ] = 5

Substituting these values into the equation above, we get A = (10 - 15)² + (5 - 15)²= 100, which is Olga's walkie-talkie range. Therefore, Neil will be able to receive Olga's weather updates for a distance of 10 miles on the road.

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Answer:

5) 59.7 in

6) 39.0 mi

7)

8) 50.3 mi

Step-by-step explanation:

5) C = [tex]\pi (19)[/tex]

C = 59.7 in

6) C = [tex]2\pi (6.2)[/tex]

C = 39.0 mi

7) RADIUS IS CUT OFF

use C = [tex]2\pi r[/tex]

8) C = [tex]2\pi (8)[/tex]

C = 50.3 mi

According to the given information, the equation is [tex]V = 15,000(1-0.12)^t[/tex], the car is worth $7,156.67 in 5 years and will be worth $1000 in 24 years.

What is the depreciation rate?

Depreciation rate is a mathematical process in which a quantity decreases over time in a manner proportional to its current value. This means that the rate of decay is proportional to the amount of the substance remaining, and as the amount of the substance decreases, the rate of decline also decreases

a) V = P(1-r)^t, where V is the value of the car, P is the initial price ($15,000), r is the depreciation rate (0.12), and t is the time in years.

[tex]V = 15,000(1-0.12)^t[/tex]

b) To find the value of the car in 5 years, substitute t = 5 into the equation:

[tex]V = 15,000(1-0.12)^5[/tex]

V = 7,156.67

The car is worth approximately $7,156.67 in 5 years.

c) To find when the car will be worth $1000, we need to solve for t in the equation:

[tex]1000 = 15,000(1-0.12)^t[/tex]

[tex]0.067 = (1-0.12)^t[/tex]

Take the natural logarithm of both sides:

ln(0.067) = t ln(0.88)

t = ln(0.067) / ln(0.88)

t ≈ 23.7

Therefore, the car will be worth $1000 in approximately 24 years.

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the direct variation equation relating weight x and stretch y is: y = 0.5x , we can estimate that the spring will stretch 21cm when a 42 gram weight is attached.  

A) We can use the given information to write a direct variation equation as follows:

y = kx

where y represents the amount of stretch of the spring, x represents the weight attached to the spring, and k is the constant of variation.

Using the given information, we know that when a 10 gram weight is attached, the spring stretches 5cm. Therefore:

5 = k(10)

Solving for k, we get:

k = 0.5

So the direct variation equation relating weight x and stretch y is:

y = 0.5x

B) To estimate the amount of stretch when a 42 gram weight is attached, we can use the direct variation equation we just derived:

y = 0.5x

Substituting x = 42, we get:

y = 0.5(42)

y = 21

Therefore, we can estimate that the spring will stretch 21cm when a 42 gram weight is attached.

It's important to note that this is an estimate, and there may be other factors that could affect the actual amount of stretch, such as the quality and condition of the spring. Additionally, the direct variation equation assumes that the spring behaves in a perfectly linear manner, which may not always be the case in reality. However, for simple applications like this, the direct variation equation can provide a useful estimate of the relationship between weight and stretch.

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The probability of choosing letter other than 's' from srinivasa ramanujan is 0.888889 ( nearest millionth)

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probability = sample space / total outcome

For example if a fair die is rolled, the total outcome is 6, because a die has 6 faces. The probability of getting 1 = 1/6

Similarly, The number of times s appeared in the name is 2. This means sample space is 2. The total outcome is 18.

The probability of picking letter 's' out of the name is 2/18 = 1/9 = 0.111111

Therefore the probability of picking letter other than 's' is 1-0.111111 = 0.888889( nearest millionth)

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The probability of choosing a letter other than s in the name srinivasa ramanujan is 0.89

The name "srinivasa ramanujan" contains 2 instances of the letter "s" and a total of 18 letters.

So, the bag contains 16 letters that are not "s".

Therefore, the probability of choosing a letter other than "s" from the bag is:

16/18 = 8/9

So the probability of choosing a letter other than "s" is 8/9, which is already in its lowest terms.

Alternatively, as a decimal rounded, it is 0.89.

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The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

The solution to the quadratic equation is determined as follows;

2x² + 12x - 3 = 0

2x² + 12x = 3

divide through by 2

x² + 6x = ³/₂

take half of coefficient of x, square it and add it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

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The roots of the given quadratic functions are -

x = (- 6 ± √42)/2.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that Inga is solving the quadratic equation -

2x² + 12x - 3 = 0

The quadratic equation is given as -

2x² + 12x - 3 = 0

We can writ its solution as -

x = {- 12 ± √(144 + 24)}/4

x = (- 12 ± √168)/4

x = (- 12 ± 2√42)/4

x = (- 6 ± √42)/2

Therefore, the roots of the given quadratic functions are -

x = (- 6 ± √42)/2.

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To determine the most likely distribution of the colors of candies in the bag before it was opened, we can analyze the data from the table and try to find a distribution that would result in the observed frequencies.

If we add up the number of candies of each color that were pulled out by the four students, we get:

Red: 75 + 80 + 85 + 90 = 330

Blue: 45 + 55 + 60 + 50 = 210

Green: 50 + 45 + 40 + 55 = 190

Yellow: 20 + 20 + 30 + 25 = 95

Orange: 10 + 5 + 25 + 30 = 70

We can see that the most frequently pulled color was red, followed by blue and then green. This suggests that the bag may have had more red candies than the other colors before it was opened.

Looking at the answer choices, the distribution in option B (300 red, 250 blue, 200 green, 100 yellow, and 150 orange) seems to match the observed frequencies the closest, as it has the highest number of red candies. Therefore, option B is the most likely distribution of the colors of candies in the bag before it was opened.

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Correct question:

A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table.

According to this data, which was the most likely distribution of the colors of candies in the bag before it was opened?

A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange

B. 300 red, 250 blue, 200 green, 100 yellow, and 150 orange

C. 200 red, 200 blue, 200 green, 200 yellow, and 200 orange

D. 200 red, 200 blue, 200 green, 100 yellow, and 100 orange

Normal distribution, the quartiles lie at roughly 0.675 standard deviations below the mean and 0.675 standard deviations above the mean, which corresponds to 25% and 75% of the data, respectively.

To determine the number of standard deviations above and below the mean that the quartiles of any normal distribution lie, use the closest available values (the applet cannot hit every value exactly).

The quartiles of a normal distribution are separated by 1.5 IQR, where IQR is the interquartile range. In a standard normal distribution, the interquartile range spans from approximately -0.675 to 0.675, which corresponds to roughly 0.675 standard deviations above and below the mean.

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Answer:

  60.3°

Step-by-step explanation:

You want the measure of angle B in right triangle ABC with leg BC = 8 and leg AC = 14.

The tangent relation is ...

  Tan = Opposite/Adjacent

Applying this to the given triangle, we have ...

  tan(B) = 14/8

The arctangent function gives you the angle from the tangent.

  B = arctan(14/8) ≈ 60.3°

The measure of angle B is about 60.3°.

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Answer: 163.36 in

Step-by-step explanation: Using the formula C=2πr you can plug in the radius and get your answer.

C=2 x pi x 26

C = 163.362817987

round as needed

Answer: 163.36

Im pretty sure all you have to do is use the formula

C=2πr

Step-by-step explanation:

C=2π(26)

163.36

It is more likely for Jenna's coin to land on tails than for Shay's coin to land on heads. This can be solved by concept of Probability.

To determine the likelihood of each event, we need to calculate the probabilities of the outcomes. For Jenna's coin, the probability of landing on tails can be calculated as 17 tails out of 36 flips, which is approximately 0.47 or 47%.

For Shay's coin, the probability of landing on heads can be calculated as 12 heads out of 22 flips, which is approximately 0.55 or 55%.

Therefore, the probability of Shay's coin landing on heads is higher than Jenna's coin landing on tails. However, the question asks which event is more likely to occur, which means we need to compare the probabilities of the opposite outcomes.

For Jenna's coin, the probability of landing on heads is 19 out of 36, which is approximately 0.53 or 53%. For Shay's coin, the probability of landing on tails is 10 out of 22, which is approximately 0.45 or 45%.

Since the probability of Jenna's coin landing on heads is closer to 50% than Shay's coin landing on tails, we can conclude that it is more likely for Jenna's coin to land on tails than for Shay's coin to land on heads.

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Each slice has an exterior edge that measurement roughly 0.6981 feet in length. Hence, the price per slice is around $11.11.

What does measurement and example mean?

Comparison of a parameter with a predetermined reference value is the process called measurement. For instance, when a measurement is represented as 10 kg, kg is the accepted unit of mass and 10 represents the physical quantity's size. Make correction suggestions.

The formula for calculating the arc length of the a sector, which is as follows, may be used to get the measurement of each slice's outer edge:

arc length is equal to (angle/360) x 2r.

when r is the pizza's radius, which is equal to its diameter. When we replace r with 2 feet & angle with 40 degrees, i get:

arc length is (40/360) x 2 x 2 feet, which is rounded to 0.6981 feet with 4 decimal places.

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Answer:

The angles are 60° and 120°.

Step-by-step explanation:

"supplementary" means that the two angles add up to 180°.

One angle can be x.

The other angle can be x+60° bc its 60° more.

Write an equation.

x + x + 60 = 180

combine like terms.

2x + 60 = 180

subtract 60

2x = 120

divide by 2

x = 60.

Since x = 60, one angle is 60° and the other is 120° (that's 60° more) and they are supplementary.

60° + 120° = 180°

The angles are 60° and 120°.

The probability that the first arrival will not occur until at least the fifth one-second interval is 1/32.

This is calculated by the following equation:
P(First arrival in at least the fifth one-second interval) = 1 - P(First arrival in first 4 one-second intervals)
P(First arrival in first 4 one-second intervals) = 4/32
Therefore, P(First arrival in at least the fifth one-second interval) = 1 - 4/32 = 1/32

Therefore, the probability that the first arrival will not occur until at least the fifth one-second interval is 1/32.

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Answer:

To find the answer, you need to multiply the fractions 3/7 and 1/5 together:

3/7 * 1/5 = (31) / (75) = 3/35

Therefore, the answer to 3/7 of 1/5 is 3/35.

Answer:

The word "of" in math means to multiply.

3/7*1/5= 3/35

Step-by-step explanation:

Hope this helps!! Mark me brainliest!!

Answer:2/30

Step-by-step explanation:

1/15*1/15=2/30

There are 2 x 120 = 240 possible arrangements in which Maria and Olivia are adjacent.

An order of award presentations has been devised for seven people, including Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. We must find out how many different orders the awards can be presented in if Maria and Olivia will be one after the other.There are six possible pairs:

{M, O}, {O, M}, {J, M}, {M, K}, {L, M}, and {M, N}.

In the total number of arrangements, these pairs can occur in two different ways. They are:-

The pair can come first, and the remaining people can be arranged in the rest of the arrangement- The pair can come last, and the remaining people can be arranged in the rest of the arrangement.That is, each pair may appear at the beginning or end of the arrangement, and the remaining persons may be arranged in the remaining positions in any order.

The arrangements would be the same for all six pairs, so we can choose any pair and multiply the outcome by 6.Choose the pair {M, O}. The pair may appear at the start or end of the sequence. There are 2 ways to pick which pair appears first or second.There are 5 individuals left to be arranged. The remaining 5 people can be arranged in 5! = 120 ways.

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Answer:180

Step-by-step explanation:

The value of the cube root [tex]343x^9y^{12}z^6[/tex] is [tex]7x^3y^4z^2[/tex]

A number's cube root is a quantity that when multiplied by itself three or more times, returns the original quantity. The cube root of 27, represented as 327, for instance, is 3 because 3 x 3 x 3 = 27 = 33 when we multiply 3 by itself three times. As a result, we can state that the cube root yields a value that is essentially cubed. Thus, 27 is referred to as the ideal cube. We may deduce what the cube's root is from the word "cube root." It denotes the integer that brought about the cube under the root.

The cube root 0f  [tex]343x^9y^{12}z^6[/tex]

[tex]\sqrt[3]{343x^9y^{12}z^6} \\\sqrt[3]{(7x^3y^4z^2)^3} \\\\\\7x^3y^4z^2[/tex]

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Answer:

m<NPQ= 82°

Step-by-step explanation:

Below is the explanation for the answer to the assignment.