Write a recursive formula for An, the nth
a
an the nth term of the sequence 12,3, -6, ....

The chance that you will win the show even if you pick 34.

As given in the question, there are 500,000 people in the game show, and the host is asking everyone to pick a number from one to 100. The person who picks the number that's close to two-thirds of the average is the winning number, and he or she will win the show. So, what number should you pick?The average of all the numbers that everyone picks is (1 + 2 + 3 + ....... + 100)/N, where N is the number of people participating in the show. Therefore, the average is (1 + 2 + 3 + .....+ 100)/500,000, which is 50.5.Now, you have to pick a number that's close to two-thirds of 50.5. So, two-thirds of 50.5 is 33.67. As you need to pick a number close to this, you should go for 33 or 34. Since it's impossible for anyone to choose 33.67, you need to pick a number close to either 33 or 34.

Therefore, the number that you should pick is 33 or 34.If you pick 33, then two-thirds of the average will be (2/3) × 50.5 = 33.67, which is very close to 33. Therefore, it's highly likely that you will win the show. However, if you pick 34, then two-thirds of the average will be (2/3) × 50.5 = 33.67, which is close to 34. Therefore, there is still a chance that you will win the show even if you pick 34.

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Answer: C

The denominator is just the number on the bottom. In this case its \(2\sqrt{2}\)

Answer:

I got C.

Step-by-step explanation:

Calculator.

Answer:

C. -2

Step-by-step explanation:

Subtract 3c from -8c, and add -6 to 16 to simplify the equation.

The probability value of (m, n) is (1, 2^1005).

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

(1/2) ⋅ (2^1004 + (-1)^1005)

Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).

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Complete question:

If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?

The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

\((1/2) * (2^{1004} + (-1)^1005)\)

Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)

Hence, (m, n) = (\(1, 2^{1005\)).

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The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.

The formula for the confidence interval is:

CI = p1 ± Z * √((p1 * (1 - p1)) / n)

Where:

CI is the confidence interval,

p1 is the sample proportion (proportion of accidents involving teenage drivers),

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),

n is the sample size (number of accidents checked).

Given:

Number of accidents checked (sample size), n = 582

Number of accidents involving teenage drivers, x = 91

First, we calculate the sample proportion:

p1 = x / n = 91 / 582 ≈ 0.1566

Now we can calculate the confidence interval:

CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)

Calculating the standard error of the proportion:

SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184

Substituting the values into the formula:

CI = 0.1566 ± 1.96 * 0.0184

Calculating the values:

CI = 0.1566 ± 0.0361

Finally, we can simplify the confidence interval:

CI = (0.1205, 0.1927)

Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

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Answer:

B) 17

Step-by-step explanation:

3 (12 - 8) + 5

(3 x 12) - (3 x 8) + 5

(36 - 24) + 5

12 + 5

17

If UV = x and TW = x+99 ,using triangle proportional theorem, then the value of x is 99

Triangle proportion theorem states that if a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

since TU = TS and S W = VW. This show that triangle SUV is an isosceles triangle

then TW / UV = 1/2

therefore x/-x+99 = 1/2

2x = -x+99

Collect like terms

2x- x = 99

x= 99

therefore the value of x is 99

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Answer: -25

Step-by-step explanation:

I used point-slope form [y-3=2(x-14)] and the Y intercept is -25

The expression equivalent to the 5ⁿ/2ⁿ will be (5/2)ⁿ , (2/5)⁻ⁿ ,  (2.5)ⁿ , 2⁻ⁿ/5⁻ⁿ.Options A, B, D, and F are correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the expression is, 5ⁿ/2ⁿ

The expression can be written in different ways as,

5/2)ⁿ

(2/5)⁻ⁿ

(2.5)ⁿ

2⁻ⁿ/5⁻ⁿ

Thus, the expression equivalent to the 5ⁿ/2ⁿ will be (5/2)ⁿ , (2/5)⁻ⁿ ,  (2.5)ⁿ, 2⁻ⁿ/5⁻ⁿ. Options A, B, D, and F are correct.

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a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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65°

Step-by-step explanation:

just have to rest 115° from 180°

Answer:

the area = 28.27 or you can write the answer out as 28.2744 or also 28.27433

Step-by-step explanation:

start with what we know. the formula for solving this is A=pi R squared

so, area= pi (3.1416)

then, multiply that by the radius given, which is 3.

So, 9.4248 × 3 = 28.2744 square inches

or 28.27 sq.in.

HOPE THIS HELPS... HAVE A GREAT DAY!!

The symbol for proportionality is "∝". It is read as "is proportional to" or "varies in proportion to".

Proportionality is a mathematical concept that describes the relationship between two quantities. When two quantities are proportional, it means that they have a constant ratio. For example, the distance traveled by a car is proportional to the time it takes to travel that distance. This means that if the time taken to travel doubles, then the distance traveled also doubles.

In mathematics, we use the symbol "∝" to represent proportionality. This symbol is read as "is proportional to" or "varies in proportion to". So, if we say that A ∝ B, it means that A is proportional to B. This implies that if B increases or decreases, then A also increases or decreases, but the ratio of A to B remains constant.

The concept of proportionality is used in various mathematical fields, such as algebra, geometry, and physics. It is a powerful tool for solving problems that involve relationships between quantities, and it is widely used in real-world applications, such as in engineering, economics, and statistics.

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Answer:

Step-by-step explanation:

I'll give a couple answers so you get the gist of things.

All you have to do is substitute 1/2 for x and 3/4 for y.

Ex - 30. x × y = 1/2 × 3/4 = 3/8

Answer:

y=3x+1 or 3x-y=-1

Step-by-step explanation:

Hello,

We are given the line 3y+x=-2, and we want to write an equation of the line that is perpendicular to 3y+x=-2, and contains the point (-2, -5)

First, we'll need to find the slope of 3y+x=-2, as perpendicular lines have slopes that multiply to -1

In order to find the slope of 3y+x=-2, let's convert the equation of the line from standard form to slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

y is isolated by itself in slope-intercept form, so let's subtract x from both sides of the equation

3y=-x-2

Now divide both sides by 3

y=\(-\frac{1}{3}x - \frac{2}{3}\)

The slope of the line is -1/3

Now to find the slope of the line perpendicular to it, use this formula:

-1/3m=-1

Multiply both sides by -3

m=3

So the slope of the line perpendicular to it is 3

We can write the equation of this new line in slope-intercept form; substitute 3 as m in y=mx+b:

y=3x+b

Now we need to find b

As the equation passes through the point (-2, -5), we can use its values to help solve for b

Substitute -2 as x and -5 as y:

-5=3(-2)+b

Multiply

-5=-6+b

Add 6 to both sides

1=b

Substitute 1 as b:

y=3x+1

The equation can be left as this, or we can write it in standard form, if you wish

In standard form, x and y are on the same side; so we'll subtract 3x from both sides in order to have both variables on the same side

-3x+y=1

However, a (the coefficient in front of x) cannot be negative; so we'll multiply both sides by -1 to change the sign of the variable.

3x-y=-1

Hope this helps!

The null space of A is a subspace of\(R^2\\\).

The dimension of the null space of A is given by k = n - r, where n is the number of columns of A and r is the rank of A. To calculate the rank of A,

we need to perform row reduction operations on A.

After row reduction operations, the matrix A becomes:

A = [2 -6 -1 0 4 8 0 0 12].

From the above matrix, it can be seen that the rank of A is r = 3, as there are three non-zero rows. Therefore, the dimension of the null space of A is k = n - r = 5 - 3 = 2.

Therefore, the null space of A is a subspace of \(R^2\).

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Answer:

1. D

2.B

3.0.1081 (the one with a line over it)

Answer:

the awnser is:30° yup it is

Answer:

30°

Step-by-step explanation:

We Know

(4x - 2) + (20x - 10) = 180°

4x - 2 + 20x - 10 = 180

24x - 12 = 180

24x = 192

x = 8

Find m∠EBD

∠ABC is a vertical angle to ∠EBD, meaning they will equal it.

4(8) - 2

32 - 2

30°

So, m∠EBD is 30°

Answer:

b i think

Step-by-step explanation:

The average number of trees planted by students at Arlington High School decreased by 20% when comparing the first planting session (5 trees per participant) to the upcoming session (4 trees per participant).

To calculate the percent of decrease, we can use the following formula:

Percent decrease = ((Initial value - Final value) / Initial value) * 100

For the first planting session, the initial value is 5 trees per participant, and for the upcoming session, the final value is 4 trees per participant. Plugging these values into the formula:

Percent decrease = ((5 - 4) / 5) * 100 = (1 / 5) * 100 = 20%

Therefore, the percent of decrease in the average number of trees planted is 20%. This means that the average number of trees planted per participant decreased by 20% from the first planting session to the upcoming session

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Location in the classroom has no impact final grade and the P-Value = 0.58609.

Null Hypothesis:

The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

Here null hypothesis is the ratio that is equal for all rows (No impact)

Alternate Hypothesis: At least one is different

Event     Observed    Expected       Expected     (0-E)^r     (0-E)^r/E

             frequency    probability      frequency

 1 - 2         14                0.2                  12               4             0.3333

 3 - 4          8                 0.2                  12              16            1.3333

 5 - 6         13                0.2                  12               1              0.0833

 7 - 8         10                0.2                  12               4              0.3333

 9 - 10       15                0.2                  12               9              0.75

Total         60                                       60                               2.83333

The corresponding P-Value = 0.586093

Reject Null Hypothesis if P < ∝ (0.05)

Here P > ∝ (we do not reject Null hypothesis)

All proportions are same

Hence the answer is, Location in the classroom has no impact final grade and the P-Value = 0.58609.

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Answer:

-2 5/6

Step-by-step explanation:

First, you have to change the fraction 2/3 to have a common denominator with 1/6. 2/3 x 2/2 = 4/6.

Second, now your equation is -2 1/6 + ( -4/6 ).

Third, you have to add -2 1/6 and -4/6 which gets you -2 5/6

Hope this helps!

Answer:

8

Step-by-step explanation:

8 x .50 = 4

Answer:

8

Step-by-step explanation:

ANSWER

$28

EXPLANATION

We have that the entry fee is $10 and for each ride, $6 must be paid.

We want to complete the table by finding the cost of 3 rides.

First, let us represent the cost of going to the fair and taking the ride.

Let the number of rides a person takes by x.

We have that the cost of taking x rides will be the entry fee plus the cost of each ride taken:

Cost = 10 + 6x

So, for taking 3 rides, it will cost:

Cost = 10 + 6(3)

Cost = 10 + 18

Cost = $28

That is the cost of taking 3 rides.

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

Answer:

Step-by-step explanation:

Replace x

x=-y+21

2(-y+21)-15=y

Then solve the rest

Answer: 6

Step-by-step explanation: 22 / 6 = 3.6666666666666666666666666667

Based on the information given, the equation will be 3x + 10y = 22.

Let the number of times she walks be x.

Let the number of times she rides be y.

Since she runs 3miles, therefore, from the information given, the equation will be 3x + 10y = 22.

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Answer:

= 0 and k = -59.

Step-by-step explanation:

The equation y = x^2 - 82 -- 8.0 + 15 can be written as y = (x - 0)^2 - 82 + 15 + 8.0.

The value of h is the number that is subtracted from x in the square term. In this case, h = 0.

The value of k is the constant term that is added to the square term. In this case, k = -82 + 15 + 8.0 = -59.

Therefore, the values of h and k are h = 0 and k = -59.

the values of h and k in the equation y = x^2 - 82x - 8.0 + 15 converted to the form y = (x - h)^2 + k are h = 41 and k = -162.

To convert the equation y = x^2 - 82x - 8.0 + 15 to the form y = (x - h)^2 + k, we need to complete the square.

First, let's rearrange the terms:

y = x^2 - 82x + 7

To complete the square, we need to add and subtract a constant term that will allow us to factor the quadratic expression as a perfect square trinomial.

We can rewrite the quadratic expression as:

y = (x^2 - 82x + 169) - 169 + 7

Now, let's factor the perfect square trinomial within the parentheses:

y = (x - 41)^2 - 162

Comparing this form to the form y = (x - h)^2 + k, we can identify the values of h and k:

h = 41

k = -162

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Answer:

1. no

2. 36+196=232    c=441 Obtuse.

3. x is greater than 3, less than 21.

Step-by-step explanation:

1. no

2. 36+196=232    c=441 Obtuse.

3. x is greater than 3, less than 21. is the correct answer to the question