11 inches in miles?
24.5 km in miles?

We prove with the help of Strong Induction.

Let P(n) be the statement that Pn+1/Pn E N.

In order to prove this statement, we will utilize strong induction.So we are given that p + 1/p E N. We will show that P(n) is true for all n >= 1.

Let's consider the base case

P(1):P2/P1 = (p + 1/p)^2 - 2 = (p^2 + 2 + 1/p^2) - 2p/p = (p^2 + 1/p^2) - (2p - 2/p)

Since p + 1/p E N, both p and 1/p must be integers.

Hence, p^2 and 1/p^2 are also integers. This implies that (p^2 + 1/p^2) is an integer.

It only remains to show that (2p - 2/p) is an integer. This is equivalent to showing that 2p^2 - 2 E 0 mod p. But this is clearly true, since 2p^2 - 2 = 2(p^2 - 1) and p^2 - 1 is divisible by p.

Let's assume that P(k) is true for all k such that 1 <= k <= n. We need to prove that P(n+1) is true as well.

Now we need to prove that P(n+1) is true. In other words, we need to show that P(n+2)/P(n+1) E N, assuming that P(n+1)/P(n) E N and P(n)/P(n-1) E N.

Using the definition of P(n), we have:P(n+1)/P(n) E N and P(n)/P(n-1) E N imply that P(n+1) = aP(n) and P(n) = bP(n-1) for some integers a and b. Then:P(n+2)/P(n+1) = (P(n+2)/P(n+1)) * (P(n)/P(n)) = (P(n+2)P(n))/(P(n+1)P(n)) = (aP(n+1)P(n))/(bP(n)P(n+1)) = a/bIf we can show that a/b E N, then P(n+2)/P(n+1) E N, and P(n+1) satisfies the inductive hypothesis.

But this follows from the fact that a and b are integers and the product of two integers is always an integer.

Hence, P(n+1) is true for all n >= 1, by strong induction.Therefore, by strong induction, we have proved that if p + 1/p E N, then Pn+1/Pn EN for all nEN.

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9514 1404 393

Answer:

Step-by-step explanation:

The base of each triangle is half the difference between the bases of the trapezoid:

  (29 in -22 in)/2 = 7 in/2 = 3.5 in

The area of the triangle is given by the formula ...

  A = 1/2bh

  A = 1/2(3.5 in)(17 in) = 29.75 in² . . . triangle area

__

The area of the central rectangle is the product of its base and height.

  A = bh = (22 in)(17 in) = 374 in² . . . rectangle area

__

The total area of the trapezoid is the sum of the areas of the two triangles and the area of the rectangle.

  total area = 2(29.75 in²) + 374 in² = 433.5 in² . . . total trapezoid area

Answer:

a(n) = n/8

Step-by-step explanation:

64/8 = 8, 8/8 = 1, 1/8 = 0.125.…

Explicit Equation: a(n) = n/8

Recursive Equation: a(1) = 64; a(n) = n/8

i dont know if this is correct or not but here you go!

Answer: S > 22

Step-by-step explanation:

Answer:

s = 23 and above

Step-by-step explanation:

2s + 5 > 49

      -5     -5

2s > 44

44/2

= 22

However, the answer for s is not 22

Since it has this sign > not ≥ then that means s = 23 and above

Check:

2(23) + 5 > 49

46 + 5 > 49

51 > 49

Given, an equivalence relation ~ on a set S. Let a and b be two elements in the set S. Assuming that [a] and [b] are two equivalence classes under the equivalence relation ~. Now we need to prove that either [a] = [b] or [a] ∩ [b] = ∅ (disjoint).

Proof:If [a] and [b] are not equal, then there must be some element c in the intersection of the equivalence classes [a] and [b]. i.e, c belongs to [a] and c belongs to [b].Thus, [a] ∩ [b] is not empty.

Let x be an element in [a], then x~a, and a~c (since c belongs to [a]) and hence x~c. So, x belongs to [c] which implies that [a] is a subset of [c].Now, let y be an element in [b], then y~b, and b~c (since c belongs to [b]) and hence y~c. So, y belongs to [c] which implies that [b] is a subset of [c].Thus, both [a] and [b] are subsets of [c].

Therefore, if [a] and [b] are not equal, then [a] and [b] are both subsets of [c] and hence the intersection of [a] and [b] is not empty. Thus, [a] and [b] are not disjoint. Hence, the proof by contradiction.

Conversely, if [a] and [b] are disjoint, then [a] ∩ [b] = ∅. And thus, [a] is not equal to [b].Therefore, two equivalence classes under the equivalence relation ~ are either equal or disjoint.

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Answer:

A radius(radius) = 3The radius of a balloon (which depends on the amount of air inside) is 3

inches

Answer:

c the ratio of the measure of arc QR and the circle

Step-by-step explanation:

i just took the quiz

hope this helps (:

Answer:

D) 156/100 = n/70

Step-by-step explanation:

n = 156% of 70

% indicates a fraction over 100.

"of" indicates multiplication.

n = 156/100 • 70

Let's divide both sides by 70 to have one fraction one each side.

n/70 = 156/100

This is equal to D) [tex](\frac{156}{100}) = (\frac{n}{70})[/tex]

The fund balance at the end of 2019 will be $8,000.

The given problem has four different parts, where we are supposed to calculate the accumulation of funds at the end of 2019 in different scenarios.

Scenario 1In the first scenario, the first deposit is made on December 31, 2016, and interest is compounded annually.

Using the FVA of $1 table; Payment: $2,000n = 4i = 12%

Fund balance 12/31/2019: $9,559

Hence, the fund balance at the end of 2019 will be $9,559.Scenario 2In the second scenario, the first deposit is made on December 31, 2015, and interest is compounded annually.

Using the FVAD of $1 table;Payment: $2,000n = 4i = 12%

Fund balance 12/31/2019: $10,706 Therefore, the fund balance at the end of 2019 will be $10,706.Scenario 3In the third scenario, the first deposit is made on December 31, 2015, and interest is compounded quarterly. Using the FV of the $1 chart, we get the following calculation:

Deposit Date i = n = Deposit Fund Balance 12/31/2015 3% 16 $2,000 $3,20912/31/2016 3% 12 $2,000 $2,85212/31/2017 3% 8 $2,000 $2,53412/31/2018 3% 4 $2,000 $2,251

The interest rate is 3%, and the payment is $2,000. Hence, the fund balance at the end of 2019 will be $10,846.Scenario 4In the fourth scenario, the first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.

Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019$2,000 $8,000 Hence, the fund balance at the end of 2019 will be $8,000.

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Answer:

108+x=180

X=180-108

X=72

The value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.

Given is a regular heptagon with one of the exterior angle be x we need to find the value of x

To find the value of the exterior angle of a regular heptagon, we can use the formula:

Exterior Angle = 360 degrees / Number of Sides

In this case, the heptagon has seven sides, so we can substitute the values into the formula:

Exterior Angle = 360 degrees / 7

Exterior Angle ≈ 51.43 degrees

Therefore, the value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.

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Null hypothesis (H0): µ ≤ 1825, the alternative hypothesis is µ > 1825.

The hypotheses are given below:

Null hypothesis (H0): µ ≤ 1825

Alternative hypothesis (Ha): µ > 1825 where µ represents the population mean amount spent by Amazon Prime members on Amazon.com.

As given in the question, the company believes that due to the pandemic, Amazon Prime members have spent more on average at Amazon.com compared to last year.

Therefore, the alternative hypothesis is µ > 1825.

The null hypothesis is that there is no significant difference or increases in the mean amount spent on Amazon.com by Amazon Prime members last year and this year or that the mean amount spent this year is less than or equal to that of last year, which is µ ≤ 1825.

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Answer:

The median is 2

Step-by-step explanation:

Arrange your numbers in numerical order.

0011112233445

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

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The correct option to the sentence "The percentage of people who have an IQ between 70 and 130 ?" is:

b. 95%.

To solve for the percentage of people who have an IQ between 70 and 130, we will have to use the standard deviation and the mean IQ.

It is given that: Mean = 100, Standard deviation = 15

Now we will use these values to find the percentage of people who have an IQ between 70 and 130.

The first step to this process is to standardize the IQ scores by converting them to Z-scores.

The formula for Z-score is:

Z = (X - µ) / σ, where X represents the IQ score, µ represents the mean IQ, and σ represents the standard deviation.

IQ score of 70:

Z = (70 - 100) / 15

Z = -2

IQ score of 130:

Z = (130 - 100) / 15

Z = 2

Now that we have the Z-scores for IQ scores of 70 and 130, we can find the percentage of people who have an IQ between these two scores. We will use the Z-table to do this. The Z-table provides the area under the standard normal distribution curve for a given Z-score.

From the Z-table, we can find that the area under the curve between Z = -2 and Z = 2 is approximately 0.9545. This means that approximately 95.45% of people have an IQ between 70 and 130.

Therefore, the correct option is: b. 95%.

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The optimal solution to minimize cost while meeting the building code is to use 0 Sitka spruce planks and 150 basswood planks.

To minimize the cost while meeting the building code, let's assume we use x Sitka spruce planks and y basswood planks.

We want to minimize the cost, so our objective function is the cost of the planks. The cost is given by:

Cost = 3.25x + 3.75y

We also have the constraint that the total weight of the planks must be between 600 and 900 pounds:

3x + 4y ≥ 600

3x + 4y ≤ 900

To solve this optimization problem, we can use linear programming. We'll use the Simplex method to find the optimal solution.

Let's rewrite the constraints in standard form:

-3x - 4y ≤ -600

3x + 4y ≤ 900

Now we have the following system of equations:

-3x - 4y ≤ -600

3x + 4y ≤ 900

The feasible region is a quadrilateral with vertices at (0, 150), (0, 225), (300, 150), and (225, 0).

To minimize the cost, we need to find the corner point of the feasible region that lies on the cost line, which is given by 3.25x + 3.75y.

Let's evaluate the cost at each corner point:

Cost at (0, 150) = 3.25(0) + 3.75(150) = 562.50

Cost at (0, 225) = 3.25(0) + 3.75(225) = 843.75

Cost at (300, 150) = 3.25(300) + 3.75(150) = 1500.00

Cost at (225, 0) = 3.25(225) + 3.75(0) = 731.25

From the evaluations, we can see that the minimum cost is achieved at (0, 150), which means we should use 0 Sitka spruce planks and 150 basswood planks.

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Answer:

Step-by-step explanation:

let CP of the article = x

at 5% gain, SP of article = x + (5/100)x = 1.05x

at 5% loss, SP of article = x - (5/100)x = 0.95x

given that 1.05x - 0.95x = 16.5

⇒ 0.1x = 16.5

⇒ x = 16.5/0.1

⇒ x = Rs. 165.

The cost price of the article is Rs. 165.

Answer:

if simplest form by you mean fraction then the answer is 2/5

hope this is the answer you are looking for

Step-by-step explanation:

Answer:

Least Likely: Arrow lands on a section labeled with an odd number.

_____: Arrow lands on a section labeled with the number 1.

Most Likely: Arrow lands on a section labeled with a number less than 4.

Step-by-step explanation:

The spinner:

There are 8 sections, 4 labeled with the number 1, 2 labeled with the number 3, 1 labeled with the number 3, and 1 labeled with the number 4.

Probabilities of the spinner:

The options:

A - Arrow lands on a section labeled with an odd number.

B - Arrow lands on a section labeled with the number 1.

C - Arrow lands on a section labeled with a number less than 4.

The probabilities are:

P(0 < z < 1.96) = 0.4750

P(-1.23 < z < 0) = 0.3907

P(z > 0.82) = 0.2061

P(z < -1.77) = 0.0384

P(-0.20 < z < 1.56) = 0.5199

P(1.12 < z < 1.43) =0.0550

P(z > -1.43) = 0.9236

To locate the chances of the usage of the same old ordinary distribution, we will use a well-known normal desk or a calculator. Here are the calculations for the given possibilities:

P(0 < z < 1.96):

Using the standard everyday desk, the place to the left of one.Ninety-six is 0.9750, and the vicinity to the left of zero is 0.5000. Therefore, the chance between zero and 1.96 is:

P(0 < z < 1.96) = 0.9750 - 0.5000 = 0.4750

P(-1.23 < z < 0):

Using the usual ordinary table, the vicinity to the left of -1.23 is 0.1093, and the area to the left of zero is zero.5000. Therefore, the possibility between -1.23 and 0 is:

P(-1.23 < z < 0) = 0.5000 - 0.1093 = 0.3907

P(z > 0.82):

Using the standard everyday table, the region to the left of zero.82 is zero.7939. Therefore, the possibility of z being extra than 0.82 is:

P(z > 0.82) = 1 - 0.7939 = 0.2061

P(z < -1.77):

Using the same old regular desk, the vicinity to the left of -1.Seventy-seven is zero.0384. Therefore, the chance of z being much less than -1.77 is:

P(z < -1.77) = 0.0384

P(-zero.20 < z < 1.56):

Using the standard ordinary desk, the area to the left of -0.20 is 0.4207, and the area to the left of 1.56 is 0.9406. Therefore, the opportunity between -0.20 and 1. Fifty-six is:

P(-0.20 < z < 1.56) = 0.9406 - 0.4207 = 0.5199

P(1.12 < z < 1.43):

Using the standard regular desk, the place to the left of 1.12 is 0.8686, and the location to the left of one. Forty-three is zero.9236. Therefore, the opportunity between 1.12 and 1. Forty-three is:

P(1.12 < z < 1.43) = 0.9236 - 0.8686 = 0.0550

P(z > -1.43):

Using the same old normal desk, the location to the left of -1.43 is zero.0764. Therefore, the possibility of z being greater than -1. Forty-three is:

P(z > -1.43) = 1 - 0.0764 = 0.9236

Please word that the chances are rounded to 4 decimal locations for clarity.

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The correct question is:

"Find the probability using the standard normal distribution. P(0 < z <1.96), P(-1.23 < z < 0), P(z > 0.82), P(z < -1.77), P(-0.20 < z < 1.56), P(1.12 < z < 1.43), P(z > -1.43)"

Answer:

Step-by-step explanation:

38 − 7x = −2(x − 29)

=> 38 - 7x = -2x + 58

=> 38 - 58 = 7x - 2x

=> -20 = 5x

[tex] = > x = \frac{ - 20}{5} [/tex]

=> x = -4 (Ans)

Your read from left to right. Read intensively if you want to practice the fundamentals and learn vocabulary. Intensive reading is focused more on individual details of what you’re reading.

hope this helped <3

Answer:

This is how to read a

Pronounce it with your mouth open as in "ah" then smile with an "ee" sound. Say "Ay" and that's how you say A or "Ah"

How to read Q? Just pronounce it as "Kyuu" or when reading it say "Ck" with a sharper sound.

Hope this helped!

Answer:

72 degrees

Step-by-step explanation:

To determine the value of DBC, we first have to determine the value of q

Angle on a straight line = 180 degrees

7q - 46 + 3q + 6 = 180

10q - 40 = 180

collect like terms

10q = 180 + 40

10q = 220

q = 22

Substitute for q in angle dbc

3(22) + 6 = 72 degrees

a) The x-intercepts of p(x) are x = 3 and x = -4/3.  b) The y-intercept of p(x) is y = -12.

a) To find the x-intercepts, we set p(x) = 0 and solve for x:

x + 3x² - 4x - 12 = 0

Simplifying the equation, we get:

3x² - 3x - 12 = 0

Factoring, we have:

(x - 3)(3x + 4) = 0

Setting each factor equal to zero, we find the x-intercepts:

x = 3 and x = -4/3

b) The y-intercept is the value of p(0), so we substitute x = 0 into the equation:

p(0) = 0 + 3(0)² - 4(0) - 12 = -12

Therefore, the y-intercept is -12.

c) To sketch the graph, we plot the x-intercepts (x = 3 and x = -4/3) and the y-intercept (y = -12) on a coordinate plane.

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Answer:

(0, 1)

Step-by-step explanation:

All other choices do not match the two possible vertices of the square.

Answer:

3.14 * r * r = area of circle, 2 * 3.14 * r = circumference

Step-by-step explanation:

Remember these formulas, very important.

Answer:

6

Step-by-step explanation:

27/9 =3

now 18/3

=6

Answer:

60

Step-by-step explanation:

Answer:

(a) Mean = 541.00

(b) Median = 535.00

(c) Mode: 530

(d) Range = 230

(e) Variance = 5340.40

(f) Standard deviation = 73.10

(g) IQR = 100

(h) Upper fence = 740.00

Step-by-step explanation:

Answer:

The numbers are 3 and 27.

Step-by-step explanation:

The explanation is attached below.

The equation of the regression line is: y = 1.5 + 0.95x

To find the equation of the regression line, we can use the formulas:

b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²]

a = [(Σy)(Σx²) - (Σx)(Σxy)] / [n(Σx²) - (Σx)²]

Given the following data:

n = 4

Σx = 20

Σy = 25

Σxy = 144

Σx² = 120

Let's calculate the values step by step:

b = [4(144) - (20)(25)] / [4(120) - (20)²]

  = (576 - 500) / (480 - 400)

  = 76 / 80

  = 0.95

a = [(25)(120) - (20)(144)] / [4(120) - (20)²]

  = (3000 - 2880) / (480 - 400)

  = 120 / 80

  = 1.5

Therefore, the equation of the regression line is:

y = 1.5 + 0.95x

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Answer:

2

Step-by-step explanation:

it's literally 6-4 = 2

Answer: 2

Step-by-step explanation: +6 is simply 6 and 6-4 is 2.