how do i solve this???

The answer is two base cases, using induction.

What is induction ?

Weak induction is when an inductive mathematical proof holds true for all integers in a set of countable proofs. Natural numbers typically use this. The base step and inductive step are used to prove a set, making it the simplest type of mathematical induction.

Two examples make up an induction proof. Without requiring any prior knowledge of other examples, the first, or base case, establishes the claim for n = 0. The induction process, which is used in the second case, demonstrates that if the assertion is true for any particular scenario where n = k, it must also be true for the subsequent case where n = k + 1.

If a statement true  for n= k, accordily to induction it have to hold good for n = k+1,

Hence, base cases does a proof by the weak form of the principle of mathematical induction requires 2 bases.

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Answer:

A. y= 1x + 5

Step-by-step explanation:

Answer:

A. y=x+5

Step-by-step explanation:

(0,5):

x=0

y=(0)+5=5

(3,8):

x=3

y=(3)+5=8

I hope this help you

Answer:

your going to do super good and get %100

Step-by-step explanation:

Answer:

Did you ace it? %100?

Step-by-step explanation:

The expected payout for one draw is $0.19327.

To calculate how much Mark should pay for one draw, we need to determine the probability of drawing each type of card and the corresponding payouts, and then take a weighted average.

There are 13 clubs in the deck, so the probability of drawing a club is 13/52 = 1/4. The payout for a club is $0.50.

There are 4 aces in the deck, so the probability of drawing an ace is 4/52 = 1/13. The payout for an ace is $0.65.

There is only one ace of clubs in the deck, so the probability of drawing the ace of clubs is 1/52. The payout for the ace of clubs is $0.95.

To calculate the weighted average payout, we can multiply the probability of each outcome by its corresponding payout, and then add up the products:

(1/4) x $0.50 + (1/13) x $0.65 + (1/52) x $0.95 = $0.125 + $0.05 + $0.01827

So the expected payout for one draw is $0.19327.

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Answer:

the third one

Step-by-step explanation:

first you would multiply the mass and the "amu" of both of the isotopes of copper when you have what you multiplyed, you add that product and get your answer.

In order to view more detail in the condensed data columns, we can expand the columns by clicking on the arrow icon located on the right side of the column header.

By clicking on the arrow icon located on the right side of the column header, this can expand column and show more detailed information of the fever report.

Effectively, the feature allows to easily access all the relevant data without having to switch between different views or reports which makes it more efficient and user-friendly. Also, we can also customize the columns and choose which data to display based on your preferences and needs.

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According to the question,  solution for the inverse variation function. Using standard concept which defines inverse variation function is as follows:

Inverse variation function: \(yx=k\)

Therefore, the number of inverse variation function which has\((2,3)\) as a solution is : one

What is inverse variation function?

Inverse variation function defines the relationship which are in inverse function. Like, direct variation define direct relationship between the two variables. In inverse variation function, one variable is inversely related to the another variable.

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Answer:

X=15 since it the same

Step-by-step explanation:

X is simply equal to 15 because it an equilateral triangle

Answer:

There is convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327.

Step-by-step explanation:

Because the p-value of 0.045 < α = 0.05 we have convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327.

4 is 90

1 is 37

3

2 is 127

3 is 23

Answer:

The standard deviation of the critical path = 5

Step-by-step explanation:

The formula for the standard deviation of a critical path is given as:

Standard deviation of a path

=√(sum of variances of activities on path)

Variance = (Standard deviation)²

In the above question, we are given:

Standard deviation of 1, 2, 4 and 2 days

Standard deviation of a critical path

=√(sum of variances of activities on path)

= √1² + 2² + 4² + 2²

= √1 + 4 + 16 + 4

= √25

= 5

Mark wants to fence 4 rectangular gardens. So we calculate the perimeter of the each garden by this formula

P = 2(L) + 2(W)

Total Length of the garden =

=

Length = 18.5 feet

Total width of the garden =

=

Width = 9.0 feet

Perimeter of the garden = 18.5 + 9 = 27.5 feet

Mark wants to fence 4 garden

Therefore, 27.5 × 4 = 110 feet.

Mark needs 110 ft. fencing to surround all 4 gardens.

Answer:

4 1/2 +1 1/2= 5 1/2

Step-by-step explanation

The angle ABC in the circle is 17 degrees.

The inscribed angle is ∠ABC and the arc angle is AC.

Therefore, the inscribed angle theorem states that an angle x inscribed in a circle is half of the central angle 2x that subtends the same arc on the circle.

Therefore,

∠ABC = 1 / 2 (34)

Hence,

∠ABC =  17 degrees.

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Answer:

f(g(x))=6x-1

Step-by-step explanation:

Replace all x's in f(x) with g(x):

f(g(x))=2(3x-2)+3 = 6x-4+3=6x-1

Answer:

180%

Step-by-step explanation:

Answer:

180%

Step-by-step explanation:

Answer:

11/10 is greater than 1

Step-by-step explanation:

For reference, 10/10 = 1, 8/8 = 1. So when looking at these:

11/10 is 1 and 1/10

7/8 is less than 1

Answer:

D

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = - 3 , then

\(a_{n}\) = 8 - 3(n - 1) = 8 - 3n + 3 = - 3n + 11 → D

If PQRS are points on a circle with the centre O, PS is a diameter of the circle Angle PQR=136, the measure of angle RPS is 88 degrees.

Since QR is parallel to PS, we can use alternate interior angles to determine that angle QPS is equal to angle PQR. This means that angle QPS is also 136 degrees.

Angle PQR and angle QPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

We can use this fact to find the measure of angle RPS. First, we know that the sum of angles in a quadrilateral is 360 degrees. Therefore, we can find the measure of angle PSR as follows:

Angle PSR = 360 degrees - Angle PQR - Angle QPS

Angle PSR = 360 degrees - 136 degrees - 136 degrees

Angle PSR = 88 degrees

Next, we use the fact that angles at the circumference of a circle subtended by the same arc are equal. Angle PSR and angle RPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

Angle RPS = Angle PSR = 88 degrees

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Complete question is:

PQRS are points on a circle with the centre O PS is a diameter of the circle Angle PQR=136 Work out the size of angle RPS

The margin of error for the 95% confidence interval used to estimate the population proportion, given n = 186 and x = 103, is approximately 0.0643 (option b).

To find the margin of error for a confidence interval, we use the formula:

Margin of Error = \(Z * \sqrt{((p-hat * (1 - p-hat)) / n)}\),

where Z represents the z-score corresponding to the desired confidence level, p-hat is the sample proportion, and n is the sample size.

In this case, the sample size is n = 186 and the sample proportion is p-hat = x/n = 103/186.

First, we need to find the z-score corresponding to a 95% confidence level. The z-score for a 95% confidence level is approximately 1.96.

Substituting the values into the formula, we have:

Margin of Error = \(1.96 * \sqrt{ ((103/186 * (1 - 103/186)) / 186)}\) ≈ 0.0643.

Therefore, the margin of error for the 95% confidence interval is approximately 0.0643 (option b).

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The probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States, is approximately 0.267 or 26.7%.

To find the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States, we need to consider the percentage distribution provided in the table.

From the table, we can see that the probability of selecting a restaurant from the southwestern United States (SW) is 3%. Within the southwestern region, the probability of selecting a restaurant in a city with a population over 100,000 is given as 8%.

To calculate the conditional probability, we use the formula:

Probability (A|B) = Probability (A ∩ B) / Probability (B),

where A is the event of selecting a restaurant in a city with a population over 100,000 and B is the event of selecting a restaurant from the southwestern United States.

Applying the formula, we have:

Probability (A|B) = (Probability of selecting a restaurant in the southwestern United States with a population over 100,000) / (Probability of selecting a restaurant from the southwestern United States).

Probability (A|B) = 8% / 3%.

Simplifying, we find:

Probability (A|B) ≈ 0.267.

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Note the full question is 1) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. Region <10,000 Population of City 10,000 - 100,000 >100,000 NE 6% 15% 20% SE 6% 1% 4% SW 3% 12% 8% NW 0% 5% 20% What is the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States?

Question:

780 people wanted cranberry blast 220 wanted melon splash,

in the taste test % of the people wanted cranberry blast.

Answer:

78% of people wanted cranberry blast.

the  Answer C: 4

Step-by-step explanation:

Answer:

6*4 = 24

Step-by-step explanation:

Hopefully that helps, and you can write fractions as x/y.

Answer:

6×3 because 6 is one third of the whole loaf and 6×3 are 18.

Step-by-step explanation:

The coordinate vector of b relative to F is:

bf = [ 4 ]
      [-2]

To find the coordinates of b with respect to the basis F, we need to express b as a linear combination of f1 and f2:

b = a1f1 + a2f2

where a1 and a2 are scalars. We want to find a1 and a2.

Substituting in the given values for b, f1, and f2, we get:

[-2] = a1[0] + a2[-1]
[0]  = a1[-1] + a2[-1]

Simplifying these equations, we get:

a2 = 2
a1 + a2 = 0

Solving for a1, we get:

a1 = -2

Therefore, we can express b as:

b = -2f1 + 2f2

To find the coordinate vector of b with respect to the basis F, we simply put the coefficients of f1 and f2 into a column vector:

bf = [-2]
    [ 2]
To find the coordinates of b relative to the ordered basis F, we need to express b as a linear combination of f1 and f2. We have:

b = [-2]
   [-2]

f1 = [ 0]
    [-1]

f2 = [ 1]
    [-1]

We want to find scalars x and y such that:

b = x * f1 + y * f2

Substituting the values, we get:

[-2] = x * [ 0] + y * [ 1]
[-2]       [-1]       [-1]

Solving for x and y:

-2 = 0x + 1y => y = -2
-2 = -1x + (-1y) => -2 = -x + 2 => x = 4

So, we have:

b = 4 * f1 + (-2) * f2

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Answer:

second that -x is the correct answer

The net force acting on the box is <10, 50> Newtons. Rounded to 2 decimal places, the magnitude of the net force is approximately 50.99

To find the net force acting on the box, we need to sum up the individual forces exerted by the ropes. We can do this by adding the corresponding components of the forces.

Given:

F₁ = <20, 30> Newtons

F₂ = <-10, 20> Newtons

To find the net force, we can add the corresponding components of the forces:

Net force = F₁ + F₂

= <20, 30> + <-10, 20>

= <20 + (-10), 30 + 20>

= <10, 50>

Therefore, the net force acting on the box is <10, 50> Newtons.

To calculate the magnitude of the net force, we can use the Pythagorean theorem:

Magnitude of the net force = √(10² + 50²)

= √(100 + 2500)

= √2600

≈ 50.99

Rounded to 2 decimal places, the magnitude of the net force is approximately 50.99 (without the unit).

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Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, the change in the mean is calculated as follows:

Change in mean = Mean of second data set - Mean of first data set

Since none of the values in the second data set have changed, the mean of the second data set is the same as the mean of the first data set. Therefore, the change in the mean is:

Change in mean = Mean of second data set - Mean of first data set

= Mean of first data set - Mean of first data set

= 0

Thus, the change in the means between Kelly's original survey and her second survey is zero.

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The value of v will be - 6.

What is Equation of line?

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Slope of line = - 8

And, Line is passes through the points (8, v) and (6, 10).

Now,

Since, The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is defined as;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, The slope of the line passing through the points (8, v) and (6, 10) is;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

⇒ m = (10 - v) / (6 - 8)

⇒ m = (10 - v) / (-2)

Since, Slope of line (m) = - 8

We get;

⇒ m = (10 - v) / (-2)

⇒ - 8 = (10 - v) / (-2)

Multiply by - 2, we get;

⇒ - 8 x - 2 = 10 - v

⇒ 16 = 10 - v

Add v both side;

⇒ 16 + v = 10

Subtract 16 both side, we get;

⇒ v = - 6

Thus, The value of v will be - 6.

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Answer:

150 and 2/3 or 150.6666...

Step-by-step explanation:

1/6 + 1/2 = 1/6 + 3/6.

1/6 + 3/6 = 4/6 = 2/3

150 + 2/3 = 150 and 2/3

Mark as brainliest please

Answer: exact form is 452/3

decimal form is 150.6

Step-by-step explanation:

Answer:

i think you have written wrong equation

Step-by-step explanation: