Martin finds a shirt on sale

By considering the cases of including and excluding the 'n-th' element, we obtain the recurrence relation is C(n) = C(n-1) + C(n-1).

The first term, C(n-1), represents the number of subsets that exclude the 'n-th' element. Since we exclude this element, we are essentially counting the subsets of a set with 'n-1' elements.

The second term, C(n-1), represents the number of subsets that include the 'n-th' element. Since we include this element, we need to count the subsets of a set with 'n-1' elements as well.

By adding these two terms, we obtain the total number of subsets for a set with 'n' elements.

To use the recurrence relation, we need to establish initial conditions or base cases. These are specific values of C(n) that we know beforehand.

For the subsets of a set with 0 elements, there is only one possible subset: the empty set {}. Therefore, we have:

C(0) = 1

With this initial condition, we can start using the recurrence relation to calculate the number of subsets for sets with larger numbers of elements.

To use the recurrence relation, we start with the initial condition C(0) = 1. Then, we can iteratively calculate C(n) for larger values of 'n' using the recurrence relation:

C(1) = C(0) + C(0) = 1 + 1 = 2

C(2) = C(1) + C(1) = 2 + 2 = 4

C(3) = C(2) + C(2) = 4 + 4 = 8

And so on.

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Answer:

0, -2, 2, -1

Step-by-step explanation:

You are trying to make it so that the one of the (  )= 0.

An example is (x+15) or (2x+3)

the first l one would be x= -15 since -15+15 would equal 0.

The second one is -3/2 since it would be -3+3 which would equal 0.

also since the equation starts with x( or -x it doesn't really matter) one of the zeros would also be 0.

Hope this helps!

Answer:

6x2 − 12x − 30

Answer:

−2x^2 + x + 4

Step-by-step explanation:

(i) Let W be the event that the wind is blowing and H be the event that she hits the target. Using the multiplication rule: Probability of wind and hitting target

= P(W) x P(H|W) = 0.3 x 0.4 = 0.12

(ii) Probability of hitting the target on the first shot:

P(H) = P(not windy) x P(H|not windy) + P(windy) x P(H|windy)

= (1 - 0.3) x 0.7 + 0.3 x 0.4= 0.58

(iii) There are two cases to consider: She hits the target on the first shot and misses on the second, or she misses on the first shot and hits the target on the second.

P(hits target exactly once in two shots)

= P(H1, not H2) + P(not H1, H2)

= [P(not windy) x P(H1, not H2|not windy) + P(windy) x P(H1, not H2|windy)] +[P(not windy) x P(not H1, H2|not windy) + P(windy) x P(not H1, H2|windy)]

= [(1 - 0.3) x 0.7 x 0.6 + 0.3 x 0.4 x 0.6] + [(1 - 0.3) x 0.3 x 0.4 + 0.3 x 0.6 x 0.4]

= 0.282

(iv) Probability of no wind given that she missed:

=P(not W|not H)

= P(not H|not W) x P(not W) / P(not H)

= [P(not windy) x P(not H|not windy) + P(windy) x P(not H|windy)] x [1 - P(H)]

= [(1 - 0.3) x 0.3 + 0.3 x 0.6] x [1 - 0.58]= 0.112

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Answer:

y-(-3)= -4(x-1)

Step-by-step explanation:

i got it correct

The statements that can be used to determine independent events are given as follows:

If two events are independent, the multiplication of the probabilities of each event is equals to the probability of both events, that is:

P(A and B) = P(A) x P(B).

Which means that the first statement is correct.

The conditional probability formula is given as follows:

P(B|A) = P(A and B)/P(A).

However, for independent events, we know that:

P(A and B) = P(A) x P(B).

Hence:

P(B|A) = P(A) x P(B)/P(A).

P(B|A) = P(B).

The same is true for the opposite, meaning that:

P(A|B) = P(A).

Meaning that the last statement is correct.

The Venn probability P(A or B) = P(A) x P(B) - P(A and B) can also be used to determine if the events are independent, when it assumes a value of zero.

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The probability of getting at least one head in two flips of a coin is 3/4 or 0.75, which means that there is a 75% chance of getting at least one head in two flips of a coin.

To find the probability of at least one head in two flips of a coin, we can use the complement rule. The complement of the event "at least one head" is "no heads."

The probability of getting no heads in two flips of a coin is (1/2) x (1/2) = 1/4.

Therefore, the probability of getting at least one head in two flips of a coin is:

1 - (probability of no heads) = 1 - 1/4 = 3/4

The probability of getting at least one head in two flips of a coin is 3/4 or 0.75, which means that there is a 75% chance of getting at least one head in two flips of a coin.

In other words, if you flip a coin twice, the probability of getting at least one head is relatively high, and you are more likely to get at least one head than to get no heads at all.

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Answer:Corporations step up their expansion plans and thus increase their demand for capital.

Step-by-step explanation:

its 6 Step-by-step explanation:

The scale factor of the drawing of the house given the scale of the drawing is 1cm : 0.29m.

A scale drawing is a smaller image of a larger image or object. The scale drawing is usually reduced at a constant dimension.

The scale factor is the ratio of the dimension of the scale drawing to the original object. The scale factor is the measurement used to convert the larger image into a smaller version of the original object.

The scale factor is usually written in this format - 1, a colon (:), then the matching length on the original image. e.g. 1 : 10

The scale factor of the drawing = original dimensions/dimensions of the scale drawing

2 / 7 = 0.29

The complete question is given below.

Colette made a scale drawing of a house. The scale of the drawing was 7 centimeters = 2 meters. What is the scale factor of the drawing?

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Answer:Let x be the price the trader paid for the toaster.

If he sold it for $10,000 and lost 15% of the original price, then he received 85% of the original price:

0.85x = $10,000

If we divide both sides by 0.85, we get:

x = $11,764.71

Therefore, the trader paid $11,764.71 for the toaster.

Step-by-step explanation:

Answer: Hello Luv......

C.  (y x 40)+(y x 8)

Step-by-step explanation:

Hope this helps. Please mark me brainest.

Anna ♥

a. two critical points are (0,0) and (-2, -4). b. H has two positive eigenvalues, and (-2,-4) is a local minimum of f(x,y).

(a) To find the critical points of f(x,y), we need to find the partial derivatives of f(x,y) with respect to x and y, and then set them equal to zero.

∂f/∂x = 4x^3 - 8y

∂f/∂y = 4y - 8x

Setting these partial derivatives equal to zero and solving for x and y, we get:

4x^3 - 8y = 0 => y = x^3/2

4y - 8x = 0 => y = 2x

Substituting y = 2x into y = x^3/2, we get:

2x = x^3/2 => x(x^2 - 4) = 0

So we have two critical points: (0,0) and (-2, -4).

(b) To classify the critical points, we need to use the second partial derivative test. The Hessian matrix of f(x,y) is:

H = [12x^2 -8 -8-8 4 0-8 0 0]

At (0,0), we have H = [-8 -8; -8 4], which has determinant (-8)(4)-(-8)(-8) = 0 and trace -4. Since the determinant is zero, we cannot use the second partial derivative test at (0,0). Instead, we can observe that f(0,0) = 0, and f(x,y) is positive for all (x,y) not equal to (0,0). Therefore, (0,0) is a saddle point. At (-2,-4), we have H = [44 -8; -8 0], which has determinant (44)(0)-(-8)(-8) = 64 > 0 and trace 44 > 0. Therefore, H has two positive eigenvalues, and (-2,-4) is a local minimum of f(x,y).

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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To estimate the standard deviation of the entire population with a 97.4% confidence level, we can use a formula called the confidence interval formula.

It involves calculating a range of values within which the true population standard deviation is likely to lie.Let's begin with the given data of weights of cereal boxes:2.10, 1.14, 1.03, 1.01, 0.95, 1.12, 0.91, 1.06, 0.88, 1.09To calculate the standard deviation with 97.4% confidence, we need to first find the sample mean and sample standard deviation of this data. Then we can use these values in the confidence interval formula to get the range within which the population standard deviation is likely to be. Using a chi-square table, we find χ²(9, 0.013) = 2.821 and χ²(9, 0.987) = 19.022.Substituting the given values, we get: Confidence interval = (0.417 × √9) / √2.821, (0.417 × √9) / √19.022Confidence interval = 0.483, 1.062Therefore, with 97.4% confidence, we can say that the population standard deviation lies within the range of 0.483 to 1.062.

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Answer:Arnold earns $87 of interest in 5 years.

Step-by-step explanation:

If 10p equals 2, then p would equal 0.2

Answer:

Step-by-step explanation:

Start by isolating the variable (in this case, "p") on one side of the equation. To do this, divide both sides of the equation by 10:

10p/10 = 2/10

Simplify both sides of the equation:

p = 0.2

So the solution is p = 0.2.

Answer:

hy are u indian ?

------------------------

(a) The figure is line Segment

(b)The figure is line.

(c )The figure is ray.

Line segment: An part of a line with two endpoints is called a line segment. Different shapes, including triangles, polygons, hexagons, and squares, are constructed using a variety of line segments. A line segment's length is its measurement.

Line: A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

Ray: Ray is a further link in the chain. It consists of a line and a line segment combination with one terminating end and an eternally extending end. Its length cannot be calculated since one of its ends is non-terminating.

Line segment, Line and Ray:

A line segment is a section of a line with two ends that has a quantifiable length. A ray, on the other hand, has only one fixed point (its starting point), but no endpoint. Therefore, its length cannot be determined.A line can be extended on both sides and has no ends. In contrast, a line segment cannot be extended on both sides because it has two endpoints.

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(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

The steps for using a compass and straightedge to construct a square are as follows :-

1. Use a straightedge to draw line a and label a point on the line as point P.

2. Construct a line perpendicular to line a through point P.

3. Label a point on this line as point R.

4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.

5. Label the points of intersection as points S and T.

6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.

7. Label the point of intersection as point Q.

8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .

9. Use the straightedge to draw QS ,QT,SR and RT.

In geometry, a square is a plane figure with four equal sides and four right angles (90°). A square is a special kind of parallelogram as well as an equilateral rectangle.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

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Answer:

x= -2

Step-by-step explanation:

7x-3=4x-9

3x-3= -9

3x= -6

x= -2

Answer:

x=-2

Step-by-step explanation:

7x=4x-6

7x-4x=4x-6-4x

3x=-6

3x/3 = -6/3

x=-2

Answer:

y - 2 = 3(x + 5)

Step-by-step explanation:

The given equation has slope -1/3.  Any line perpendicular to the given line has a slope which is the negative reciprocal of -1/3, which comes out to +3.

Use the point-slope formula y - k = m(x - h):

y - 2 = 3(x + 5)

Answer:

7

Step-by-step explanation:

140 / 20 = 7

so, you need to ride 7 laps per day :)

Heyo! ;D

In order to solve this problem, we simply need to follow the rule of division.

140 ÷ 20 = 7

Hence, if your goal is to ride your bike 140 laps around your block over a 20 day period, you must ride your bike 7 total laps a day to do so.

Hope this helped! If so, please lmk! Tysm and good luck!

Answer:

8

Step-by-step explanation:

this is because If you multiply the denominator by 2 you will get 32

so if you likewise multiply the numerator by 2 you will get 8

The options are  correct: 1. There are infinitely many polynomial p(x) of degree three such that p(4) = 0, p(5) = 0, p(6) = 0, and p(0) = 1.4. If (x - 1) is a factor of 2x³ + x² + 7x + k, then the value of k is -10.

1. The statement is true because there are infinitely many polynomials of degree three that can satisfy the given conditions by adjusting the coefficients of the polynomial.

4. If (x - 1) is a factor of 2x³ + x² + 7x + k, it means that when x = 1, the polynomial evaluates to zero. Substituting x = 1 into the polynomial, we get:

2(1)³ + (1)² + 7(1) + k = 0

2 + 1 + 7 + k = 0

10 + k = 0

k = -10

Therefore, the value of k is -10.

The other options are incorrect:

2. The statement is incorrect because there can be multiple polynomials of degree three that satisfy the given conditions.

3. The number of turning points of f(x) = (x - 5) is 1, not 8.

5. The statement is incomplete and cannot be determined based on the given information.

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The options are  correct: 1. There are infinitely many polynomial p(x) of degree three such that p(4) = 0, p(5) = 0, p(6) = 0, and p(0) = 1.4. If (x - 1) is a factor of 2x³ + x² + 7x + k, then the value of k is -10.

1. The statement is true because there are infinitely many polynomials of degree three that can satisfy the given conditions by adjusting the coefficients of the polynomial.


4. If (x - 1) is a factor of 2x³ + x² + 7x + k, it means that when x = 1, the polynomial evaluates to zero. Substituting x = 1 into the polynomial, we get:

2(1)³ + (1)² + 7(1) + k = 0

2 + 1 + 7 + k = 0

10 + k = 0

k = -10

Therefore, the value of k is -10.

The other options are incorrect:

2. The statement is incorrect because there can be multiple polynomials of degree three that satisfy the given conditions.

3. The number of turning points of f(x) = (x - 5) is 1, not 8.

5. The statement is incomplete and cannot be determined based on the given information.

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Answer:

Step-by-step explanation:

remember,

x^(a/b) corresponds to

bth root of x^

7.

x^(2/3) × y^(5/3)

= 3rd root of (x²y⁵)

8.

(a³b⁷/(a²b^-3))

= a¹×b¹⁰

so, the whole expression is

a^(1/5) × b^(10/5) = a^(1/5) × b²

9.

(2^(1/2) × 3^(5/2))^(1/3)

= (2^(1/6) × 3^(5/6))

the whole expression is

6th root of (2 × 3⁵)

Answer:

b

Step-by-step explanation:

5 5/16

Answer:

5 and 5/16

Step-by-step explanation:

Answer:

2.4 hours

Step-by-step explanation:

6 3/10 divided by 5 1/4 is 1.2. So 6 3/10 is 1.2 times more than 5 1/4. We then take the 1.2 and multiply it by 2 hours because we need to find what's 1.2 times more than 2 hours. So then you get 2.4 hours.