How Do you solve this?

Using the addition principle, we have proven that nk = n-1k-1 + n-1k.

To prove that nk = n-1k-1 + n-1k using the addition principle, we can follow these steps:

1. Start with the left side of the equation: nk

2. Apply the addition principle by breaking down n into (n-1) + 1: (n-1 + 1)k

3. Use the distributive property to distribute the k: (n-1)k + 1k

4. Simplify 1k to 1: (n-1)k + 1

5. Substitute n-1 for n and k-1 for k in the first term: n-1k-1 + n-1k

6. This gives us the right side of the equation, proving that nk = n-1k-1 + n-1k.

Therefore, using the addition principle, we have proven that nk = n-1k-1 + n-1k.

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Answer: he rose up the trail and descended and rose again and descended again

i hope this helps???

Answer:

Slope = -2/3

Step-by-step explanation:

You can use the slope formula to find the slope. y2-y1 / x2-x1

Substitute and you get m= -2/3

Answer:

2/-3

Step-by-step explanation:

(6,-2)(3,0)

[tex]\frac{0+2}{3-6}[/tex] =[tex]\frac{2}{-3}[/tex]

slope=2/-3

We first write the system of equations in matrix form, then use elementary row operations to transform the matrix to reduced echelon form.

To solve the system by transforming the augmented matrix to reduced echelon form, we first need to write the system of equations in matrix form. Then, we will use elementary row operations to transform the augmented matrix to reduced echelon form. Once the matrix is in reduced echelon form, we can easily solve for the variables.

Write the system of equations in matrix form.
For example, if the system of equations is:
x + 2y + 3z = 4
2x + 3y + 4z = 5
3x + 4y + 5z = 6
The augmented matrix would be:
[1 2 3 | 4]
[2 3 4 | 5]
[3 4 5 | 6]

Use elementary row operations to transform the augmented matrix to reduced echelon form.
We can use the following elementary row operations:
- Swap two rows
- Multiply a row by a nonzero constant
- Add a multiple of one row to another row
Using these operations, we can transform the matrix to reduced echelon form, which looks like this:
[1 0 0 | a]
[0 1 0 | b]
[0 0 1 | c]

Solve for the variables.
Once the matrix is in reduced echelon form, we can easily solve for the variables. The solution will be:
x = a
y = b
z = c

In conclusion, to solve the system by transforming the augmented matrix to reduced echelon form, we first write the system of equations in matrix form, then use elementary row operations to transform the matrix to reduced echelon form, and finally solve for the variables.

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Alice's percentage profit is approximately 32.91%, rounded to one decimal place.

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

Alice bought the pack of 14 candy bars for £6.32, which means she paid:

[tex]$\frac{6.32}{14} \approx 0.4514$[/tex] per candy bar

She sells each candy bar for 60p, which is equivalent to:

[tex]$\frac{60}{100} = 0.6$[/tex] pounds per candy bar.

So her revenue from selling all 14 candy bars is:

[tex]$14 \times 0.6 = 8.4$[/tex] pounds.

Her profit is then:

[tex]$8.4 - 6.32 = 2.08$[/tex] pounds.

To find the percentage profit, we need to calculate the profit as a percentage of the cost:

[tex]$\frac{2.08}{6.32} \times 100 \approx 32.91%$[/tex]

Therefore, Alice's percentage profit is approximately 32.91%, rounded to one decimal place.

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A matrix A such that its image is spanned by the vector [1/5] is the following:
A =
 [1/5  0]
 [0   0]

The image of A is spanned by the vector [1/5] because it is the only column of the matrix A.
If A is an m x n matrix, then the image of A is the subspace of R^n consisting of all linear combinations of the columns of A. It is the column space of A. We denote it by im(A).

So, in short, the Image of A is the span of the column vectors of A.

The span of a set of vectors is the set of all linear combinations of the vectors. This means that each vector in the span is a linear combination of the original set of vectors.A vector v is in the span of a set of vectors v1, v2, ..., vn if v can be written as a linear combination of the vi’s. That is, there are constants c1, c2, ..., cn such thatv = c1v1 + c2v2 + ... + cnvn

A matrix A such that im(A) spanned by the vector [1/5] is given as follows:[1/5]We know that the span of a vector is a set of all linear combinations of the vector. So, since the span of the Image of A is given by the vector [1/5], A must be a 1 x n matrix with a single row that is equal to the vector [1/5].

Thus, the matrix A such that im(A) spanned by the vector [1/5] is: [1/5]

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Answer:

Step-by-step explanation:

[tex]2x^{2}[/tex]+[tex]7x[/tex]+3

If the NCAA has applications from 6 universities for hosting its intercollegiate tennis championship in 2008 and 2009.

a. There are 30 ways they are not both to be held at the same university.

b. There are 21 ways they may both be held at the same university.

a) If the NCAA wants to select two different universities to host the intercollegiate tennis championship in 2008 and 2009, then the first host can be chosen in 6 ways, and the second host can be chosen in 5 ways (since one university has already been chosen). Therefore, the total number of ways to select the hosts is:

6 x 5 = 30

So there are 30 ways to select two different universities to host the championship in 2008 and 2009.

b) If the NCAA allows the same university to host both championships, then there are two cases to consider:

Case 1: One university hosts both championships. In this case, there are 6 ways to choose the university that will host both championships.

Case 2: Two different universities each host one championship. In this case, the first host can be chosen in 6 ways, and the second host can be chosen in 5 ways (since one university has already been chosen). However, since the order in which the championships are held does not matter, we need to divide by 2 to avoid counting the same pair of universities twice. Therefore, the total number of ways to select the hosts is:

(6 x 5) / 2 = 15

So there are 15 ways to select two different universities to host the championship, with each university hosting one championship.

The total number of ways to select the hosts for the championships, allowing for the possibility of the same university hosting both championships, is:

6 + 15 = 21 ways.

The complete question is:-

If the NCAA has application from 6 universities for hosting its intercollegiate tennis championship in 2008 and 2009 how many ways may they select the hosts for these championship. a) if they are not both to be held at the same university? b) if they may both be held at the same university?

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a) the first question she gets right is question number 3 = 0.6875,

b) she gets all of the questions right = 0.0156

c) she gets at least one question right = 0.5782

n = 3,

a) p (first question gets right is question no. 3)

= p (first question wrong) × p (second question wrong) × p (third question wrong)

= (1-0.25) × (1-0.25) × 0.25

= 0.6875

b) p (all questions right)

= p (first question right) × p (second question right) × p (third question right)

= (0.25)³

= 0.0156

c) p (atleast one question right)

= 1 - p (all questions wrong)

= 1 - p (first question wrong) × (second question wrong) × (third question wrong)

=1 - 0.75 × 0.75 × 0.75

=1 - 0.4218

= 0.5782

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Answer: 320

Step-by-step explanation:

64 x 5

Answer:

Answer:d)  320

Step-by-step explanation:

64x5

Answer: X-intercepts: (10/3)

Y-intercepts: (0,-2)

Step-by-step explanation:

The speed at which a car travel in 2hours 35minutes if it travelled 2hours 45 minutes at a speed of 106 km/hour is 112.8 km/hour.

The algorithm is as follows:

speed = Distance / Time

Distance = speed * time.

Distance = 106 km/h * 2.75 hours

Distance = 291.5 km

Now we can apply the algorithm determine the vehicle's overall speed:

Speed = Distance / Time

The Total time = 2 hours 35 minutes = 2.5833 hours 

Speed = Distance / Total time

Speed = 291.5 km / 2.5833 hours

Speed = 112.8 km/h

The vehicle will therefore with the speed of approximately  112.8 km/h for the duration of the 2 hours 35 minute trip.

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this is your explanation and answer.

The confidence interval on the mean weight of buttercups with confidence levels of 90%, 95%, and 99% is (7.947981, 8.052019), (7.938019, 8.061981) and (7.918413, 8.081587).

The confidence level identifies the likelihood that an estimate of a statistical parameter's location in a sample survey is accurate for the entire population.

Confidence levels must be decided upon in advance when conducting a survey since they affect the survey's essential scope and error margin.

A determined statistical value based on a sample would have a 95% probability of being true for the entire population within the defined confidence level if the confidence level were set at 95%. In other words, there is a very strong likelihood that the population's arithmetic mean will fall inside the survey's defined margins of error.

For 90% confidence level:

Given a=0.1, |Z(0.05)|=1.645 (from standard normal table)

So 90% CI is

[tex]\bar x \pm Z\frac{s}{\sqrt{n} }[/tex]

8 ± 1.645*0.2/√(40)

(7.947981, 8.052019)

For 95% confidence level:

Given a=0.05, |Z(0.025)|=1.96 (from standard normal table)

So 95% CI is

[tex]\bar x \pm Z\frac{s}{\sqrt{n} }[/tex]

8 ± 1.96*0.2/√(40)

(7.938019, 8.061981)

For 99% confidence level:

Given a=0.01, |Z(0.005)|=2.58 (from standard normal table)

So 99% CI is

[tex]\bar x \pm Z\frac{s}{\sqrt{n} }[/tex]

8 ± 2.58*0.2/√(40)

(7.918413, 8.081587).

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Answer:

Step-by-step explanation:

Find the area of EACH square? each? If that's so the answer is already in the question. 1 square unit.

But if you want to find the area of the ENTIRE square (which is made of many squares) then you count them. That's 256 squares my guy. So 256 square units.

If my counting is adequate that answer should be correct.

If there are 20 items, then mοst prοbably the weight οf her suitcase wοuld be c) 20 lbs.

An algebraic expressiοn is a cοmbinatiοn οf variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. It can include numbers, variables, and symbοls that represent mathematical οperatiοns.

Fοr example, the expressiοn 3x + 5 is an algebraic expressiοn where 3 and 5 are cοnstants, x is variable, and + represents additiοn. Similarly, the expressiοn 2a - b/3 is an algebraic expressiοn where 2 and 1/3 are cοnstants, a and b are variables, and - and / represent subtractiοn and divisiοn, respectively.

Assuming that Karen's items are typical travel items such as clοthing, tοiletries, and shοes, the mοst reasοnable predictiοn fοr the tοtal weight οf her suitcase wοuld be arοund 11 lbs (οptiοn c), which is a reasοnable weight fοr a small tο the medium-sized suitcase.

Optiοn d, 26 lbs, cοuld be a pοssibility if the items were heavy οr if the suitcase is large, but it is less likely than οptiοn c.

Optiοn a, 17 lbs, seems tοο light, while οptiοn b, 36 lbs, may be pοssible but less likely than οptiοn c 20 lbs.

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Complete question:

Answer:

346m^2

Step-by-step explanation:

this is a rectangular prism, find the area of each face and add it up you'll get 346m^2

Answer: 48

Step-by-step explanation:

If we use process of elimination we can eliminate 138 and 96 since there obtuse angles which leads us to two answers since 84 is the peak X whould be 48 hope this helps.

Using the law of cosines with the given values, the length of side x is found to be approximately 23.4 cm.

To solve for the length of side x, we can use the law of cosines, which states:
c² = a² + b²  - 2ab cos(C)
where c is the side opposite to the angle we know (x in this case), a and b are the other two sides, and C is the angle opposite to side c.
In this case, we know a = 18 cm, b = 15 cm, and C = 105 degrees. We want to solve for c, which is x.

x² = 18² + 15² - 2(18)(15)cos(105°)
x² = 324 + 225 - 540cos(105°)
x² = 549.66

Taking the square root of both sides, we get:
x = 23.4 cm (rounded to 1 decimal place)

Therefore, the length of side x is approximately 23.4 cm.

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The missing figure is in the image attached below

Therefore, the completed table is Number of hours Wage in Rand

2 160

3 240

7 560

4 320

An hour is a unit of time that is equal to 60 minutes or 3,600 seconds. It is commonly used to measure the duration of an event, the length of a class or meeting, or the time of day. The term "hour" is derived from the Latin word "hora," which means "time of day." There are 24 hours in a day, and the hours are typically divided into two 12-hour periods, AM and PM, to represent the time before and after noon.

by the question.

To complete the table, we need to multiply the number of hours worked by the wage rate per hour:

Number of hours Wage in Rand

2 2 *80 = 160

3 3 × 80 = 240

7 7 × 80 = 560

4 4 × 80 = 320

Therefore, the completed table is:

Number of hours Wage in Rand

2 160

3 240

7 560

4 320

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The integer values of x that satisfy the inequality 3x - 3 > 12 are 6, 7, 8, 9, 10

To solve the inequality 3x - 3 > 12, we can isolate the variable x on one side of the inequality by adding 3 to both sides:

3x - 3 + 3 > 12 + 3

3x > 15

Next, we can divide both sides by 3 to get x by itself:

x > 5

So we know that any integer value of x in the interval [4, 10] that is greater than 5 will satisfy the inequality.

Therefore, the integer values of x that satisfy the inequality are:

6, 7, 8, 9, 10

Note that 5 is not included in this list, since the inequality is strict (i.e., x is greater than 5, not greater than or equal to 5).

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The net charge on a 3.9-cm diameter isolated metal sphere is 0.86 μc.

To calculate the number of excess electrons on the sphere, we use the formula Q = ne, where Q is the total charge, n is the number of excess electrons, and e is the charge of a single electron.

Therefore, the number of excess electrons on the sphere can be calculated as follows:

n = Q/e

n = 0.86 μc/1.6022*10^-19 C

n = 5.35*10^13

Therefore, there are 5.35*10^13 excess electrons on the 3.9-cm diameter isolated metal sphere.

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Both functions are differentiable at all x-values, or (-∞, ∞) in interval notation.

The function y = x^2 is differentiable at all x-values because it is a polynomial function, and polynomial functions are differentiable everywhere.

This means that the function has a derivative at every point on its graph. Therefore, the x-values at which the function is differentiable are all real numbers, or (-∞, ∞).

The function y = x^2 − 49 is also differentiable at all x-values because it is also a polynomial function. Like the first function, it has a derivative at every point on its graph. Therefore, the x-values at which this function is differentiable are also all real numbers, or (-∞, ∞).

In conclusion, both functions are differentiable at all x-values, or (-∞, ∞) in interval notation.

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Answer:

I am pretty sure they are both true! If not please correct me.

Step-by-step explanation:

Therefore , the solution of the given problem of coordinates comes out to be we can infer that option C reaction time 2 seconds, stopping distance 67 feet .

A reference frame can accurately identify position in combination with other mathematical components on this location, including Euclidean space, by using a number of components or coordinates. During mirrored flight, one can locate an item or point by using its coordinates, which appear to be assemblages of numbers. The y or x coordinates can be used to determine an object's location using a double surface.

Here,

According to the scatterplot, reaction time as well as stopping distance generally have a negative trend,

which indicates that as reaction time goes up, stopping distance tends to go down.

The choice with the greatest deviation from the overall trend of the data is option C (reaction time 2 seconds, stopping distance 67 feet), which can be seen when examining the available options. T

his point is an outlier in the scatterplot because it has a comparatively high reaction time but a very large stopping distance.

As a result, we can infer that option C (reaction time 2 seconds, stopping distance 67 feet) is the setting where the scatterplot's correlation is most likely to decline.

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Case 1: The two right triangles are similar.

Case 2: The value of the variable x is equal to 49 / 5 meters.

Case 3: The height of the tree is equal to 91 / 2 meters.

In this problem we need to determine when two triangles are similar and how to find the value of a variable related to a system of two similar triangles.

Case 1 - There is a geometric system formed by two right triangles, whose internal angles are congruent and whose sides are not congruent though proportional. Thus, we conclude that the two right triangles are similar.

Case 2 - The value of the variable can be found by means of the following proportion formula:

8 / 40 = x / 49

x = (8 / 40) × 49

x = 49 / 5

Case 3 - The height of the tree is found by this proportion formula:

h / 260 m = 1.75 m / 10 m

h = (1.75 m / 10 m) × 260 m

h = 91 / 2 m

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To make a tape diagram to solve this problem, you can start by drawing a rectangle to represent the total number of boats in the marina. Then, you can divide the rectangle into four equal parts to represent the fraction of boats that are white.

Next, you can shade in a portion of the remaining three parts to represent the boats that are not white. Since the problem states that the remaining boats are blue and red, you can divide the shaded area into two equal parts and label one part as blue and the other as red.

Finally, you can label the given quantity of red boats (9) on the tape diagram and use it to find the total number of boats in the marina.

Here's an example of how the tape diagram could look like:

_________________________________

|            Total boats           |

|---------------------------------|

|    |    |    |         |         |

|    |    |    |   Red   |         |

|____|____|____|_________|_________|

   4    4    4         3/4      1/4

(Each line represents one boat)

To find the total number of boats, you can set up an equation using the information given in the problem:

3/4 of the boats are white

1/4 of the boats are not white

Out of the non-white boats, some are blue and some are red

There are 9 red boats

So, we have:

1/4 x Total boats = Blue boats + Red boats

1/4 x Total boats = (Total boats - (3/4 x Total boats)) - 9

1/4 x Total boats = 1/4 x Total boats - 9

9 = 0.5 x Total boats

Total boats = 18

Step 1: Draw a rectangle to represent the total number of boats in the marina.

Step 2: Divide the rectangle into four equal parts to represent the fraction of boats that are white.

Step 3: Shade in a portion of the remaining three parts to represent the boats that are not white. Divide the shaded area into two equal parts and label one part as blue and the other as red.

Step 4: Label the given quantity of red boats (9) on the tape diagram.

Step 5: Use the tape diagram to set up an equation. Since we know that 3/4 of the boats are white and the remaining boats are either blue or red, we can write:

1/4 x Total boats = Blue boats + Red boats

Step 6: Use the information given in the problem to simplify the equation. We know that 1/4 of the boats are not white, so we can substitute (Total boats - (3/4 x Total boats)) for Blue boats + Red boats:

1/4 x Total boats = (Total boats - (3/4 x Total boats)) - 9

Step 7: Simplify the equation by combining like terms:

1/4 x Total boats = 1/4 x Total boats - 9

Step 8: Solve for Total boats by isolating it on one side of the equation:

9 = 0.5 x Total boats

Total boats = 18

Step 9: Check your answer. We can verify that our answer is correct by using the tape diagram. If there are 18 boats in the marina, then 3/4 of them (or 13.5 boats) should be white. The remaining 4.5 boats should be split evenly between blue and red (since we divided the non-white area of the tape diagram into two equal parts). 9 of those 4.5 boats are red, which matches the given information in the problem. Therefore, our answer of 18 boats is correct.

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To make a tape diagram for the given problem, draw a rectangle to represent the total number of boats in the marina and divide it into four equal parts to represent the three-quarters of white boats and one quarter of blue and red boats combined.

What is ractangle?

A rectangle is a 2-dimensional shape that has four sides and four angles, where opposite sides are parallel and of equal length, and opposite angles are of equal measure.

To create a tape diagram for this problem, you can start by representing the whole marina as a rectangle. Then, divide the rectangle into four equal parts to represent the boats in the marina.

Since three-quarters of the boats are white, shade in three of the four parts of the rectangle to represent the white boats. This leaves one part of the rectangle unshaded, which represents the remaining boats that are not white.

Next, you are told that of the remaining boats, some are blue and some are red. Let's represent the blue boats as a part of the unshaded area. If x represents the total number of boats in the marina, then the number of blue boats is (1/4)x - 9, since 9 boats are red.

Finally, you are told that the remaining boats are red. Since there are 9 red boats, we can add a label to the tape diagram that shows 9 boats in the red section.

The completed tape diagram should show a rectangle divided into four equal parts, with three parts shaded to represent white boats and one part unshaded to represent the remaining boats. Within the unshaded area, a section labeled "blue" represents (1/4)x - 9 blue boats, and a section labeled "red" represents 9 red boats.

To find the total number of boats in the marina, you can add up the number of boats in each section of the tape diagram. The equation would be:

(3/4)x + (1/4)x - 9 + 9 = x

Simplifying this equation, you get:

(4/4)x = x = 36

Therefore, there are 36 boats in the marina.

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If the speed "v" of train is 68 km/h, then the inequality that shows the error interval is  67.5 ≤ v < 68.5.

The speed of train being reported as 68 km/h, correct to the nearest km/h, the possible error interval for the true speed of the train can be expressed as : 67.5 ≤ v < 68.5,

The lower bound of interval, 67.5 km/h, is obtained by rounding down the true speed of the train to the nearest km/h.

The upper bound of interval, 68.5 km/h, is obtained by rounding up the true speed of the train to the nearest km/h.

Therefore, the error interval inequality is 67.5 ≤ v < 68.5.

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