Let v1 and v2 be two vectors in a vector space V. Show that v1 and v2 are linear dependent if and only if one of the vectors is a scalar multiple of the other.

The resultant vector of A+B is C (5,3) with the length of √34.

Resultant vector is the sum of 2 or more vectors. In this case, we give the name of the resultant vector as C.

Please refer to the attached picture below.

Vector C is the resultant vector of A+B and we will use the tail-to-head appraoch.

From the given graph, we know that:

vector A = (2 - 0) = (2)

                 (4 - 0)    (4)

Vector B = (5 - 2) = (3)

                 (3 - 4)     (-1)

Vector C = Vector A + Vector B

Vector C = (2 + 3)

                  (4 + (-1))

Vector C = (5,3)

The length of Vector C can be calculated using the phytagoras theorem:

Length of vector C = √(5² + 3²)

Length of vector C = √(25 + 9)

Length of vector C = √34

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A student who is chosen at random has a 2/5 chance of playing neither instrument.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, a group of 30 pupils, 13 play the flute only. 1 plays the piano only. 4 play both instruments

From the general formula of probability:

Probability = desired outcome / total outcomes

Total outcomes = 30

In our case desired outcome = is chosen student plays neither instrument

desired outcome =  30 - 13 -1 -4

desired outcome = 12

thus,

Probability = 12/30

probability = 2/5

Therefore, the probability of a randomly selected student playing neither instrument is 2/5.

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Answer: either, because the broken pipe is 2.51 meters long either, because the broken pipe is 2.67 meters long

Step-by-step explanation:

The advantage of a larger sample size is that the estimate covers more ground and is more reliable.Answer:a) 0.6180 b) 0.7817 c) 0.9484 d) 0.994

z = (x - xbar)/σ

Standard deviation = σ = √variance = √[(p)(1-p)/n]

p = population proportion = 0.3

n = sample size

Sample proportion = (x - xbar) = ± 0.04

z = (sample proportion)/(standard deviation)

a) sample proportion = ± 0.04

n = 100

Standard deviation = √[(0.3)(1 - 0.3)/100] = 0.0458

z = ± 0.04/0.0458 = ± 0.873

Using normal probability distribution tables

P(|x- xbar| < 0.04) = P(-0.873 < z < 0.873) = P(z < 0.873) - P(z < -0.873) = 0.809 - 0.191 = 0.6180

b) sample proportion = ± 0.04

n = 200

Standard deviation = √[(0.3)(1 - 0.3)/200] = 0.0324

z = ± 0.04/0.0324 = ± 1.23

Using normal probability distribution tables

P(|x- xbar| < 0.04) = P(-1.23 < z < 1.23) = P(z < 1.23) - P(z < -1.23) = 0.891 - 0.1093 = 0.7817

c) sample proportion = ± 0.04

n = 500

Standard deviation = √[(0.3)(1 - 0.3)/500] = 0.0205

z = ± 0.04/0.0205 = ± 1.95

Using normal probability distribution tables

P(|x- xbar| < 0.04) = P(-1.95 < z < 1.95) = P(z < 1.95) - P(z < -1.95) = 0.974 - 0.0256 = 0.9484

d) sample proportion = ± 0.04

n = 1000

Standard deviation = √[(0.3)(1 - 0.3)/1000] = 0.0145

z = ± 0.04/0.0145 = ± 2.76

Using normal population proportion tables

P(|x- xbar| < 0.04) = P(-2.76 < z < 2.76) = P(z < 2.76) - P(z < -2.76) = 0.997 - 0.0029 = 0.9941

e) the advantage of a larger sample size is that the estimate covers more ground and is more reliable.

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a. Steady state concentration = 10/0.23 = 43.48 kg/m^3

b. Concentration 3 hrs later = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3

a. The steady state concentration of the air pollutant can be found by the equation C = M/k, where C is the concentration, M is the mass loading rate, and k is the reaction rate. In this case, C = 10 kg/s/0.23/hr = 43.48 kg/m^3. b. To calculate the concentration of the pollutant 3 hours later, we can use the equation C = M/k * e^(-kt), where t is the time in hours. In this case, C = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3. This equation takes into account the decrease in wind speed and the decrease in reaction rate due to the decrease in concentration.

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The area of the walkway around the garden is 17x+14.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, the area of the garden is 2(5.5x +3.5). The combined area of the garden and the walkway is 3.5(8x + 6).

Area of a walkway = The combined area of the garden and the walkway - The area of the garden

= 3.5(8x+6)-2(5.5x +3.5)

= 28x+21-11x-7

= 17x+14

Therefore, the area of the walkway around the garden is 17x+14.

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a. The two numbers whose product is 24 and whose sum is 14 are 6 and 4

b. 14x = 6x + 8x

c. 8x²2² + 6x + 8x + 3

=8x²2² + (6x + 8x) + 3

=8x²2² + 14x + 3

The trinomial 8x²2² + 14x + 3 can be factored by grouping as (8x²2² + 14x) + 3

The delta is the difference between the values of x and f(z)-f(1.382). To find the largest delta, incrementally increase x by delta until it is less than 0.0008.

A pre-defined Oracle function is a function that may be used to conduct a specific operation or computation on data contained in an Oracle database. Oracle functions are frequently used to change data from a query result or to conduct computations such calculating the average, sum, or count of a group of numbers.

The delta is the difference between the two x values. To determine the biggest delta such that f(z)-f(1.382)0.0008 when |x-1.382|8, we must first enter x=1.382 into the oracle function and note the result of f. (1.382). Then we must gradually increase x by delta, inserting the new value into the Oracle function and noting the result. Then we may compute f(x)-f(1.382) to determine if it is less than 0.0008. This method may be repeated, increasing the delta each time, until we obtain the greatest delta where f(x)-f(1.382)0.0008. The greatest delta that meets this requirement is the answer.

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(a) P(0≤Z≤2.54) represents the area under the standard normal curve between 0 and 2.54 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2.54, which is approximately 0.4966.

(b) P(0≤Z≤2) represents the area under the standard normal curve between 0 and 2 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2, which is approximately 0.4772.

(c) P(−2.40≤Z≤0) represents the area under the standard normal curve between −2.40 and 0 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 0, which is approximately 0.3821.

(d) P(−2.40≤Z≤2.40) represents the area under the standard normal curve between −2.40 and 2.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 2.40, which is approximately 0.7621.

(e) P(Z≤1.36) represents the area under the standard normal curve to the left of 1.36 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the left of 1.36, which is approximately 0.9155.

(f) P(−1.25≤Z) represents the area under the standard normal curve to the right of −1.25 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of −1.25, which is approximately 0.1151.

(g) P(−1.40≤Z≤2.00) represents the area under the standard normal curve between −1.40 and 2.00 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −1.40 and 2.00, which is approximately 0.7170.

(h) P(1.36≤Z≤2.50) represents the area under the standard normal curve between 1.36 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 1.36 and 2.50, which is approximately 0.0951.

(i) P(1.40≤Z) represents the area under the standard normal curve to the right of 1.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of 1.40, which is approximately 0.0821.

(j) P(|Z|≤2.50) represents the area under the standard normal curve between −2.50 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.50 and 2.50, which is approximately 0.5199.

In all cases, a standard normal table or calculator is used to find the area under the standard normal curve. The area represents the probability of the given event.

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The length and width of the given rectangle are 11 units and 8 units.

Let the length and breadth of rectangle be l and b.

The perimeter of a rectangle is given by the formula:

P=2( l + b )

It is given that Perimeter of the rectangle is 38.

2( l + b ) = 38

( l + b ) = 19

l = 19 - b

Also, length is 5 less than twice the width.

l = 2b - 5

⇒19 - b = 2b - 5

⇒3b = 24

⇒b = 8

Now, The length can be calculated as:

⇒l = 19 - b

⇒l = 19 - 8

⇒l = 11

Therefore, The length and Width of the rectangle are 11 and 8 respectively

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Based on the graph which shows the relationship between time and the number of soda bottles a machine can make, this machine can make 20 soda bottles each minute.

In Geometry, the rate of change of any straight line simply refers to the  slope and it can be calculated by using this mathematical equation (expression);

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the graph above, we can logically deduce the following data points located on the line:

Substituting the given data points into the rate of change formula, we have the following;

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope), m = (140 - 100)/(7 - 5)

Rate of change (slope), m = 40/2

Rate of change (slope), m = 20.

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Step-by-step explanation:

(sinθ + cosθ)^2 + (sinθ − cosθ)^2

= (sin^2 θ + cos^2 θ + 2sinθ cosθ)+(sin^2 θ+cos^2 θ − 2sinθ cosθ)

= (1 + 2sinθ cosθ) + (1 − 2sinθ cosθ)

= 1 + 2sinθ cosθ + 1 − 2sinθ cosθ

= 1 + 1 = 2

Therefore, (sinθ+cosθ)^2 + (sinθ−cosθ)^2 = 2

6 is the number of ways described when There are 3 children, 3 pets, and 3 favorite colors. We can represent the children, pets, and colors in a list and explained below .

Children:

1. Angela

2. Lisa

3. Susan

Pets:

1.Cat

2. Dog

3. Fish

Colors:

1.Blue

2.Green

3. Red

We can use the combination rule to find the number of ways to assign a child, a pet, and a color to each other. The combination rule states that if we have n items and want to choose k items at a time, the number of ways to do this is given by the formula:

n! / (k! (n-k)!)

Where n! denotes the factorial of n, meaning the product of all positive integers less than or equal to n.

In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:

3! / (1! (3-1)!) = 3! / (1! 2!) = 3 * 2 * 1 / (1 * 2) = 3

So there are 3 ways to assign a child, a pet, and a color to each other.

We can also use the permutation rule to find the number of ways to assign a child, a pet, and a color to each other. The permutation rule states that if we have n items and want to choose k items at a time and order matters, the number of ways to do this is given by the formula:

n! / (n-k)!

In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:

3! / (3-3)! = 3! / 0! = 3 * 2 * 1 / 1 = 6

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11. The ΔACD is not equal and congruent to ΔBCD.

12. The ΔXYZ is equal and congruent to ΔPQZ.

13. The ΔMNL is not equal and congruent to ΔRSL.

What is congruency?

Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

It is known that -

If two triangles are congruent, when they meet one of the following criteria -

a) All three pairs of corresponding sides should be equal.

b) Two pairs of corresponding sides and the corresponding angles between them should be equal.

c) Two pairs of corresponding angles and the corresponding sides between them should be equal.

11. In the first diagram, it is given that line segments -

AD = BD

CD = CD (common in both the triangles)

It is given that angles -

∠A ≅ ∠B

This proves that AD ≅ BD and CD = CD.

If ΔACD is congruent with ΔBCD then ∠ADC ≅ ∠BDC.

But not enough information is given about ∠ADC and ∠BDC.

Therefore, ΔACD is not congruent with ΔBCD.

12. In the second diagram, it is given that -

Z is the midpoint of line segment XQ and YP.

This means that line segments -

XZ = ZQ

YZ = ZP

It is also given that ∠XZY = ∠PZQ as they form a pair of vertically opposite angles which are equal.

So, the criteria two pairs of corresponding sides and the corresponding angles between them should be equal is fulfilled.

Therefore, ΔXYZ is congruent with ΔPQZ.

13. In the third diagram, it is given that line segments-

MN ≅ LR

LN ≅ LS

It is given that angles -

∠LMN ≅ ∠LRS

If the line segments MN ≅ LR and LN ≅ LS, then ∠MNL ≅ ∠NLS

But not enough information is given about ∠MNL and ∠NLS being equal.

Therefore, ΔMNL is not congruent with ΔRSL.

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Answer:

C

Step-by-step explanation:

Answer:

23/33

Step-by-step explanation:

The copper keys and the silver keys in total is 23 and the amount of keys in total is 33.

Step-by-step explanation:

soln on

n(s)=6

n(p)=3

therefore

probability =6/3

The APR (Annual Percentage Rate) is 4.08% while the APY (Annual Percentage Yield) is 4.16%.

The annual percentage yield (APY) is the normal annual percentage rate (APR) based on a compounding period of one year.

The annual percentage rate (APR) represents the cost of borrowing expressed as a percentage.

Thus, while APY considers compound interest, APR does not.

MPR = 0.34%

APR = 4.08% (0.34 x 12)

The formula for computing the APR is as follows:

APY = (1 + APR/N)^N - 1

Where APR is the normal interest rate, N is the number of compounding period in a year.

= (1 + 0.0408/12)^12 - 1

= (1 + 0.0034)^12 - 1

= (1.0034)^12 = 1

= 1.0416 - 1

= 0.0416

= 4.16%

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Answer -4

Step-by-step explanation:

The system is inconsistent for k=0.

The system has a unique solution when k=1 and k=-3. To see this, we plug in these values of k into the system and solve the resulting three equations in three unknowns. For k=1, we have x=2, y=1, and z=0. For k=-3, we have x=3, y=2, and z=0.

The system has infinitely many solutions when k=5. In this case, we have x+y-5z=2, x+2y+z=3, and x+y+25z=5, which yields the solution x=2, y=1, and z=0/5. Since any non-zero value of z will also satisfy the system, the system has infinitely many solutions.

The system is inconsistent when k=0. In this case, we have x+y=2, x+2y+z=3, and x+y-z=0, which has no solution. Therefore, the system is inconsistent for k=0.

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The conditional probability that the selected student is male and got grade A is 2/7.

P(A|M) stands for the probability of such a considering that M has happened.

Then, formula for the conditional probability is-

P(A|M) = P(A∩M) / P(M)

P(A∩M)  = Probability that the student is male M and got grade A = 4/25.

P(M) =  Probability that the student is male M = 14/25.

Then,

P(A|M) = 4/25 / 14/25

P(A|M) = 4/14 = 2/7

Thus, the conditional probability that the selected student is male and got grade A is 2/7.

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The data can be analyzed to determine the distribution of the data.

In order to construct a histogram for the daily sales of IPA beer, in pints, for the first three years of operations of Red Banjo Brewing Company, the lower bin limit is set to 0 and the bin width is set to 50. The data can be analyzed to determine the distribution of the data. To calculate the distribution, the data points are counted and the number of occurrences of each data point is divided by the total number of data points.

Using this formula, the data can be analyzed to determine if the data is symmetric, negatively skewed, positively skewed, or flat. The formula used is:

(Number of Occurrences / Total Number of Data Points) * 100

In the case of the Red Banjo Brewing Company data, the data is found to be positively skewed. This means that there are more data points in the higher range than in the lower range. This suggests that the brewery has seen a steady increase in the sale of IPA beer over the past three years.

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The domain of y = 3 * (2) ^ x is set of all real numbers i.e. (-∞,∞) and the range is (0,∞).

What is domain and range of a function?

The domain is the set or a collection of all the possible values that can go in the function.

The range is collection of all the output values of a function.

Domain

For the given function, the domain is the set of all real numbers because there is no value for 'x' where the function is not defined.

Thus, the domain is (-∞,∞).

Range

For the given function, the values for y range from 0 to infinity.

Therefore, the range is (0,∞).

Hence, the domain of y = 3 * (2) ^ x is (-∞,∞) and the range is (0,∞).

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The amount of money with the simple interest is A = $ 1,780

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as I

Now , the amount with simple interest A = P + I

Now , the principal P = $ 1,000

The interest rate R = 13 %

The number of years T = 6 years

And , Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

Simple Interest I = ( 1000 x 13 x 6 ) / 100

On simplifying the equation , we get

Simple Interest I = $ 780

Now , the amount after 6 years = $ 1,000 + $ 780

The amount after 6 years = $ 1,780

Hence , the simple interest is $ 780

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Answer:M<R corresponds to M<T, meaning M<R is 4x+1.

Step-by-step explanation:

In parallelogram of 17th problem the x is 12 and y is 14 and in 18th problem value of x is 8 and y is 29.

polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length

4x-9=3x+3

4x-3x=9+3

x=12

2y-3=2x+1

2y-3=24+1

2y=28

Divide both sides by 2

y=14

The opposite angles of a parallelogram are of equal measure.

7x+8=8x

x=8

and y+87=4y

87=3y

Divide both sides by 3

29=y

Hence, in parallelogram of 17th problem the x is 12 and y is 14 and in 18th problem value of x is 8 and y is 29.

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Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.

Two lines are parallel if they have the same slope. The slope of a line is represented by the letter "m" in the equation y = mx + b.

In this case, Y=2x + 9 has a slope of 2 and 4x -2y = 3 has a slope of -1/2, these slopes are different, which means that these two lines are not parallel.

On the other hand, 6x -3y = 0 and 2x -4y -3 are parallel because they have the same slope, -3/2. The slope of a line is the amount of change in the y coordinate for each unit of change in the x coordinate.

Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.

In the case of 6x -3y = 0, the slope is -3/6 = -1/2. In the case of 2x -4y -3, the slope is -4/2 = -2. Since both lines have the same slope, they are parallel. This means that they never intersect and have the same direction.

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The tangent line to the given circle passing through the point B is given by the image presented at the end of the answer.

A tangent line to a circle is a line that only touches the circumference of the circle, not crossing.

If the line crosses the circle, then the line is called a secant line, which crosses the circumference of the circle twice.

Then the tangent line, only touching the circumference of the circle, is given by the image presented at the end of the answer.

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The  basic formula that is used to find out  the area of a triangle is:

Area = (1/2) * base * height.

where "base" is one of the sides of the triangle, and "height" is the perpendicular distance from the vertex opposite the base to the line formed by the base. This formula is based on the fact that the area of a triangle is equal to half of the product of its base and its height. The height is also known as the altitude, and it is the distance from the vertex opposite the base to the line formed by the base. It is important to note that the height must be perpendicular to the base. This formula is valid for any type of triangle, whether it is right-angled or not, and it works well when the base and the height are known. This formula can be used in any triangle, and can be applied to any side as base, not only the bottom side. Another important formula is Heron's formula which is used to find the area of a triangle when the lengths of all three sides are known. Heron's formula is given by:

Area = √(s(s-a)(s-b)(s-c))

where s is said as semi-perimeter of the triangle, and a, b and c are the lengths of the three sides of a given  triangle.

Finally, trigonometric functions like sine, cosine, and tangent can also be used to find the area of a triangle when we know two sides and the angle formed between them. The formula used is:

Area = (1/2) * a * b * sin(C)

where  let us assume a and b are the lengths of two sides of the  given triangle and C is the angle which is  between them.

In conclusion, there are different formulas for calculating the area of a triangle, the most common one is the base times height formula, but depending on the information you have, you can also use Heron's formula or trigonometric functions.

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