2. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v=4i+j, w = i - 4j A. Not enough information B. Parallel O C. Orthogonal D. Neither orthogonal nor paralle

\(\huge\fbox{Answer ☘}\)

number of marks available = 140

percentage secured = 70%

therefore marks secured =

\(70\% \: \: of \: 140 \\\\ =>\frac{70}{100} \times 140 \\ \\ = > 98 \: marks\)

hope helpful~

Answer:

B

Step-by-step explanation:

Thomas is 49 years old.

What is equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

Given:

Huilan is 11 years older than Thomas.

The sum of their ages is 109.

We have to find the Thomas's age in years.

Let x be the Thomas age.

Then the age of Huilan is x + 11.

As the sum of their ages is 109.

⇒ x + (x + 11) = 109

         2x + 11 = 109

               2x = 98

                 x = 49

Hence, Thomas is 49 years old.

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Answer:

7 feet

Step-by-step explanation:

10 - 3 = 7

The augmented matrix for the system of equations is:

| 1  2 -2  2 -1 | 0 |
| 1  2 -1  3 -2 | 0 |
| 2  4 -7  1  1 | 0 |

A basis for the solution space S is {(-2, 1, 0, 0, 4), (2, 0, 1, 0, -4), (3, 0, 0, 1, -4)}. The dimension of the solution space S is 3, since there are 3 free variables and 3 basis vectors.

To solve the system by Gauss elimination method, we first need to eliminate the x1 term from the second and third equations. To do this, we can subtract the first equation from the second and third equations:

| 1  2 -2  2 -1 | 0 |
| 0  0  1  1 -1 | 0 |
| 0  0 -3 -3  3 | 0 |

Next, we can eliminate the x3 term from the third equation by adding 3 times the second equation to the third equation:

| 1  2 -2  2 -1 | 0 |
| 0  0  1  1 -1 | 0 |
| 0  0  0  0  0 | 0 |

Now, we can see that the third equation is redundant, so we can ignore it. The remaining equations give us:

x1 + 2x2 - 2x3 + 2x4 - x5 = 0
x3 - x4 + x5 = 0

We can solve for x3 and x5 in terms of x1, x2, and x4:

x3 = x4 - x5
x5 = 2x1 + 4x2 - 4x3 - 4x4

Substituting these equations back into the first equation gives us:

x1 + 2x2 - 2(x4 - x5) + 2x4 - (2x1 + 4x2 - 4x3 - 4x4) = 0

Simplifying gives us:

-2x1 - 4x2 + 4x3 + 6x4 = 0

We can solve for x1 in terms of x2, x3, and x4:

x1 = -2x2 + 2x3 + 3x4

Now, we can express the solution space S in terms of the free variables x2, x3, and x4:

S = {(-2x2 + 2x3 + 3x4, x2, x3, x4, 2x1 + 4x2 - 4x3 - 4x4) | x2, x3, x4 ∈ R}

A basis for the solution space S is:

{(-2, 1, 0, 0, 4), (2, 0, 1, 0, -4), (3, 0, 0, 1, -4)}

The dimension of the solution space S is 3, since there are 3 free variables and 3 basis vectors.

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Answer:

are those fractions or division signs

Step-by-step explanation:

.........................

Answer:

5/21

Step-by-step explanation:

4/7 - 1/3

12/21 - 7/21

5/21

Best of Luck!

The limit of cos(πx) as x approaches -2 is option C 1/16.

What is limit?

A limit in mathematics is a point at which a function approaches the outcome for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

To find the limit of the function cos(πx) as x approaches -2, we can simply evaluate the function at x = -2, since cos(πx) is a continuous function.

cos(πx)

= cos(π(-2))

= cos(-2π)

We know that the cosine function has a period of 2π, meaning that cos(x + 2π) = cos(x) for any value of x.

Therefore, we can add any multiple of 2π to -2π without changing the value of cos(-2π).

cos(-2π)

= cos(-2π + 2π)

= cos(0)

= 1

So, the limit of cos(πx) as x approaches -2 is equal to cos(-2π) = 1.

Therefore, the value is obtained as 1/16.

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The solution for the linear inequality is provided in the graph.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given linear inequality is x+2y>5

So the solution can be represented by a graph.

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Answer:

The answer is actually not an option here. The answer is y=-1/3x+16

The Risk Matrix lists the relative probability of a risk occurring and the relative impact of the risk occurring.

The Risk Matrix is a tool commonly used in risk management to assess and prioritize risks based on their likelihood of occurrence and potential impact.

It typically consists of a two-dimensional grid, with one axis representing the likelihood of the risk occurring, and the other axis representing the potential impact of the risk.

Each cell in the grid represents a specific level of risk, and is typically color-coded or labeled to indicate the severity of the risk. By using a Risk Matrix.

Organizations can prioritize their risk management efforts by focusing on the risks that are most likely to occur and have the greatest potential impact.

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The nurse manager approves two staff nurses to attend a national conference.

The nurse manager has given their authorization or consent for two staff nurses to participate in and attend a national conference. This decision indicates that the nurse manager recognizes the value and relevance of the conference for professional development and sees the benefit of the staff nurses' participation. By approving their attendance, the nurse manager demonstrates support for their growth, learning, and exposure to new knowledge, experiences, and networking opportunities available at the conference.

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Answer:

A

Step-by-step explanation:

The way to find your nswer would be multiplying because if you did any other option it wouldent make any sense.

a. The correct equation is option (b) 17,000f + 21,000g = 316,000. b. The number of Electra Glide bikes sold is approximately 11. c. Kenny sold 25 Electra Glide motorcycles to make a total of $525,000.

a. To express the number of bikes sold if Kenny sold $316,000 in his first month of business, we can set up an equation using the given prices and variables:

Let f represent the number of Fat Boy motorcycles sold.

Let g represent the number of Electra Glide Classic bikes sold.

Since each Fat Boy motorcycle is sold for $17,000 and each Electra Glide Classic bike is sold for $21,000, we can write the equation:

17,000f + 21,000g = 316,000

b. If 5 Fat Boy bikes were sold, we can substitute the value of f = 5 into the equation to determine the number of Electra Glide bikes sold:

17,000(5) + 21,000g = 316,000

85,000 + 21,000g = 316,000

21,000g = 316,000 - 85,000

21,000g = 231,000

g = 231,000 / 21,000

g ≈ 11

c. If Kenny sold only Electra Glide motorcycles making a total of $525,000, we can set up a new equation using the given prices and variables:

Let g represent the number of Electra Glide Classic bikes sold.

The total revenue from selling Electra Glide bikes is $525,000.

21,000g = 525,000

g = 525,000 / 21,000

g = 25

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The length of the fence in yards, using all 144 feet of material, is 12 yards. Jason will have a fence with a length of 21 yards if he uses all 144 feet of material to build the fence around his rectangular garden.

Let's denote the length of the fence as L in feet. The width of the fence is given as 9 feet. The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

In this case, we have P = 144 feet and W = 9 feet. We want to find the value of L that satisfies the equation 2L + 2W = P.

Substituting the given values, we have:

2L + 2(9) = 144

2L + 18 = 144

2L = 144 - 18

2L = 126

L = 126/2

L = 63

So the length of the fence is 63 feet.

To convert this length from feet to yards, we know that 1 yard is equal to 3 feet. Therefore, to obtain the length in yards, we divide the length in feet by 3:

63 feet / 3 = 21 yards

Therefore, the length of the fence, using all 144 feet of material, is 21 yards.

Jason will have a fence with a length of 21 yards if he uses all 144 feet of material to build the fence around his rectangular garden.

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Answer:

Step-by-step explanation:

the answer willbe 80

The form of the partial fraction decomposition for the rational function "(18x - 29)/((x - 6)(5x - 4))" is A/(x - 6) + B/(5x - 4) .

The partial fraction decomposition is defined as a way to write a rational function as a sum of simpler fractions.

The general form of the partial fraction decomposition for a rational function with distinct linear factors in the denominator is:

⇒ R(x)/[(x - a)(x - b)(x - c) ...] = A/(x - a) + B/(x - b) + C/(x - c) + ...

where R(x) = numerator of the rational function, and A, B, C, etc. are constants .

The function is (18x - 29)/((x - 6)(5x - 4)) ,

the denominator (x-6)(5x-4) is already expressed in the factor form ,

So , we can write in partial fraction decomposition as :

⇒ (18x - 29) / ((x - 6)(5x - 4)) = A/(x - 6) + B/(5x - 4)

where A and B are constants that we are not required to solve .

Therefore , the form of partial fraction decomposition for this rational function is "A/(x - 6) + B/(5x - 4)" .

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The given question is incomplete , the complete question is

Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. (18x - 29)/(x-6)(5x-4)

Answer:

0.6 repeating as a fraction is equal to 2/3.

Step-by-step explanation:

In order to change a repeating decimal into a fraction, we can set the decimal equal to x and then solve...

Answer:

Fghcv

Step-by-step explanation:

Gvhv

Answer:

The second option and the last option

Step-by-step explanation:

10^5 equals 100000 and if you try all options the only 2 that also equal 100000 is those two.

The estimated cost of the new 3000-ft2 heat exchange system for the plant retrofit can be calculated using the power-sizing exponent and the price index. Based on the given information, the rough estimate for the cost of the new heat exchanger system is approximately $108,984.

To estimate the cost of the new heat exchange system, we need to consider the price index and the power-sizing exponent. The price index provides a measure of the change in prices over time. In this case, the price index 7 years ago was 1360, and the current price index is 1478.

To calculate the cost estimate, we can use the following formula:

Cost estimate = (Cost of previous heat exchanger) × (Current price index / Previous price index) × (New size / Previous size) ^ power-sizing exponent

Using the given information, the cost of the previous heat exchanger was $75,000, the previous size was 1200 ft2, and the new size is 3000 ft2.

Plugging in these values into the formula, we get:

Cost estimate = ($75,000) × (1478 / 1360) × (3000 / 1200) ^ 0.55

Simplifying the calculation, we find:

Cost estimate ≈ $108,984

Therefore, a rough estimate for the cost of the new 3000-ft2 heat exchanger system for the plant retrofit is approximately $108,984. It's important to note that this is just an estimate and the actual cost may vary based on specific factors and market conditions.

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Answer:

864

Step-by-step explanation:

First, you multiply 2 and 6, so it's 12, and multiply it by 144, so it's 1728, and divide it by 2. Therefore, it's 864!

So, the exact acute angle 0 for the given function value is 60°. Therefore, the answer is 60.

A function in mathematics seems to be a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a particular member in the second set (called the range). A function, in other words, receives input from one set and produces outputs from another.

The variable x has been frequently used to represent the inputs, and the changeable y is used to represent the outputs. A function can be represented by a formula or a graph. For example, the calculation y = 2x + 1 represents a functional form in which each value of x yields a distinct value of y.

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Answer:

15 is the answer

Answer:

The hypotenuse length = 2

To answer your question if a side is given as a square root of a number, squaring that side will be the number under the square root

Thus (√3)² = 3

Step-by-step explanation:

The Pythagorean theorem states that :

c² = a² + b²

Once we find c² by adding a² and b² we take the square root of the sum

where
c= hypotenuse and a, b the other two sides

In the figure

a = √3, b = 1

a² = (√3)² = 3    (because (√a)² = a)

b² = 1² = 1

a²  + b² = 3 + 1 = 4

Therefore
c² = 4

c = √4 = 2

The standard matrix of a linear transformation T can be found by using the formula A = [T(e1) T(e2) ... T(en)], where A is the standard matrix, e1, e2, ..., en are the columns of the identity matrix, and T(e1), T(e2), ..., T(en) are the images of the identity matrix columns under the transformation T.

1. For the first transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(3,1,3,1) (-5,2,0,0)] = [[3 -5] [1 2] [3 0] [1 0]]. Therefore, the standard matrix of T is [[3 -5] [1 2] [3 0] [1 0]].

2. For the second transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2) T(e3)] = [(1,3) (4,-7) (-5,4)] = [[1 4 -5] [3 -7 4]]. Therefore, the standard matrix of T is [[1 4 -5] [3 -7 4]].

3. For the third transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)], where cos(31/2) and sin(31/2) are the cosine and sine of 31/2 radians, respectively. Therefore, the standard matrix of T is [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)].

4. For the fourth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)], where cos(-1/4) and sin(-1/4) are the cosine and sine of -1/4 radians, respectively. Therefore, the standard matrix of T is [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)].

5. For the fifth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (2,1)] = [[1 2] [0 1]]. Therefore, the standard matrix of T is [[1 2] [0 1]].

6. For the sixth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (3,1)] = [[1 3] [0 1]]. Therefore, the standard matrix of T is [[1 3] [0 1]].

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Identify the smallest multiple that is common to both numbers

The least common multiple (LCM) of two numbers is the smallest positive number that is a multiple of both numbers. To find the LCM of each pair in exercise 24, you can use the following steps:

1. List the multiples of each number in the pair.
2. Identify the smallest multiple that is common to both numbers.
3. This is the least common multiple of the pair.

For example, if the pair is 6 and 8, the multiples of 6 are 6, 12, 18, 24, 30, and so on, and the multiples of 8 are 8, 16, 24, 32, and so on. The smallest multiple that is common to both numbers is 24, so the LCM of 6 and 8 is 24.

Without knowing the specific numbers in exercise 24, it is not possible to provide the exact LCM for each pair. However, you can use the steps outlined above to find the LCM for each pair in the exercise.

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Out of the given options, (a) and (d) are examples of time series while (b) and (c) are not.

A time series is a set of data points collected at regular intervals of time, with the aim of analyzing trends, patterns, and changes over time. In other words, it's a sequence of data points recorded at successive intervals of time. Here's a detailed explanation of each option:

a) The number of daily visitors to Niagara Falls during the month of April: This is an example of a time series. It shows the number of visitors to Niagara Falls every day in the month of April. The data points are collected at regular intervals of time (daily) and can be used to analyze patterns, trends, and changes in the number of visitors over time.

b) The recorded exam scores of students in a class: This is not an example of a time series. The data points represent a one-time measurement of exam scores and do not change over time.

c) The sales prices of single-family homes sold last month in Florida: This is not an example of a time series. The data points represent a one-time measurement of sales prices and do not change over time.

d) The current average prices of regular gasoline in different states of the U.S.: This is an example of a time series. The data points represent the current average prices of regular gasoline in different states of the U.S. The data points are collected at regular intervals of time and can be used to analyze patterns, trends, and changes in gasoline prices over time.

Therefore, Out of the given options, (a) and (d) are examples of time series while (b) and (c) are not.

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For the first question: the probability of showing a 1 on the first roll and an even number on the second roll is 1/12.

For the second question: the probability that Jose reaches into the bag and randomly selects a sugar cookie, eats it, and then selects a chocolate chip cookie is approximately 0.0516.

For the first question:

When rolling a die twice, the probability of getting a 1 on the first roll is 1/6, since there is only one side with a 1 out of the six possible outcomes.

The probability of getting an even number on the second roll is 3/6, as there are three even numbers (2, 4, and 6) out of the six possible outcomes.

To find the probability of both events occurring, we multiply the probabilities:

P(1st roll = 1 and 2nd roll is even) = (1/6) * (3/6) = 1/12

Therefore, the probability of showing a 1 on the first roll and an even number on the second roll is 1/12.

For the second question:

The probability of randomly selecting a sugar cookie from the bag is 7/24, as there are 7 sugar cookies out of the total 24 cookies.

After eating the sugar cookie, there are now 6 sugar cookies left in the bag.

The probability of randomly selecting a chocolate chip cookie from the remaining cookies is 4/23, as there are 4 chocolate chip cookies left out of the remaining 23 cookies.

To find the probability of both events occurring, we multiply the probabilities:

P(selecting sugar cookie and then chocolate chip cookie) = (7/24) * (4/23) ≈ 0.0516 (rounded to four decimal places)

Therefore, the probability that Jose reaches into the bag and randomly selects a sugar cookie, eats it, and then selects a chocolate chip cookie is approximately 0.0516.

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Parallelograms are shapes with equal and parallel opposite sides

The most descriptive name for the quadrilateral is rhombus

The endpoints of the diagonals are given as:

Next, we plot the endpoints on a coordinate plane (see attachment)

From the attached figure, we can see that the quadrilateral is a rhombus

Hence, the most descriptive name for the quadrilateral is rhombus

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By using the volume of a right circular cone, it can be calculated that

Height of the right circular cone is 14 units

What is volume of a right circular cone?

Volume of a right circular cone is the total space taken by the right circular cone.

If r is the radius of the right circular cone and h is the height of the right circular cone, then volume of the right circular cone is calculated by the formula

\(v = \frac{1}{3}\pi r^2h\)

Let the height of the right circular cone be h units

Diameter of cone = 12 units

Radius of cone = \(\frac{12}{2}\) = 6 units

Volume of cone = \(\frac{1}{3} \times \pi \times 6^2 \times h\)

By the problem,

\(\frac{1}{3} \times \pi \times 6^2 \times h = 168 \pi\)

h = \(\frac{168 \pi\times 3}{6 \times 6 \times \pi}\)

h = 14 units

Height of the right circular cone is 14 units

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