If m 3 = 74 degrees, find each measure

The cross product of the unit vectors j and k is i.

The cross product of two vectors a and b is defined as:

a x b = |a| |b| sin(theta) n

where |a| and |b| are the magnitudes of vectors a and b, theta is the angle between the two vectors, and n is a unit vector perpendicular to both a and b, with a direction given by the right-hand rule.

Here, j and k are unit vectors in the y and z directions, respectively. Since j and k are perpendicular to each other, the angle between them is 90 degrees, and the sin(theta) term in the cross product formula is equal to 1.

Thus, we have:

j x k = |j| |k| sin(90) n

Since j and k are unit vectors, their magnitudes are both equal to 1. Substituting these values into the equation above, we get:

j x k = 1 x 1 x 1 n = n

Therefore, the cross product of j and k is a unit vector n that is perpendicular to both j and k.

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Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Answer: x=3 ; y=13

Step-by-step explanation:

1. isolate y from equation to substitute into the second equation

y= 16-x ---> (16-x) = 3x+4

2. move to one side and solve for x

4x=12 --> x=3

3. plug in x value to solve for y

3+y=16 or 3(3)+4

y=13

Answer:

3.8

Step-by-step explanation:19 divided by 5 equals 3.8

Answer:

5

Step-by-step explanation:

I think 5 sorry if I am wrong

The cost of filling your gas tank if it is already 38 38 full. $48.88 required to fill the gas tank if it is already 38% full.

Money do you spend on gasoline is $72.46 is spends on that trip.

Given that

To find

So according the question

We have

Now, for finding

a.) The cost of filling your gas tank if it is already 38 % full.

      38 % of 25 gallon = 9.5 gallon

      the unfilled part of the tank  = 25-9.5 = 15.5 gallon

      So the tank can filled 15.5 gallon of gasoline more now.

      The cost of 15.5 gallon of gasoline

                                   = 15.5 × cost of 1 gallon of gasoline

                                   = 15.5 × 2.96

                                   = $45.88

b.) How much money spend on gasoline on the trip of 705 miles.

    ∵ Car can travelled in 1 gallon of gasoline = 28.8 miles.

    ∴ Gasoline required to travel 705 miles = \(\frac{705}{28.8}\)

                                                                        = 24.48 gallon.

      The cost of 24.48 gallon of gasoline

                                   = 24.48 × cost of 1 gallon of gasoline

                                   = 24.48 × 2.96

                                   = $72.46    

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Answer:

-2

Step-by-step explanation:

El sótano, se entiende, esta por debajo del nivel de la superficie. La superficie, en la recta numérica representa al número cero, es decir, por encima de está encontramos los números positivos y por debajo de está encontramos los números negativos.

Por tanto al estar en el segundo sótano, el número asociado es:

-2

I think I misread this.......

'How to associate an integer of the following statement: I have a car parked in the second basement'

I need to work on my Spanish....

Answer:

It is ...

Step-by-step explanation:

The required fraction at which lettuce will be divided in is 5/12.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,

A chef divides 5 heads of lettuce equally among 12 salad plates. ,
The ratio in which 5 heads of lettuce will be divided in 12 plates is given as,
= 5 / 12

Thus, the required fraction at which lettuce will be divided in is 5/12.

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Step-by-step explanation:

1- The probability of obtaining at most 2 red balls is equal to the probability of obtaining 0 red balls plus the probability of obtaining 1 red ball plus the probability of obtaining 2 red balls. Since there are a total of 12 balls in the urn and each ball has an equal chance of being drawn, the probability of drawing a red ball is

4/12 = 1/3.

Using the binomial formula, we can calculate that

P(J) = (3C0)(1/3)^0(2/3)^3 + (3C1)(1/3)^1(2/3)^2 + (3C2)(1/3)^2(2/3)^1

= 26/27.

2- The probability of getting a red ball followed by a white ball then a black ball is equal to the product of the probabilities of each event happening. Since there are 4 red balls out of 12 total balls, the probability of drawing a red ball is

4/12 = 1/3.

Similarly, the probability of drawing a white ball is 5/12 and the probability of drawing a black ball is 3/12.

Therefore, P(K) = (1/3)(5/12)(3/12)

= 5/108.

3- The probability that the first ball drawn is the only black ball can be calculated as follows: There are three possible sequences in which this can happen: BBW, BWB and WBB. The probability for each sequence happening is

(3/12)(2/9)(5/9) =

10/108.

Therefore P(L) = 3(10/108)

= 5/18.

4- The easiest way to calculate P(M) would be to calculate the complement event: neither red nor white balls are drawn or only one color (either red or white) is drawn. The probability that no red or white balls are drawn is

(3C0)(3C0)(6C3)/(12C3)

=1/220.

The probability that only red balls are drawn is

(4C1)(8C2)/(12C3)

=56/220 and similarly for only white balls being drawn.

Therefore P(M)=1-(1+56+56)/220

=107/220.

I hope this helps!

PLS MRK ME BRAINLIEST

Answer:

24:1 or 24/1

Step-by-step explanation:

288/12 = 24

This is the unit rate.  There are 24 tennis balls for each racket.

Answer: 24

Step-by-step explanation:

288/12=24

THERE ARE 24 BALLS PER TENNIS RACKET.

Solutions of given exponents are :

1.  \(9^{18}\)   2. \(16x^4\)   3.  \(\frac{6561}{y^2}\)

In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as \(a^x\)

where, a = the base of function

            x = exponential

Important properties of exponential :

According to the question,

1. given, \((9^{3})^6\)

  use the property, \((a^n)^m = a^{nm}\)

   \((9^{3})^6\) = \(9^{3.6} = 9^{18}\)

2. Given, \((2x)^4\)

   use the property, \((ab)^n = a^n.b^n\)

    \((2x)^4\) = \(2^4.x^4 = 16x^4\)

3. Given , \((\frac{3^4}{y}) ^{2}\)

    use the property, \((\frac{a}{b})^n = \frac{a^n}{b^n}\)

     \((\frac{3^4}{y}) ^{2}\) = \(\frac{(3^4)^2}{y^2}\)

    now use ,  \((a^n)^m = a^{nm}\)

     = \(\frac{3^8}{y^2} = \frac{6561}{y^2}\)

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Answer:

C. 3/4

Step-by-step explanation:

Using the SOH CAH TOA identity;

tan theta = opposite/adjacent

From the diagram

Opposite = x

Adjacent = 12

tan <B  = x/12

Since cot <B = 1/tan <B

cot <B = 12/x

Get x using pythagoras theorem

x² = 20²-12²

x² = 400 -144

x² = 256

x = 16

Hence cot <B = 12/16

cot <B =3/4

Answer:

3rd one

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

2e-3c

=10-9

=1

2x5 - 3x3

10-6=4

replace the letter with the numbers

Semantic Tableaux are decision-making tools for checking if an argument in a logical language is valid. Semantic tableaux provide an algorithmic method for determining whether a formula in propositional logic is satisfiable (i.e., whether it is possible to find a truth value for each propositional variable that makes the formula true).Explanation:A semantic tableau is a diagram that determines whether a formula is a tautology or not.

The tableau method is an algorithmic technique for determining the validity of a propositional or predicate logic formula. The tableau algorithm produces a tree of sub-formulas of the formula being analyzed, the branches of which represent the possible truth values of the sub-formulas of the formula to be determined.In this process, the formula's truth tables are created with the help of branches. The logical operators contained in the formula's truth tables are negation, conjunction, and disjunction. To test the validity of a formula, the semantic tableau method is a common method.

The decision problem for satisfiability and validity in classical first-order logic is solved using this method.A semantic tableau or a truth tree is a way of visually representing logical proofs to determine the consistency, completeness, or satisfiability of formulas. Semantic tableaux, often known as truth tables, are tree-like data structures that show the possible truth values of the sub-formulas of a formula. The technique starts with the formula to be tested at the root of a tree, and a proof of the formula's validity is constructed by recursively examining the truth values of its sub-formulas.The main advantage of the semantic tableau is its systematic and intuitive character. Semantic tableaux offer a streamlined and intuitive way to show the internal mechanics of logical proofs, providing a foundation for automating the process. For logical proofs, they may be generated automatically by computer algorithms, and their use is becoming increasingly popular in computer science, artificial intelligence, and related fields. Semantic tableaux are a simple yet effective tool for demonstrating the validity of a proposition

The semantic tableau provides a simple and intuitive method for determining the validity of logical formulas. Semantic tableaux are tree-like data structures that show the possible truth values of the sub-formulas of a formula. The technique begins with the formula to be tested at the root of a tree, and a proof of the formula's validity is constructed by recursively examining the truth values of its sub-formulas. Semantics tableaux provide a foundation for automating logical proof generation and are becoming more common in computer science, artificial intelligence, and related fields.

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Answer:

p = 1

Step-by-step explanation:

Given that the system intersect at (4, q) then this point satisfies both equations, that is

q = 4² - 4(4) + 3

q = \(\frac{1}{2}\) (4) + p

Equating both gives

16 - 16 + 3 = 2 + p, that is

3 = 2 + p ( subtract 2 from both sides )

p = 1

Given: 2n = m + h, h = n + m, n = 2m is proven below.

Given: a - b = c -d, b = d - 1, c = 6; a = 5 is proven below.

Given: 2n = m + h, h = n + m; Prove: n = 2m

Statements:

2n = m + h (Given)

h = n + m (Given)

2n = m + n + m (Substituting the value of h from statement 2)

2n = 2m + n (Combining like terms in statement 3)

2n - n = 2m (Subtracting n from both sides of statement 4)

n = 2m (Simplifying statement 5)

Reasons:

Statement 1 is given

Statement 2 is given

Statement 3 is obtained by substituting the value of h from statement 2 in statement 1

Statement 4 is obtained by combining like terms in statement 3

Statement 5 is obtained by subtracting n from both sides of statement 4

Statement 6 is obtained by simplifying statement 5

Therefore, n = 2m is proven.

Given: a - b = c -d, b = d - 1, c = 6; Prove: a = 5

Statements:

a - b = c - d (Given)

b = d - 1 (Given)

c = 6 (Given)

a - b = c - d (Repeating statement 1)

a - (d - 1) = 6 - d (Substituting b with d - 1 in statement 4)

a - d + 1 = 6 - d (Expanding the bracket in statement 5)

a + 1 = 7 (Adding d to both sides of statement 6 and simplifying)

a = 6 (Subtracting 1 from both sides of statement 7)

Reasons:

Statement 1 is given

Statement 2 is given

Statement 3 is given

Statement 4 is repeating statement 1

Statement 5 is obtained by substituting b with d - 1 in statement 4

Statement 6 is obtained by expanding the bracket in statement 5

Statement 7 is obtained by adding d to both sides of statement 6 and simplifying

Statement 8 is obtained by subtracting 1 from both sides of statement 7

Therefore, a = 5 is proven.

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Answer:

cos^2 (x)

Step-by-step explanation:

Use two of the Pythagorean Identities. See image.

You can rearrange the Pyth Identities. Like subtract the same thing from both sides.

Your question simplifies in just two steps. See image.

The gross monthly salary of a clerk earning an annual salary of $22,320 is $1,860.

To determine the clerk's gross monthly salary, divide her annual salary by the number of months in a year. There are 12 months in a year, so the clerk's monthly salary is as follows:$22,320 / 12 = $1,860

Given, the clerk is paid an annual salary of $22,320.To find the gross monthly salary of the clerk, we will divide the annual salary by the number of months in a year, i.e., 12 months.Gross monthly salary = Annual salary / 12Gross monthly salary = $22,320 / 12Gross monthly salary = $1,860Thus, the gross monthly salary of the clerk is $1,860.

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Answer:

You will be paying 60 percent more than the original price

Step-by-step explanation:

Here you go hope it helps

The probability of flipping heads and rolling a three is zero. These are two independent events, and the probability of each event occurring is 1/2 for flipping heads and 1/6 for rolling a three. Therefore, the probability is 1/12, which can be written as a fraction.

To calculate the probability of two independent events occurring simultaneously, we multiply the probabilities of each event. In this case, flipping heads and rolling a three are two independent events. The probability of flipping heads is 1/2 because there are two possible outcomes (heads or tails), and assuming a fair coin, each outcome has an equal chance of occurring. Similarly, the probability of rolling a three on a fair six-sided die is 1/6 because there are six possible outcomes (numbers 1 to 6), and each outcome has an equal chance of occurring.

When we want to find the probability of both events happening, we multiply the individual probabilities. In this case, (1/2) * (1/6) = 1/12. This means that out of all the possible outcomes of flipping a coin and rolling a die, only one out of twelve outcomes satisfies the condition of getting heads and rolling a three simultaneously.

Therefore, the probability of flipping heads and rolling a three is 1/12.

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In mathematics, the point below which a specified percentage of the observations fall is commonly referred to as the percentile.

A percentile is a measure that indicates the relative position of a particular value within a dataset.

For example, if a value is at the 80th percentile, it means that 80% of the observations in the dataset are below that value, and only 20% of the observations are above it.

Percentiles are often used to analyze and understand the distribution of data, especially in fields such as statistics, probability, and data analysis. They provide insights into how individual data points compare to the overall dataset and help identify outliers or extreme values.

A percentile is a statistical measure that indicates the relative standing of a particular value within a dataset. It represents the point below which a specified percentage of the observations or data points fall. Percentiles are primarily used to understand the distribution of data and analyze how individual values compare to the overall dataset.

To calculate a percentile, the dataset is arranged in ascending order, from the smallest value to the largest value. The position of a specific percentile is then determined based on the percentage of data points below it. For example, the 75th percentile represents the value below which 75% of the data points fall.

Percentiles are commonly used in various fields, including statistics, probability, and data analysis. They provide valuable insights into the spread, variability, and distribution of data. Here are a few key points to consider:

1. Median: The median is the 50th percentile, representing the value that divides the dataset into two equal halves. It is a measure of central tendency and provides information about the middle point of the distribution.

2. Quartiles: Quartiles divide the dataset into four equal parts. The first quartile, or the 25th percentile (Q1), represents the value below which 25% of the data points fall. The third quartile, or the 75th percentile (Q3), represents the value below which 75% of the data points fall. The difference between Q3 and Q1 is known as the interquartile range (IQR) and provides insights into the spread of the middle 50% of the data.

3. Percentile Ranks: Percentile ranks indicate the percentage of data points that are below a specific value. For example, if a student scores in the 80th percentile on a standardized test, it means they performed better than 80% of the test-takers.

4. Outliers: Percentiles can be useful in identifying outliers, which are data points that significantly deviate from the rest of the dataset. Extremely high or low percentiles may indicate unusual or extreme values that warrant further investigation.

5. Normal Distribution: In a normal distribution, the 50th percentile (median) coincides with the mean and mode, and specific percentiles have known standard deviations from the mean (e.g., the 68-95-99.7 rule).

Percentiles are versatile tools for summarizing and analyzing data, providing valuable insights into the distribution and relative positions of individual values. They enable comparisons and help make informed decisions based on the characteristics of a dataset.

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The rate of interest for 2nd year is 4.1%

From the given parameters;

Rate of interest for 1st year = 2.5

As we know the formula for Simple interest is given by

                         => I = (PTR)/100

We will use this formula in the following problem

Let 100 be Feri's investment

At the Rate of interest of 2.5  

Interest on 100 = [(100(1)(2.5)]/100 = 2.5

Total amount at end of 1st year = 100 + 2.5 = 102.5

Let x be the rate of interest for 2nd year

At the rate of interest of x

interest on 100 = [(100(1)(x)]/100 = x

Total amount at end of 2st year = 102.5 + x  

Given that, at end of the 2 years, the rate of interest becomes 6.6%  

Interest on 100 at the rate of 6.6%  

=>  [(100(1)(6.6)]/100 = 6.6

=> total amount = 100 + 6.6 = 106.6

As we know in both cases, the amount must be equal

=> 102.5 + x  = 106.6  

=> x = 4.1

Therefore, The rate of interest for 2nd year = 4.1

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Answer:

2/3

Step-by-step explanation:

0.6666667 as a fraction is 2/3

Answer:

Part A = 2/3

Part B = 12

Step-by-step explanation:

2/3 of 18 would be 12

Hope this helped, have a great day

Answer:

7.1

Step-by-step explanation:

if we put this into a number sentence it will be 0.71*10 which is 7.1

Regular maintenance and inspections are essential to ensure the systems are functioning effectively and meeting the required standards.

The dining area and the kitchen used to prepare food in a university dining center have different lighting and ventilation needs due to their distinct purposes and requirements. Here's how and why their needs may differ:

1. Lighting:

- Dining Area: The dining area is primarily a space for eating and socializing. It requires comfortable and pleasant lighting to create a welcoming and inviting atmosphere.

The lighting should be evenly distributed to ensure visibility and allow people to see their food and interact with others. Warm and soft lighting can enhance the ambiance and promote a relaxed dining experience.

- Kitchen: The kitchen is a functional area where food is prepared, cooked, and plated. It requires bright and focused lighting to ensure proper visibility and facilitate safe and efficient food handling.

Bright task lighting is necessary for food preparation areas, cooking stations, and cutting surfaces to ensure accuracy, cleanliness, and food safety. Additionally, proper lighting helps staff identify food quality, monitor cooking processes, and prevent accidents.

2. Ventilation:

- Dining Area: The dining area typically requires adequate ventilation to maintain a comfortable and pleasant environment for diners. Ventilation systems in the dining area primarily focus on maintaining air circulation, controlling temperature, and removing odors.

- Kitchen: The kitchen, on the other hand, has more stringent ventilation requirements due to the nature of food preparation. A commercial kitchen generates heat, steam, smoke, and food odors, which can affect air quality and pose health risks if not properly managed.

The kitchen requires specialized ventilation systems, such as exhaust hoods, fans, and ductwork, to remove heat, steam, and grease-laden air. This helps maintain a clean and safe working environment, minimize odors, control humidity, and prevent the buildup of harmful contaminants.

It's important to note that specific regulations and guidelines may vary depending on local health and safety standards. Therefore, it's crucial for dining centers in universities to comply with applicable codes and regulations regarding lighting and ventilation in both the dining area and the kitchen.

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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