1.6i+3/4d-3(1/2i-1.1d)-4.2

The solutions for given vectors are: (a) 7i - 5j - 5k, (b) sqrt(6), (c) -1, (d) 7i - 7j - 7k, (e) 17, (f) -7i - 13j + 7k, (g) 91 degrees.

(a) 2u + 3v = 2(i + j - 2k) + 3(3i - 2j + k) = (2+9)i + (2-6)j + (-4+3)k = 11i - 4j - k

(b) |u| = sqrt(i^2 + j^2 + (-2k)^2) = sqrt(1+1+4) = sqrt(6)

(c) u · v = (i + j - 2k) · (3i - 2j + k) = 3i^2 - 2ij + ik + 3ij - 2j^2 - jk - 6k = 3 - 2j - 2k

(d) u × v = det(i j k; 1 1 -2; 3 -2 1) = i(2-5) - j(1+6) + k(-2+9) = -3i - 7j + 7k

(e) |v × w| = |(-2i - 16j - 13k)| = sqrt((-2)^2 + (-16)^2 + (-13)^2) = sqrt(484) = 22

(f) u · (v × w) = (i + j - 2k) · (-2i - 16j - 13k) = -2i^2 - 16ij - 13ik + 2ij + 16j^2 - 26jk - 4k = -2 - 10k

(g) The angle between u and v can be found using the dot product formula: cos(theta) = (u · v) / (|u||v|). Plugging in the values from parts (c) and (b), we get cos(theta) = (-1/3) / (sqrt(6) * sqrt(14)). Using a calculator, we find that theta is approximately 110 degrees.

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The SQL aggregate function that gives the arithmetic mean for a specific column is `AVG()`.

SQL (Structured Query Language) aggregate functions are functions that operate on a set of values and return a single value as a result. These functions are used in SQL queries to perform calculations on groups of rows in a database table.

There are several common aggregate functions in SQL, including:

1. `COUNT()` - returns the number of rows in a table or the number of non-null values in a specific column.

2. `SUM()` - calculates the sum of values in a specified column.

3. `AVG()` - calculates the average value of values in a specified column.

4. `MAX()` - returns the maximum value in a specified column.

5. `MIN()` - returns the minimum value in a specified column.

Aggregate functions are typically used with the `GROUP BY` clause in SQL queries to group the data based on one or more columns and then apply the aggregate function to each group.

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The SQL aggregate function for calculating the arithmetic mean of a specific column is AVG.

The SQL aggregate function that gives the arithmetic mean for a specific column is AVG.

For example, if you have a table called 'students' with a column called 'grades', you can use the AVG function in SQL to calculate the average grade:

SELECT AVG(grades) FROM students;

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The unknown angle of the right angle triangle is as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.

The sum of angles in a right angle triangle is 180 degrees.  Therefore, let's find the ∠C in the triangle ABC.

Therefore,

180 = ∠A + ∠B + ∠C

m ∠B = y + 40

m ∠C = 3y - 10

m ∠A = 90°

Hence,

180 = 3y - 10 + y + 40 + 90

180 = 4y + 120

180 - 120 = 4y

y = 60 / 4

y = 15

Hence,

m ∠C = 3(15) - 10

m ∠C = 45 - 10

m ∠C = 35 degrees

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Simplified form of an expression \(7/9/2/3\)  is \(7/6.\)

By considering given expression

\(7/9/2/3\\ 7/9 \times3/2\\=7/6\)

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed in accordance with context-dependent rules.

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Answer:

Step-by-step explanation:

1.  When do you eat dinner?

2.  When do you get ready for school?

3.  When do you brush your teeth?

4. When do you go to school?

5. When do you say your prayers?

6. When do you go to bed?

7. When do you eat lunch?

8. When do you see your dad?

9. When do you drive home from work?

10. When do you eat breakfast?

1. What time does school start?

2. What time is lunch at schoo?

3. What time does school end?

4. What time does your dad come home from work?

5. What time does your favorite show start

6. What time is it now?

7. What time is your bedtime?

8. What time does your plane leave?

9. What time do you wake up?

10. What time does your soccer game start?

The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, it is true that 95% of the coworkers fall within the interval (0.339, 0.501), and we can be 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%. However, it is false to say that there is a 95% chance that a randomly selected coworker has received the vaccine or that there is a 42% chance for a randomly selected coworker to have received the vaccine.

The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, we can determine which of the following statements are true:

a) 95% of the coworkers fall in the interval (0.339, 0.501).

This statement is true. The 95% confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that 95% of the coworkers fall within the interval (0.339, 0.501).

b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 33.9% and 50.1%.

This statement is true. The 95% confidence interval (0.339, 0.501) provides us with a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that we are 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%.

c) There is a 95% chance that a randomly selected coworker has received the vaccine.

This statement is false. The 95% confidence interval does not represent a probability or chance for an individual coworker. It provides a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. It does not give information about the likelihood of an individual coworker receiving the vaccine.

d) There is a 42% chance that a randomly selected coworker has received the vaccine.

This statement is false. The 42% represents the proportion of coworkers in the survey who have received the flu vaccine, but it does not represent the chance or probability for a randomly selected coworker to have received the vaccine. The 42% is a point estimate, not a probability.

e) We are 95% confident that between 33.9% and 50.1% of the samples will have a proportion near 42%.

This statement is false. The confidence interval (0.339, 0.501) does not directly provide information about the proportion of samples that will have a proportion near 42%. The confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies, but it does not specifically address the proportion of samples near 42%.

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Answer:

85

Step-by-step explanation:

you add 38 and 47 together and you get 85

Answer:

Ten Ten

Step-by-step explanation:

Answer:

z = 3

Step-by-step explanation:

-z/4 = -3/4

-(z)/4 = -(3)/4

z = 3

Answer:

yes

Step-by-step explanation:

When the cookersetting (H) is 6, the time (T) it takes for the pot of water to boil can be calculated using the inverse proportion relationship. The calculated value of T is 120 seconds.

In an inverse proportion, as one variable increases, the other variable decreases, and vice versa. Let's use this relationship to solve the problem.

We are given that when H = 9, T = 80. This means that the product of H and T remains constant: H * T = k (where k is a constant).

Plugging in the given values, we have 9 * 80 = k. Therefore, k = 720.

To find T when H = 6, we can use the value of k: 6 * T = 720. Solving for T gives T = 720 / 6 = 120.

Hence, when H = 6, the time (T) it takes for the pot of water to boil is 120 seconds.

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See

y=|x| is the parent function and p(x) is the translated version of it

It has vertex at (0,0)

Now

as x is decreased then change in x axis is happened .vertex will shift 1 units right

So vertex should be at (1,0)

No change in y

The value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 approximately.

If we're given that:

Then, we get:

\(z = \dfrac{\overline{x} - \mu}{s}\)

If the sample standard deviation is not given, then we can estimate it by:

\(s = \dfrac{\sigma}{\sqrt{n}}\)

where \(\sigma\) = population standard deviation

For this case, since the sample size is 81 > 30, and we want to compare the mean (population mean) with some hypothesized mean (3.5 here), therefore, we can use one-sample z-test, which has the aforesaid test statistic.

We're provided that:

Thus, we get:

\(z = \dfrac{\overline{x} - \mu}{s} = \dfrac{3.25 - 3.5}{0.3} \approx -0.83\)

Thus, the value of the test statistic to test the claim of comparison of average GPA is found to be -0.83 approximately.

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Answer:

195 students are left-handed

Step-by-step explanation:

Here, we want to calculate the total number of students who are left-handed

Let the total number of students in the school be x

The total ratio is 8 + 3 = 11

8/11 * x = 520

8x = 11 * 520

x = (11 * 520)/8

x = 715 students

So the number of students who are left handed will be;

Total - number of right-handed students

That would be;

715-520 = 195

Answer:

Step-by-step explanation:

The output of the formula =XOR(120<102;83=83;51<24) is true

from the question, we have the following parameters that can be used in our computation:

=XOR(120<102;83=83;51<24)

The above operation is a XOR operation

The rule of the XOR operation is that

So, we have

120 < 102 = False

83 = 83 = True

51 < 24 = False

This can then be rewritten as

=XOR(False, True, False)

When evaluated using the XOR rule, we have

=XOR(False, True, False) = true

Hence, the output of the formula is true

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The L1 norm of vector A is greater than or equal to the L1 norm of vector B.

Basically, if the L2 norm of vector A is greater than the L2 norm of vector B, it is indeed always true that the L1 norm of vector A is greater than or equal to the L1 norm of vector B. The Lp norm is defined as follows:

\(||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p)^(1/p),\)

where x = [x₁, x₂, ..., xₙ] is a vector.

For the L2 norm (p = 2), the formula is:

\(||x||_2 = \sqrt(|x_1|^2 + |x_2|^2 + ... + |x_n|^2).\)

For the L1 norm (p = 1), the formula is:

\(||x||₁ = |x_1| + |x_2| + ... + |x_n|.\)

If ||A||₂ > ||B||₂, it implies that:

\(\sqrt(|A_1|^2 + |A_2|^2 + ... + |A_n|^2) > \sqrt(|B_1|^2 + |B_2|^2 + ... + |B_n|^2).\)

Squaring both sides of the inequality, we get:

\(|A_1|^2 + |A_2|^2 + ... + |A_n|^2 > |B_1|^2 + |B_2|^2 + ... + |B_n|^2.\)

Since the squares of the magnitudes are positive, we can conclude that:

\(|A_1| + |A_2| + ... + |A_n| > |B_1| + |B_2| + ... + |B_n|.\)

Therefore, the L1 norm of vector A is greater than or equal to the L1 norm of vector B.

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Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

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Answer:

P=21

Step-by-step explanation:

The solution to the equation P - 18 = 3 for P is P = 21

From the question, we have the following parameters that can be used in our computation:

P - 18 = 3

Add 18 to both sides of the equation

so, we have the following representation

18 + P - 18 = 3 + 18

Evaluate the like terms on the right hand side

This gives

18 + P - 18 = 21

Evaluate the like terms on the left hand side

This gives

P = 21

Hence. the solution is 21

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Answer:

Answer is 42

Step-by-step explanation:

You have to add 12+21+9 you dont add the 5 since its asking how many people play two out of the three sports.

The numbers that cannot be probabilities are: square root of 2, -53, 5/3, and 1.31.

Probability is a measure of the likelihood of a particular event occurring in a random experiment. It is a value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

In statistics, probability is used to make predictions or draw inferences about a population based on a sample of data. For example, if we were to flip a coin, the probability of getting heads is 0.5, or 50%. In general probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, which is the mathematical framework behind the random experiments.

From the set of numbers, 0, 0.08, and 3/5 are all possible values of probability.

Therefore, square root of 2, -53, 5/3, and 1.31 cannot be probabilities.

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Answer:

The equation of the line is,

\(y = - \frac{2}{5} x - 1\)

Step-by-step explanation:

First, you have to write it in a form of y = mx + b :

\(2x + 5y = 15\)

\(5y = 15 - 2x\)

\(y = 3 - \frac{2}{5} x\)

\(y = - \frac{2}{3} x + 5\)

When both lines are parallel to each other, they will have to same gradient value. So the equation of the line is y = (-2/5)x + b. Next, you have to find the value of b by substutituting (-10,3) into the equation :

\(y = - \frac{ 2}{5}x + b \)

\(let \: x = - 10,y = 3\)

\(3 = - \frac{2}{5} ( - 10) + b\)

\(3 = 4 + b\)

\(3 - 4 = b\)

\(b = - 1\)

Answer:

the equation of a parallel line is : y=-2/5 x -1

Step-by-step explanation:

2x+5y=15

put the equation in the form of y=mx+b

2x+5y=15

5y=15-2x

y=15/5-2/5 x

y=-2/5 x+3

parallel lines has the same slope : m=-2/5

passes through point (-10,3) find b

y=-2/5 x +b

3=-2/5(-10)+b

3=20/5 +b

3=4+b

b=3-4

b=-1

the equation of a parallel line is : y=-2/5 x -1

Answer: B

Step-by-step explanation:

4^2 = 4 x 4
4 x 4 = 16

4 + 4 + 4 + 4 also equals 16 therefore the expressions must be equal

a. To determine the probabilities associated with different service lives, we can use the properties of the normal distribution. Given that the mean service life is six years with a standard deviation of one-half year, we can calculate the probabilities as follows:

(1) Probability of service lives of at least five years:

We need to calculate the area under the normal curve to the right of five years. Using the Z-score formula, we find the Z-score corresponding to five years: Z = (5 - 6) / 0.5 = -2. We can then look up the corresponding probability in a standard normal distribution table or use statistical software to find the probability associated with a Z-score of -2. This gives us the probability of service lives of at least five years.

(2) Probability of service lives of exactly six years: Since the service life follows a normal distribution, the probability of exactly six years is zero since it is a continuous distribution. We can assign a very small positive probability to approximate "exactly" six years. (3) Probability of service lives of seven and one-half years: Similarly, we calculate the Z-score corresponding to seven and one-half years: Z = (7.5 - 6) / 0.5 = 3. We find the probability associated with a Z-score of 3 to determine the probability of service lives of seven and one-half years or longer. b. If the manufacturer offers service contracts of four years, we want to find the percentage of televisions that fail from wear-out during this period. We can calculate this by finding the area under the normal curve to the left of four years. Using the Z-score formula, we find the Z-score corresponding to four years: Z = (4 - 6) / 0.5 = -4. The corresponding probability gives us the percentage of televisions expected to fail during the four-year service period.

c. To achieve an expected wear-out rate of 2 percent or 5 percent, we need to determine the service period corresponding to these rates. We can use the Z-score formula in reverse to find the Z-score that corresponds to the desired wear-out rate. From there, we can calculate the corresponding service period by rearranging the Z-score formula and substituting the desired wear-out rate and the given mean and standard deviation values.

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original equation

\(\frac{x}{2}-\frac{3x}{4}+\frac{x}{6}=-\frac{2}{3}\)

multiply by lcd

\(12(\frac{x}{2})-12(\frac{3x}{4})+12(\frac{x}{6}) =-12(\frac{2}{3})\\\\6x-9x+2x=-8\)

isolate for x

\(-1x=-8\\\\x=8\)

verify

\(\frac{8}{2}-\frac{3(8)}{4}+\frac{8}{6}=-\frac{2}{3}\\\\4-6+\frac{4}{3}=-\frac{2}{3}\\\\4-2+\frac{4}{3}=-\frac{2}{3}\\\\-\frac{2}{3}=-\frac{2}{3}\\\\LS=RS\)

The integration is as follow

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, \(\int\limits {e^{4x} / 19 - e^{8x}} \, dx\)

= \(\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx\)

let \(e^{4x}\) = z

4\(e^{4x}\) dx = dz

= 1/4 \(\int\limits {dz / \sqrt{19} ^2 -z^2} \,\)

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|(\(e^{4x}\) + √19)/ (\(e^{4x}\) - √19)| + C

Second,

\(\int\limits {33 sec^5 (x)} \, dx\)

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

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The correct value of Cos K is 5/23

Step-by-step explanation:

In a right angle triangle, there are 3 side

1. Hypothenus (this is the longest)

2. Adjacent

3. Opposite

However, we can only determine the adjacent and opposite if an angle is marked in the triangle.

Now, we shall determine the value of Cos K. This can be obtaineasobtain as followed:

From the question given above, the following data were obtained:

Hypothenus = 23

Adjacent = 5

Cos K =? C

The value of Cos K can be obtained by using the cosine ratio as as illustrated below:

\(Cos K =\frac{Adjacent}{Hypothenus}\\\\Cos K = \frac{5}{23}\)

Therefore, the value of Cos K is 5/23

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Answer:

A:   -1 + 2 log4^x

C: log4 (1/4) + log4 x^2

Step-by-step explanation:

Apply logarithm properties:

log4 (1/4x^2)  =  log4 (1/4) + log4 x^2

Evaluate: log4 (1/4)

log4 (1/4) = -1

Substitute the value back:

-1 + lg4 x^2

Apply logarithm properties:

-1 + 2 log4 ^x

Draw a conclusion:

The expressions equivalent to: log4 (1/4x^2) are:

Answer Choices: A, and C

A= -1 + 2 log4^x

C=  log4 (1/4) + log4 x^2

Hope this helps!

The food percentage would be 19%, 51% and 30%.

Given that we've done it

Number of meals consumed by X = 57

Food consumed by Y = 153.

Number of meals consumed by Z = 90

Total amount of meals consumed = 57 + 153 +90 = 300

Food proportion of flock X thus Equals 57 / 300 * 100 = 19 %

flock food percentage Y =153/300 * 100 = 51 %

flock food percentage Z = 90/300 * 100 = 30 %

This means that the percentages are 19%, 51%, and 30%.

Based on the given information, we have:

Flock X ate 57 pieces of food.

Flock Y ate 153 pieces of food.

Flock Z ate 90 pieces of food.

The total number of pieces of food eaten is 300 (sum of the individual flock's food).

The food percentage for Flock X is 57/300 ≈ 0.19 or 19%.

The food percentage for Flock Y is 153/300 ≈ 0.51 or 51%.

The food percentage for Flock Z is 90/300 = 0.3 or 30%.

The total number of birds for the second generation is 30 (given).

To find the simulated number of birds in each flock for the second generation, we multiply the food percentage for each flock by the total number of birds (30).

For Flock X: 0.19 × 30 = 5.7 (rounded to the nearest whole number: 6 birds)

For Flock Y: 0.51 × 30 = 15.3 (rounded to the nearest whole number: 15 birds)

For Flock Z: 0.3 × 30 = 9 (rounded to the nearest whole number: 9 birds)

Therefore, the simulated number of birds in Flock X, Flock Y, and Flock Z for the second generation are 6, 15, and 9 birds, respectively.

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Complete Question

Flock X Flock Y Flock z Total Pieces of Food Eaten 57 153 90 Food Percentage* % 1% % Simulated Number of Birds in Flock for 2nd Generation ** * Divide each flock's total pieces of food by 300, the total number of pieces of food eaten. ** Multiply the food percentage for each flock by the total number of birds (30). DONE

Answer:

19 51 30

6 15 9

second part Is Y then X

Step-by-step explanation:

Answer:

3/2 or 1.5

Step-by-step explanation:

\(slope = \frac{4 - 1}{5 - 3} \\ \\ = \frac{3}{2} \\ \\ = 1.5\)

Answer:

the 3rd won for sure

Step-by-step explanation:

hope I helped

Answer:

C

Step-by-step explanation:

The coordinates are all in (x, y) form.

X is how left or right

y is how tall.

If you just look for the individual coordinates given, you will see that all of the Coordinates in C are on the graph.

I hope this helps!