Find the absolute maximum and minimum values of the function f(x,y) = x^2+y^2-2x

The median salary of the workers is P11,000.

In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.

To calculate the median of a set of numbers:

In the given question,

To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.

The salaries are:

P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500

There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.

Median salary = (P11,000 + P11,000)/2

= P11,000

Therefore, the median salary of the workers is P11,000.

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The composite function is obtained applying the inner function as the input to the outer function.

The functions for this problem are defined as follows:

Hence the composite function is obtained replacing the two instances of T on the function N(t) by the definition of T(t), hence:

N(T(t)) = 20(6t + 1.2)² - 128(6t + 1.2) + 77

N(T(t)) =  720t² + 288t + 28.8 - 768t - 204.6.

N(T(t)) = 720t² - 480t - 175.8.

For a population of 18413 bacteria, we have that N(T(t)) = 18413, hence:

720t² - 480t - 175.8 = 18413

720t² - 480t - 18588.8 = 0.

The coefficients of the quadratic function are given as follows:

a = 720, b = 480, c = -18.588.8.

Using a quadratic function calculator, the positive solution is given as follows:

t = 4.76 hours.

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The slope of the function is 12. Because of the slope, Jennifer will require 12 extra meters of tape for each additional office she needs to tape the baseboards in.

A line's slope on a graph is its steepness or inclination. It may be derived from any two locations on a line by dividing the vertical change (rise) by the horizontal change (run). Positive, negative, zero, or undefinable slopes are all possible for lines. A line on a graph with a positive slope is growing as you travel from left to right, while one with a negative slope is declining. A line has a slope of zero when it is horizontal and a slope of infinity when it is vertical.

The given function is y = 12x + 25.

The standard equation of the line is given as:

y = mx + b

where, m is the slope.

Comparing the equation with the given equation the slope of the function is 12.

Because of the slope, Jennifer will require 12 extra metres of tape for each additional office she needs to tape the baseboards in. In other words, if more offices need to be painted, the amount of sellotape required also grows linearly.

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you need to match it to the percentage of the fraction for example 1/2 is 50 percentage and than you do 1/4 is 25 percent.

The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

What is gravitational force?

Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.

The gravitational force that the moon produces on the Earth can be calculated using the formula:

[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]

where:

[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]

[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]

[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]

[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]

Substituting these values into the formula, we get:

[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]

Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

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The volume of the solid is given by the equation V = 36π (√2 - 1) using the triple integral.

A three-dimensional object's volume in three-dimensional space may be determined using the triple integral. The three-variable function is represented by the triple integral. If in space is a closed region, the region's entire volume may be expressed as V = Ddv, which is equivalent to V = D d x d y d z.

Cone: z = [tex]\sqrt{x^2+y^2}[/tex]

sphere: x² + y² + z² = 18

Here, we will use cylindrical coordinates to evaluate volume:

x = rcosθ , y = rsinθ, z = z

so, z = [tex]\sqrt{r^2cos^2\theta+r^2sin^2\theta} =r[/tex]

z = [tex]\sqrt{18-(x^2+y^2)} =\sqrt{18-r^2}[/tex]

r = [tex]\sqrt{18-r^2}[/tex]

r = 3

Finding limits,

[tex]Volume = \int\limits^2_0 \int\limits^3_0\int\limits^a_r {rdzdrd\theta} \, \\\\= \int\limits^2_0 \int\limits^3_0rz \ drd\theta\\\\= \int\limits^2_0 \int\limits^3_0 r(\sqrt{18-r^2}-r ) \ drd\theta\\\\[/tex]

Now, we have

[tex]\int\limits^3_0 {r\sqrt{18-r^2} } \, dr = -(9-18\sqrt{2} ) = 18\sqrt{2} -9[/tex]

Now the integral becomes,

Volume = 2π [(18√2-9) - 9]

= 2π x 18√2 - 18

V = 36π (√2 - 1)

Therefore, the volume of the solid is given by V = 36π (√2 - 1).

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Answer:

The value could be any length between 3 and 15

Step-by-step explanation:

9 - 6 = 3

and

9 + 6 = 15

Step-by-step explanation:

Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:

P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.

Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.

Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).

However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.

Answer:

Given: Angle 1 = 32, Angle 2 = x + 29 ----- Answer is x = 119°

Given: 54 + x = 90 ----- Answer is x = 36°

Given: Angle 1 = x, Angle 2 = 24 + 2x ----- Answer is x = 22°

Step-by-step explanation:

1. Supplementary angle = 180°

Angle 1 = 32°    Angle 2 = x + 29

Angles 1 + 2 = 180°

32° + x + 29° = 180°

32° + x = 180° - 29°

32° + x = 151°

x = 151° - 32°

x = 119°

2. Complementary angle = 90°

Given: 54 + x = 90

90 - 54 = x

x = 36°

3. Complementary angle = 90°

Given: Angle 1 = x, Angle 2 = 24 + 2x

Angles 1 + 2 = 90°

x + 24 + 2x = 90°

3x + 24 = 90°

3x = 90° - 24

3x = 66°

x = 66°/3

x = 22°

Hope it helps!

In response to the stated question, we may state that As a result, the equation's answer is x = 0.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

4x = 864x is the provided equation.

This equation may be simplified by deleting 4x from both sides:

[tex]860x = 0[/tex]

This equation may now be rewritten in factored form:

[tex]860x = 0 \sx(860) = 0[/tex]

We know from the zero-product principle that if the product of two elements is zero, then at least one of them must be zero. As a result, we may set each component to zero and solve for x:

x = 0 or 860 = 0 (which is impossible) (which is impossible)

As a result, the equation's answer is x = 0.

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Answer:

Step-by-step explanation:

The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:

Protein: 1x + 1y ≥ 8 (at least 8 units of protein)

Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)

Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)

The inequalities that x and y must satisfy because they cannot be negative are:

x ≥ 0

y ≥ 0

Step-by-step explanation:

To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:

1. 1x + 1y ≥ 8 (At least 8 units of protein)

2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)

3. 1x + 1y ≤ 10 (No more than 10 units of fat)

To ensure that x and y are non-negative, the following inequalities must be satisfied:

x ≥ 0y ≥ 0

Therefore, the complete set of inequalities for x and y are:

x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0

If 2 books are chosen at random, then the probability that both are statistics books is (a) 1/21.

The number of statistics book in bookcase is = 2;

The number of biology books in bookcase is = 5;

So, the total number of books is = 7;

The Probability of choosing a statistics book on the first draw is 2/7, since there are 2 statistics books out of a total of 7 books.

After the first book is chosen, there will be 6 books left, including 1 statistics book out of a total of 6 books.

So, the probability of choosing another statistics book on the second draw is 1/6.

In order to find the probability of both events happening together (i.e. choosing 2 statistics books in a row), we multiply the probabilities of each event:

So, P(choosing 2 statistics books) = P(1st book is statistics) × P(2nd book is statistics given that the 1st book was statistics);

⇒ (2/7) × (1/6)

⇒ 1/21

Therefore, the required probability is (a) 1/21.

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The given question is incomplete, the complete question is

A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is

(a) 1/21

(b) 10/21

(c) 11

(d) 21/11

Answer:

X=18

Step-by-step explanation:

Answer:

x = 3.5 units (nearest tenth)

Step-by-step explanation:

The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.  

Therefore, the formula for the ratio of the sides is x : x : x√2 where:

As the hypotenuse of the given right triangle is 5 units:

[tex]\implies x\sqrt{2} = 5[/tex]

To find the measure of x, solve for x:

[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]

[tex]\implies x =3.5355339...[/tex]

[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]

Therefore, the length of side x to the nearest tenth is 3.5 units.

Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.

To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.

First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.

The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.

We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:

z = (p - P) / sqrt(P(1-P)/n)

where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).

Plugging in the values, we get

z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39

Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.

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Answer:5

Step-by-step explanation:5555555

The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.

Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.

To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.

From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.

So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:

0.16 / 0.96 ≈ 0.17

Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.

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(a) The theoretical probability of getting a 5 or 6 is 1/5

(b) The experimental probability of getting a 5 or 6 is 1/5

(c) The true statement is the first statement.

A subfield of statistics known as probability studies random events and their likelihood of happening. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

(a) Assuming that the machine is fair, the theoretical probability of getting a 5 or 6 is:

P(5 or 6) = P(5) + P(6) = 1/10 + 1/10 = 1/5

(b) From the results, we can see that out of the 50 trials, there were 10 trials where the machine output a 5 or a 6.

The experimental probability of getting a 5 or 6 is:

P(5 or 6) = 10/50 = 1/5

(c) A large number of trials, might be a difference between the experimental and theoretical probabilities, but the difference should be small. This is because the theoretical probability is based on the assumption of a fair machine, while the experimental probability is based on actual results.

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Answer:

10 metres

Step-by-step explanation:

All sides are equal in Rhombus

So, the length of one side= 40m÷4

=10 metres

Step-by-step explanation:

7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd

Conversely, as the confidence level decreases, the margin of error becomes smaller, and the confidence interval becomes narrower.

In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a mean or a proportion), based on a sample from that population. The confidence interval is typically expressed as an interval around a sample statistic, such as a mean or a proportion, and is calculated using a specified level of confidence, typically 90%, 95%, or 99%.

Here,

To develop a confidence interval, we need to use the following formula:

Confidence Interval = sample mean ± margin of error

where the margin of error is calculated as:

Margin of Error = z* (sample standard deviation/ √n)

where z* is the critical value from the standard normal distribution table based on the chosen confidence level.

a. For a 90% confidence interval, the critical value (z*) is 1.645. Thus, the margin of error is:

Margin of Error = 1.645 * (4 / √25) = 1.317

So, the 90% confidence interval for the population mean is:

30 ± 1.317, or (28.683, 31.317)

b. For a 95% confidence interval, the critical value (z*) is 1.96. Thus, the margin of error is:

Margin of Error = 1.96 * (4 / √25) = 1.568

So, the 95% confidence interval for the population mean is:

30 ± 1.568, or (28.432, 31.568)

c. For a 99% confidence interval, the critical value (z*) is 2.576. Thus, the margin of error is:

Margin of Error = 2.576 * (4 / √25) = 2.0656

So, the 99% confidence interval for the population mean is:

30 ± 2.0656, or (27.9344, 32.0656)

d. As the confidence level increases, the margin of error also increases, because we need to be more certain that our interval includes the true population mean. This means that the confidence interval becomes wider as the confidence level increases.

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Answer:

What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←​

Step-by-step explanation:

To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.

We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.

To do this, we need to find the angle between these two vectors. Using the dot product, we have:

<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0

Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.

To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:

[0 -1]

[1 0]

Multiplying this matrix by the vector <4, -7>, we get:

[0 -1] [4] = [-7]

[1 0] [-7] [ 4]

which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.

Answer:

90° counterclockwise

Step-by-step explanation:

I am not sure if the picture helps or not.  I am trying to show that I traced the point (4,-7).  Then I have a plus sign at (0,0).  I start rotating the tracing paper counterclockwise until  I get to the point (7,4).  I needed to turn one turn of the plus sign.  That would be 90°

Helping in the name of Jesus.

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.

Expanding the left side of the equation we have:

[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)

= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12

= [tex]e^2[/tex] - 4e√3 + 12

Substituting back in the function

[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3

[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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Answer:

Step-by-step explanation:

Answer:

Hence, factors are 3x,(x−4y).

Step-by-step explanation:

We need to factorise 3x 2 −12xy

Here we can take 3x common.

Thus we have 3x 2−12xy=3x(x−4y)

Hence, factors are 3x,(x−4y).

Answer: 3x ( x - 4y )

Step-by-step explanation:

Factorizing 3x²-12xy

3x ( x - 4y )

Answer:

15.8823% error

Step-by-step explanation:

Percent Error Formula

abs([tex]\frac{(a-x)}{x}[/tex]) * 100%

abs:  absolute value

a:  actual value

x:  expected value

Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%

                       = abs(-0.158823) * 100%

                       15.8823% error

The area of the right triangle given in this problem is given as follows:

21 units squared -> Option A.

To calculate the area of a triangle, you can use the formula presented as follows:

Area = (1/2) x base x height

In which the parameters are given as follows:

For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5 x 7 x 6 = 21 units squared.

The complete problem is defined as follows:

"Calculate the area of the given triangle".

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Answer: 62°

Step-by-step explanation:

All angles of a triangle add up to 180°.

So, add up all the other angles.

15 + 25 + 39 = 79

180 - 79 = 101

Then, to find x, subtract 39 from 101, to get 62!

There are 81 potential outcomes in Andy's sample space.

Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.

The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.

We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.

For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.

9 × 9 = 81.

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Answer:

It means the point x = 5 and y = 10

Answer: The place 5 units right and 10 units up from the center of the graph (the origin).

Step-by-step explanation:

Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.

Hi Martin,

To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.

The total purchase cost of all three items is:

Snow shovel: $28.61

Winter coat: $23.27

Rock salt: $7.96

Total purchase cost: $59.84

Now, we apply the applicable taxes:

State tax: 5% of $59.84 = $2.99

County tax: 0.5% of $59.84 = $0.30

City tax: 2.5% of $59.84 = $1.49

Total taxes: $2.99 + $0.30 + $1.49 = $4.78

Therefore, the total purchase price is:

Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62