Find the absolute maximum and minimum of f (x, y) = x^2 + 2y^2 − 2x − 4y +1 on D = {(x, y) 0 ≤ x ≤ 2, 0 ≤ y ≤ 3} .

None of the options are reducible polynomial

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

The list of options

The variable Q means rational numbers

So, we can use the rational root theorem to test the options

So, we have

(a) 4x³ + x - 2

Roots = ±(1, 2/1, 2, 4)

Roots = ±(1, 1/4, 2, 1, 1/2)

(b) 3x³ - 6x² + x - 2

Roots = ±(1, 2/1 ,3)

Roots = ±(1, 1/3, 2, 2/3)

(c) 5x³ + 9x² - 3

Roots = ±(1, 3/1 ,5)

Roots = ±(1, 1/5, 3, 3/5)

See that all the roots have rational numbers

And we cannot determine the actual roots of the polynomial.

Hence, none of the options are reducible polynomial

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The graph is a downward-opening parabola opening downward with its vertex at (2,0). Therefore, the correct option is C.

The equation y = -16t^2 + 64t + 16 represents the path of a projectile launched from a 16-ft-tall tower. To determine the correct graph, we can analyze the equation. The coefficient of t^2 (-16) is negative, indicating a downward-opening parabola. The coefficient of t (64) determines the horizontal shift of the graph, and in this case, t = 4 represents the maximum height of the projectile. The constant term (16) represents the initial height of the tower.

Considering these factors, we find that the correct graph of the equation is option C. It depicts a downward-opening parabola with its vertex at (2,0). The parabola starts at an initial height of 16 ft (the tower's height) and descends symmetrically from its vertex.

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Answer:

Step-by-step explanation:

59 apples two times = 59 x 2 = 118 apples

Total apples = 118 + 60 = 178 apples

Answer:

however much the Child's pass is x 3 = Adult Pass cost

Step-by-step explanation:

Answer:

5/11 is 0.4555555555555555555555555

so basically the first option out of the two.

U do know you can just calculate this with the calculator right?

Answer:

V = 960 cm^3

Step-by-step explanation:

Volume of a rectangular prism = L * W * H

V = 12 * 8 * 10

V = 960 cm^3

Answer:

d. 960 cm^3

Step-by-step explanation:

The formula for volume is length x width x height. To solve you have to multiply 12 by 8 by 10 to get 960

The expected number of women in the survey who have group A blood is 48.

To calculate the expected number, we assume that sex and blood type are independent variables. This means that the proportion of women with group A blood would be the same as the proportion of men with group A blood.

Out of 100 men surveyed, 40 had group A blood. This corresponds to a proportion of 40/100 = 0.4.

Since sex and blood type are assumed to be independent, we can assume that the proportion of women with group A blood is also 0.4.

To find the expected number of women with group A blood, we multiply the proportion by the total number of women surveyed:

Expected number of women with group A blood = Proportion of women with group A blood * Total number of women surveyed

Expected number of women with group A blood = 0.4 * 120 = 48

Therefore, the expected number of women in the survey who have group A blood is 48.

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The steps necessary for graphing parametric equations include creating a table, solving the equations for t and plotting those points, connecting the points with a smooth curve, and setting up the coordinate plane with t on the horizontal axis (c, d, f, h).

Create a table: Choose a range of values for t and calculate the corresponding values for x and y using the parametric equations. List these values in a table.

Solve the equations for t and plot those points: Solve the parametric equations separately for t to obtain the x and y coordinates. Plot these points on the coordinate plane.

Connect the points with a smooth curve: Once all the points are plotted, connect them with a smooth curve. This curve represents the graph of the parametric equations.

Set up the coordinate plane with t on the horizontal axis: Label the horizontal axis as t and the vertical axis as either x or y. This allows you to visualize how the x and y values change with respect to the parameter t.

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Answer:

27.

Step-by-step explanation:

3^3 = 3 * 3 * 3

= 9 * 3

= 27.

Answer:

IMAO YOU GAVE UP, PSY

Step-by-step explanation:

Answer:

45 minutes

Step-by-step explanation:

1 1/2 hours = 90 minutes

90 - 45 = 45

The the success rate of the student is PHYS>MATH. Therefore, the correct answer is Option A.

We can calculate the success rate of the student by calculating the z-score of each of the courses. The z-score is calculated as (x-μ)/σ, where x is the individual score, μ is the mean of the data, and σ is the standard deviation of the data.

For Physics, we have x=60, μ=49, and σ=11. So the z-score is (60-49)/11=1.09.

For Mathematics, we have x=58, μ=55, and σ=16. So the z-score is (58-55)/16=0.19.

Since the z-score of Physics is greater than the z-score of Mathematics, the student's success rate in Physics is greater than the student's success rate in Mathematics.

Therefore, the correct answer is Option A.

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The 99% confidence interval of the true mean is given as follows:

8.56 million < μ < 16.78 million.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 10 - 1 = 9 df, is t = 3.2498.

The parameter values for this problem are given as follows:

[tex]\overline{x} = 12.67, s = 4, n = 10[/tex]

The lower bound of the interval is then given as follows:

[tex]12.67 - 3.2498 \times \frac{4}{\sqrt{10}} = 8.56[/tex]

The upper bound of the interval is then given as follows:

[tex]12.67 + 3.2498 \times \frac{4}{\sqrt{10}} = 16.78[/tex]

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Answer: 140,  220,  220,  140

Step-by-step explanation:

All you have to do is double the numbers.

The forecasted sales for February through April are as follows:

February: 19.5, March: 25.65, April: 30.755. The forecasted sales for May is approximately 35.928.

Exponential smoothing is a time series forecasting method that assigns weights to past observations, with the weights decreasing exponentially as the observations get older. The smoothed value for a particular period is a weighted average of the previous smoothed value and the actual value for that period.

To calculate the smoothed values and forecast sales using exponential smoothing with α = 0.3, we start with the initial forecast for January, which is given as 18. Then, for February, we use the formula:

Smoothed value (February) = α * Actual sales (February) + (1 - α) * Smoothed value (January)

= 0.3 * 25 + 0.7 * 18 = 19.5

Similarly, for March:

Smoothed value (March) = α * Actual sales (March) + (1 - α) * Smoothed value (February)

= 0.3 * 34 + 0.7 * 19.5 = 25.65

And for April:

Smoothed value (April) = α * Actual sales (April) + (1 - α) * Smoothed value (March)

= 0.3 * 40 + 0.7 * 25.65 = 30.755

Finally, for the forecasted sales in May:

Forecasted sales (May) = Smoothed value (April) = 30.755

Therefore, the forecasted sales for May, using exponential smoothing with α = 0.3, is approximately 35.928.

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just the first one 11 ........

Answer:

Maximum, and (0, -2)

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

15h - 25 dollars is an expression to describe his spendings and earnings in a day.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Peter makes 15 dollars an hour, so if he works for h hours, he earns:

15h dollars

Peter spends 25 dollars a day on transportation and food, so his total spending can be expressed as:

25 dollars

Therefore, his total earnings minus his total spending can be expressed as:

15h - 25 dollars

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Answer:

Step-by-step explanation:

a = 32 ÷ 4

a = 8

all i know is that it would not be 13.9

Answer:

12in

Step-by-step explanation:

this is the only subject i'm good at in math XDDD.

By applying the principle of inclusion-exclusion, we can show that for any events E1, E2,..., EM, the inequality P(E1 or E2 or ... or EM) < P(EM) holds. This result holds true for any integer M ≥ 1.

To prove the statement by induction, we will assume that for M = 1, the inequality holds true. Then we will show that if the statement holds for M, it also holds for M + 1.

Base case (M = 1):

For M = 1, we have P(E1) ≤ P(E1), which is true.

Inductive step:

Assuming that the inequality holds for M, we need to show that it holds for M + 1. That is, we need to prove P(E1 or E2 or ... or EM or EM+1) < P(EM+1).

Using the principle of inclusion-exclusion, we can express the probability of the union of events as follows: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1) - P((E1 or E2 or ... or EM) and EM+1). Since events E1, E2, ..., EM, and EM+1 are mutually exclusive, the last term on the right-hand side becomes zero: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1)

Since we assumed that P(E1 or E2 or ... or EM) < P(EM), we can rewrite the inequality as: P(E1 or E2 or ... or EM or EM+1) < P(EM) + P(EM+1)

Now we need to show that P(EM) + P(EM+1) < P(EM+1) for the inequality to hold. Simplifying the expression, we have: P(EM) + P(EM+1) < P(EM+1)

Since P(EM+1) is a probability and is always non-negative, this inequality holds true. Therefore, by the principle of mathematical induction, we have shown that for any integer M ≥ 1, the inequality P(E1 or E2 or ... or EM) < P(EM) holds.

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a. Using intersection of events probability of FUA is 0.0165

b. Using complement rule, the probability of F'UA is 0.9835

To find the probabilities, we can use the given information and apply the appropriate probability rules.

(a) FUA represents the event that the driver is female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the formula: P(FUA) = P(F ∩ A), where ∩ denotes the intersection of events.

P(FUA) = P(F) * P(A|F)

Given information:

P(F) = 0.2868 (probability that the driver is female)

P(A) = 0.1828 (probability that the driver is 24 years old or less)

P(A|F) = 0.0576 (probability that the driver is 24 years old or less given that the driver is female)

P(FUA) = 0.2868 * 0.0576 ≈ 0.0165

Therefore, the probability of FUA is approximately 0.0165.

(b) F'UA represents the event that the driver is not female, 24 years old or less, and is involved in a fatal vehicle accident.

We can calculate this probability using the complement rule: P(F'UA) = 1 - P(FUA).

P(F'UA) = 1 - P(FUA) ≈ 1 - 0.0165 ≈ 0.9835

Therefore, the probability of F'UA is approximately 0.9835.

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Answer:

3. The equivalent fractions are presented as follows;

[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

4.  The equivalent fractions are presented as follows;

[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

5. The reason why it works is because [tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]

Step-by-step explanation:

3. Based on the shaded region of the given figures, the two fractions are equivalent

Mathematically, we can show the equivalency of the two fractions as follows;

[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

Therefore;

[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

4. From the shaded region of the given figure, the fractions are equivalent

Mathematically, we have;

[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{4}{4} \times \dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

Therefore;

[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

5. The amount of salt required by the recipe = 1/4 teaspoon of salt

The measure of the spoon Jonas has = 1/8 teaspoon

When Jonas adds two 1/8 teaspoons, he gets;

[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1 + 1}{8} = \dfrac{2}{8} = \dfrac{2 \times 1}{2 \times 4} = \dfrac{2}{2} \times \dfrac{1}{4} = 1 \times \dfrac{1}{4} = \dfrac{1}{4}[/tex]

Therefore;

[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]

Two 1/8 measuring teaspoons are equivalent to one 1/4 teaspoons and therefore Jonas is able to get the 1/4 teaspoons of salt the recipe asks for b combining two 1/8 measuring teaspoons of salt he has because 1/8 + 1/8 = 1/4.

Answer:

Dining Hall = 24 square meters

Kitchen = 48 square meters

Together = 72 square meters

A method of assigning probabilities based upon personal judgment is referred to as the subjective method. The correct answer is a.

The subjective method of assigning probabilities is based on personal judgment or subjective beliefs about the likelihood of events occurring. It involves incorporating individual knowledge, experience, and intuition to estimate the probabilities of different outcomes.

Unlike the classical method, which assigns probabilities based on equally likely outcomes, or the relative frequency method, which uses observed frequencies to determine probabilities, the subjective method relies on individual opinions and subjective assessments of probabilities.

In the subjective method, probabilities are not determined through mathematical calculations or empirical data. Instead, they are based on an individual's expertise, opinions, and subjective reasoning.

This method is commonly used in situations where objective data or historical information is limited or unavailable, such as in decision-making under uncertainty or when dealing with complex and uncertain scenarios.

The correct answer is a.

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Answer:

5. B

6. A

7. C

Step-by-step explanation:

Answer:

5.) b. 12 - 2x

6.) a. 8x

7.) c. 5d + 3c = 66

Step-by-step explanation:

uhm, I don't really have proof, i've just been doing this for a long time, you're just gonna have to trust me on this one

Answer:

8

Step-by-step explanation:

0.20 x 40 = 8

Therefore, 20% of 40 is 8

Answer:

2,125,760

Step-by-step explanation:

The first term (a) is 8

The fourth term is 216

Hence the sum of the first 12 term can be calculated as follows

= 8-8(3)^12/1-3

= 8-24^12/-2

= 2,125,760

The sum of first 12 terms is 2,125,760

Sum of the first 12 term  =  2,125,760

For geometric sequence,

aₙ = arⁿ⁻¹

where

a = first term

r = common ratio

n = number of terms

Therefore,

a = 8

a₄ = 216

let's find the common ratio

216 = 8 × r⁴⁻¹

216 = 8 × r³

r³ = 216 / 8

r³ = 27

r = [tex]\sqrt[3]{27}[/tex]

r = 3

Let's find sum of the first 12 terms.

Sₙ = a (rⁿ - 1) / r - 1

S₁₂ = 8(3¹² - 1) / 3 - 1

S₁₂ = 8(531440) / 2

S₁₂ = 4251520 / 2

S₁₂ = 2,125,760

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a) The equation of the line passing through the point (3, 2) with slope 4 is y - 2 = 4(x - 3).

b. The equation of the line passing through (4, -2) and (5,6) is y + 2 = 8(x - 4).

c) The slope of the line 6x +2y +4 is -3.

a. To derive the equation, we use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m represents the slope.

Substituting the given values into the equation, we have:

y - 2 = 4(x - 3)

This equation can be further simplified if required.

b) The equation of the line passing through the points (4, -2) and (5, 6) can be found using the slope-intercept form, y = mx + b.

First, we calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁).

m = (6 - (-2)) / (5 - 4) = 8.

Next, we substitute one of the given points and the calculated slope into the slope-intercept form:

y - y₁ = m(x - x₁).

y - (-2) = 8(x - 4).

Simplifying the equation:

y + 2 = 8(x - 4).

c) To find the equation of the line passing through the point (3, -1) and parallel to the line 6x + 2y + 4 = 0, we first need to determine the slope of the given line.

Rearranging the equation 6x + 2y + 4 = 0, we have:

2y = -6x - 4,

y = -3x - 2.

The given line has a slope of -3.

Since parallel lines have the same slope, the line we are looking for will also have a slope of -3. Using the point-slope form with the given point (3, -1), the equation becomes:

y - (-1) = -3(x - 3).

Simplifying:

y + 1 = -3(x - 3).

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