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The reduced gradient is analogous to the residual for linear models.

In linear regression, the residual represents the difference between the observed values and the predicted values of the dependent variable. Similarly, in optimization, the reduced gradient represents the difference between the current solution and the optimal solution. It is a measure of how far the current solution is from the optimal solution in the direction of the search. By minimizing the reduced gradient, we can move closer to the optimal solution.

The reduced gradient is a widely used optimization technique in non-linear programming that allows for efficient computation of the descent direction at each iteration while accounting for constraints. It involves calculating a partial derivative of the objective function with respect to the variables that are not restricted by the constraints, and then projecting the resulting gradient onto the space defined by the constraints. The resulting vector is called the reduced gradient, and it points in the direction of the steepest descent that is feasible.

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Answer:

the best anime is death note.

Step-by-step explanation:

Answer:

My hero Achadamia is my fav. um Attack of the titan Black Clover and Fruits basket thats all i can name lol

Step-by-step explanation:

The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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The initial temperature of the inside room is 65.56° F. we can use Newton's Law of Cooling to solve problems

To solve the problem, we can use the formula for Newton's Law of Cooling:  T(t) = T(∞) + (T(0) - T(∞))e^(-kt)

where T(t) is the temperature at time t, T(0) is the initial temperature, T(∞) is the outside temperature, and k is a constant.

We can set up two equations using the given information:

75 = 25 + (T(0) - 25)e^(-k)

50 = 25 + (T(0) - 25)e^(-5k)

We can solve for k by dividing the second equation by the first equation:

50 / 75 = e^(-5k) / e^(-k)

2 / 3 = e^4k

Taking the natural logarithm of both sides, we get:

ln(2/3) = 4k

k = -ln(2/3) / 4

Then, we can substitute k into one of the equations to solve for T(0):

75 = 25 + (T(0) - 25)e^(-k)

T(0) = 65.56° F (rounded to two decimal places).

In summary, we can use Newton's Law of Cooling to solve problems involving temperature changes. We can set up equations using the given information and then solve for the constants using algebraic methods.

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Answer:

1 dollar is equal to 0.75 E

Step-by-step explanation:

120$ = 90 e -----> 4$ = 3E

250$ = 187.50 e -----> 4$ = 3E

400$ = 300 e -----> 4$ = 3E

----------------------------------

from this we know 4$ = 3E

1 E = 4$/3

1 E = 1.33...$

---------------------

1 $ = 3/4 E

1 $ = 0.75 E

---------------------

1.33...$ dollars is equal to 1 E and

1 $ is equal to 0.75 E

-----------------------------------

90 x 1.33... =120

187.50x1.33...= 250

300 x 1.33... = 400

--------------------------

Answer: σ: 2.76

Step-by-step explanation:

Count, N: 5

Sum, Σx: 125

Mean, μ: 25

Variance, σ2:  7.6

Steps

look at attached pic for formula

σ^2 = \(\frac{Σ(xi - μ)^{2} }{N}\)

\(\frac{(21 - 25)2 + ... + (29 - 25)2}{5}\)

⇒ \(\frac{38}{5}\)

⇒ 7.6

σ =  \(\sqrt{7.6}\)

⇒   2.756809750418

⇒ or 2.76

The total amount of money earned by Kerri is $135.

Given that, Kerri earns $15 an hour tutoring.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the total amount of money earned by Kerri be x.

Now, total number of hours = 2+3+4=9 hours

Total money = Number of hours worked × Amount earned in an hour

x=9 × 15

⇒ x = 135

Therefore, the total amount of money earned by Kerri is $135.

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Each cube in the pattern has an area of 3 square inches.

To determine the area of each cube in the pattern, we need to find the area of each rhombus formed by the pattern.

The pattern consists of rhombuses, and we know that the diagonals of each rhombus are 2 inches and 3 inches.

The formula to find the area of a rhombus is given by:

Area = (d1 * d2) / 2,

where d1 and d2 are the lengths of the diagonals.

In this case, d1 = 2 inches and d2 = 3 inches.

Plugging the values into the formula, we get:

Area = (2 * 3) / 2

= 6 / 2

= 3 square inches.

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The angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.

How to calculate angle of elevation?

We can use trigonometry to calculate the angle of elevation:

tan(angle) = opposite/adjacent

In this case, the opposite is the height of the tower (199 feet) and the adjacent is the distance from Josh to the base of the tower (125 feet). So:

tan(angle) = 199/125

We can solve for the angle by taking the inverse tangent (tan^-1) of both sides:

angle = tan^-1(199/125)

Using a calculator, we find that:

angle ≈ 58.7 degrees

Therefore, the angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.

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Answer: A

Step-by-step explanation:

Answer:

-1 and 21

Step-by-step explanation:

Let the numbers be x and y.

x + y = 20

xy = -21

Solve the first equation for x and substitute in the second equation.

x = 20 - y

(20 - y)y = -21

20y - y^2 = -21

y^2 - 20y - 21 = 0

(y - 21)(y + 1) = 0

y - 21 = 0 or y + 1 = 0

y = 21 or y = -1

For y = 21:

x = 20 - y

x = 20 - 21

x = -1

For y = -1:

x = 20 - y

x = 20 - (-1)

x = 21

Solutions: (-1, 21) and (21, -1)

Answer: the numbers are -1 and 21

In mathematics, linear programming is a technique for maximizing operations under certain restrictions.

Using the mathematical modeling technique of linear programming, a linear function is maximized or minimized depending on the restrictions it is subjected to. This method has proved helpful for directing quantitative judgments in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

In mathematics, linear programming is a technique for maximizing operations under certain restrictions. Maximizing or minimizing the numerical value is the primary goal of linear programming. It comprises of linear functions that are subject to restrictions in the form of inequalities or linear equations.

Therefore, the correct answer is option A. this is a binding constraint, so there is no slack or surplus.

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Answer:

it would be 4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4*2/4*25= 8/100=0.08 or 8%

The random variable X is the number of rolls needed to obtain the first occurrence of a 4 or 5. The values that X can take on are 1, 2, 3, 4, ... The probability of success is 2/6 = 1/3. The probability of failure is 4/6 = 2/3. The probability that the first occurrence of event F is on the fourth trial is 2/3 * 2/3 * 2/3 * 1/3 = 16/81.

(a) The random variable X is the number of rolls needed to obtain the first occurrence of a 4 or 5. This means that X can take on the values 1, 2, 3, 4, ..., where 1 represents the first roll, 2 represents the second roll, and so on.

(b) The probability of success (event F occurs) is the probability of rolling a 4 or a 5 on any given roll. There are 2 outcomes that satisfy this condition, and there are a total of 6 possible outcomes, so the probability of success is 2/6 = 1/3.

The probability of failure (event F does not occur) is the probability of not rolling a 4 or a 5 on any given roll. There are 4 outcomes that satisfy this condition, and there are a total of 6 possible outcomes, so the probability of failure is 4/6 = 2/3.

(d) The probability that the first occurrence of event F (rolling a four or five) is on the fourth trial is the probability of failing to roll a 4 or 5 on the first three rolls and then rolling a 4 or 5 on the fourth roll. The probability of failing to roll a 4 or 5 on the first three rolls is (2/3)^3 = 8/27.

The probability of rolling a 4 or 5 on the fourth roll is 1/3. So, the probability that the first occurrence of event F is on the fourth trial is (8/27) * (1/3) = 16/81.

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Answer:

1.125

Step-by-step explanation:

1 and 3/4 = 1.75

2 and 7/8 = 2.875

So

2.875 - 1.75 = 1.125

The trigonometric ratio for cos D is 24/25

To find the trigonometric ratio of cos D, we need to use the cosine function

cos D = adjacent / hypotenuse

In this case, the adjacent side is EF, which has a length of 72 units, and the hypotenuse is DF, which has a length of 75 units. Therefore, we have

cos D = EF / DF

Substitute the values in the equation

cos D = 72 / 75

To simplify this fraction, we can divide both the numerator and the denominator by the greatest common factor, which is 3

cos D = (72/3) / (75/3)

cos D = 24 / 25

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The given question is incomplete, the complete question is:

What is the trigonometric ratio for cosD ? Enter your answer, as a simplified fraction, in the boxes.

Answer:7/25

Step-by-step explanation:

i took the test

The probability that a pupil uses neither pool nor gym is 11/70

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.

Number of pupil that can use pool and gym = 28

Number of people that can use pool = 48

Number of people that can use gym = 39

Number of people that can use pool only = 48 - 28 which is 20

Number of people that can use gym only = 39 - 28 = 11

Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59

Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.

Probability = required outcome / possible outcome

Required outcome = 11

possible outcome = 70

Probability = 11/70

In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70

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Answer: 1/10

Step-by-step explanation:

(1 x 4)/(8x5)

4/40

1/10

Answer: 5n+2. 5×3+2=$. 15+2=$. 17=$.

Answer:

B is the correct answer

Step-by-step explanation:

same as above

The interval of convergence is (-18/5, 18/5).

To express f(x) as a power series, we first need to decompose it into partial fractions:

f(x) = 11/(x^2 - 7x - 18) = 11/[(x - 9)(x + 2)]

Using partial fractions, we can write:

11/[(x - 9)(x + 2)] = A/(x - 9) + B/(x + 2)

Multiplying both sides by the denominator (x - 9)(x + 2), we get:

11 = A(x + 2) + B(x - 9)

Setting x = 9, we get:

11 = A(9 + 2)

A = 1

Setting x = -2, we get:

11 = B(-2 - 9)

B = -1

Therefore, we have:

f(x) = 1/(x - 9) - 1/(x + 2)

Now, we can write the power series of each term using the formula for a geometric series:

1/(x - 9) = -1/18 (1 - x/9)^(-1) = -1/18 * sigma^n=0 to infinity (x/9)^n

1/(x + 2) = 1/11 (1 - x/(-2))^(-1) = 1/11 * sigma^n=0 to infinity (-x/2)^n

So, putting everything together, we get:

f(x) = 1/(x - 9) - 1/(x + 2) = -1/18 * sigma^n=0 to infinity (x/9)^n + 1/11 * sigma^n=0 to infinity (-x/2)^n

The interval of convergence can be found using the ratio test:

|a_n+1 / a_n| = |(-x/9)^(n+1) / (-x/9)^n| + |(-x/2)^(n+1) / (-x/2)^n|

= |x/9| + |x/2|

= (|x|/9) + (|x|/2)

For the series to converge, we need |a_n+1 / a_n| < 1. This happens when:

(|x|/9) + (|x|/2) < 1

Solving for |x|, we get:

|x| < 18/5

Therefore, the interval of convergence is (-18/5, 18/5).

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y = | x + 5 | - 4

You subtract 4 outside the abs val to move the graph down.

You add 5 inside the abs val to move the graph left.  (Inside translations are the opposite of what you'd expect.)

SOLUTIONS

Quartile is also called as Quarter

A quartile divides data into three points—a lower quartile, median, and upper quartile—to form four groups of the dataset. The lower quartile, or first quartile, is denoted as Q1 and is the middle number that falls between the smallest value of the dataset and the median. The second quartile, Q2, is also the median.

Quartiles are values that divide your data into quarters. However, quartiles aren't shaped like pizza slices; Instead they divide your data into four segments according to where the numbers fall on the number line. The four quarters that divide a data set into quartiles are: The lowest 25% of numbers.

Therefore Quartile is also called as Quarter

Answer:

x = c/3 - k/3

Step-by-step explanation:

Solve for x:

k + 3 x = c

Subtract k from both sides:

3 x = c - k

Divide both sides by 3:

Answer: x = c/3 - k/3

The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Generally, the equation for three points is mathematically given as

a+2b+4c=1.....1  for the variable (1, 2)

4a+4b+4c=1.....2  for the variable (2, 2)

9a+3b+c=1.....3  for the variable (3, 1)

Step 1

Here we solve equations 1 and 2 simultaneously to find the value of b

Therefore

equ 2-equ1

3a+2b=0

b=-1.5a....4

Step 2

We solve equations 1 and 3 simultaneously to find the value of c

Where

9*equ1-equ3 gives

-15b-35c=-8

c=8-15b

subbing equ 4 we have

c=8+22.5a ....5

Step 3

Put values of b and c in equation 2, and we have

4a-6a+32+90a=1

a=-31/88

a=-0.3523

The value of b will be

b=-1.5*a

b=0.5284

The value of b will be

c=8-22.5*a

c=15.9268

Step 4

In conclusion, the equation is given as

By substituting the values of a b and c into the general formula we have

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

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Answer:

x+ 3/2y= 15

Step-by-step explanation:

8x+12y=120

To put the equation into standard form, the leading coefficient has to be 1. So, divide the whole equation by 8.

x+ 3/2y= 15