a factory bottles 360 bottles of juice in 5 minutes find the factory’s into rate bottles per minute

A.  u is a linear combination of u+v, v+w, and w+u.

B. u is a linear combination of av and bw.

(a) Since u is a vector in ℝ, we can write it as a linear combination of any three vectors in ℝ. So, let's try to express u as a linear combination of the given three vectors:

u = α(u+v) + β(v+w) + γ(w+u)

where α, β, and γ are some real numbers that we need to find.

Expanding this expression using vector addition and scalar multiplication, we get:

u = αu + αv + βv + βw + γw + γu

Rearranging terms, we get:

(1 - γ)u + (α + β)v + (β + γ)w = 0

Since u, v, and w are linearly independent (otherwise, we could not represent u as a linear combination of them), the coefficients of u, v, and w must all be zero. Thus, we have the following system of equations:

1 - γ = 0

α + β = 0

β + γ = 0

Solving for α, β, and γ in terms of γ, we get:

γ = 1

α = -1

β = -1

Substituting back into the original expression, we get:

u = (-1)(u+v) + (-1)(v+w) + (1)(w+u)

Therefore, u is a linear combination of u+v, v+w, and w+u.

(b) Suppose u is a linear combination of v and w, i.e., there exist some real numbers α and β such that:

u = αv + βw

We want to show that u is also a linear combination of av and bw, i.e., there exist some real numbers λ and μ such that:

u = λ(av) + μ(bw)

= (aλ)v + (bμ)w

We can choose λ and μ as follows:

λ = α/a

μ = β/b

Then, we have:

(aλ)v + (bμ)w = (aα/a)v + (bβ/b)w = αv + βw = u

Therefore, u is a linear combination of av and bw.

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(i) The dual of the given LP problem can be found by following these steps:

1. For each constraint in the primal problem, create a dual variable. In this case, we have three constraints, so we'll have three dual variables: y1, y2, and y3.
2. The objective function of the dual problem will be the sum of the products of the primal variables and their corresponding dual variables. So, the dual objective function is:
  Maximize w = 3y1 + 2y2 + y3.
3. For each primal variable x, create a constraint in the dual problem with the coefficient of the corresponding dual variable equal to the coefficient of x in the primal objective function. So, the dual constraints are:
  y1 + 2y2 - y3 ≤ -2
  y1 + y2 + y3 ≤ -1
  y1, y2, y3 ≥ 0.

(ii) To find the optimal solution to the dual problem, we need to solve the optimal tableau of the dual problem. From the given information, we know that Row 0 of the optimal tableau is:
  w = 4x1 + e2 + (M-1)a2 + (M+2)a3 = 0.
 
  However, the given information does not provide any details about the values of x1, e2, a2, or a3. Therefore, without this information, we cannot determine the specific optimal solution to the dual problem.

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Answer:

B. x<27

Step-by-step explanation:

300-165=135

135/5=27

Answer:

B. x<27

Step-by-step explanation:

The shelter has 165 animals.  The shelter must keep its total occupancy below 300.  The shelter takes in an average of 5 animals per day. If x is the number of days, then in x days the shelter takes 5x animals. In total there will be  165+5x animals. This number must be less  than 300

         X<27

Answer:

x = 6.8829

Step-by-step explanation:

\(\frac{sin\left(35\right)}{x}=\frac{sin\left(90\right)}{12}\)

Answer:

x ≈ 6.8

Step-by-step explanation:

Label each side of the triangle with "a" (adjacent), "o" (opposite), or "h" (hypotenuse).

Side x is the opposite, side 12 is the hypotenuse, and the other side is the adjacent.

Use SOH-CAH-TOA to find the missing side (Sin, Cos, Tan).

To find x, we need to use SOH or Sin(a)= O/H

Plug in the adjacent angle for a and 12 for h then solve:

Sin(35)=O/12

The calculator approximation of Sin(35) is 0.5735.

0.5735  ≈ O/12

Multiply both sides by 12:

12 * 0.5735  ≈ O/12 * 12

O ≈ 6.882

Round to nearest tenth:

O ≈ 6.8

Answer:

(a) The unit rate for car B is greater because the slope is greater than the slope for car A.

Step-by-step explanation:

We have been given a graph that represents the distance cars A and B travel. We are asked to choose the correct option about our given graphs.

Since slope represents the change in y-value with respect to change in per unit x value, so slope is also unit rate of the graph.

Let us find the slope of car A using points (8,5) and (0,0).

Let us find the slope of car B using points (5,8) and (0,0).

We can see that slope of car B is greater than slope of car A, therefore, option A is the correct choice.

Step-by-step explanation:

After a three-day visit to a hacienda, the student finds themselves approximately 14.2 km away from the barn, in a direction of 43 degrees south of east.

Let's break down the three days of travel. On the first day, the student walks 5 km southeast from the barn. This creates a right-angled triangle with one leg of length 5 km. On the second day, they walk 12 km in a 30-degree north-east direction. This adds another leg to the triangle, forming a parallelogram. Using trigonometry, we can determine that the second leg has a length of approximately 10.4 km. On the third day, the student walks 12 km west, which completes the triangle.

To find the total distance and direction from the barn, we can combine the lengths and directions of the three sides. By adding the horizontal components and vertical components separately, we get approximately 12 km east and 12 km south. Applying Pythagoras' theorem, the total distance from the barn is approximately 16.97 km. To find the direction, we use inverse trigonometry, which yields approximately 43 degrees south of east.  

To return to the starting point, the student needs to retrace their steps. Since the third day's walk was in the opposite direction, they need to travel a distance of approximately 12 km west. Combining this with the 10.4 km north-east component from the second day, we get a total distance of approximately 20.4 km. To find the direction, we again use inverse trigonometry, which gives us approximately 57 degrees north of west.

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Answer:

102

Step-by-step explanation:

Answer:

there is no remainder

Step-by-step explanation:

Answer:

x = - 2

Step-by-step explanation:

Givens

(2,5)

(x,3)

m = 1/2

Formula

m = (y2 - y1)/(x2 - x1)

Solution

y2 = 3

y1 = 5

x2 = x

x1 = 2

1/2 = (3 - 5)/(x - 2)                 Cross multiply

1*(x - 2) = 2 (-2)                      Combine and remove the brackets.

x - 2 = - 4                               Add 2 to both sides

x = - 4 + 2

x = - 2

Answer:

after 25 minutes the temperature was at 78 degrees

Step-by-step explanation:

Answer:

-76

Step-by-step explanation:

Answer:

Degree: 5

Leading Coefficient: -7

Step-by-step explanation:

The two situations which would result in a solution of 0 include the following:

B. On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?

D. A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

For this exercise, the expression which represents the first situation is given by:

Amount of money left = $35 - $35

Amount of money left = 0

For this exercise, the expression which represents the second situation is given by:

Amount of money owed = $7.50 - $7.50

Amount of money owed = 0.

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The mass of the entire archway is 585.32 grams. This is calculated by (275 x 1.2 x 0.1785) + 45 = 585.32 grams.

1. Calculate the mass of the helium in the balloons: (275 x 1.2 x 0.1785) = 49.38 grams

2. Calculate the mass of the string and fixings: 45 grams

3. Add the mass of the helium and the mass of the string and fixings: 49.38 + 45 = 585.32 grams

4. The mass of the entire archway is 585.32 grams.

The mass of the entire archway is 585.32 grams. This is calculated by (275 x 1.2 x 0.1785) + 45 = 585.32 grams.

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Answer:

Step-by-step explanation:

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Answer:

Kites are a special type of quadrilateral with two distinct pairs of consecutive sides the same length. ... Similarly, every kite is not a parallelogram, because the opposite sides of a kite are not necessarily parallel.

Answer:

No

Step-by-step explanation:

All parallelograms are not a kite.

A kite is a quadrilateral with two disjoint pairs ( no side is in both pairs ) of equal-length, adjacent ( sharing a vertex ) sides. A parallelogram also has two pairs of equal-length sides, however they must be opposite, as opposed to adjacent.

( See the attached image )

Answer:

H is equal to and greater than 48 the last one because you must be equal to 48 inches or greater than 48 inches so = would be equal to and < would mean that you must be greater than

Step-by-step explanation:

Answer:

h ≥ 48

Step-by-step explanation:

Height must be greater than or equal to 48 inches tall to ride.

Answer:

UTR and UTW, hope this helped!

Step-by-step explanation:

Idk what to explain here...

Answer:

XWY and VWT

Step-by-step explanation:

Vertical angles are formed from the same lines but are opposite each other

XWY and VWT  are formed by the same lines but are opposite each other

The values of the given quantities calculated using permutation and combination are a. P(6,3) = 20 b. P(8,5) = 1120 c. P(10,8) = 1814400 d. C(8,4) = 70 e. C(12,6) = 924

a. P(6,3) represents the permutation of 3 elements taken from a set of 6 elements. The formula to calculate permutations is given by P(n,r) = n! / (n-r)!, where n! denotes the factorial of n. In this case, P(6,3) = 6! / (6-3)! = 6! / 3! = (6 * 5 * 4) / (3 * 2 * 1) = 120 / 6 = 20.

b. P(8,5) represents the permutation of 5 elements taken from a set of 8 elements. Applying the permutation formula, we have P(8,5) = 8! / (8-5)! = 8! / 3! = (8 * 7 * 6 * 5 * 4) / (3 * 2 * 1) = 6720 / 6 = 1120.

c. P(10,8) represents the permutation of 8 elements taken from a set of 10 elements. Using the permutation formula, we get P(10,8) = 10! / (10-8)! = 10! / 2! = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2) / (2 * 1) = 3628800 / 2 = 1814400.

d. C(8,4) represents the combination of 4 elements taken from a set of 8 elements. The formula for combinations is given by C(n,r) = n! / (r! * (n-r)!). Thus, C(8,4) = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70.

e. C(12,6) represents the combination of 6 elements taken from a set of 12 elements. Applying the combination formula, we have C(12,6) = 12! / (6! * (12-6)!) = 12! / (6! * 6!) = (12 * 11 * 10 * 9 * 8 * 7) / (6 * 5 * 4 * 3 * 2 * 1) = 924

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The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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A quantitative variable x is a "Random Variable" if the value that x takes on in a given experiment or observation is a chance or random outcome.

A random variable is one with an unknown value or a function which assigns qualities to each of the outcomes of an experiment.

Some key features regarding the Random Variable are-

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Answer:

Step-by-step explanation:

Dimensions of rectangle:

The area is the product of the two dimensions:

Answer:

3/10

Step-by-step explanation:

12/40, divide by four on the top and bottom -> 3/10

Answer:

the ratio as a fraction in simplest form :12/40=3/10

Answer:

I zont know i need points

Step-by-step explanation:

Yea im srry

Answer:

slope is 3

y-intercept =-24

Step-by-step explanation:

solve for y

y+3=3(x-7)

y+3=3x-21

y=3x-21-3

y=3x-24

Answer:

Step-by-step explanation:

A linear function is a line which, in slope-intercept form, follows

y = mx + b,

where m is the slope and b is the y-intercept.

The only one that follows that form is B. B can be rewritten as

\(y=\frac{1}{3}x+2\)

and in that form we see that the slope value is 1/3 and the y-intercept is 2. The choice is B.

A is a radical function moved up from its originating spot; C is an inverse function moved down 4 units from its originating spot with a vertical asymptote at x = 0; and D is a cubic moved down 10 units from its originating spot.

B is the one you want.

Answer:

C on edge

Step-by-step explanation:

The domains of f(x) and g(x) are different. (answer)

The domains of graph f(x) and g(x) are different.

A mathematical operation is commutative if the numbers used can be changed without changing the outcome. As illustrated here, addition and multiplication are two examples of commutative operations. 2+3 = 5

3+2 = 5

2*3 Equals 6

3*2 Equals 6.

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Vertical angulation refers to the angle at which the x-ray beam is directed when taking dental radiographs. It is an important factor in obtaining clear and accurate images.

In both the paralleling and bisecting techniques, the group of answer choices remains the same. However, the vertical angulation is generally greater for images taken with the paralleling technique compared to the bisecting technique.

This is because the paralleling technique requires the x-ray beam to be directed more vertically in order to capture the entire tooth structure on the film. On the other hand, the bisecting technique involves angling the x-ray beam downward to intersect the imaginary bisector between the long axis of the tooth and the film.

Therefore, the vertical angulation differs depending on which technique is being used.

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Triangle JKL is congruent to triangle MLK based on angle - angle - side congruency theorem

A triangle is a polygon that has three sides and three angles. Types of triangles are equilateral, isosceles, scalene, right angled triangle. In an equilateral triangle, two sides are equal.

Two triangles are said to be congruent, if all angles and all sides are congruent to each other.

From the diagram:

∠KJL = ∠LMK (Given)

∠JKL = ∠MLK (Given)

KL ≡ KL

PS = QS (Definition of equilateral triangle)

ΔJKL ≅ ΔMLK (angle - angle - side congruency theorem)

Triangle JKL is congruent to triangle MLK

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