Divide.

(−16)÷(−56)

What is the quotient?

Enter your answer as a simplified fraction in the box.

Answer:

To calculate the total amount, first find out how much you contribute and then add the amount your employer contributes.

Your contribution: 10% of $50,000

= ($50,000 * 10) / 100

= $5,000

Employer's contribution: 3% of $50,000

= ($50,000 * 3) / 100

= $1,500

Total contribution:

= Your contribution + Employer's contribution

= $5,000 + $1,500

= $6,500

So, the total amount being put away in your account each year is $6,500.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

it's 4 because I'd you put the numbers from least to greatest its in the middle

Answer:

2

Step-by-step explanation:

arrange the numbers in order

count how many numbers you have

if have ood number divide by 2 and round up to get the position of the median number

Answer:

The maximum number of visits for a member of science museum is 36.

Step-by-step explanation:

Given,

Membership fee = $8

Per visit fee = $1

Total cost = $44

Let,

x be the number of visits

y be the total cost

Total cost = per visit fee*number of visits + membership fee

y = x+8

The maximum number of visits for a member of science museum is 36.

Keywords: variable, addition

Answer:

x = 37

37 visits

y = 1x + 8

(45) = x + 8

45 - 8 = x

37 = x

Step-by-step explanation:

Answer:

16.09N

Step-by-step explanation:

Answer:

\(\boxed{\purple{\textsf{The weight of the dog on moon is \textbf{10 Newtons. }}}}\)

Step-by-step explanation:

Given that the weight of the dog on the earth is 60N . We need to find the weight of dog on the moon. So we know that the weight of an object is one sixth the weight of an object on the moon. In other words the acceleration due to gravity is one sixth on the moon that of earth. We can use a formula as ,

\(\qquad\boxed{\boxed{\sf Weight_{(On \ moon )}= \dfrac{1}{6}\times Weight_{(On \ earth )}}}\)

On substituting the respective values :-

\(\sf\implies Weight_{(On \ moon )} = \dfrac{1}{6}\times Weight_{(On \ earth )} \\\\\sf\implies Weight_{(On \ moon )} =\dfrac{1}{6}\times 60 N \\\\\sf\implies\boxed{\pink{\frak{ Weight_{(On \ moon )}= 10 \ Newtons }}}\)

5.25 or 5 1/4

I worked it out I hope this helps :)

The aggregate demand curve shifts to the left, indicating a decrease in overall demand in the economy.

A decrease in U.S. net exports would result in a decrease in aggregate demand.

This is because net exports are a component of aggregate demand, which is the total amount of goods and services demanded in an economy.

When net exports decrease, it means that fewer goods and services are being exported from the U.S.

This, in turn, means that there is less demand for U.S. goods and services from foreign buyers.

As a result, the aggregate demand curve shifts to the left, indicating a decrease in overall demand in the economy.

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The domain of the function here is {0 ≤ x ≤ 600}. The first option is the right answer.

The domain of a function is the set of all input values (or independent variables) for which the function is defined and produces a valid output (or dependent variable). It is the set of values that can be plugged into a function and yield a valid result.

The domain of this function in this context is {0 ≤ x ≤ 600}.

This is because x represents the number of t-shirts Henry sells and he has ordered 600 shirts. So, he can only sell a non-negative number of shirts (x ≥ 0) and a maximum of 600 shirts (x ≤ 600). Any values outside this range are not meaningful in this context, hence they are not part of the domain.

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Answer:

Final equation: y = -7x -19

Step-by-step explanation:

You are looking for slope intercept correct?

Formula: y = mx + B

Y = y-value of point ( coordinates )

M = slope

X = x - value of point ( coordinates )

B = Y - intercept

Equation:

2 = -7(-3) + B

2 = 21 + B

-21 = -21 = B

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

-19 = B

Final equation: y = -7x -19

Unless if it asks you to plug back the numbers for anything else then you do that but this is how you get slope intercept.

In a queueing system with customer arrivals every 6 seconds and service times of 4 seconds, the task is to calculate the average number of customers in the queue

To calculate the average number of customers in the queue, we can use Little's Law, which states that the average number of customers in a stable queueing system is equal to the average arrival rate multiplied by the average time spent in the system.

First, we need to calculate the average arrival rate. Since customers arrive once every 6 seconds, the arrival rate is 1 customer per 6 seconds or 1/6 customers per second.

The total service time is 4 seconds, and the standard deviation is 5.9. Therefore, the average service time is 4 seconds.

Using Little's Law, we multiply the average arrival rate (1/6 customers per second) by the average service time (4 seconds) to obtain the average number of customers in the queue.

Average number of customers in the queue = (1/6) * 4 = 2/3 ≈ 0.667

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Answer:

See below

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

2a +3b

let a=-4 and b=3

2(-4) +3(3)

Multiply

-8 +9

Add

1

536.2  cubic inches  is the volume of a cube with surface area of 396.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given,

\(A=6V^{\frac{2}{3}}\)

A is surface Area ‘A’, in square units, of a cube

V is  volume of cube in cubic units.

We need to find the volume, in cubic inches, of a cube with surface area of 396.

A=396

We need to find V

\(V^{\frac{2}{3} } =A/6\)

=396/6

=66

\(V=66^{\frac{3}{2} }\)

V=536.2  cubic inches

Hence, 536.2  cubic inches  is the volume of a cube with surface area of 396.

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Answer:

(x-3) (x-2)

Step-by-step explanation:

\(x^{2}\) - 5x + 6

How to break down the equation and factorise it:

-3 x -2 = 6

-3 + -2 = -5

Final Answer:

(x-3) (x-2)

It will take 4 months for the total cost for both gyms to be equal.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's assume that the total cost for both gyms will be equal after "x" months.

For Gym A, the total cost after "x" months can be calculated as follows:

Total cost for Gym A = Joining fee + Monthly charge * Number of months

Total cost for Gym A = $20 + $40x

For Gym B, the total cost after "x" months can be calculated as follows:

Total cost for Gym B = Monthly charge * Number of months

Total cost for Gym B = $45x

Now we can set up an equation to find when the total cost for both gyms will be equal:

$20 + $40x = $45x

To solve for "x", we can first subtract $40x from both sides:

$20 = $5x

Then divide both sides by $5:

x = 4

Therefore, it will take 4 months for the total cost for both gyms to be equal.

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Answer:

\(\displaystyle 36° = m∠NQS\)

Step-by-step explanation:

Apply the Midsegment Theorem:

\(\displaystyle \frac{1}{2}[96 - 4x]° = [5x + 6]° → [48 - 2x]° = [5x + 6]° → -42 = -7x; 6 = x \\ \\ [48 - 2(6)]° = [48 - 12]° = 36° \\ \\ AND/OR \\ \\ [5(6) + 6]° = [30 + 6]° = 36°\)

I am joyous to assist you at any time.

Answer:

AB = 24

Step-by-step explanation:

AB = EB x 2 = 24

Answer:

AB equals 24.

Step-by-step explanation:

Fill in the blank would be 24

Answer: -5

Step-by-step explanation:

9514 1404 393

Answer:

  (b)  The independent variable is time and the dependent variable is distance

Step-by-step explanation:

When you have an equation of the form ...

  <single variable or function name> = <expression involving another variable>

we take this to mean the <single variable> is the dependent variable. The <other variable> involved in the expression on the right is considered to be the independent variable. The variable on the left depends on the variable on the right.

Here, that means ...

Answer:

Least= -6

Middle= -3

Greatest= -2

Answer:

Quotient = x² + x + 3

Reminder = 10

Step-by-step explanation:

We need to divide , x³ - 4x² - 2x - 5 by x - 5

x - 5) x³ - 4x² - 2x - 5 ( x² + x + 3

- x³ -(+)5 x²

_______________

0 + x² - 2x - 5

x² -5x

__________________

0 +3x - 5

+3x -15

__________________

+10

it A

Step-by-step explanation:

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}\)

Answer: m²-mn

Explanation: multiply the letter outside the brackets by everything inside the brackets, so, m×m = m² and m×n = mn, altogether it is m²-mn.

The determinant of the matrix a with 8's on the diagonal, 1's above the diagonal, and 0's below the diagonal is det(a) = 8ⁿ, where n is the dimension of the matrix.

To find the determinant of the n×n matrix a with 8's on the diagonal, 1's above the diagonal, and 0's below the diagonal, we can use the property that the determinant of a triangular matrix is equal to the product of its diagonal elements.

Since the matrix a is an upper triangular matrix, its determinant is the product of its diagonal elements.

The diagonal elements of matrix a are all 8's. Therefore, the determinant of matrix a can be computed as follows:

det(a) = 8 * 8 * 8 * ... * 8 (n times)

      = 8ⁿ

Hence, the determinant of the matrix a is 8 raised to the power of n (det(a) = 8ⁿ).

This means that the determinant of matrix a is simply 8 raised to the power of the dimension of the matrix (n).

The specific values of the elements above and below the diagonal (1's and 0's, respectively) do not affect the determinant, as they do not contribute to the product when computing the determinant of an upper triangular matrix.

In summary, the determinant of matrix a is det(a) = 8ⁿ, where n represents the dimension of the matrix.

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Answer:

x= 0.9

step-by-step explanation:

LCM=3x

use the lcm to multiply each term

3x×1/3+3x×3=3x×3/x

cancel out

x+9x=9

10x=0

divide both side by the coefficient of x

10x/10=9/10

x=0.9

The linear program has an optimal solution of 28.5 at (A, B) = (2, 5) when the right-hand side for constraint 1 is 10. If the right-hand side is increased to 11, the optimal solution remains 28.5 at the same point.

The dual value for constraint 1 stays the same as long as the right-hand side stays within the range 8.4 to 11. The value of the optimal solution will increase by 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is within the range 23 to 27.

a) To find the new optimal solution, we need to graph the feasible region and find the new corner points. After the change, the first constraint becomes 1A + 1B ≤ 11. The other two constraints remain the same. The corner points can be found by substituting the bounds of each variable into the constraints and solving for the other variable. The feasible region can then be graphed, and the maximum of the objective function can be found at one of the corner points.

The new corner points are (0,0), (0,9), (6,0), and (2,5). The feasible region can be graphed as a triangle with these corner points. The maximum of the objective function 3A + 2B occurs at the point (2,5), where the value of the objective function is 28.5.

b) The value of the objective function at the optimal solution is 28.5, at (A, B) = (2, 5).

c) The right-hand side range information for constraint 1 tells us that if the right-hand side is increased from 10 to 11, the dual value will remain the same (since the allowable increase is 2.6 and the right-hand side only increases by 1). The range for constraint 1 is 8.4 to 11. As long as the right-hand side stays within this range, the dual value of 2.6 is applicable.

d) The dual value for constraint 2 is 0.5. Using this dual value and the right-hand side range information, we can conclude that the value of the optimal solution will increase by 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is within the range 23 to 27.

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Complete question:

Consider the following linear program.

Max 3A + 2B s.t.

1A + 1B ≤ 10

3A + 1B ≤ 27

1A + 2B ≤ 18

A, B ≥ 0

The value of the optimal solution is 28.5. Suppose that the right-hand side for constraint 1 is increased from 10 to 11.

(a) Use the graphical solution procedure to find the new optimal solution.

What is the value of the objective function at the optimal solution?

(blank) at (A, B) =

Use the solution to part (a) to determine the dual value for constraint 1.

(c) The computer solution for the linear program provides the following right-hand side range information

. Constraint RHS Value Allowable Increase Allowable Decrease

1 10.00000 2.60000 1.00000

2 27.00000 3.00000 13.00000

3 18.00000 Infinite 6.50000

What does the right-hand side range information for constraint 1 tell you about the dual value for constraint 1?

The range for constraint 1 is (blank) to (blank) . As long as the right-hand side stays (within/outside) this range, the dual value of (blank) is applicable.

(d) The dual value for constraint 2 is 0.5. Using this dual value and the right-hand side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2?

The value of the optimal solution will increase by (blank) for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is (within/outside) the range (blank) to (blank).

It turns out that the dynamo effect depends on the presence of up to 20% nickel in the Earth's core, a metal that behaves very differently from iron under extreme temperatures.  Unlike the northern hemisphere mineral-rich crust and mantle, the core is made almost entirely of metal—specifically, iron and nickel. The shorthand used for the core's iron-nickel alloys is simply the elements' chemical symbols—NiFe. Elements that dissolve in iron, called siderophiles, are also found in the core.

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At a significance level of 5%, with a sample size of 800 items produced on a new machine and 48 of them being defective, the null hypothesis is that the proportion of defective items is not significantly more than 5%, while the alternative hypothesis is that it is significantly more than 5%. The level of significance is 0.05. Using a z-test for proportion with a one-tailed test, the calculated test statistic is 3.45. Since the calculated test statistic is greater than the critical value of 1.645, we reject the null hypothesis. Therefore, there is enough evidence to get rid of the machine.

Null Hypothesis: p = 0.05

Alternative Hypothesis: p > 0.05

Level of Significance: α = 0.05

Sample Size: n = 800

Number of Defective Items: x = 48

Sample Proportion:P= x/n = 48/800 = 0.06

Since the sample size is large, we can use the normal distribution to approximate the binomial distribution.

Test Statistic: z = (P - p) / sqrt(p * (1 - p) / n)

Under the null hypothesis, the test statistic follows a standard normal distribution.

Decision Rule: Reject the null hypothesis if z > zα, where zα is the z-score that corresponds to a cumulative probability of 1 - α.

From the standard normal distribution table, we have:

zα = 1.645

Computation:

z = (0.06 - 0.05) / sqrt(0.05 * 0.95 / 800) = 1.33

Since z (1.33) is less than zα (1.645), we fail to reject the null hypothesis.

Conclusion: At a significance level of 5%, there is not enough evidence to conclude that the proportion of defective items produced by the new machine is significantly more than 5%. Therefore, the factory should not get rid of the machine based on this sample data.

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[ 18  5  2  ] is  the sum of a vector .

What, in the simplest terms, is a vector?

A quantity or phenomena with both magnitude and direction being independent of one another is called a vector.

                           The phrase also describes how such a quantity is represented mathematically or geometrically.

                                  Velocity, momentum, force, electromagnetic fields, and weight are some natural examples of vectors.

Since u₁ , u₂ = 0

So, u₁, u₂ is an orthogonal set is W .

Since orthogonal  vector are linearly independent , it follows that { u₁, u₂} is linearly independent set .

 \(\frac{u_{1} . y}{u_{1} u_{1} } u_{1} + \frac{u_{2}. y }{u_{2}u_{2} } u_{2}\)

\(\frac{19 + 0 - 3}{1 + 0 + 1} [ 1 0 -1 ] + \frac{38 + 1 + 6}{4 + 1 + 4} [ 2 1 2 ]\)

 = 16/2 [ 1 0 1 ]  + 45/9  [ 2 1 2 ]

  = 8 [ 1 0  - 1 ] + 5 [ 2  1   2  ]

  = [ 18  5  2  ]

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The chance of drawing a white counter after drawing a white counter from the bag is 1

Let's assume that the probability of drawing a white counter from the bag is represented by the symbol P(W), and the probability of drawing a black counter is represented by P(B).

Initially, there is a 50% chance that the counter in the bag is white and a 50% chance that it is black. Therefore, we can represent the probability of initially having a white counter as P(W) = 0.5 and the probability of initially having a black counter as P(B) = 0.5.

After adding the white counter to the bag, we now have two possible scenarios

The counter in the bag was originally white, and we added another white counter. The probability of this scenario is P(W) × 1 = 0.5 × 1 = 0.5.

The counter in the bag was originally black, and we added a white counter. The probability of this scenario is P(B) × 1 = 0.5 × 1 = 0.5.

Thus, the probability of drawing a white counter after drawing a white counter from the bag is the probability of scenario 1 divided by the probability of both scenarios

P(W|W) = P(W and W) / P(W and W) + P(B and W)

P(W|W) = (0.5 × 1) / ((0.5 × 1) + (0.5 × 0))

P(W|W) = 1

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