Write equations to show how the commutative and associative properties of multiplication are involved when you calculate 40.800 mentally by relying on basic multiplication facts (such as 4.8). Write your equations in the form 40.800 = some expression = :
=some expression Indicate specifically where the commutative and associative properties of multiplication are used.

To obtain the following tableau, we pivot around the element at the intersection of the x1 column and the x6 row:

| BV | x1 | x2 | x3 | x4 | x5 | x6 | x7

A variable (from the Latin variabilis, "changeable") is a mathematical symbol. A variable can be a number, a vector, a matrix, a function, its argument, a set, or an element of a set.

To solve the given linear programming problem using the Big M method, we need to convert the problem into standard form by adding slack, surplus, and artificial variables as needed. Then, we use the simplex algorithm to iteratively improve the solution until we reach an optimal solution.

Let's first write the problem in standard form by introducing slack and artificial variables as follows:

Maximize Z = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + 3x3 + 2x4 + x5 = 4

x1 - x3 + x4 - x6 = -1

2x1 + x2 + x7 = 2

x1 + 2x2 + x3 + 2x4 = 2

where x5, x6, x7 are slack and artificial variables.

We can see that the problem is infeasible because the last equation is inconsistent with the second equation. To make the problem feasible, we need to introduce artificial variables for the second equation and modify the objective function to penalize their use. This leads us to the following modified problem:

Maximize Z = -2x1 + x2 - 4x3 + 3x4 - M(x6 + x8)

Subject to:

x1 + x2 + 3x3 + 2x4 + x5 = 4

x1 - x3 + x4 + x6 - x8 = -1

2x1 + x2 + x7 = 2

x1 + 2x2 + x3 + 2x4 = 2

where x5, x6, x7, x8 are slack and artificial variables, and M is a large positive constant.

Now, we can construct the initial simplex tableau as follows:

| BV | x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | RHS |

|----|----|----|----|----|----|----|----|----|-----|

| x5 | 1  | 1  | 3  | 2  | 1  | 0  | 0  | 0  |  4  |

| x6 | 1  | 0  | -1 | 1  | 0  | 1  | 0  | -1 | -1  |

| x7 | 2  | 1  | 1  | 0  | 0  | 0  | 1  | 0  |  2  |

| x8 | 1  | 1  | 2  | 1  | 0  | 0  | 0  | -1 |  2  |

| Z  | -2 | 1  | -4 | 3  | 0  | M  | 0  | -M |  0  |

The column for the objective function includes the coefficients of the original variables and the artificial variables, with the artificial variables having a coefficient of M in the objective function.

To perform the simplex algorithm, we select the most negative coefficient in the bottom row, which corresponds to x1, as the entering variable. We then select the row with the smallest nonnegative ratio of the RHS to the coefficient of the entering variable, which corresponds to x6, as the leaving variable. We pivot around the element in the intersection of the x1 column and the x6 row to obtain the next tableau:

| BV | x1 | x2 | x3 | x4 | x5 | x6 | x7

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The given null hypothesis statement a. true, statement b. true and finally statement c. true.

a. False. Rejection of the null hypothesis using ANOVA only tells us that at least one group mean is different from the others, but it doesn't necessarily mean that all means are different from each other. Additional post-hoc tests, such as Tukey's HSD or Bonferroni, are needed to identify which specific means are different from each other.

b. True. If the null hypothesis is rejected using ANOVA, it means that there is significant variability between the groups. This variability is measured by the F-statistic, which is the ratio of between-group variability to within-group variability. A high F-statistic indicates that the standardized variability between groups is higher than the standardized variability within groups.

c. True. If the null hypothesis is rejected using ANOVA, it means that there is at least one significant difference between the means of the groups. Pairwise comparisons can be conducted using post-hoc tests to identify which specific pairs of means are significantly different. However, it's important to adjust the significance level for multiple comparisons to avoid making Type I errors.

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Answer:

The answer to your problem is, B. 20

Step-by-step explanation:

Well by looking at the graph we can tell that it is not labeled so we will go to our estimate which is on the left side

2 + 3 + 4 + 5 + 6 = 20

Which we can look at our options and see we have a 20.

Thus the answer to your problem is, B. 20

The new basis is x₂, x₄, and x₆, with a non-artificial cost of 3x₂ - M/2x₃ + M/2.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

(a) Using the Big M method, we first rewrite the constraints in standard form by introducing slack variables x₄ and x₅ as follows:

x₁ - 2x₂ + x₃ + x₄ = 20

2x₁ + 4x₂ + x₃ + x₅ = 50

We then introduce artificial variables x₆ and x₇ to handle the inequalities in the first constraint as follows:

x₁ - 2x₂ + x₃ + x₄ - x₆ = 20

2x₁ + 4x₂ + x₃ + x₅ + x₇ = 50

We can now construct the initial simplex tableau as follows:

BV    x₁   x₂   x₃   x₄   x₅   x₆   x₇   RHS

x₄ 1 -2 1 1 0 0 0 20

x₅ 2 4 1 0 1 0 0 50

x₆ 1 -2 1 0 0 1 0 20

x₇ 2 4 1 0 0 0 1 50

Zj-Cj -M M -M 0 0 M M 0

where BV denotes the basic variables, RHS denotes the right-hand side coefficients, and Zj-Cj denotes the relative profits or costs. We set M to a large positive number (e.g., M=1000) to penalize the artificial variables. The initial artificial basic feasible solution is x₄ = 20, x₅ = 50, x₆ = 20, x₇ = 0, with an artificial cost of Mx₆ + Mx₇ = 2000.

The initial entering basic variable is x₂, which has the most negative relative profit of -M. To determine the leaving basic variable, we compute the minimum ratio test for each row:

x₁: 20/1 = 20

x₂: 50/4 = 12.5

x₆: 20/1 = 20

x₇: 50/4 = 12.5

The minimum ratio is 12.5 for x₂ and x₇, which means either of these variables can leave the basis. Since x₇ has a higher index, we choose it to leave the basis. To perform the pivot operation, we divide row 3 by 2 and subtract 2 times row 1 from it:

BV    x₁   x₂   x₃   x₄   x₅   x₆   x₇   RHS

x₄ 0 -2 0 -1 0 1 0 0

x₅ 0 8 0 2 1 0 0 50

x₂ 1 -2 1 0 0 0.5 -0.5 10

x₁ 0 8 -1 0 0 -0.5 0.5 10

Zj-Cj -M 3 -M/2 0 0 M/2 -M/2 2000

The new basis is x₂, x₄, and x₆, with a non-artificial cost of 3x₂ - M/2x₃ + M/2.

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Answer:

(1,-1)

Step-by-step explanation:

Substituting the given point into the equation

[tex]-5/6x=y+1/6\\-5/6(1) = -1 + 1/6\\-5/6 = -5/6[/tex]

This means that if you get strong, then you are guaranteed to win races, according to the original statement.

a) We can convert the statement into propositional logic using the following symbols:

T: You train hard

E: You eat good food

S: You get strong

W: You win races

Using these symbols, the original statement can be represented as follows:

((T ∧ E) → S) ∧ (S → W)

This can be read as "If you train hard and eat good food, then you will get strong, and if you get strong, then you will win races."

b) We can use the propositional logic statement to answer this question. If you don't win races but do train hard, we know that the second part of the statement (S → W) is false, because if S (you get strong) were true, then W (you win races) would have to be true as well. Therefore, we can conclude that S (you get strong) must also be false. In plain English, this means that if you don't win races but do train hard, then you didn't get strong.

c) If you do get strong, we know that the second part of the statement (S → W) must be true, because if S (you get strong) is true, then W (you win races) must also be true. Therefore, we can conclude that if you get strong, then you will win races. In plain English, this means that if you get strong, then you are guaranteed to win races, according to the original statement.

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The amount that is Nick's hourly wage would be = $9.

The total number of hours that Nick works a day = 6 hours

The total amount of money that Nick earned for those hours = $54

That is;

6 hours = 54

1 hours = X

Mark X the subject of formula;

X = 54/6

= $9

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the answer to your question is  130

The value of the identity sin N = 3/5

To determine the value of the identity, we need to know the different trigonometric identities. These identities are;

From the information given, we have that;

The angle of the triangle is N

The opposite side of angle N is 3

The hypotenuse side of angle N is 5

Using the sine identity, we have;

sin N = 3/5

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The non-permissible values are any values of n that would make the original equation undefined. In this case, there are no such non-permissible values.

a.

The given equation is:

[tex]1 + x^4 = x[/tex]

Rearranging terms, we get:

[tex]x^4 - x + 1 = 0[/tex]

To solve this equation, we can use the quartic formula:

x = [ -b ± sqrt( b^2 - 4ac ) ] / 2a

Here, a = 1, b = -1, and c = 1, so we have:

x = [ -(-1) ± sqrt( (-1)^2 - 4(1)(1) ) ] / 2(1)

x = [ 1 ± sqrt( -3 ) ] / 2

Since the discriminant is negative, the solutions are complex:

x = [ 1 ± i*sqrt(3) ] / 2

Therefore, the non-permissible values are any values of x that would make the original equation undefined. In this case, there are no such non-permissible values.

b.

The given equation is:

3^(n-1) / (3^n + 6) + 2^n = 0

To solve for n, we can start by simplifying the first term:

3^(n-1) / (3^n + 6) = 3^(-1) / (1 + 2*3^(-n))

Substituting this into the original equation, we get:

3^(-1) / (1 + 2*3^(-n)) + 2^n = 0

Multiplying both sides by (1 + 23^(-n)), we get:

3^(-1) + 2^n(1 + 2*3^(-n)) = 0

Simplifying, we get:

2^n + 2*3^(n-1) = 0

Dividing both sides by 23^(n-1), we get:

(1/2)(1/3)^n + 1 = 0

Multiplying both sides by -2 and taking the logarithm of both sides, we get:

n = log(2/3) / log(3) - log(2)

Therefore, the solution is:

n = log(2/3) / log(3) - log(2)

The non-permissible values are any values of n that would make the original equation undefined. In this case, there are no such non-permissible values.

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When a $10 check written on the First National Bank is deposited in an account at the Second National Bank, the correct option is C) the liabilities of the Second National Bank decrease by $10. This is because the Second National Bank's liability to the account holder increases by $10, while its liability to the First National Bank decreases by $10. However, none of the other options are correct.

Option A) is incorrect because the liabilities of the First National Bank do not decrease as a result of the check being deposited in the Second National Bank. The liability of the First National Bank to the account holder is transferred to the Second National Bank.

Option B) is incorrect because the reserves of the First National Bank do not increase by $10 when the check is deposited in the Second National Bank. Reserves refer to the amount of money that banks hold in order to meet their depositors' demands for cash withdrawals. When the check is deposited in the Second National Bank, the reserves of the First National Bank remain the same.

Option D) is incorrect because the assets of the Second National Bank do not decrease by $10 when the check is deposited. The asset of the Second National Bank increases by $10 due to the deposit of the check.

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Answer:

1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)

Step-by-step explanation:

The first digit can be any of the numbers between 10 and 40, except for those that end in 6 (since the last digit of all three numbers is 6). This leaves us with 30 numbers to choose from for the first digit. Similarly, the second digit can be any of the numbers between 10 and 40, except for those that end in 6 and the one chosen for the first digit. This leaves us with 29 numbers to choose from for the second digit.

For the third digit, we have only one option since we know it ends in 6.

So the total number of possible combinations is:

30 * 29 * 1 = 870

Out of these, only one combination is the correct one. Therefore, the probability of guessing the combination correctly on the first try is:

1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)

$134

$110+$24=$134

if Bob had 110 in his account and found he had a -24 balance, you would need to add the two together to find the check amount written.

The correct graph of function f(x) =-3ˣ - 2 is shown in option 4.

We have to given that;

Function is,

⇒ f(x) = -3ˣ - 2

Now, In option 4;

Take a point (0, - 3) into function as;

Plug x = 0, y = - 3;

⇒ f(x) = -3ˣ - 2

⇒ - 3 = - 3⁰ - 2

⇒ - 3 = - 1 - 2

⇒ - 3 = - 3

Thus, The correct graph of function f(x) =-3ˣ - 2 is shown in option 4.

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We are similar to gram-negative. It must be noted that we are neither and have different cell characteristics compared to bacteria.

The bacterial cells are classified as gram postive and gram negative depending on their cell membrane structure. The gram negative bacteria are rich in lipid layer and thin peptidoglycan while gram postive have more peptidoglycan content.

Now, peptidoglycan are responsible for gram staining. Human epithelial cells do not have peptidoglycan which do not let them take up the stain. Hence, humans will be considered gram negative while noting the identity will be completely different.

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The value of z is given as follows:

z = 38.

We have two secants in this problem, and point C is the intersection of the two secants, hence the angle measure of z is half the difference between the angle measure of the largest arc by the angle measure of the smallest arc.

The arc measures are given as follows:

138º and 62º.

Hence the value of z is obtained as follows:

z = 0.5 x (138 - 62)

z = 38.

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The distance between the opposite corners of the windowpane would be 17 inches.

If the windowpane is divided diagonally, we see that the distance between the opposite corners can be be the hypotenuse of a right angle triangle.

This allows us to use the Pythagorean theorem to find that distance between opposite sides. The distance is:

d ² = 15 ² + 8 ²

d ² = 225 + 64

d ² = 289

d = √ 289

d = 17 inches

In conclusion, the distance between the opposite corners is 17 inches.

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We can make 4 servings of chicken noodle soup using 20 oz of egg noodles.

To determine how many servings of chicken noodle soup can be made from 20 oz of egg noodles, we need to divide the total amount of noodles by the amount required for each serving.

Given that 5 oz of egg noodles are needed for one serving, we can divide 20 oz by 5 oz/serving to get the total number of servings.

20 oz ÷ 5 oz/serving = 4 servings

The serving size may vary depending on the recipe and the individual's appetite, so this calculation is an estimate. Other ingredients such as chicken, vegetables, and broth will also affect the overall serving size and number of servings.

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Answer: 62

Step-by-step explanation:

top row has 12

the next row has 1 more =13

and it alternates

12+13+12+13+12=62

Answer:

[tex] \sqrt{175 {x}^{2} {y}^{3} } = \sqrt{175} \sqrt{ {x}^{2} } \sqrt{ {y}^{3} } = \sqrt{25} \sqrt{ {x}^{2} } \sqrt{ {y}^{2} } \sqrt{7} \sqrt{y} = 5xy \sqrt{7y} [/tex]

The differential dy for y = tan(4x + 6) when x = 4 and dx = 0.2 is 3.22, the differential dy for y = 3x² + 5x + 4 when x = 5 and dx = 0.2 is 30.20, and the change in y [tex]∆y[/tex] for y = [tex]4√x[/tex] when x = 2 and[tex]∆x = 0.3 is 0.848[/tex].

To find the differential of a function, we use the derivative, which is defined as the limit of the ratio of the change in y to the change in x as the change in x approaches zero. The differential dy is then given by the product of the derivative and the change in x, or simply dy = f'(x) dx.

For the function y = tan(4x + 6), we can find the derivative as follows: f'(x) = sec²(4x + 6) * 4 = 4 sec²(4x + 6) Substituting x = 4 and dx = 0.2, we get: dy = f'(4) * 0.2 = 4 sec²(22) * 0.2. Rounding to two decimal places, we get dy = 3.22.

For the function y = 3x² + 5x + 4, we can find the derivative as follows: f'(x) = 6x + 5 Substituting x = 5 and dx = 0.2, we get: dy = f'(5) * 0.2 = 6(5) + 5 * 0.2 Rounding to two decimal places, we get dy = 30.20.

For the function y = [tex]4√x[/tex], we can find the derivative as follows: f'(x) = 2/√x Substituting x = 2 and[tex]∆x = 0.3[/tex], we get: ∆y = f'(2) *[tex]∆x = 2/√2 * 0.3 = 0.848[/tex] Rounding to three decimal places, we get [tex]∆y = 0.848[/tex].

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To find the z-value needed to calculate one-sided confidence bounds for an 81% confidence level, we first need to determine the area under the normal distribution curve to the left of the confidence level. Since we are looking for one-sided confidence bound, we only need to consider the area to the left of the mean.

Using a standard normal distribution table or calculator, we can find that the area to the left of the mean for an 81% confidence level is 0.905.

Next, we need to find the corresponding z-value for this area. We can use the inverse normal distribution function to do this.

z = invNorm(0.905)

Using a calculator or a table, we can find that the z-value for an area of 0.905 is approximately 1.37.

Therefore, the z-value needed to calculate one-sided confidence bounds for an 81% confidence level is 1.37 (rounded to two decimal places).
The z-value needed to calculate a one-sided confidence bound with an 81% confidence level.

1. First, since it's one-sided confidence bound, we need to find the area under the standard normal curve that corresponds to 81% confidence. This means the area to the left of the z-value will be 0.81.

2. Now, to find the z-value, we can use a z-table or an online calculator that provides the z-value corresponding to the cumulative probability. In this case, the cumulative probability is 0.81.

3. Using a z-table or an online calculator, we find that the z-value corresponding to a cumulative probability of 0.81 is approximately 0.88.

So, the z-value needed to calculate a one-sided 81% confidence bound is 0.88, rounded to two decimal places.

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Where the logistic growth function is f( t) = 116000/(1+5200e⁻t)

a) 22 people were initially affected

b) after 4 weeks the numbers increased to 1,205 approximately

c) the limiting size of the population that becomes ill is 116,000.

The logistic equation (also known as the Verhulst model or logistic growth curve) is a population growth model developed by Pierre Verhulst (1845, 1847).

a) since when the epidemic began, the initial number of infection will always be zero, thus:

f( t) = 116000/(1+5200e⁻t )

Note that e is the mathematical constant known as Euler's number or the natural base. e = 2.71828

f(0) = 116000/(1+5200e⁻0 )

f(0) = 116000/(1+5200 (2.71828)⁻0 )

f(0) = 116000/(1+5200 (1) )

f(0) = 116000/(1+5200 )

f(0) = 116000/(5201 )

f(0) = 22.3034031917

f (0) [tex]\approx[/tex] 22

B) by the fourth week,

the expression became f(4) = 116000/(1+5200e⁻4 )

f (4) = 116000 /(1+5200 (e)⁻4 )
f (4) = 1205.30347384
f (4)  [tex]\approx[/tex] 1205

C)

Since the logistic curve is given as....

f(t) = 116000/(1+5200e⁻t )

as t becomes smaller and smaller nearing 0, the denominator will be almost 1

So
f(t) = 116000/(1+5200e⁻ ∞ )

f(t) = 116000/(1+0 )

f(t) = 116,000

As you can see, the limit to the size of the population that can fall ill is 116,000 peple.

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Answer:

1/7

Step-by-step explanation:

7/7-3/7=4/7

[tex]\frac{4}{7} /2[/tex]=2/7

4/7+2/7=6/7

7/7-6/7=1/7

So the housewife has 1/7 of the money left

Clark would spend about $420 on these items in a year.

Given that Clark finds that in an average month, he spends $35 on things he really doesn't need and can't afford.

If Clark spends $35 on things he doesn't need or can't afford in an average month, then he would spend:

$35/month x 12 months/year = $420/year

Therefore, Clark would spend about $420 on these items in a year.

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The value of the variable x is 8

To determine the value, we have to take note that the sum of the angles in polygon is determined with the formula

(n -2 )180

Such that the variable, 'n' is the number of sides of the polygon

From the information given, we have that;

n = 4

Substitute the values

(4-2) 180 = 360

Now, equate the measures to the angle, we have;

9x + 5 + 14x + 3 + 15x -11 + 7x + 3 = 360

collect the like terms

9x + 14x + 15x + 7x = 360

Add the like terms

45x = 360

Make 'x' the subject of formula

x = 8

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The equation that represents the same relationship is D. 3x−4y=2

It should be noted that the equation of the line in slope-intercept form is:

y = (3/4)x - 1/2

Multiplying both sides of this equation by 4 to eliminate the fraction, we get:

4y = 3x - 2

Rearranging this equation to the standard form, we get:

3x - 4y = 2

Therefore, the answer is D. 3x - 4y = 2.

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