2. A company owns two flourmills (A and B) which have different production capacities for HIGH, MEDIUM and LOW grade flour. This company has entered contract supply flour to a firm every week with 12, 8, and 24 quintals of HIGH, MEDIUM and LOW grade respectively. It costs the Co. $1000 and $800 per day to run mill A and mill B respectively. On a day, mill A produces 6, 2, and 4 quintals of HIGH, MEDIUM and Low grade flour respectively. Mill B produces 2, 2 and 12 quintals of HIGH, MEDIUM and LOW grade flour respectively. How many days per week should each mill be operated in order to meet the contract order most economically. Solve the problem graphically.​

slope 35 and 6 negative on x ies

The steps required to expand and simplify the difference between two polynomials are listed below:

Step 1: Definition of subtraction / Associative and distributive properties / (- 1) · x = - x

Step 2: Associative property

Step 3: Commutative and associative properties

Step 4: Distributive property / Definitions of addition and subtraction

Step 5: Commutative property

In this problem we must determine all steps needed to find the result of subtracting a polynomial by another polynomial. Each step is defined by a series of algebra properties:

Step 1: Definition of subtraction / Associative and distributive properties / (- 1) · x = - x

(- 3 · x³ + 5 · x² + 4 · x - 7) + (- 6 · x³ + 2 · x - 3)  

Step 2: Associative property

(- 3 · x³) + 5 · x² + 4 · x + (- 7) + (- 6 · x³) + 2 · x + (- 3)

Step 3: Commutative and associative properties

[(- 3 · x³) + (- 6 · x³)] + (4 · x + 2 · x) + [(- 7) + (- 3)] + 5 · x²

Step 4: Distributive property / Definitions of addition and subtraction

- 9 · x³ + 6 · x - 10 + 5 · x²

Step 5: Commutative property

- 9 · x³ + 5 · x² + 6 · x - 10

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The graphs that represent functions in this problem are given as follows:

Graph B and Graph D.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

Hence the graphs that do not represent functions are given as follows:

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Answer: 16.26 degrees

Step-by-step explanation:

Sin^-1 (7/25)

SOH

Sin= Opposite/Hypotenuse

Answer:

Answer: 16.26 degrees

Step-by-step explanation:

Sin^-1 (7/25)

Step-by-step explanation:

Answer:

20.83

Step-by-step explanation:

Certainly! Here's the math involved in calculating the infusion rate in drops per minute:

1. Convert 8 hours to minutes:

8 hours * 60 minutes/hour = 480 minutes

2. Calculate the total number of drops:

Total drops = 500 mL * 20 drops/mL

Total drops = 10,000 drops

3. Determine the infusion rate:

Infusion rate (drops per minute) = Total drops / Total time (minutes)

Infusion rate = 10,000 drops / 480 minutes

Infusion rate ≈ 20.83 drops per minute

So, the infusion rate is approximately 20.83 drops per minute.

longer explanation

To calculate the infusion rate in drops per minute, we need to determine the total number of drops in 8 hours and then divide it by the total time in minutes.

Given:

- Volume: 500 mL

- Drops per mL: 20

- Time: 8 hours

First, let's convert 8 hours into minutes:

8 hours * 60 minutes/hour = 480 minutes

Now, calculate the total number of drops:

Total drops = Volume (mL) * Drops per mL

Total drops = 500 mL * 20 drops/mL

Total drops = 10,000 drops

Finally, divide the total number of drops by the total time in minutes to find the infusion rate:

Infusion rate (drops per minute) = Total drops / Total time (minutes)

Infusion rate = 10,000 drops / 480 minutes

Infusion rate ≈ 20.83 drops per minute

Therefore, the infusion rate is approximately 20.83 drops per minute.

chatgpt

The expression 2 - 5(x - 1) is a linear expression

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

2 - 5(x - 1)

The general rule is that

Using the above as a guide, we have the following:

2 - 5(x - 1) is a linear expression

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The sequence of transformations that proves that the shapes are similar is given as follows:

B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5

First, we have that the orientation of the figure, hence it was reflected.

The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.

The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:

3/2 = 1.5.

Hence option B is the correct option for this problem.

The missing parts of the problem are given by the image presented at the end of the answer.

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The value of tan(60) in the right triangle is √3.

The figure in the image is a right triangle, having one of its interior angles at 90 degrees.

To determine the value of tan( 60° ), we first need to find the measure of length side opposite to angle 60 degrees.

Using trigonometric ratio:

tanθ = opposite/adjacent

Plug in: opposite = x and adjacent = 5

tan(60) = x / 5

x =  tan(60) × 5

x = 5√3

Now, we find tan( 60° ):

Using trigonometric ratio: tanθ = opposite/adjacent

tan( 60° ) = [tex]\frac{5\sqrt{3} }{5}[/tex]

Simplify:

tan( 60° ) = √3

Therefore, the value of tan( 60° ) is √3.

Option C)√3 is the correct answer.

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The APR of the credit card that has a monthly rate of 3.5% is 42%. The correct option is therefore;

B. 42%

The APR (Annual Percentage Rate) can be calculated from the monthly interest rate using the formula;

Monthly interest rate = APR/12

Therefore; APR = 12 × The monthly interest rate

The monthly interest rate charged by the credit card = 3.5%

The number of months in a year = 12

Annual percentage rate = The monthly interest rate × Number of months

Therefore, the annual percentage rate of the credit card = 3.5% × 12 = 42%

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Answer:

Set your calculator to degree mode.

x/sin(120°) = 5/sin(23°)

x = 5sin(120°)/sin(23°) = about 11.08

11.08 belongs in the green box.

The solution of the inequality equation is x > -π/2 or x > 3π/2.

The value of x in the inequality is calculated by applying the following formula as follows;

Given 0 ≤ x < 2π,

tan (x/2) > - 1

To determine the value of x take the arc tan of (-1) as follows;

x/2 > arc tan (-1)

x/2 > -π/4

x > -π/2

In the interval π/2 ≤ x < π:

x/2 > arc tan (-1)

x/2 > 3π/4

x > 3π/2

Thus, the solution of the inequality equation is x > -π/2 or x > 3π/2.

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The graphed velocity function ​v(t)=ds/dt=f'(t) and the acceleration function ​ is attached.

we start by  Plotting  the position function

Choosing a set of time values within the given interval [0, 9.5] and find the corresponding position values by substituting each time value into the position function s(t) = 152t - 16t².

We then plot the points (t, s) on a coordinate system.

We go ahead to Plot the velocity function by calculating  the derivative of the position function to obtain the velocity function v(t) = ds/dt = f'(t).

Plot the acceleration function by calculating the second derivative of the position function to obtain the acceleration function a(t) = d²s/dt² = f''(t).

We then connect the points representing the various function to create the needed graph.

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The solution to the given system of equations is (1,3). This is the intersection point of the two equations: y = 3x² - 8x - 2 and 2x - y = 5. Therefore, the correct answer is (1,3).

The given system of equations is: y = 3x² - 8x - 2 and 2x - y = 5

We can substitute y in the second equation with the expression obtained in the first equation.

2x - (3x² - 8x - 2) = 5 ⇒ 3x² - 10x - 7 = 0

This is a quadratic equation that can be solved using the quadratic formula.

x = (-(-10) ± sqrt((-10)² - 4(3)(-7))) / (2 * 3) ⇒ x = (10 ± sqrt(124)) / 6

Therefore, the two possible solutions for x are x = (10 + sqrt(124)) / 6 or x = (10 - sqrt(124)) / 6.

When we plug these values of x in the first equation, we can obtain the corresponding values of y. It can be observed that only one of these solutions, x = (10 - sqrt(124)) / 6 ≈ 1.166, gives a real value of y.

Therefore, the intersection point of the two equations is (1,3).

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The expression (2.7 x 10⁴) x (9.1 x 10³) in standard form is 245700000

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

(2.7 x 10⁴) x (9.1 x 10³)

The expressions in standard form, we have

(2.7 x 10⁴) x (9.1 x 10³) = 27000  x 9100

Evaluatet the products

(2.7 x 10⁴) x (9.1 x 10³) = 245700000

Hence, the expression in standard form is 245700000

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The equation log₄(x²) = log₂(x - 4) does not have a solution in the real number system.

To solve the equation log₄(x²) = log₂(x - 4), we can use the property of logarithms that states if logₐ(M) = logₐ(N), then M = N.

Let's apply this property to the given equation:

log₄(x²) = log₂(x - 4)

We can rewrite the equation using the change-of-base formula to convert both logarithms to a common base.

Let's convert them to base 10:

log₄(x²) = log₂(x - 4)

(log(x²) / log(4)) = (log(x - 4) / log(2))

Now, we can simplify the equation further:

(log(x²) / log(4)) = (log(x - 4) / log(2))

Using the quotient rule of logarithms, we can rewrite the equation as:

log(x²) / log(4) = log(x - 4) / log(2)

Now, we can eliminate the logarithms by cross-multiplying:

log(x²) [tex]\times[/tex]log(2) = log(x - 4) [tex]\times[/tex] log(4)

Since the logarithms have the same base (log base 10), we can equate the arguments:

log(x²) [tex]\times[/tex] log(2) = log(x - 4) [tex]\times[/tex] log(4)

By simplifying the equation further and applying properties of logarithms, we can solve for x:

2 [tex]\times[/tex]log(x) = log(x - 4) [tex]\times[/tex]2

log(x) = log(x - 4)

From this point, we can conclude that the equation does not have a unique solution.

It implies that there is no value of x that satisfies the equation log₄(x²) = log₂(x - 4).

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Minimum sample size required: 2124. Confidence level: 99%, margin of error: 0.028. Assumed worst-case scenario for population proportion.

To find the minimum sample size required to estimate the population proportion with a given margin of error and confidence level, we can use the formula:

n = [tex](Z^2 * p * q) / E^2[/tex]

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level

p is the estimated proportion of the population

q is the complement of p (1 - p)

E is the desired margin of error

In this case, the margin of error is given as 0.028 and the confidence level is 99%, which corresponds to a Z-score of approximately 2.576 (obtained from a standard normal distribution table).

Since the proportion p and its complement q are unknown, we can assume the worst-case scenario where p = q = 0.5. This ensures the maximum sample size needed.

Substituting the values into the formula:

n = ([tex]2.576^2[/tex] * 0.5 * 0.5) / 0.028^2

n = (6.656576 * 0.25) / 0.000784

n = 1.664144 / 0.000784

n ≈ 2123.47

Rounding up to the nearest whole number, the minimum sample size required is 2124.

Therefore, to estimate the population proportion with a margin of error of 0.028 and a confidence level of 99%, a minimum sample size of 2124 is needed. This ensures a reliable estimate with the desired level of precision and confidence.

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The graph that shows a direct variation is the one in which a straight line passes through the origin, with the equation y = kx and the slope equal to k.

The graph that shows a direct variation is the one in which a straight line passes through the origin.

A direct variation is a type of relationship between two variables in which their ratio is constant.

It means that as one variable increases, the other variable increases proportionally, and as one variable decreases, the other variable decreases proportionally.
In a direct variation, the equation is usually in the form y = kx, where k is the constant of proportionality. The graph of a direct variation is a straight line that passes through the origin, or (0,0). This means that when x = 0, y = 0. The slope of the line is equal to k.
For example, if we have a direct variation between the number of miles driven and the amount of gas used, the equation would be y = kx, where y is the amount of gas used, x is the number of miles driven, and k is the constant of proportionality, which represents the gas mileage of the car.

The graph of this direct variation would be a straight line passing through the origin.

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Answer: 40 cups of trail mix

Step-by-step explanation:

To solve the problem, we can set up a proportion. We know that Orla uses 2 cups of raisins for every 8 cups of trail mix, which can be written as:

2/8 = 10/x

Where x is the number of cups of trail mix Orla will make if she uses 10 cups of raisins.

To solve for x, we can cross-multiply:

2x = 8 * 10

2x = 80

Then divide by 2:

x = 40

Therefore, if Orla uses 10 cups of raisins, she will make 40 cups of trail mix.

Matching of the polygon coordinates with their perimeters are:

38 units → U(4, -1), V(12, -1), W(20,-7), X(8, -7), Y(4,-4)

25.4 units → P(7,2), Q (12,2), R(12,6), S(7,10), T(4,6)

50 units → A( 1, 1), B(6,13), C(8,13), D(16,-2) E(1, -2 )

19.24 units → K(4,2), L(8,2), M(12,5), N(6,5), O(4,4)

The formula to find the distance between two coordinates is:

Distance = √(y₂ - y₁)² + (x₂ - x₁)²

1) The coordinates are given as:

A( 1, 1), B(6,13), C(8,13), D(16,-2) E(1, -2 )

Using the earlier formula we have:

Perimeter = AB + BC + CD + DE + EA

Perimeter = 13 + 2 + 17 + 15 + 3

Perimeter = 50 units

2) The coordinates are given as:

K(4,2), L(8,2), M(12,5), N(6,5), O(4,4)

Perimeter = KL + LM + MN + NO + OK

Perimeter = 4 + 5 + 6 + √5 + 2

Perimeter = 17 + 2.24

Perimeter = 19.24 units

3) The coordinates are given as:

F(14,-10), G(16, -10), H(19,-6), I (14,-2), J(11,-6)

Perimeter = FG + GH + HI + IJ + JF

Perimeter = 2 + 5 + √41 + 5 + 5

Perimeter = 19 + 6.40

Perimeter = 25.40

4) The coordinates are given as:

P(7,2), Q (12,2), R(12,6), S(7,10), T(4,6)

Perimeter = PQ + QR + RS + ST + TP

Perimeter = 5 + 4 + √41 + 5 + 5

Perimeter = 19 + 6.40

Perimeter = 25.40 units

5) The coordinates are given as:

U(4, -1), V(12, -1), W(20,-7), X(8, -7), Y(4,-4)

Perimeter = UV + VW + WX + XY + YU

Perimeter = 8 + 10 + 12 + 5 + 3

Perimeter = 38 units

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Here, we just need to add x and y and subtract it from 180.

x + y = 91 + 42 = 133.

180 - 133 = 47.

Hence, z = 47 degrees.

Answer:

Step-by-step explanation:

straight line = 180° we remove the angles x and y and find z

180 - 91 - 42 =

47°

Answer:

412.92

Step-by-step explanation:

[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

[tex]A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92[/tex]

Answer:

it's a Parallelogram

Explanation

A parallelogram has two pairs of opposite sides that are parallel. PV is parallel to QU. UV is parallel to PQ.

The parallelogram, its opposite sides are equal in length. This property distinguishes a parallelogram from other quadrilaterals.

Answer:

90

Step-by-step explanation:

0.5 tablets twice a day ⇒ 1 tablet per day

so in 90 tablets will be needed for 90 days

Answer:Step-by-step explanation:

90, this is due to the fact you newd 1 entire one a day. 0.5+0.5 =1

1*90=990

The expression (x + 1) divided by (x + 1) simplifies to just 1.

The expression that is equivalent to (x + 1) divided by (x + 1) is 1.

When we divide a number by itself, the result is always 1.

In this case, we have (x + 1) divided by (x + 1), which means we are dividing a quantity by itself. Regardless of the value of x, the numerator and denominator are the same, so the result will always be 1.

Therefore, the expression (x + 1) divided by (x + 1) simplifies to just 1.

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The pattern is as follows: Start with 3, square it, subtract 10.

Looking at the given sequence: -7, 103, -997, 10003, -99997, we can observe a pattern emerging. Let's break it down:

The first number, -7, can be obtained by starting with 3, squaring it, and then subtracting 10: (-7 = 3^2 - 10).

The second number, 103, is obtained by starting with -7, adding 110, and then subtracting 10: (103 = -7 + 110 - 10).

The third number, -997, is obtained by starting with 103, subtracting 1110, and then subtracting 10: (-997 = 103 - 1110 - 10).

The fourth number, 10003, is obtained by starting with -997, adding 11110, and then subtracting 10: (10003 = -997 + 11110 - 10).

The fifth number, -99997, is obtained by starting with 10003, subtracting 111110, and then subtracting 10: (-99997 = 10003 - 111110 - 10).

From this analysis, we can see that each subsequent number in the sequence is obtained by alternately adding a positive integer (110, 1110, 11110) and subtracting 10 from the previous number. The pattern continues in this manner.

Then, alternate between adding increasingly larger positive integers and subtracting 10 to obtain subsequent numbers in the sequence.

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The expression "[tex]\sqrt[4]{9}^1^/^2[/tex]" simplifies to 81, but none of the given options represents this value.

The correct answer is option E.

The expression "[tex]\sqrt[4]{9}^1^/^2[/tex]" represents the fourth power of the square root of 9 raised to the power of one-half. Let's simplify this expression step by step.

First, let's simplify the square root of 9:

[tex]\sqrt{9}[/tex] = 3

Next, let's simplify the exponent one-half:

[tex]3^1/2 = \sqrt{3}[/tex]

Now, we have the expression "[tex]\sqrt[4]{3}[/tex]". This means we need to raise the square root of 3 to the fourth power.

[tex]\sqrt{(3)^4 }[/tex]= [tex](\sqrt{3})(\sqrt{3})(\sqrt{3})(\sqrt{3})[/tex]= 3*3*3*3 = 81

Therefore, "^[tex]\sqrt[4]{9}^1^/^2[/tex]" simplifies to 81.

Among the given options, none of them matches the simplified expression of 81.

Therefore, none of the options A, B, C, or D is equivalent to the expression "^[tex]\sqrt[4]{9}^1^/^2[/tex]".

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The question probable may be:

Which is equivalent to [tex]\sqrt[4]{9}^1^/^2[/tex]?  

A.g2x

B. [tex]9^1/2[/tex]

C.[tex]\sqrt{9}[/tex]

D[tex]\sqrt[5]{9}[/tex]

E. None of the above

Answer:

option C.

Step-by-step explanation:

To calculate the net change in elevation from the Atacama trench to the Mariana trench, we subtract the elevation of the Atacama trench from the elevation of the Mariana trench.Net change in elevation = Elevation of Mariana trench - Elevation of Atacama trench

= (-11.033 kilometers) - (-8.065 kilometers)

= -11.033 kilometers + 8.065 kilometers

= -2.968 kilometersTherefore, the net change in elevation from the Atacama trench to the Mariana trench is -2.968 kilometers. This corresponds to option C.

        Hence, AGNES's ANNUAL TAXABLE INCOME is:   346560

MAKE A PLAN:

Calculate AGNES's Total Monthly Income, Subtract her Deductions and Personal Relief, and Then Find Her Annual Taxable Income:

1) - Calculate AGNES's Total Monthly Income:

     20000  +  15000  =  35000

2) - Calculate AGNES's  Total Monthly Deductions:

      960  +   3500  +  400  =  4860

3) - Calculate AGNES's MONTHLY TAXABLE INCOME:

     35000  -   4860  -  1260  =  28880

4) - Calculate AGNES's ANNUAL TAXABLE INCOME:

     28880  *   12   =    346560

       Hence, AGNES's ANNUAL TAXABLE INCOME is:   346560

       I hope this helps you!

A) the total number of boxes in the bottom 2 layers is 100 + 80 = 180 boxes. B) Number of boxes in each layer = W(n) * D C) the total number of boxes needed to make up the 4 layers is 280 boxes.

A) To determine the number of boxes in the bottom 2 layers:

The bottom layer has a width of 20 boxes and is 5 boxes deep.

The second layer has a width of 16 boxes and is also 5 boxes deep.

Number of boxes in the bottom layer = 20 boxes wide * 5 boxes deep = 100 boxes

Number of boxes in the second layer = 16 boxes wide * 5 boxes deep = 80 boxes

Therefore, the total number of boxes in the bottom 2 layers is 100 + 80 = 180 boxes.

B) To develop a formula to calculate the number of boxes in n layers:

Let's denote the width of each layer as W and the depth of each layer as D.

The width of each layer follows the pattern: 20, 16, 12, 8.

We can observe that the width decreases by 4 units for each consecutive layer.

The formula to calculate the width of the nth layer can be written as:

W(n) = 20 - 4 * (n - 1)

Since each layer has a depth of 5 boxes, the number of boxes in each layer can be calculated as:

Number of boxes in each layer = W(n) * D

C) To use the formula from part B to solve for the total number of boxes needed to make up the 4 layers:

We want to calculate the total number of boxes in 4 layers.

Number of boxes in 4 layers = Number of boxes in the first layer + Number of boxes in the second layer + Number of boxes in the third layer + Number of boxes in the fourth layer

= W(1) * D + W(2) * D + W(3) * D + W(4) * D

= (20 - 4 * 0) * 5 + (20 - 4 * 1) * 5 + (20 - 4 * 2) * 5 + (20 - 4 * 3) * 5

= 20 * 5 + 16 * 5 + 12 * 5 + 8 * 5

Simplifying the expression, we get:

Number of boxes in 4 layers = 100 + 80 + 60 + 40 = 280 boxes

Therefore, the total number of boxes needed to make up the 4 layers is 280 boxes.

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The inverse of the given function is: f⁻¹(x) = 4x² - 3 for x ≤ 0

The inverse of a function is defined as a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f' produces the output x. A function f' that has an inverse is referred to as invertible and the inverse is denoted by f⁻¹.

The given function is:

f(x) = -¹/₂√(x + 3)

To find the inverse of the function we replace the value of x and y and then find y in terms of x which is the inverse of the function.

Let f(x) = y

Thus:

x = -¹/₂√(y + 3)

Multiply both sides by -2 to get:

-2x = √(y + 3)

Square both sides to get:

4x² = y + 3

y = 4x² - 3

Thus, the inverse of the function is:

f⁻¹(x) = 4x² - 3 for x ≤ 0

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