A chemical company manufactures silicon carbide and silicon tetrachloride. It takes 1.5 kg of silica and 0.6 kg of carbon to make 1 kg of silicon carbide. On the other hand, 1 kg of silicon tetrachloride requires 0.35 kg of silica, 0.14 kg of carbon, and 0.84 kg of chlorine. The manufacturer has 105 kg of silica, 84 kg of carbon, and 126 kg of chlorine in stock. If they make $320 profit on 1 kg of silicon carbide and $250 on 1 kg of silicon tetrachloride, how much of each should they produce?

[tex]\dfrac{1}{2a}t \ \text{sin} \ \text{at}[/tex] is the solution of (18s)/(s²+36)²​ using convolution property.

Convolution is a mathematical operation on two functions (f and g) that results in a third function (f×g) that expresses how the shape of one is altered by the other. It is a mathematical operation on two functions (f and g) in mathematics, more specifically in functional analysis.

Convolution is a term that describes both the method of computing a function and its result. Its definition states that it is the integral of the product of the two functions after one of them has been shifted and reflected about the y-axis. The result of the integral remains unchanged regardless of which function is chosen to be reflected and shifted before it (see commutativity). The convolution function is created by evaluating the integral across all shift values.

[tex]\begin{aligned}& =\frac{1}{a} \int_0^t \cos a u \sin a(\mathrm{t}-\mathrm{u}) \mathrm{du} \\& =\frac{1}{a} \int_0^t[\cos a u \sin (a \mathrm{t}-a u)] \mathrm{du} \\& =\frac{1}{a} \int_0^t\left[\frac{\sin (a \mathrm{t}-a u+a u)+\sin (a \mathrm{t}-a u-a u)}{2}\right] \mathrm{du} \\& =\frac{1}{2 a} \int_0^t[\sin (a \mathrm{t})+\sin a(\mathrm{t}-2 u)] \mathrm{du} \\& =\frac{1}{2 a} \int_0^t[\sin (a \mathrm{t})+\sin a(\mathrm{t}-2 u)] \mathrm{du} \\\end{aligned}[/tex]

[tex]\begin{aligned}\\& =\frac{1}{2 a}\left[(\sin \mathrm{at}) \mathrm{u}+\left(\frac{-\cos a(\mathrm{t}-2 \mathrm{u})}{-2 a}\right)\right]_0^t \\& =\frac{1}{2 a}\left[(\sin a t) \mathrm{u}+\frac{\cos a(\mathrm{t}-2 \mathrm{u})}{2 a}\right]_0^t \\& =\frac{1}{2 a}\left[t \sin \mathrm{at}+\left(\frac{\cos a t}{2 a}\right)-\left(0+\frac{\cos a t}{2 a}\right)\right] \\& \therefore L^{-1}\left[\frac{s}{\left(\mathrm{~s}^2+\mathrm{a}^2\right)^2}\right]=\frac{1}{2 a} t \sin \mathrm{at}\end{aligned}[/tex]

Thus, [tex]\dfrac{1}{2a}t \ \text{sin} \ \text{at}[/tex] is the solution of (18s)/(s²+36)²​ using convolution property.

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Answer: A. Part A:

f(4) = 9x + 27 = 9(4) + 27 = 36 + 27 = 63

g(4) = x + 3 = 4 + 3 = 7

B. Part B:

f(x) / g(x) = (9x + 27) / (x + 3) = 9

f(4) / g(4) = 63 / 7 = 9

C. Part C:

The domain of f(x) / g(x) is all real numbers except x = -3, because dividing by zero is undefined. The domain of f(x) / g(x) is all real numbers except x = -3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A: f(4) = 63, and g(4) = 7.

My work for Part A:

Step 1: Write the first function substituting x for 3: f(4) = 9 x 4 + 27.

Step 2: Solve the function: f(4) = 9 x 4 = 36, and 36 + 27 = 63.

Step 3: Write the final answer for the first function: f(4) = 63.

Step 4: Write the second function substituting x for 3: g(4) = 4 + 3.

Step 5: Solve the function: g(4) = 4 + 3 = 7.

Step 6: Write the final answer for the second function: g(4) = 7.

Part B: (f/g)(4) = 9.

My work for Part B:

Step 1: Using the numbers from Part A, simply divide f(4) by g(4) to get (f/g)(4): 63/7 = 9.

Step 2: Write the final answer of (f/g)(4): (f/g)(4) = 9.

Part C: The domain of (f/g)(x) is -3 < x ≤ ∞. So, any numbers greater than -3 and less than or equal to infinity, are possible solutions to this function. Therefore, -2, 3, 7, and many more numbers greater than -3 are possible solutions.

The area of the square is 1084 square inches.

The area of a square can be calculated as the square of the sides of a given figure. A square is always a rectangle, parallelogram, a rhombus and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square or a rhombus is a square).

The area of a square = side x side

Given;

One side of square= 33inches

Area of square= A^2

=33x33

=1089

Therefore, the area will be 1089m^2

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Answer:Let, one leg be x units.

since the other leg is 9.0 units shorter than the other,

the measure of the other leg =x-9

hypotenuse =13.0 units

According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides.  

x^2 +(x-9)^2 =13^2

x^2 + x^2 -18x +81 = 169

2x^2-18x-88=0

Divide the whole equation by 2

x^2 - 9x -44 =0  

Let's use the quadratic formula to find the roots.

formula: x= [-b ± sqrt(b^2-4*a*c)]/2*a  

a=1 b=-9 c=-44

x= [9±sqrt(81+176)]/2

=[9±sqrt(257)]/2

=[9±16.03]/2

=25.03/2 or -7.03/2

length of a triangle cannot be negative,

Therefore, x=25.03/2 =12.52

one leg =12.5 units

other leg =12.52-9 =3.5 units

Step-by-step explanation:

The angle x is in the quadrilateral is an alternate angle and x = 29°, y = 73°, and z = 102°.

Angles formed by parallel lines and a transversal as in the quadrilateral can be alternate and are said to be equal

angles x and 29° are alternate angles and

x = 29°

y + x + 78° = 180° {sum of interior angles of a triangle}

y + 29° + 78° = 180°

y + 107° = 180°

y = 180° - 107°

y = 73°

z + 78° = 180° {supplementary angles}

z = 180 - 78°

z = 102°

The measures of angles in the quadrilateral are x = 29°, y = 73°, and z = 102°.

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Given: cost of CAYMAN sleep couch with VAT is R2 699

cost without VAT is R1 999

2.1  To calculate the original price of the couch excluding VAT, we can use the following formula:

Price including VAT / 1 + (VAT rate / 100) = Price excluding VAT

In this case, the VAT rate is 15% (since it is included in the original price), so the formula is:

R2,699 / 1 + (15 / 100) = R2,346.96

2.2  To calculate the expected price of the couch including VAT at the sale price, we can use the following formula:

Price excluding VAT * (1 + (VAT rate / 100)) = Price including VAT

In this case, the VAT rate is still 15% and the sale price is R1,999 (excluding VAT), so the formula is:

R1,999 * (1 + (15 / 100)) = R2,299

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Therefore, the ratio of 5:2 is the p:q ratio of 2p=5q. When two quantities are proportionate, one rises and the other follows suit.

Relationships that have the same ratio over time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear relationship between two numbers or variables. When the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities stays the same at all values.

given

2p=5q

p/q = 5/2

Therefore, the ratio of 5:2 is the p:q ratio of 2p=5q. When two quantities are proportionate, one rises and the other follows suit.

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Resort is located on the shore in of Lake Michigan, near the town of Saugatuck, Michigan.

A unit is a distinct and indivisible quantity or measure used to express a physical quantity or attribute. It is typically used as a standard of comparison for other measurements of the same quantity. Units are used in the measurement of physical quantities such as length, time, mass, temperature, electric current and luminous intensity. Units are also used to express abstract quantities such as velocity, acceleration, and force. In mathematics, units are used to define the magnitude of a quantity.

It offers breathtaking views of the lake and surrounding woodlands.

The resort is open to guests of all ages and offers amenities such as an outdoor pool, hot tub, and private beach. Guests can also enjoy activities such as boating, fishing, biking, and hiking. The resort also offers a variety of dining options, including a full-service restaurant, a bar, and a snack bar.

Haile Resort is the perfect getaway for anyone looking to relax and enjoy nature. The area is known for its tranquil beauty and the resort's amenities and services make it easy to enjoy the outdoors. Whether guests are looking for a romantic getaway, a family vacation, or a quiet weekend away, Haile Resort can provide the perfect escape.

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Solve the equation for  x  by finding a, b, and c of the quadratic then applying the quadratic formula.

Exact Form: x = 55 + √ 3241 2 , 55 − √ 3241 2

Decimal Form: x =

55.96489065… , −0.96489065…

Answer: B. 24 - 24 x r = 4.32

Step-by-step explanation:

The percent tip can be found by using the formula: tip = bill x (tip percentage in decimal form)

In this case, Diego's bill was $24 and the tip he paid was $4.32. To find the tip percentage, we can divide the tip by the bill:

tip / bill = 4.32 / 24 = 0.18

To convert the decimal to a percentage, we can multiply the decimal by 100: 0.18 x 100 = 18%

The tip percentage is 18%

So, option B. 24 - 24 x r = 4.32 is the equation that will help find the percent tip that Diego gave the server.

Answer: 7350 mm

Step-by-step explanation:

1 meter = 1000 mm

7 meter = 7000 mm

1 cm = 10 mm

35 cm = 350 mm

7000 mm + 350 mm = 7350 mm

Answer: x=1

Step-by-step explanation:

Add\:similar\:elements:-53x+0.5x=-52.5x

Subtract\:the\:numbers:-14-38.5=-52.5

Multiply\:both\:sides\:by 10

Refine

Divide\:both\:sides\:by -525

Simplify

x=1

…………………………………Answer:

Step-by-step explanation:

Answer: 20

Step-by-step explanation: if there is a ratio of 3:2 flowers and there are 12 lilies then 12 divided by the 3 from 3:2 is 4 meaning to find the number of daisies we need to multiply by 4, the 2 from 3:2 is multiplied by 4 which makes it 8 since there are 12 lilies and 8 daisies then 12 + 8 = 20 there are 20 flowers

If on a map with a scale of 1 in = 30 mi , the distance between Norsville and Cheertown is 4 1/2 in . The actual distance, to the nearest mile, between the town is B) 135 mi.

Using this formula to find the  the actual distance, to the nearest mile, between the towns

Actual distance = Scale of 1 in × Cheertown

Where:

Scale of 1 in =30 mi

Cheertown = 4 1/2 or 4.5

Let plug in the formula

Actual distance = 30 mi × 4.5

Actual distance = 135 mi

Therefore we can conclude that the correct option is B.

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Answer:

B

Step-by-step explanation:

Using Pythagoras theorem, the length of the missing side is 16.6 units

A right-angled triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides. Pythagoras, an ancient Greek mathematician, is credited with discovering and proving the theorem, and it bears his name.

The theorem can be written as an equation:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Data;

Substituting the values and solve for a

a² + b² = c²

17² = a² + 15²

a² = 17² - 15²

a² = 274

a = √274

a = 16.6

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The errors on scale 1 and scale 2 are 15% and 6%.

This talks about how correct a scale is over a time.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Scale 1, measured weight = 85, and actual weight = 100.

Scale 2, measured weight = 47, and actual weight = 50.

Error % is given by the formula,

(Actual value - Measured value)/Actual value * 100/1

For scale 1

Measured weight = 85, and actual weight = 100.

Percentage error =(Actual value - Measured value)/Actual value * 100/1

Percentage error = (100-83)/100

Percentage error = 15%

For scale 2

Measured weight = 47, and actual weight = 50.

Measured value)/Actual value * 100/1

Percentage error = (50-47)/50

Percentage error = 6%

Thus the error in scale 1 and scale 2 is 15% and 6%. respectively

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Answer:

Decay Rate = 17 percent

Step-by-step explanation:

1.00 - 0.83 = 0.17

To calculate the state income tax owed on a $50,000 per year salary, we need to apply the progressive tax rate based on the income range.

What does money interest mean?

You pay interest on any loans or borrowings of money. the portion of the loan's value that lenders use to calculate interest. Consumers can earn interest by lending money (via a bond or certificate of deposit, for example), or by putting money into an interest-bearing bank account.

The first $10,000 of the salary will be taxed at 3%, the next $40,000 (from $10,001 to $50,000) will be taxed at 5%, and the remaining $0 will be taxed at 5.5%

Tax on first $10,000 = $10,000 x 3% = $300

Tax on next $40,000 = $40,000 x 5% = $2,000

Tax on remaining $0 = $0 x 5.5% = $0

Total tax owed = $300 + $2,000 + $0 = $2,300

Therefore, the state income tax owed on a $50,000 per year salary is $2,300.

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The extra amount paid is 30000 where total amount paid is 210000 where as the the actual amount be 180000 .

What is percentage?

percentage can be defined as the product of ratio of given value , total value and hundred.

Given ,

A radio whose cash price is 180,000 can also be bought on hire purchase paying a deposit of 35% of the cash value followed by 6 equal monthly instalments of  24,500

The 35% of 180,000 = 35/100  *  180000

= 63000

So, the amount to paid over 6 months of 24500

amount could be = 6 * 24500

= 147000

So, the total amount paid  = 63000 + 147000

= 2, 10, 000

The total amount paid is 210000 where as the the actual amount be 180000  which is paid more that is 30000

Hence, The extra amount paid is 30000 where total amount paid is 210000 where as the the actual amount be 180000 .

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Answer:

[tex]\boxed{W = \dfrac{3X^5}{Y}}[/tex]

Step-by-step explanation:

Area A = [tex]72 X^7Y^2[/tex]

Length L = [tex]24 X^2Y^3[/tex]

A = L x W where W = width

W = A/L

[tex]\dfrac{72 X^7Y^2}{24 X^2Y^3}\\\\\\= 3X^{(7-2)}Y^{(2-3)}\\\\= 3 X^5Y^{-1}\\\\\\[/tex]

[tex]\textrm{Using the identity }x^{-1} = \dfrac{1}{x}\\\\[/tex]

we get

[tex]W = \dfrac{3X^5}{Y}[/tex]

Answer: It is impossible for me to answer this question as I do not have access to the accompanying graph that Tracy is using. The graph would be needed to determine the relationship between the number of hours needed to get out a mailing and the number of campaign workers used. Without this information, it is not possible to determine how many hours it would take to do the mailing if 125 workers are used.

Step-by-step explanation:

Answer:

What atre u asking me to solve?

Step-by-step explanation:

2n + 3 = -3n + 5n

= 2n + 3 = 2n

= 3 = 0

= ø

Answer:

3√2

Step-by-step explanation:

Distance (d) = [tex]\sqrt{((1 - -2)^2 + (3 - 6)^2)}[/tex]

= [tex]\sqrt{((3)^2 + (-3)^2)}[/tex]

= √18

= 3√2

The population of the  River City expanded by 10% between 2000 and 2010, and it is anticipated to grow by 8% between 2010 and 2020.

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.

given

population increase at a rate of 6.75% per year

then divide that number by the initial population and multiply by 100.

The population of the  River City expanded by 10% between 2000 and 2010, and it is anticipated to grow by 8% between 2010 and 2020.

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