Find the slope of the line that contains the points (10, 0) and (-20, -18)

The solution to the expression (12x³ + 9x² - 3) / 3x is (4x³ + 3x² - 1) / x

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Given the expression:

(12x³ + 9x² - 3) / 3x

To solve, we need to factorize the numerator to get:

= 3(4x³ + 3x² - 1) / 3x

= (4x³ + 3x² - 1) / x

The solution to the expression is (4x³ + 3x² - 1) / x

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Water fills a tank at a rate of 150 liters during the first hour, 125 liters during the second, 150 liters during the third, and so on. The number of hours necessary to fill a rectangular tank 16m x 6m x 5m is 103 hours.

The volume of the rectangular tank can be found by multiplying its length, width, and height:

The volume of the tank = Length x Width x Height

Volume of tank = 16m x 6m x 5m

The volume of the tank = 480 cubic meters

We need to convert this volume to liters in order to compare it to the flow rate of water. Since 1 cubic meter is equal to 1,000 liters, we have:

Volume of tank = 480 x 1,000 = 480,000 liters

Now we can add up the flow rate of water over time until it exceeds the volume of the tank. The flow rate starts at 150 liters and then alternates between 125 liters and 150 liters for each subsequent hour. We can express this pattern as:

[tex]150 + 125 + 150 + 125 + 150 + ...[/tex]

This is an arithmetic sequence with a first term of 150, a common difference of -25 (since each subsequent term is 25 less than the previous one), and an unknown number of terms. We can use the formula for the sum of an arithmetic sequence to find the number of terms:

Sum = (n/2)(first term + last term)

where n is the number of terms.

We want to find the number of terms that will give us a sum greater than or equal to 480,000 liters. We can set up an inequality:

(n/2)(150 + (150 + (n-1)(-25))) ≥ 480,000

Simplifying and solving for n, we get:

n ≥ 102.4

Since we need a whole number of terms, we can round up to 103 terms. This means it will take 103 hours to fill the tank.

Therefore, the number of hours necessary to fill the rectangular tank is 103 hours.

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Answer:

orange box = [tex]1 \frac{1}{4}[/tex]

blue box = [tex]1\frac{3}{4}[/tex]

Step-by-step explanation:

We are counting up in quarters (1/4) so we add 1/4 (or a quarter) on every time.

1/4 + 1/4 = 2/4 = 1/2 (equivalent fractions)

2/4 + 1/4 = 3/4

3/4 + 1/4 = 4/4 = 1 whole = 1

1 + 1/4 = 1 1/4 = orange box

1 1/4 + 1/4 = 1 1/2 or 1 2/4

1 2/4 + 1/4 = 1 3/4 = blue box

etc

hope this makes sense.

We need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.

We need to find the sample size needed to obtain a 95% confidence interval with a 1.2 centimeters margin of error.Given that population standard deviation of student height is 9.48 centimeters.Using the formula of margin of error, we getME = z* σ/√nHere, σ = 9.48, ME = 1.2, and confidence interval = 95%.Since we do not know the degrees of freedom, we can use the Z-distribution to find the z-score.For 95% confidence interval, α/2 = 0.025The z-score for the 0.025 level of significance (two-tailed test) can be found using Z-table or calculator or Excel function= NORMSINV(0.025) = -1.96ME = z* σ/√n1.2 = -1.96 * 9.48 /√n√n = 1.96 * 9.48 /1.2= 15.42n = (15.42)^2= 238.1764≈ 239Therefore, we need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.

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Answer:

Step-by-step explanation:

x = 4 or x = -2

If a father's age is four times the age of his daughter.. After 5 more years , his age would be 5 times his daughter's age at that time.

Let's use D to represent the daughter's current age and F to represent the father's current age.

We know that the father's age is four times the age of his daughter, so we can write an equation to represent this relationship:

F = 4D

We also know that after 5 years, the father's age would be three times his daughter's age, so we can write another equation to represent this:

F + 5 = 3(D + 5)

Now we can substitute the first equation into the second equation to get an equation with only one variable:

4D + 5 = 3(D + 5)

Simplifying the equation, we get:

4D + 5 = 3D + 15

Subtracting 3D and 5 from both sides, we get:

D = 10

Therefore, the daughter's current age is 10 years old. We can use the first equation to find out the father's current age:

F = 4D = 4(10) = 40

After 5 more years, the father's age would be:

F + 5 + 5 = 40 + 10 = 50

In summary, after 5 more years, the father's age would be 50 and his daughter's age would be 10, which is 5 times younger than the father.

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Answer:

[tex]x=\frac{b-a}{ab}[/tex]

Step-by-step explanation:

[tex]\frac{1}{ax} -\frac{1}{bx} =1\\\frac{1}{ax} *\frac{b}{b} -\frac{1}{bx} *\frac{a}{a} =1\\\frac{b}{abx} -\frac{a}{abx}=1\\\frac{b-a}{abx}=1\\b-a=abx\\x=\frac{b-a}{ab}[/tex]

Answer:

74 + 4 π ft^2

Step-by-step explanation:

Just a bit of a piecemeal.

2 rectangles and a half circle. We have all the dimensions.

1. Let's solve the big one first A = lw, putting in the numbers A = 4*15 = 60

2. The smaller one A = lw, putting int eh numbers A = 2 * 7 = 14

3. Now, the semi-circle. We know the diameter by deducting 12 from the total length, which is 9 + 7 = 16 in = 4 ft

The radius of the circle is half of the diameter, so the radius is 2 ft

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Substituting the values, we get:

A = π(2)^2

A = 4π

The area of the circle is 4π square ft^2

Add: 60 + 14 + 4π = 74 + 4 π ft^2

False. The area of a circle is equal to 7.854.

The formula for the circumference of a circle is C = 2πr,

where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:

r = C/2π.

In this case, we are given that the circumference is 10, so we can calculate the radius as:

r = 10/2π

r = 5/π

To calculate the area of a circle, we use the formula

[tex]A = \pi r^2[/tex]

Substituting the value we found for r, we get:

[tex]A = \pi (5/\pi )^2\\A = \pi (25/\pi^2)\\A = 25/\pi[/tex]

This is approximately equal to 7.9577, which is not equal to 100. Therefore, the statement "A circle with a circumference of 10 has an area of 100" is false.

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The duration of the compression event is  100 degrees of crankshaft rotation by using the number of degrees of crankshaft rotation between the point where the intake valve closes (IVC) and the point where the exhaust valve opens (EVO).

To determine the duration of the compression event, we need to find the number of degrees of crankshaft rotation between the point where the intake valve closes (IVC) and the point where the exhaust valve opens (EVO).

Intake valve opens (IVO) at 8 degrees before top dead center (BTDC)

Intake valve closes (IVC) at 50 degrees after bottom dead center (ABDC)

Exhaust valve opens (EVO) at 50 degrees before bottom dead center (BBDC)

Exhaust valve closes (EVC) at 8 degrees after top dead center (ATDC)

First, we need to determine the position of the piston at each of these valve events. We know that the stroke of the engine is 180 degrees, so we can use this information to calculate the position of the piston at each event:

IVO: piston is at 8 degrees BTDC

IVC: piston is at 180 - 50 = 130 degrees ATDC

EVO: piston is at 180 + 50 = 230 degrees ATDC

EVC: piston is at 360 - 8 = 352 degrees BTDC

To find the duration of the compression event, we need to calculate the number of degrees of crankshaft rotation between IVC and EVO. We can do this by subtracting the position of the piston at IVC from the position of the piston at EVO:

Duration of compression event = EVO - IVC

= 230 - 130

= 100 degrees

Therefore, the duration of the compression event is 100 degrees of crankshaft rotation.

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In a rectangle having an area of 36 cm, if the length is three times more than the width of the rectangle is approximately 3.46 cm.

Let's assume that the width of the rectangle is "w" cm-

According to the problem, the length of the rectangle is three times longer than the width. Therefore, the length of the rectangle would be 3w cm.

The area of the rectangle is given as 36 cm². We know that the formula for the area of a rectangle is A = length x width.

So, we can substitute the values we have and get:-

36 = (3w) x w

Simplifying the equation, we get:-

36 = 3w²

Dividing both sides by 3, we get--

12 = w²

Taking the square root of both sides, we get--

w = √12

w ≈ 3.46

Therefore, the width of the rectangle is approximately 3.46 cm.

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Answer: [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

7+3(5-4)=10

2+1=3

Therefore, 10/3.

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

put the given values in the equation

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[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

To convert the salary data from different countries into US dollars, the industrial/organizational psychologist would need to use the exchange rates between each country's currency and the US dollar. Exchange rates are the value of one currency in terms of another currency.

For example, if the exchange rate between the US dollar and the British pound is 1.38, this means that one US dollar is worth 1.38 British pounds. So, to convert the average monthly salary of an accountant in the UK into US dollars, the psychologist would divide the salary in pounds by the exchange rate.
Once the psychologist has converted all of the salary data into US dollars, she can then compare the average monthly salaries of accountants across the five different countries and analyze the relationships between job satisfaction, job performance, and job compensation.

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The probability of getting a sum that is a divisor of 10 is:P(sum is a divisor of 10) = 4/36= 1/9.

The sample space for the experiment "Toss three coins" is given by:{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}b. The event, E: "Get exactly two heads" consists of the following elements:{HHT, HTH, THH}c. The probability of the event, E: "Get exactly two heads" is given by:P(E) = number of favorable outcomes / number of possible outcomes= 3/8For the experiment of rolling two dice, the sample space is given by the set of all possible ordered pairs {(i, j)}, where i and j are numbers from 1 to 6. Thus, the sample space contains 6*6 = 36 elements.a. For the sum to be 10, the pairs that satisfy the condition are (4, 6), (5, 5), and (6, 4). Thus, the probability of getting a sum of 10 is:P(sum = 10) = 3/36= 1/12b. For the sum to be a divisor of 10, we need the pairs (2, 8), (4, 6), (6, 4), and (8, 2). Thus, the probability of getting a sum that is a divisor of 10 is:P(sum is a divisor of 10) = 4/36= 1/9.

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By answering the presented question, we may conclude that  For slope example, if a figure's measures are in metros, the volume will be in cubic metros (m3).

The slope of a line determines how steep it is. The gradient is expressed mathematically as gradient overflow. The slope is computed by dividing the vertical difference (run) between two locations by the height difference (rise). The curve form of an expression is used to describe the straight line equation, which is written as y = mx + b. The y-intercept of the line is located where the inclination is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7. (0, 7). The y-intercept is placed where the slope of the path is m, b is b, and (0, b).  

When we calculate the volume of a 3D figure, we call our solution "units 3 (cubed)".

The term "cubed" is used since volume is calculated by multiplying three dimensions (length, breadth, and height), resulting in a unit raised to the power of three. For example, if a figure's measures are in metres, the volume will be in cubic metros (m3).

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Answer:

Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.

Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.

Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.

Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.

ion:

Answer:

Its the 3rd one

Step-by-step explanation:

I had this question twice

Answer:

number 3 i did this 2 days ago

Step-by-step explanation:

In response to the question, we may say that  Line A has a slope of -4, which is lower than that of line B.

The slope of a line determines how steep it is. A mathematical expression for the gradient is gradient overflow. The vertical change (run) between two spots is divided by the height change (rise) between the same two locations to get the slope. The equation of a straight line, written as y = mx + b, is represented by the curve form of an expression. The inclination is m, b is b, and the line's y-intercept is located at these points (0, b). As an example, consider the y-intercept and slope of the equation y = 3x - 7. (0, 7). The y-intercept is situated when the slope of the path is m, b is b, and (0, b).

With the two provided points, we must first establish whether of the following claims is true:

Slope of line B = (Y) / (X) = (-11 - 1) / (1 - (-2)) = -12 / 3 = -4

As a result, we can identify the following claims as being true:

The slope of line B is -5. (False)

The slope of line A is -4. (Really) The slope of lines A and B is the same. (False) Line B slopes more gently than line A. (False) Line A slopes more gently than line B. (True)

The following propositions are true:

Line A has a slope of -4, which is lower than that of line B.

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There are multiple ways to find the center and radius of a circle, depending on what information your provided.

Method 1: Reading the standard equation of a circle

Equation of a circle: [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

where h is the center's x-coordinate, k is the center's y-coordinate, and r is the radius. Here's an example:

[tex](x-5)^{2} +(y+2)^{2} =25[/tex]

In this case, the center would be (5,-2) and the radius is 5

Method 2: Reading a graph

In the attached graph, there is a circle with a labeled center point. The radius can be found by finding the distance from the center to a different point on the circle.

Distance Formula:

[tex]D = \sqrt{ (x_{2}-x_{1}) ^{2} + (y_{2}-y_{1}) ^{2}}\\[/tex]

The first point we use will be the center ( 5 , -2 ), and the second point will be a point on the circle, (10,-2).

[tex]r = D = \sqrt{ ((10)-(5)) ^{2} + ((-2)-(-2) )^{2}}\\r = D = \sqrt{ (5 ^{2} + 0)^{2}}\\r = D = \sqrt{25}\\r = 5[/tex]

Next, plug in the values into the standard equation of a circle formula

[tex](x-5)^{2} +(y+2)^{2} =5^2[/tex]

Simplify

[tex](x-5)^{2} +(y+2)^{2} =25[/tex]

From the given data, we can see that only one condition is violated, which is the sample size being less than 10% of the population size. The other conditions, such as the population distribution being approximately normal, np > 10, and n(1-p) > 10, are all satisfied. Therefore, the statement "more than one condition is violated" is incorrect.

Only one condition is violated in the given data, which is the sample size being less than 10% of the population size. The other conditions are all satisfied and do not violate any of the conditions for a representative sample.

It is important to note that in order for a sample to be representative of the population, the sample size should be at least 10% of the population size. If the sample size is less than 10% of the population size, the sample may not accurately represent the population and the results may be biased.

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Answer:

A should be 180 - 68 which is 112 degrees

Step-by-step explanation:

Answer:a=108

Step-by-step explanation:

140+(180-60)+(180-84)+(180-68)=140+120+96+112=260+208=468

sum of angles are 540, so,

540-468=180-a

72=180-a

a=108

Therefore, the total cost to make 100 wind chimes is 14,000$.

In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it.

Here,

The cost of making one wind chime is 10 + 130 = 140$.

To make 100 wind chimes, the total cost would be:

100 x 140 = 14,000$.

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The manufacturer can maximize their revenue by producing 60 road bikes and 120 touring bikes. The maximum revenue of the manufacturer is $24,000.

Revenue is the total amount of money earned by a business from its activities. It is calculated by subtracting the cost of goods sold from the total sales of goods and services. Revenue indicates how well a company is doing financially and serves as a key indicator of a company's performance. Revenue is an important factor in calculating the company's profitability.

This satisfies the minimum requirements of the supply contract, while also utilizing all of the available resources, frames and labor.

The total cost of producing 60 road bikes and 120 touring bikes is 400 frames and 900 hours of labor. This leaves no frames or labor unused. The total revenue from selling these bicycles is $24,000 (60 x $400 + 120 x $200). Therefore, the maximum revenue of the manufacturer is $24,000.

To maximize their revenue, the manufacturer should produce 60 road bikes and 120 touring bikes. This will ensure that all of their resources are used and they will get the highest return on their investment. This will also help them meet the minimum requirements of the supply contract.

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The three options of exterior angles are m∠5 + m∠6 =180°,

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

The angles that are created οutside οf a triangle are its exteriοr angles. In οther wοrds, the angle fοrmed between οne οf a triangle's sides and its adjacent extended side is the triangle's exteriοr angle.

Given that the exteriοr angles are m∠1, m∠4, and m∠6.

The interiοr angles οf the triangle are angles m∠2, m∠3, and m∠5.

The sum οf all angles οf a triangle is 180°.

Thus m∠2 + m∠3 + m∠5 = 180°

The interiοr angle and the cοrrespοnding exteriοr angle in a triangle make up a linear pair. Exteriοr Angle plus Interiοr Angle equals 180°, sο.

The exteriοr angle at angle 5 is angle 6.

Thus m∠5 + m∠6 =180°

The interiοr and exteriοr angles that make up a triangle are always added tοgether tο fοrm the exteriοr angle. The term "exteriοr angle prοperty" refers tο this feature. If twο triangles' cοrrespοnding angles tend tο be cοngruent and their side lengths are prοpοrtiοnal, any twο triangles will be similar tο οne anοther.

The οppοsite interiοr angles οf m∠6 are m∠2,  m∠3.

Thus m∠2 + m∠3 = m∠6

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Answer:

Step-by-step explanation:

tan^2 x +1=sec^2 x

1= sec^2 x-tan^2 x

Part a: the success, with a probability of p = 1/5.

Part b:The mean of X is μ = np = 6(1/5) = 1.2.

Part c:The probability of at least two customers receiving the coupon can be computed using the binomial distribution formula, P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - [tex](6C1)(1/5)^1(4/5)^5 - (6C0)(1/5)^0(4/5)^6[/tex]

Part A: Yes, X is a binomial random variable. A binomial random variable is the number of successes in a sequence of n independent trials, where each trial has a probability p of success. In this case, X is the number of customers that receive the 50% off coupon, which is the success, with a probability of p = 1/5. There are also a total of n = 6 independent trials, which is the number of customers that made purchases from the website.

Part B: The mean of X is μ = np = 6(1/5) = 1.2. This means that, on average, the store can expect 1.2 customers to receive the 50% off coupon. The standard deviation of X is σ = √(np(1 - p)) = √(6(1/5)(1 - 1/5)) = 0.9. This means that there is a large degree of variability in the number of customers that receive the 50% off coupon.

Part C: The store's claim is accurate. The probability of at least two customers receiving the coupon can be computed using the binomial distribution formula, P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - [tex](6C1)(1/5)^1(4/5)^5 - (6C0)(1/5)^0(4/5)^6[/tex]

≈ 0.477,

which is close to the claimed probability of 1/5.

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Answer:

x = 13

Step-by-step explanation:

To find the value of x we need to isolate it! To do this we have to get rid of any other value around it...

Firstly we need to get rid of the ' -2 '. We have to add 2 to both sides!

Now we are left with 3x = 39 so we have to get rid of the 3. We have to divide 3 from both sides!

x = 13!

Hope this helps, have a lovely day! :)

The equivalent rate measured in qt/wk is 5.25 qt/wk, which is closest to option C. 12 qt/wk.

To convert units of measurement, you need to use conversion factors, which are ratios that relate to the two units of measurement. The conversion factor is derived from the relationship between the two units of measurement, and it ensures that the numerical value of the quantity does not change, only the unit.

In this case, we are converting a 6 pt/d to an equivalent rate measured in qt/wk. We need to use conversion factors for both volume and time to do this.

First, we need to convert pints to quarts. Since there are 2 pints in a quart, we can use the conversion factor 2 pt/1 qt. Multiplying by this conversion factor gives:

Therefore, the equivalent rate measured in qt/wk is 5.25 qt/wk, which is closest to option C. 12 qt/wk.

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Answer:

a. The x-values are equally spaced, and the y-values change by equal differences, so the function is linear.

Step-by-step explanation:

A linear function is categorized by a function which has a constant factor separating all coordinates. In this table, each x-value increases by 1 while each y-value increases by 2. So, it is linear.

The probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles is 0.066, rounded to three decimal places.

We can model the number of raindrops that fall on the picnic table as a Poisson distribution with parameter a, where a is the expected number of raindrops that fall on a 1 square meter area during a rainstorm. Since 462 raindrops fell over an area of 55 square meters, the average number of raindrops per square meter is:

a = 462/55 ≈ 8.4

Therefore, the probability that exactly 11 raindrops fall on the picnic table during a rainstorm is:

P(X = 11) = (eᵃ * a¹¹) / 11!

= (e⁻⁸ ⁴ * 8.4¹¹) / 11!

≈ 0.066

Rounding to three decimal places, we get the probability that exactly 11 raindrops fall on the picnic table as 0.066.

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