Find the slope of a line with the cordnates of (6,1) and (-3,5)

The initial amount of salt in the tank is 60 kg, calculated using the formula M = ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank.

Initially, the tank contains 60 kg of salt and 2000 liters of water. The amount of salt in the tank can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The density of salt is 2270 kg/m3. Assuming the tank has a constant volume, the mass of the salt in the tank is 60 kg.

The amount of salt in the tank changes due to the addition of pure water and mixing of the solution. The amount of salt in the tank at any given time can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The rate at which the salt is added to the tank is equal to the rate at which the salt-water solution is drained from the tank.

Therefore, the rate of change of the mass of the salt in the tank is equal to 8 liters/minute of pure water entering the tank minus 4 liters/minute of salt-water solution draining from the tank. Thus, the amount of salt in the tank initially is 60 kg.

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Hence, in answering the stated questiοn, we may say that If yοu're unitary methοd  satisfied with yοur line plοt, save it and distribute it as needed.

The unit technique is a prοblem-sοlving apprοach that invοlves finding the value οf a single unit and then multiplying that value by the needed value. Tο put it simply, the unit technique is used tο extract a single unit value frοm a given multiple. 40 pens, fοr example, wοuld cοst 400 rupees, οr the cοst οf οne pen. The prοcess fοr achieving this may be standardized. A single cοuntry. anything that has an identity element. Its adjοint and reciprοcal are equal in mathematics and algebra.

a general methοd fοr prοducing a line plοt:

First, cοllect yοur data. Stοck prices, temperature readings, and survey results are all examples οf this. The crucial thing is that yοu have a set οf values tο plοt οn a graph.

Enter yοur x and y values intο the plοt. The exact prοcedure depends οn the graphing prοgrammed yοu're using, but yοu shοuld be able tο enter yοur values intο a data table οr spreadsheet.

Make any changes yοu want tο yοur plοt. Adding labels tο the x and y axes, tweaking the plοt's scale, changing the line cοlοur οr thickness, οr adding a title are all pοssibilities.

If yοu're satisfied with yοur line plοt, save it and distribute it as needed.

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Complete question:

Answer:

To simplify the expression x - 15 + 2x + 6, you can combine like terms. Here are the steps to do that:

Group the x terms and the constant terms separately:

(x + 2x) + (-15 + 6)

Simplify the terms inside the parentheses:

3x - 9

So the simplified expression is 3x - 9.

Therefore, x - 15 + 2x + 6 equals 3x - 9.

Answer:

3(x-3)

Step-by-step explanation:

given : x-15+2x+6

factorize using like terms : x-15+3x+6 = 3x-9

= 3x - 9
=3(x-3)

[tex]t_2023[/tex] will be equal to the expression[tex]: t_2023 = [k*t_2022 + 1] / [k^2 * t_2021][/tex]. in terms of k.

The sequence given is defined by the recurrence relation:  [tex]t_n[/tex] = [tex][kt_(n−1)+ 1] /[k^2 t_(n−2)] for n ≥ 3,with t_1 = 1[/tex] and [tex]t_2[/tex] = 2, and [tex]t_3=(2k+1)/k^2[/tex], and [tex]t_4=(3k+1)/2k^3[/tex], and [tex]t_5=(k+1)/2k^2[/tex], and [tex]t_6[/tex]=1 and [tex]t_7[/tex]=2 and [tex]t_8=(2k+1)/k^2, t_9=(3k+1)/2k^3[/tex]. To find the value of [tex]t_2023[/tex], we need to find the values of the previous two terms, [tex]t_2022[/tex] and [tex]t_2022[/tex] . We can do this by using the recurrence relation, starting at n = 3 and going up until n = 2022.

Therefore,[tex]t_2022 = [k*t_2021 + 1] / [k^2 * t_2020][/tex].

Similarly, [tex]t_2021 = [k*t_2020 + 1] / [k^2 * t_2019[/tex]].

We can now plug in the values of [tex]t_2021[/tex] and [tex]t_2020[/tex], which can be found by continuing to work backwards in the recurrence relation until n = 9, and then we have the initial conditions of the sequence. Once we have the values of [tex]t_2021[/tex] and [tex]t_2021[/tex] , we can substitute them into the recurrence relation for[tex]t_2023[/tex] to get the desired result. Therefore, [tex]t_2023 = [k*t_2022 + 1] / [k^2 * t_2021].[/tex]

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Answer:

Slope m = 1/3

Step-by-step explanation:

Slope of the line can be found by taking two points on the line, (x1, y1) and (x2, y2)

Find the difference in y coordinates, y2 - y1  (called rise)

Find the difference in corresponding x coordinates x2 - x1 (called run)

Rise/Run gives the slope

Two distinguishable points on the line graph are (0, 2) and (3, 3)

rise = 3 - 2 = 1

run = 3 - 0 = 3

Slope = 1/3

Answer: Scootering is faster

Step-by-step explanation: If it takes 20 minutes to go around walking going through the middle would technically split the time in half and 20 divided by 2 is 10 which is more than 8 therefore scootering is faster.

If A, B, and C lie on a straight line, the sum of angles y, x, and z will be 180 degrees:

y + x + z = 180

Substituting the values given in the problem:

95 + x + 330 = 180

Simplifying:

425 + x = 180

Subtracting 425 from both sides:

x = -245

Therefore, x is -245 degrees.

However, since x represents an angle on a straight line, we can add 180 degrees to get an equivalent angle:

x + 180 = -245 + 180 = -65

Therefore, x is -65 degrees.

Answer:

1.  C.

2. D.

3. D.

Step-by-step explanation:

A.  Round both dimensions the nearest whole number. 8 1/3 rounds to 8,     6 3/4 rounds to 7. Multiply these two and your estimate for the tarp area is 56 sq yds. Option C.

B. Convert both mixed numbers to improper fractions. Multiply whole number by divisor and add the dividend. (8*3) + 1 = 25. First number is 25/3.(6*4) + 3 = 27. Second number is 27/4. Multiply these two numbers fractions  and get 225/4. Convert to a mixed number, 56 1/4. Option D.

C. This answer is reasonable. 56 1/4 is pretty close to our estimate of 56 sq yds. Or just choose the option that corresponds to your estimate from part A. Option D.

The probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1/1.

The reason for this is that if any letter of the alphabet is selected at random, the probability of getting an "r" is 1/26, or 0.0385. Since letters can be used more than once, this probability remains the same regardless of how many letters are selected. Thus, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1.

In summary, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1. This is because, when a letter is selected at random, each letter has an equal chance of being chosen (1/26), and since the probability of selecting an "r" remains the same regardless of how many letters are selected, the probability of getting at least one "r" is also 1.

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Answer:

the answer to ur question is: 36

The expected value and standard deviation of x are 1.6 and 0.66, respectively.

Given that:

Jimmy volunteers at events at the hospital each year.

The random variable x is the number of hospital events Jimmy works at each year.

We understand that he does not work for more than two events in a year

So, x can take on the values 0, 1, or 2.

From the question, we have:

Over the past ten years

So, the table is

X P(X)

0 0.1

1 0.2

2 0.7

To find the expected value, we take the sum of the products of x and P(x)

So, we have

E(x) = 0(0.1) + 1(0.2) + 2(0.7)

E(x) = 1.6

To find the standard deviation, we need to first calculate the variance:

Var(X) = E(x^2) - [E(x)]^2

Where

E(x^2) = 0^2(0.1) + 1^2(0.2) + 2^2(0.7)

E(x^2) = 3

So, we have

Var(X) = 3 - (1.6)^2

Var(X) = 0.44

This means that

SD(x) = √0.44

SD(x) = 0.66

Hence, the standard deviation is 0.66

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Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.        

Let's denote the number of points scored by Donovan as "D".    

According to the problem, Jeremy scored triple the number of points as Donovan, so he scored 3D points.

Similarly, Kolby scored double the number of points as Donovan, so he scored 2D points.

We also know that the total number of points scored by all three boys is 36. So we can write an equation:

D + 3D + 2D = 36

Simplifying this equation, we get:

6D = 36

Dividing both sides by 6, we get:

D = 6

So Donovan scored 6 points.

Using the values we found for Donovan's score, we can find the scores of Jeremy and Kolby:

Jeremy scored 3D = 3(6) = 18 points

Kolby scored 2D = 2(6) = 12 points

Therefore, Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.

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The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

Here the height of the tip of the hour hand of a wall clock follows a cosine function as the time progresses since the hour hand of a clock completes one full revolution in 12 hours.

We will use the general form of a cosine function to model the height has a function of time t:

Where A is the amplitude, B is the frequency and C is the vertical shift  

Here we have

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Hence, the applitude A = [9+10]/2 = 0.5.

The period of a cosine function is given by 2π/B,

Since the hour hand completes one full revolution in 12 hours, the period is 12 hours or 2π.

=> B = π/6.

The vertical shift is C = 9.

Thus, the equation that models the height h as a function of time t is:

h = 0.5 cos(π/6 t) + 9.

Therefore,

The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

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Answer:

Side 3 is:  5x^3 - 4x^2 +3x - 12

Note that the answer options do not include this result, but it is likely that the second option is simply missing the square term for the -4x, and it should read -4x^2.

Step-by-step explanation:

The perimeter is the sum of all three sides.  To find Side 3, subtract Sides 1 and 2 from the perimeter:

5x^3 - 2x^2 +3x - 8 - (3x^2-4x-1) - (4x-x^2+5)      = Side 3

  Perimeter             -      Side 1    -     Side 2        = Side 3

5x^3 - 2x^2 +3x - 8 - 3x^2+4x+1 - 4x+x^2-5        [Remove parentheses]

5x^3 - 3x^2 +x^2 - 2x^2 +3x +4x - 4x - 8 +1 -5     [Combine like terms]

5x^3 - 4x^2 +3x - 12                       [Simplify]       = Side 3

Answer:

The required amount Ahmet needs to pay after 6 years is $1619.14.

What is compound interest?

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,

From the given data,

P = 700, r = 15% and t = 6 (n =1)

Now,

Amount = principal[1 + r/n]ⁿᵃ

Amount = 700(1 + 0.15)⁶

Amount = $1619.14

Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.

Step-by-step explanation:

The two primary components of an angle are the limbs and the vertex. The angle sum property of a triangle is 20+21+29=180 70x=180 x=180/70.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.

According to the given question,

angle sum property of triangle-

20+21+29=180

70x=180

x=180/70.

Hence, With the angle sum property of triangle, x=180/70.

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The actual distance of 6 cm, given the scale of the map, would be 30 km .

The distance on the map, given the actual distance on the ground and the scale, would be 6 inches .

The scale is that for every 1 cm on the map, the actual distance is 5 kilometers. When given 6 cm therefore, the actual distance is :

= 6 x 5

= 30 km

The scale of the second map is such that 1 inch on the map is 3 actual kilometers so 18 km on the ground would be :

= 18 / 3

= 6 inches

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The domain and range of g of x equals the square root of the quantity x plus 4, g(x) = √x + 4, are equal to d: [–4, [infinity]) and r: [0, [infinity]). Thus, the right choice of answer is option (c).

We have a function g(x) and defined as square root of the quantity x plus 4, i.e.,

g(x) = √x + 4

We have to determine the domain and range of function g(x).

The domain of function is all input values of x that make the expression defined. The range is the set of all output values that valid g(x) values. A square root limits the function because we can't have negative numbers under the square root (they become imaginary numbers). Let y = g(x) = √x +4

the square root '√ 'sign must be implies ≥ 0, therefore, x + 4 ≥ 0

Subtracting the 4 from both sides

=> x + 4 -4 ≥ 0 - 4

=> x ≥ -4

The domain is x∈ [-4,+∞)

When x = -4, g(x) = 0

Therefore, The range is y∈ [0, 00)

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The point one tick mark to the left of negative 3 on the number line is -3.25.

Number lines are horizontal straight lines in math where the intervals between the integers are equal. A number line can be used to show all of the numbers in a sequence. At both ends, this line continues indefinitely.

Each tick mark on the number line represents one-fourth of a unit, so the distance between negative 4 and negative 3 can be divided into 4 parts, each with a length of one-fourth of a unit. Starting from negative 4, the tick marks would be labeled as -4, -3.75, -3.5, -3.25, -3, and so on. Therefore, the point one tick mark to the left of negative 3 is at -3.25 on the number line.

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Wilbur's flight took about 43.7 seconds.

Let x be the rate of Orville in feet per second and 2x be the rate of Wilbur in feet per second. Let t be the time it took for Orville to complete the flight and t - 6 be the time it took for Wilbur to complete the flight.

We know that the distance traveled by both brothers is the same, which we can express with the equation:

distance = rate × time

For Orville:

distance = x * t

For Wilbur:

distance = 2x * (t - 6)

Since the distance is the same for both brothers, we can set the two equations equal to each other:

x * t = 2x * (t - 6)

Expanding and simplifying the right-hand side:

xt = 2xt - 12x

12x = xt

x = t/12

So, Orville's rate is x = t/12 feet per second.

Substituting this into one of the equations for distance, we can solve for t:

distance = x * t

852 = (t/12) * t

852 = t² / 12

t² = 12 * 852

t² = 10224

t ≈ 101.1 seconds (rounded to the nearest tenth)

So, Orville's flight took about 101.1 seconds.

Now we can use the equation for Wilbur's distance to find his rate:

distance = 2x * (t - 6)

852 = 2(2x) * (101.1 - 6)

852 = 4x * 95.1

x ≈ 5.64 feet per second (rounded to the nearest hundredth)

So, Orville's rate is about 5.64 feet per second, and Wilbur's rate is twice that or about 11.28 feet per second.

To find Wilbur's time, we can use the equation for distance again:

distance = 2x * (t - 6)

852 = 2(11.28) * (t - 6)

852 = 22.56t - 135.36

22.56t = 987.36

t ≈ 43.7 seconds (rounded to the nearest tenth)

So, Wilbur's flight took about 43.7 seconds.

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The value of the probability P(A ∪ B) if the events are independent events is  0.55

The formula for the probability of the union of two events is:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Since the events A and B are independent, the probability of their intersection is simply the product of their individual probabilities:

P(A ∩ B) = P(A) × P(B)

Substituting the given values, we have:

P(A ∩ B) = 0.4 × 0.25 = 0.1

Now we can use the formula for the union:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

So, we have

P(A ∪ B) = 0.4 + 0.25 - 0.1

This gives

P(A ∪ B) = 0.55

Therefore, the probability of the union of events A and B is 0.55.

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The percentage decrease in the population after on year is found to be 19%.

The percentage decrease can be found by using the formula,

Percentage decrease = change in population/initial population x 100.

Now change in population in one year is given as final population - initial population.

Putting values, change in population = 252000 - 204120

Change in population = 47880

Now, putting all the value in the formula,

percentage decrease = 47880/252000 x 100

percentage decrease = 19%

So, the decrease in the population is found to be 19%.

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Answer: To find the total area of the grass that Yuri's dad needs to fertilize, we need to calculate the area of the back yard and the area of the front yard, and then add them together.

Area of the back yard:

The back yard measures 55 feet by 30 feet, so the area is:

55 feet x 30 feet = 1650 square feet

Area of the front yard:

The front yard is a square with a length of 42 feet on each side, so the area is:

42 feet x 42 feet = 1764 square feet

Total area:

To find the total area, we add the area of the back yard and the area of the front yard:

1650 square feet + 1764 square feet = 3414 square feet

Therefore, Yuri's dad needs to fertilize a total area of 3414 square feet.

Step-by-step explanation:

Answer:a

Step-by-step explanation:its simple

If I walk 3.5 miles in 2 hours, then I can walk 14 miles in 8 hours.

If I walk 3.5 miles in 2 hours, then I can use a simple proportion to calculate how far I can walk in 8 hours. I know that in 2 hours I can walk 3.5 miles, and I want to calculate how far I can walk in 8 hours. To do this, I can set up a proportion. The fraction representing the time I spent walking and the distance I walked must be equal on both sides of the equation. On the left side of the equation, I set up 2/3.5, and on the right side I set up 8/x, where x is the unknown distance I can walk in 8 hours. I can then solve for x by cross-multiplying and dividing. After solving, I find that I can walk 14 miles in 8 hours.

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The perimeter of the rectangle is (x² + 30x + 104) in² while The area of the rectangle is (x² + 30x + 104) in²

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.

The rectangle have a length of (0.5x + 13) and width of (2x + 8)

1) Perimeter = 2(length + width)

Perimeter = 2(0.5x + 13 + 2x + 8) = 2(2.5x + 21) = (5x + 42) inches

The perimeter of the rectangle is (x² + 30x + 104) in²

2) Area = length * width

Area = (0.5x + 13) * (2x + 8) = x² + 4x + 26x + 104

Area = (x² + 30x + 104) in²

The area of the rectangle is (x² + 30x + 104) in²

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Answer:

1219.5 more centimeters of fabric

Step-by-step explanation:

First, we need to convert 12.5 meters to centimeters, since the given amount of fabric is in centimeters.

12.5 meters = 12.5 x 100 centimeters/meter = 1250 centimeters

Now we can find the difference between what Ray needs and what he has:

1250 centimeters - 30.5 centimeters = 1219.5 centimeters

Therefore, Ray needs 1219.5 more centimeters of fabric.

The lowest common denominator, 20, can be used to represent any fraction that can be stated as a ratio of integers with factors of 2 and 5 in the denominator. eg. 1/4, 1/2, 2/5 and 7/10

To find all the fractions that have 20 as the lowest common denominator, we need to identify all the prime factors of 20, which are 2, 2, and 5.

Then, we can express each fraction with these prime factors in the denominator, by multiplying the numerator and denominator by the missing factors. For example, for the fraction 1/4, we need to multiply both the numerator and denominator by 5 to get:

1/4 = 5/20

Similarly, for the fraction 3/5, we need to multiply both the numerator and denominator by 2 to get:

3/5 = 6/10 = 12/20

By doing this for all fractions, we can express them with the same denominator of 20. Here are some examples:

1/4 = 5/20

3/5 = 12/20

1/2 = 10/20

2/5 = 8/20

7/10 = 14/20

Therefore, any fraction that can be expressed as a ratio of integers with factors of 2 and 5 in the denominator can be written with 20 as the lowest common denominator.

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Complete Question

Write any two fractions which have 20 as the LCD (lowest common denominator)?

The sample space is 20, 24, 28, 32, 36, 40. There are 6 outcomes in the sample space.  In this case, the sample space is {20, 24, 28, 32, 36, 40}.

The sample space of the probability experiment is the set of all possible outcomes that can occur when randomly choosing a number from the multiples of 4 between 20 and 40, inclusive.

To determine the number of outcomes in the sample space, we simply count the number of elements in the set. In this case, there are 6 outcomes in the sample space.

Therefore, the sample space is {20, 24, 28, 32, 36, 40} and there are 6 outcomes in the sample space. After Randomly choosing a number from the multiples of 4 between 20 and 40, these values are found.

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