How do pattern in mathematic help individual better undertand the world and predict what come next?

Answer:

For 2:The y intercept is whatever the y coordinate is when x = 0. Basically, where does the line hit the line going up and down?  For number two, the y intercept is negative 3.

Slope intercept form y = mx + b

m = slope

b is y intercept

so far its

y = mx - 3

the slope is how many time you have to go up and over to get to the next number. Rise/run. For 2, the slope is negative! It is - 1/1 so

y = -1x - 3 is the first equation

For 3, the y inttercept is 0! so

y = mx + 0

or just y =mx

The slope is going to be negative

1/2

so - 1 /  2

y = -1/2x +0 or just y = -1/2x

Next one 4 is a positive slope. y intercept is 4

slope is 3 /1 or just 3

y = 3x + 4

5  is negative slope as well :)

The y intercept is 3

The slope is  - 1/3

y = - 1/3x + 3

for 6, it is going to be a positive slope

y intercept is -3

Sloep is 2/1 so

y = 2x - 3

Step-by-step explanation:

The Surface area are shown below.

The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.

Given:

1. The height of the cone shape, h = 84 inches

radius = 8 inches

The cost per cubic inch is $2.25.

The cost of nickel for the sculpture is given by

= 2.25 x 1/3πr²h

= 2.25 x 1/3 x 3.14 x 8 x 8 x 84

= $12660.48.

2. The measure of sides are

A = 12

B = 10

C= 5

D= 13

So, the Lateral Surface Area

= ( 12 + 13 + 5) x 10

= 30 x 10

= 300 cm²

and, the total surface Area

= Area of two triangles + Area of rectangle

= 2 x 1/2 x 5 x 12 + 300

= 60+ 300

= 360 cm²

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This compound inequality is the range of numbers that Penelope might be thinking of;

Compound inequalities are inequalities that have been joined by the words “and” or “or.” For example: − 2 < x ≤ 5 Read, “ is greater than -2 and less than or equal to 5.” x ≥ 3 or Read, “ is greater than or equal to 3 or less than -4.” Notice that both of these inequalities have two inequality signs.

3x + 5 > -1  and  3x + 5 < 35

This compound inequality is the range of numbers that Penelope might be thinking of; the first inequality shows that the number must be greater than -1, and the second inequality shows that the number must be less than 35.

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If we know that at least one of the dice is a 4, the probability that the sum of the two dice will be equal to 7 is 1/3.

The probability that the sum of two dice will be equal to seven if we know that at least one of the dice is a 4 can be calculated as follows:

There are two cases to consider:

Since the two events are mutually exclusive, the total probability that the sum of the dice will be equal to 7 is the sum of the individual probabilities, which is

1/6 + 1/6 = 2/6 = 1/3.

In conclusion, if we know that at least one of the dice is a 4, the probability that the sum of the two dice will be equal to 7 is 1/3. This means that there is a 1 in 3 chance of getting a sum of 7 when rolling two dice and knowing that at least one of the dice is a 4.

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Answer:

150000

Step-by-step explanation:

Slope=0.500/2.000=0.250

-6/1 = 6.00000

6/4 = 3/2 = 150000

The expression that represents the volume of the rectangular prism is given as follows:

8 x 3 x 2 units ³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

Hence the volume is given by the multiplication of these dimensions as follows:

8 x 3 x 2 units ³.

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When rotated about it’s center, a regular heptagon has 5 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 7 lines of reflectional symmetry.

The number of times an object is precisely the same as the original object during a full 360° revolution is known as rotational symmetry, a sort of symmetry. It can be found in various geometrical objects as rhombuses, squares,

A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.

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The function whose derivative is f'(x) = x^(-1) is f(x) = ln(x) + C, where C is the constant that needs to be found.

To find C, we can use the point (1, 3). Plugging x = 1 and y = 3 into the equation f(x) = ln(x) + C, we get 3 = ln(1) + C, so C = 3 - ln(1). Therefore, the function is f(x) = ln(x) + 3 - ln(1). This can also be written as f(x) = ln(x) + 2.  

The function whose derivative is f'(x) = x1/x is given by f(x) = ln|x| + c, where c is a constant. To find the constant c, we can use the point (1, 3). We know that if a function passes through the point (1, 3), then f(1) = 3. Therefore, we can substitute x = 1 into f(x) to find c.

This gives us ln|1| + c = 3, or c = 3. Therefore, the function that satisfies the given conditions is f(x) = ln|x| + 3. We can check this by taking the derivative of f(x):

To calculate the value of f(x), we can substitute the value of x into th equation. For example, to find the value o f(4), we would calculate f(4) = ln(4) + 2 = 1.38629 + 2 = 3.38629.

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Answer:

This equation has no solution.

Step-by-step explanation:

A constant zero never equals zero..

Given that, the function s(t) describes the motion of a particle along a line. s(t) = t³ − 13t² + 35t − 220

We need to find the time intervals in which the particle moves in the positive direction and the negative direction.

The given equation is s(t) = t³ − 13t² + 35t − 220

Taking the derivative,

v(t) = s'(t) = 3t² -26t + 35 = velocity at time t

s'(t) = 3t² -26t + 35 = 0

(3t -5)(t-7) = 0

t = 5/3 and 7 seconds

Therefore, the velocity > 0 when s'(t) > 0, when t>7 or t < 5/3 seconds

velocity <0 when 5/3 < t < 7 seconds

When moving in a positive direction, the intervals :-

(-∞, 5/3) ∪ (7, ∞)

When moving in a negative direction, the interval :-

(5/3, 7)

Hence, the time intervals are; positive direction (-∞, 5/3) ∪ (7, ∞) and negative direction (5/3, 7)

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The question was incomplete, so I solved for the question;

The function s(t) describes the motion of a particle along a line.

s(t) = t³ − 13t² + 35t − 220

(a) Find the velocity function v(t) of the particle at any time t ≥ 0.

(b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.)

(c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.)

The ΔDEF is mapped onto ΔD'E'F' by translation and rotation rules of triangle.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As the figure is rotated by 90 degree and translated by moving from 2nd and 3rd quadrant to 1st and end quadrant.

Hence,

           The ΔDEF is mapped onto ΔD'E'F' by translation and rotation rules of triangle.

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To convert a decimal number to binary, start by dividing by the highest binary place value and writing a 1 in that place value if the result is greater than 0. the converted values is 10111011, 10111011 , 10110101 , 11011101.

187:

Start with the binary place values equal to or less than the number: 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 128 and subtract from 187. 187 - 128 = 59.

Since 59 is greater than 0, a 1 is placed in the 128 place value.

Next, subtract the next binary place value, 64, from 59. 59 - 64 = -5.

Since -5 is less than 0, a 0 is placed in the 64 place value.

Continue this process until all of the place values are filled.

The binary number for 187 is 10111011.

891:

Start with the binary place values equal to or less than the number: 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 512 and subtract from 891. 891 - 512 = 379.

Since 379 is greater than 0, a 1 is placed in the 512 place value.

Next, subtract the next binary place value, 256, from 379. 379 - 256 = 123.

Since 123 is greater than 0, a 1 is placed in the 256 place value.

Continue this process until all of the place values are filled.

The binary number for 891 is 1110100011.

2014:

Start with the binary place values equal to or less than the number: 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 1024 and subtract from 2014. 2014 - 1024 = 990.

Since 990 is greater than 0, a 1 is placed in the 1024 place value.

Next, subtract the next binary place value, 512, from 990. 990 - 512 = 478.

Since 478 is greater than 0, a 1 is placed in the 512 place value.

Continue this process until all of the place values are filled.

The binary number for 2014 is 10111011.

20486:

Start with the binary place values equal to or less than the number: 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1.

Begin with the highest place value of 16384 and subtract from 20486. 20486 - 16384 = 4102.

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An equation which can be used to determine the number of hours for both DJ's charges to be equal to each other is: B. 20h + 60 = 15h + 80.

In order to write an equation that model this situation, we would assign variables to the cost charged by DJ Ralph and DJ Felicia, and the number of hours respectively, and then translate the word problem into algebraic equation as follows:

Since DJ Ralph charged a $60 event fee plus $20 per hour while DJ Felicia charges an $80 event fee plus $15 per hour, a system of equations that models their charges is given by:

T = 20h + 60     ..............equation 1.

T = 15h + 80     ..............equation 2.

By equating the system of equations, we have:

20h + 60 = 15h + 80

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A segment that connects the vertex of a triangle with the opposite side so it makes a 90-degree angle is called Altitude.

In geometry, Altitude is used to describe the height of a polygon, triangle, or other two-dimensional shapes. The altitude of a figure is a line segment perpendicular to the base and passes through the vertex of the constitution. It is used to calculate the area of the figure and to determine the lengths of the sides and angles.

In three-dimensional figures, the altitude can also refer to the distance between the highest and lowest points of the constitution. The concept of altitude is widely used in mathematics, particularly in geometry, trigonometry, and related fields.

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Complete Question:

A line that connects the vertex of a triangle with the opposite side so it makes a 90 degree angle_____.

The statement Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2) is correct.

The probability that an event will occur is equal to the ratio of positive outcomes to all outcomes, according to the probability formula. The proportion of positive outcomes to overall outcomes, or P(E), determines the likelihood that an event will occur.

Given three softball players discussed their batting averages after a game.

Probability

Player 1 is seven elevenths = 7/11

P(Player 1) = 0.636

Player 2 is six ninths = 6/9

P(Player 2) = 0.666

Player 3 is = five sevenths = 5/7

P(Player 3) = 0.714

so the probability of P(Player 3) > P(Player 2) > P(Player 1).

so Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).

Hence option D is correct.

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f (2) = 2^2 = 2 * 2 = 4

f (3) = 3^2 = 3 * 3 = 9

f(2) + f(3) = 4 + 9 = 13

f (5) = 5^2 = 5 * 5 = 25

13 does not equal 25

a. 4

b. 9

c. f(2) + f(3) ‡ f(5) can be stated as 13 does not equal 25

A: The model for the temperature of the juice is:

T = 36 + (85 - 36)e^(-0.2659t)

B: Rounding to the nearest degree, we have:

T = 51 degreeF

C: The temperature of the juice will be 51 degreeF after 20 minutes.

What is temperature ?

Temperature is a measure of the average thermal energy of the particles in a substance or system. It is an intensive property, meaning that it does not depend on the amount of matter in the system. The unit of temperature in the International System of Units (SI) is the kelvin (K).

a. To find the value of k in the model, we can use the initial temperature and time given in the problem: T = 56 degreeF, t = 10 minutes. Plugging these values into the equation, we get:

56 = 36 + (85 - 36)e^(10k)

20 = 49e^(10k)

ln(20/49) = 10k

Solving for k, we get:

k = ln(20/49) / 10

Rounding to four decimal places, we have:

k = -0.2659

Hence, the model for the temperature of the juice is:

T = 36 + (85 - 36)e^(-0.2659t)

b. To find the temperature of the juice after 15 minutes, we plug in t = 15 into the model:

T = 36 + (85 - 36)e^(-0.2659 * 15)

Rounding to the nearest degree, we have:

T = 51 degreeF

c. To find when the temperature of the juice will be 51 degreeF, we solve for t in the model:

51 = 36 + (85 - 36)e^(-0.2659t)

15 = 49e^(-0.2659t)

ln(15/49) = -0.2659t

Solving for t, we get:

t = ln(15/49) / -0.2659

Rounding to the nearest minute, we have:

t = 20 minutes

Hence, the temperature of the juice will be 51 degreeF after 20 minutes.

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The number of solutions to the system of linear equations shown on the graph is given as follows:

D. One solution at (2, −3).

The number of solutions of the system of equations is given by the number of times which the two functions intersect.

From the image given at the end of the answer, the two functions intersect once, at x = 2 and y = -3, hence the correct option is given by option D.

The graph is given by the image presented at the end of the answer.

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Answer:

3.

x −4 0 4

y 1 0 −1

-----------------------

The graph of function f is shown. If g(x) = -2f(x), which graph is the graph of function g is show on the attachment

Note that the new function, g(x), provides a value for y that is -2 times the value returned by f(x).  That means that for the same value of x, the resulting value of g(x) will be -2 times that provided by f(x).

See the attached image.  The table shows how the values of y change for each value of x used in the respective function.  Plot those new values to produce the graph.

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Two different age brackets (18-21 and 22-29) were surveyed and the number of people who responded and refused to respond was recorded.

We can use the formula for probability:

Probability = Number of favorable outcomes by Total number of outcomes, P(A) = f / N

First, let's find the number of people in the 22-29 age bracket who agreed to respond:

238 out of 268 people in this age bracket agreed to respond.

Next, let's find the number of people in the 18-21 age bracket who agreed to respond:

70 out of 83 people in this age bracket agreed to respond.

So, the total number of people who agreed to respond is 238 + 70 = 308 out of 351 people.

Therefore, the probability of getting someone in the 22-29 age bracket or someone who agreed to respond is 308/351.

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Answer: 0.8  miles

Step-by-step explanation:

The system Ax = b is consistent, we use matrix multiplication and the Gauss Jordan Elimination method.

Given a matrix A, and a vector b, we can determine whether b is in the column space of A by performing a matrix multiplication. The column space of A is the set of all linear combinations of the columns of A. We can represent this set by multiplying A by a vector x, such that Ax = b. If the result of the matrix multiplication yields b, then b is in the column space of A.

We can determine whether the system Ax = b is consistent by evaluating the rank of A and the rank of the augmented matrix, [A|b]. If the rank of A is equal to the rank of [A|b], then the system is consistent. To determine the rank of A, we can use the Gauss Jordan Elimination method to find the reduced row echelon form of A and then count the number of non-zero rows.

In summary, to determine whether b is in the column space of A, and whether the system Ax = b is consistent, we use matrix multiplication and the Gauss Jordan Elimination method.

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The graph of the model is illustrated below and  the resistance when x = 85 is 1.12

The resistance of a conductor (such as a wire) is a measure of the opposition it presents to the flow of electric current. The resistance of a wire is dependent on various factors such as its length, cross-sectional area, and material. In this case, we are looking at the resistance of 1000 feet of solid copper wire, where the diameter of the wire is given in mils (0.001 inches).

The resistance of the wire can be approximated using the mathematical model:

=> y = 10,770/x² - 0.375,

where x is the diameter of the wire in mils and y is the resistance in ohms. The model is valid for values of x ranging from 5 to 100.

To complete the table, you need to plug in different values of x into the model and solve for y. For example, when x = 10,

=> y = 10,770/(10²) - 0.375 = 106.975 ohms.

The graph of the model can then be plotted by plotting the points (x,y) from the table and connecting them with a smooth curve. The graph can be used to estimate the resistance of the wire when x = 85.5 mils by finding the y-coordinate of the corresponding point on the graph.

Finally, you can use the model to algebraically confirm the estimate you found from the graph by plugging in the value x = 85.5 into the model and solving for y then we get the value as 1.12. This should give you the same answer as you found from the graph.

In conclusion, the resistance of a wire can be estimated using the mathematical model and can be used to make predictions about the resistance for different wire diameters.

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Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.

Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

When assessed in terms of standard deviation units, a raw score's location in relation to its distance from the mean is indicated by a z-score.

If a value is above the mean, the z-score is positive; if it is below the mean, it is negative.

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150 kg of bluegrass seed should be mixed with 200 kg of ryegrass seed to make a blend that costs of amount $7.00 per kg.

To calculate, use the following formula:

7.60x + 6.25(200 - x) = 7.00(200)

7.60x + 1,250 - 6.25x = 1,400

1.35x = 1,400

x = 1,040/1.35

x = 770/1

x = 770

Therefore, 770 kg of bluegrass seed should be mixed with 200 kg of ryegrass seed to make a blend that costs of amount $7.00 per kg.

The complete question is :

Speed Seed Company mixes bluegrass seed that costs $7.60 per kilogram with ryegrass seed that costs $6.25 a kg. How many kiolgrams of bluegrass seed should be mixed with 200 kg of ryegrass seed to make a blend that costs $7.00 per kg?

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Sam owes his dad $12.50 represents the correct situation.

Given are the situations about Sam's money that could be described using the sum of -2.5 and -10.

The sum of - 2.5 and -10 is :

{x} = - 2.5 + (- 10) = - 12.5

{x} = - 12.5

Sam owes his dad $12.50 represents the correct situation.

Therefore, Sam owes his dad $12.50 represents the correct situation.

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{Complete question -

Which situation about Sam's money could be described using the sum of -2.5 and -10?

A. Sam owes his dad $12.50

B. Sam earned $12.50

C. Sam owes his dad $7.50

D. Sam earned $7.50​}

The number of tiles that will fit along the edge of the square mosaic is 28 tiles.

The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.

To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:

sqrt(196) = 14

So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.

Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

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The number of tiles that will fit along the edge of the square mosaic is 28 tiles.

The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.

To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:

sqrt(196) = 14

So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.

Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

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