A taste test asks people from Texas and California which pasta they prefer brand A or brand B. This table shows the results

Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.

What is slope ?

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

he equation of the position y (in meters) of a submarine after x minutes can be represented as:

y = -8x - 12

Where x is the time in minutes and y is the position in meters. To solve for y, we can substitute a specific value of x and calculate the corresponding value of y.

For example, if we substitute x = 0, we can find the initial position of the submarine:

y = -8 * 0 - 12

y = -12

So, the initial position of the submarine is -12 meters.

In general, the slope of the line represented by this equation is -8, meaning that for every one unit increase in x (i.e., one minute), the position of the submarine decreases by 8 meters.

Equation represents position of submarine vs time, slope of -8 means position decreases 8m per minute.

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The position y (8 meters per minute) of a submarine after x minutes is y = -8x - 12,

given that:

The position y (in meters) of a submarine after x minutes is y = -8x - 12

The slope of the equation y = -8x - 12 represents the rate of change of the position of the submarine. It tells us the amount by which the position of the submarine changes for each unit change in time that is (minutes).

In this case, the slope is -8, which means that for each 1-minute increase in time, the position of the submarine decreases by 8 meters. This indicates that the submarine is descending at a rate of 8 meters per minute. Hence our result is 8 meters per minute.

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a) class interval that contains the median is: 2 ≤ h ≤ 3

b) An estimate for the mean numbers of hours: 23

In statistics, the median is the value that, when placed in order, falls in the centre of the supplied collection of data. Either descending or ascending order can be used to arrange the data or observations. The median of 2,3,4, for instance, is 3. The median is a form of average that is used to determine the center value in mathematics. The middle pair must be identified, added, then divided by two in order to calculate the median value in a list of even integers.

To find median class calculating cumulative freq. (cf) of less than type first:

Number of hours(h)        frequency(f)           cf

0 ≤ h ≤ 1                               4                         4

1 ≤ h ≤ 2                               8                         12

2 ≤ h ≤ 3                              11                         23

3 ≤ h ≤ 4                               7                         30

N/2 = 30/2

Where, N = ∑f

N = 15 ∑cf > N/2

so, median class is 2 ≤ h ≤ 3 since cf 23 is corresponding to this class.

Therefore class interval that contains the median is: 2 ≤ h ≤ 3.

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Since line C has a slope of -8/3 and line D is parallel to line C, the slope of line C is equal to -8/3.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of the two lines are equal and the same:

Slope of line C = Slope of line D

-8/3 = -8/3.

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The complete points of each x for the given linear function are:

Please refer to the attached graph for the graph of the function.

From the question, we have a linear function of:

y = x + 4

x points given are:

Let's try to find the output of y and the (x,y) point for each given x-point:

x = -2

y = (-2) + 4

y = 2 --> (-2, 2)

x = 0

y = (0) + 4

y = 4 --> (0, 4)

x = 2

y = (2) + 4

y = 6 --> (2, 6)

x = 6

y = (6) + 4

y = 10 --> (6, 10)

x = 8

y = (8) + 4

y = 12 --> (8, 12)

Those points are used to make a graph as attached below.

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The solution is of the function 3f(x) +2g(x) is:

=> -5x-2  

Now, According to the question:

Algebra of  functions:

Algebra of functions means the operations of the functions, specifically the arithmetic operations. Algebra of functions mainly deals with the following four arithmetic operations of functions:

The function given as:

f(x) = -3x, g(x) = 2x-1 are the two functions

then by the algebra of two functions(adding two functions) we can find the value of 3f(x) + 2g(x)

Now find

3f(x) = 3(-3x) = -9x            -----------(i)

2g(x) = 2(2x-1)

         = 2(2x)-2(1)                        

2g(x) = 4x-2                     ----------(ii)

Now, add the above two equation (i) and (ii)

3f(x) + 2g(x) = -9x + 4x - 2

                   = -5x-2  

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The given question is incomplete, complete question is:

Let f(x) = -3x and g(x) = 2x-1

Find the following: 3f(x) +2g(x)

0 6x +4

0 -5x - 2

O There is no correct answer given.

O 8x -8

O 5x+1

Generally, if the solution is composed of more ions than molecules, δsol will be positive. If the solution is composed of more molecules than ions, δsol will be negative.

The sign of δsol is dependent on the properties of the solution. δsol is a measure of the concentration of ions in the solution, and is calculated by subtracting the molar concentration of ions from the molar concentration of molecules. If the solution contains a higher molar concentration of ions than molecules, then the difference will be positive, and δsol will be positive. Conversely, if the solution contains a higher molar concentration of molecules than ions, then the difference will be negative, and δsol will be negative. It is important to note that the sign of δsol can be affected by the type of molecules and ions present in the solution. For example, if the solution contains anionic molecules, such as anions from acid-base reactions, then δsol will be negative. Conversely, if the solution contains cations, such as those from acid-base reactions, then δsol will be positive.  It is also important to note that the sign of δsol can be affected by the temperature of the solution. As the temperature increases, the solubility of the ions in the solution increases, resulting in a higher molar concentration of ions and a resulting positive.

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The final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be $70.

The final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants can be represented by the following formula:

Final Cost = Sweatshirt Cost + (2 x T Shirt Cost) + Pants Cost

For example, if the cost of a sweatshirt is $20, the cost of a T shirt is $10, and the cost of a pair of pants is $30, the final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be:

Final Cost = $20 + (2 x $10) + $30

Final Cost = $20 + $20 + $30

Final Cost = $70

Therefore, the final cost of 1 sweatshirt, 2 T shirts, and 1 pair of pants would be $70.

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Complete question:

What is the Final Cost of 1 Sweatshirt, 2 T-Shirts, and 1 Pair of Pants?

Answer:

$1,625

Step-by-step explanation:

Since the statistical survey was done with 5108 randomly selected households it can be concluded that the sample is 5108 randomly selected households.

In order to draw conclusions about the population as a whole a sample of data can be chosen.
A sample is a subset of a larger population that represents the larger population that is chosen for analysis.

In this instance, the sample consists of 5108 homes that were chosen at random for the survey to determine the proportion of homes with televisions tuned to the Super Bowl.

In order to accurately represent the number of households that watched the Super Bowl, a sample size of 5108 was used.

It should be also noted that Nielsen Media Research is a market research company that specializes in measuring media audiences, including television viewership.

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The adult male foot length of 24.2 cm is significantly low as it falls outside of the range of 26.10 cm to 28.72 cm.

The range is just the difference between the greatest and smallest data points in a set.

The square root of the variance is the standard deviation.

The standard deviation measures how far apart the data is from the mean.

The range is a less useful measure of variance than the standard deviation.

The range of data is a measure of variance that indicates the difference between the dataset's maximum and least observation.

It is based only on two observations, the maximum and minimum.

The range rule of thumb states that approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% of the data falls within two standard deviations of the mean.

So, the lower limit separating significantly low values will be:

27.41 - 1.31 = 26.10 cm

And the upper limit separating significantly high values will be:

27.41 + 1.31 = 28.72 cm.

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Answer:

D. :

x y

−2 0

−1 2

0 1

2 0

5 2

Step-by-step explanation:

That should do it.

As per the concept of permutation,  there are 362,880 possible arrangements of the letters of "sociological."

In mathematics and combinatorics, the number of arrangements of a set of objects is calculated using a formula called permutation.

When it comes to the word "sociological," there are 9 letters, and we want to calculate the number of arrangements that can be made using all 9 letters.

To find the number of arrangements, we can use the formula for permutation.

In this case, it would be

=> 9!

which is equal to

=> 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =  362,880

Complete Question:

How many arrangements are there of all the letters of word "sociological" calculate it by using the permutation method?

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Answer:

42-13 =28 so there are 28

Sanchez made more money by 3.93$

The type of function represented in the table is exponential.

The table shows an exponential function, which is a function that increases or decreases by a constant rate over a period of time. The table shows a relationship between the x-values and the y-values, where the y-values increase or decrease by a constant factor as the x-values increase. In this particular table, the y-values increase by a factor of two as the x-values increase by one. This type of function is common in mathematics and can be used to model a variety of real-world phenomena, such as population growth, compound interest, and radioactive decay.

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For the given data, probability of union of A and B (A U B) is 0.95, intersection P(A n B) = 0.75.

Set theory terms like the union and intersection are used to describe the connection between two or more sets.

The set containing all items that are a part of either set A, set B, or both sets is the union of the two sets A and B. The symbol for it is A U B.

The set containing all elements that are a part of both sets A and B is the intersection of the two sets A and B. It has the symbols A and B.

a) We may apply the formula for the union of two events to determine P(A U B), or the likelihood that either A or B will occur:

P(A U B) = P(A) + P(B) - P(A n B)

Plugging in the given values:

P(A U B) = 0.9 + 0.8 - 0.75 = 0.95

b) P(A n B), the probability of both A and B happening, is already given as 0.75. So, P(A n B) = 0.75.

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Answer:

The Mathman guy is wrong, the answer is actually 15.

Step-by-step explanation:

because from the equation that you gave, nicole started with $5 and added $15 every week
thus let y represent the total money and x represent the number of week after x week
nicole save: 15x
because at the beginning he has $5
so, y = 15x + 15
y = mx+c m is the slope c is the y intercept
so slope = 15
so we reach to the conclusion that the rate of change is 15

Answer:

A rational number is any number that can be expressed as a whole number, a fraction, or as a non repeating decimal. Otherwise, it is an irrational number.

19/5: it is a rational number because it is in fraction form

√12: this is an irrational number

√49: this is a rational number because when you simplify this you will get the answer 7, that is a whole number.

0.3425563758:  This is a decimal, hence, this is rational.

4/25 :  it is a fraction so it is a rational number.

√1/8: this is an irrational number

√0.6¯: this is an irrational number

The exponential growth factor of the given function is 7.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

The slope of the line that represents a linear relationship is equal to the growth factor. When the relationship is shown as an equation in the form y = mx + b, the growth factor is also equal to the value of m.

Given exponential function is

y = 4 * 5⁷.

Now compare the given function with y = P₀e^k

P₀ = 4

e = 5

k = 7

The growth factor is 7.

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Therefore, the value of x is established to be: x = 28 using the notion of linear pair angles.

Since that it has three sections and two vertices, a triangular qualifies as a polygon. It corresponds to the essential geometric patterns. Triangle ABC is the term used to refer to a triangle with the endpoints A, B, and C. Because when three principles are not linearly related, a unique plane composite triangle in Geometric shapes are discovered. Triangles are polygons because they have three sections and three corners. The points where it three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

given

m∠ELG = 124°

m∠ELD = 2x

Thus:

m∠ELG + m∠ELD = 180° (linear pair)

Substitute

124 + 2x = 180

2x = 180 - 124

2x = 56

x = 56/2

x = 18

Therefore, the value of x is established to be: x = 28 using the notion of linear pair angles.

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The length of any side of the square basket would be 6 feet.

What are Square roots and length?

In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.

The word "length" refers to the size of an object or the separation between two points. For instance, the length of a ruler is indicated below and indicates how long the ruler is.

You can find this by finding the square root of 36, which is 6.

The length of any side of the square basket would be 6 feet.

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For a real-valued function f, it is said that the interval's value increases for every x and y where f (x) f (y) (x). and the interval is referred to as declining if its value is f (x) f (y) for every x y.

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Corey ran 131.69 meters around a rectangular soccer field.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

Corey ran around a rectangular soccer field that measures 38.50 meters by 27.345 meters.

Corey ran = Perimeter of rectangle =2 (38.50 + 27.345)

Corey ran = 131.69 meters.

Therefore, Corey ran 131.69 meters.

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To convert 162 pounds to kilograms, you can use the following conversion factor 1 pound = 0.453592 kilograms

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The least number of terms required to compute pi as 3.14 is approx 400.

The series is π = 4 - 4/3 + 4/5 - 4/7 + .................

We have to determine the least number of terms required to compute pi as 3.14.

We can write the series as

π = 4(1 - 1/3 + 1/5 - 1/7 + .................)

The general equation of this series is

π = 4[tex]\Sigma_{k=0}^{\infty}(-1)^k(2k+1)^{-1}[/tex]

Now let S = π. So

S = 4[tex]\Sigma_{k=0}^{\infty}(-1)^k(2k+1)^{-1}[/tex]

From the Alternating series theorem

|S - S(n)| ≤ 4/(2n+1)

Hence, the accuracy should be

4/(2n+1) ≤ 1/2 × 10^{-2}

Multiply by 2 on both side, we get

8/(2n+1) ≤ 10^{-2}

We can write 10^{-2} as 1/100. Now the expression is

8/(2n+1) ≤ 1/100

Multiply by 100 on both side, we get

800/(2n+1) ≤ 1

Multiply by 2n+1 on both side, we get

800 ≤ 2n+1

Subtract 1 on both side, we get

2n ≥ 799

Divide by 2 on both side, we get

n ≥ 399.5

Hence, approx 400 terms need to compute pi as 3.14.

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The complete question is:

What is the least number of terms required to compute pi as 3.14 using the series:

π = 4 - 4/3 + 4/5 - 4/7 + .................

To travel downstream, a boat needs 2 hours while to travel back upstream, it needs 4 hours. The river flows at speed of 3.58  3.58 km/hour

The relation between distance and speed is given by:

distance = speed x travelled time

In the problem, let:

vb = boat speed

v = river speed

Then, when the boat travels downstream:

28.62 = (vb + v) x 2

2vb + 2v = 28.62   ... (Equation 1)

When the boat travels upstream:

28.62 = (vb - v) x 4

Divide both sides by 2:

14.31 = (vb - v) x 2

2vb - 2v = 14.31  ... (Equation 2)

Substract equation 1 by equation 2

2vb + 2v = 28.62

2vb  - 2v = 14.31 _

       4v  = 14.31

          v = 3.58

Hence, the speed of water = 3.58 km/hour

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Answer:

25 cents

Step-by-step explanation:

Sand sells at 8.5 cents per pound, an hundred-pound bag of this price would total $8.50 (8.5 * 100).

This is 25 cents more than buying a hundred-pound bag for 8.25, meaning you would save [25 cents]

The expected number of men who will be colorblind is 36.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

5. About 8% of males are colorblind. A researcher has a list of 12 men who have volunteered to be tested.

Here, 8% of 12

= 8/100 ×12

= 0.08×12

= 0.96

Exactly 1 of the 12 men is colorblind.

6. About 8% of males are colorblind. The researcher test 450 volunteers, hoping to find many colorblind men for their study.

Now, 8% of 450

= 8/100 ×450

= 0.08×450

= 36

The expected number of men who will be colorblind is 36.

Therefore, the expected number of men who will be colorblind is 36.

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The square root function contains a variable under the square root sign. The cube root function contains a variable under the cube root sign.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varying quantities and other variables.

A variable under the square root sign is present in a square root function, and a variable under the cube root sign is present in a cube root function.

Zero has a square root of zero, and one has a square root of one. Keep in mind that the graph only contains points where x and y are positive. For instance, using the imaginary number i is necessary when taking the square root of a negative number.

The square root function is f(x) = √x

For positive values, the graph resembles the square root graph, but cube roots can also be negative, making this equation infinite for all real numbers. Recall that a negative number will result from being multiplied an odd number of times.

The cube root function is f(x) = ³√x

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