Explain what's happening in Step 2.

[ -8, 2 ] [ -6 , 0 ] [ -4 , - 2 ] are probability of the cards into three pairs with the same total .

What is probability?

( -8 ) + 0 + ( - 6) + 2 + ( -4 ) + ( -2 )   =   -20 + 2 = -18

                                                              { addition of negative numbers }

So, each pair  =  -18 / 3  = -6  { division }

so the pairs are = [ -8, 2 ] [ -6 , 0 ] [ -4 , - 2 ]

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The amount of chemical (water with solvent) inside the tank at any instant t corresponds to the expression 260/3 - 52e⁽⁻t/⁵²⁾) pounds.

The amount of chemical (water with solvent) inside the tank at any instant t corresponds to the total amount of solution that has flowed into the tank up to that point, minus the amount that has flowed out.

Using the given information, we can calculate the amount of solution that flows into the tank per minute: 1/6 lb/gal x 52 gal = 8 2/3 lb

So, at a rate of 5 gal/min, the amount of solution that flows into the tank per minute is:

8 2/3 lb x 5 gal/min = 43 1/3 lb/min

To find the amount of chemical inside the tank at any time t, we need to integrate the rate of change of the amount of chemical over time.

Let C(t) be the amount of chemical in the tank at time t, in pounds.

Then, the rate of change of the amount of chemical inside the tank is:

dC/dt = (1/6 lb/gal) x 5 gal/min - (1/6 lb/gal) x 5 gal/min x (C/52)

The first term on the right-hand side represents the amount of chemical that flows into the tank per minute, and the second term represents the amount that flows out per minute, which is proportional to the amount of chemical inside the tank (since the concentration of the chemical is constant).

Simplifying this equation, we get:

dC/dt = 5/6 - C/52

To solve for C(t), we can use separation of variables:

dC/(5/6 - C/52) = dt

Integrating both sides, we get:

-52 ln |5/6 - C/52| = t + K

where K is a constant of integration.

Solving for C(t), we get: C(t) = 260/3 - 52e⁽⁻t/⁵²⁾

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The line integral of the vector field F = y^2 dx + x^2 dy over the square C with the given orientation is 5/3.

To compute the line integral of the vector field F = y^2 dx + x^2 dy over the square C with vertices (0,0), (1,0), (1,1), and (0,1) oriented counterclockwise, we can parameterize the boundary of the square and evaluate the line integral using the parameterization.

Let's divide the boundary of the square C into four line segments: AB, BC, CD, and DA.

On the line segment AB, we have x = t, y = 0, where t varies from 0 to 1.

On the line segment BC, we have x = 1, y = t, where t varies from 0 to 1.

On the line segment CD, we have x = t, y = 1, where t varies from 1 to 0.

On the line segment DA, we have x = 0, y = t, where t varies from 1 to 0.

Now, let's evaluate the line integral over each line segment:

∫AB F · dr = ∫[0,1] (0^2 dt) + (t^2 * 0) = ∫[0,1] 0 dt = 0

∫BC F · dr = ∫[0,1] (1^2 * 1) + (1^2 dt) = ∫[0,1] (1 + 1) dt = ∫[0,1] 2 dt = 2t | [0,1] = 2

∫CD F · dr = ∫[1,0] (t^2 * 1) + (0^2 * -1) = ∫[1,0] t^2 dt = (1/3)t^3 | [1,0] = (1/3)(0^3 - 1^3) = -1/3

∫DA F · dr = ∫[1,0] (0^2 * -1) + (t^2 * 0) = ∫[1,0] 0 dt = 0

Adding up the line integrals over each line segment, we get:

∫C F · dr = ∫AB F · dr + ∫BC F · dr + ∫CD F · dr + ∫DA F · dr = 0 + 2 + (-1/3) + 0 = 5/3

Therefore, the line integral of the vector field F = y^2 dx + x^2 dy over the square C with the given orientation is 5/3.

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Answer:

4

Step-by-step explanation:

Answer :

C

Explanation :

The length of the base edge of the square pyramid is 6 feet.

The surface area of a square pyramid is 96 square feet. The height is two thirds of the length of the base edge.

The length of the base edge can be found as follows:

Hence,

surface area of square pyramid = a² + 2al

where

Therefore,

using Pythagoras's theorem, let find the slant height of the pyramid.

c² = a² + b²

where

Hence,

height = 2 / 3 a

Therefore,

l² = (2 / 3 a)² + (1 / 2a )²

l² = 4 / 9 a² + 1 / 4 a²

l² = 25 / 36 a²

square root both sides

l = 5 / 6 a

Hence,

surface area of square pyramid = a² + 2a(5 / 6 a)

surface area of square pyramid = a² + 10 / 6 a²

surface area of square pyramid = 16 / 6 a²

96 = 16 / 6 a²

96 = 8 / 3 a²

cross multiply

96 × 3 = 8a²

288 / 8 = a²

a² = 36

a = √36

a = 6 feet

Therefore, the base length is 6 feet.

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Answer:

the y-intercept is 6 the slope is 3 / 5

Step-by-step explanation:

slope-6

y-intercept-3/5

Answer:

M = \(\frac{3}{5}\)

Step-by-step explanation:

Use the slope-intercept form y = mx + b  to find the slope m.

.

Answer:

2,4 because they are hitting each other at that point

Answer:

D

Step-by-step explanation:

The solution is where the the red and blue line intersect.

To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.

Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.

Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.

When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.

Hence the unit of analysis is objective of the section.

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The data set of the sample is

62 82 79 76 73 70 67 64 61 66 66 66 63 63 63 60 60 71 71

we have that

(84.5-59.5)/5=5

therefore

The classes are equal to

N 1) 59.5-64.5 ------> midpoint 62

N2) 64.5-69.5 -----> midpoint 67

N3) 69.5-74.5 -----> midpoint 72

N4) 74.5-79.5 -----> midpoint 77

N5) 79.5-84.5 -----> midpoint 82

Find out the frequency for each class

N 1) 59.5-64.5 ------> 8

N2) 64.5-69.5 ----->4

N3) 69.5-74.5 ----> 4

N4) 74.5-79.5 ------> 2

N5) 79.5-84.5 ----> 1

see the figure below to better understand the problem

Answer:

5000

Step-by-step explanation:

1000/2=5000

So, the array after sorting based on the 10's digit is (6, 50, 482, 14, 474, 9, 58).

To sort the array based on the 10's digit, we need to group the numbers into buckets based on their 10's digit. So, we start by looking at the second digit in each number.
We have the following buckets:
- Bucket 0: (50, 6)
- Bucket 1: (482, 14)
- Bucket 4: (474)
- Bucket 5: (58, 9)

We then need to sort each bucket based on the 1's digit. So, we have:
- Bucket 0: (6, 50)
- Bucket 1: (482, 14)
- Bucket 4: (474)
- Bucket 5: (9, 58)

Finally, we combine all the buckets in order, which gives us the sorted array:
(6, 50, 482, 14, 474, 9, 58)

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Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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(i) For the matrix A = [[-5, -1], [-4, 5]], the row echelon form can be obtained through Gauss-Jordan elimination:

Multiply the first row by -4/5 and add it to the second row: [[-5, -1], [0, 1]].

Multiply the second row by 5 and add it to the first row: [[-5, 0], [0, 1]].

Next, we perform back substitution to obtain the reduced row-echelon form:

Multiply the first row by -1/5: [[1, 0], [0, 1]].

Therefore, the inverse of matrix A is A⁻¹ = [[1, 0], [0, 1]], which is the identity matrix of the same size as A. We can verify this by multiplying A and A⁻¹:

A * A⁻¹ = [[-5, -1], [-4, 5]] * [[1, 0], [0, 1]] = [[-51 + -10, -50 + -11], [-41 + 50, -40 + 51]] = [[-5, -1], [-4, 5]].

The resulting matrix is the identity matrix, confirming that A⁻¹ is indeed the inverse of A.

(ii) For the matrix A = [[-3, -3, 1], [-2, 3, 1], [-2, -2, -3]], we perform Gauss-Jordan elimination:

Swap the first and second rows: [[-2, 3, 1], [-3, -3, 1], [-2, -2, -3]].

Multiply the first row by -3/2 and add it to the second row: [[-2, 3, 1], [0, -15/2, 5/2], [-2, -2, -3]].

Multiply the first row by -2 and add it to the third row: [[-2, 3, 1], [0, -15/2, 5/2], [0, -8, -5]].

Multiply the second row by -2/15: [[-2, 3, 1], [0, 1, -1/3], [0, -8, -5]].

Multiply the second row by 3 and add it to the first row: [[-2, 0, 0], [0, 1, -1/3], [0, -8, -5]].

Multiply the second row by 8 and add it to the third row: [[-2, 0, 0], [0, 1, -1/3], [0, 0, -19/3]].

Multiply the third row by -3/19: [[-2, 0, 0], [0, 1, -1/3], [0, 0, 1]].

Multiply the third row by 2 and add it to the first row: [[-2, 0, 0], [0, 1, -1/3], [0, 0, 1]].

Multiply the third row by 1/3 and add it to the second row: [[-2, 0, 0], [0, 1, 0], [0, 0, 1]].

Multiply the first.

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Answer:

x = ± 2

Step-by-step explanation:

Given

3x² = 12 ( divide both sides by 3 )

x² = 4 ( take the square root of both sides )

x = ± \(\sqrt{4}\) = ± 2

Answer:

\(h = 6 + 11 - 22 \\ h = 17 - 22 \\ h = - 5\)

Answer:

-5

Step-by-step explanation:

6+11 = 17↓

17-22 = -5

or

11-22 = -11↓

-11+6 = -5

The difference in temperature between London and Singapore is 38°c.

The temperature in London was -14°c, while the temperature in Singapore was 24°c. To find the difference in temperature between the two cities, we need to subtract the temperature in London from the temperature in Singapore: 24°c - (-14°c) = 24°c + 14°c = 38°c. Therefore, the difference in temperature between London and Singapore is 38°c.

Temperature is a measure of the hotness or coldness of an object or substance. It is typically measured in units such as degrees Celsius (°C) or degrees Fahrenheit (°F). The higher the temperature of an object or substance, the more energy it has, and the lower the temperature, the less energy it has.

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Answer:

m∠DBC = 46°

Step-by-step explanation:

Given:

From inspection of the given diagram, m∠ABC is a right angle.

Therefore, the sum of the two given angles is 90°:

⇒ m∠ABD + m∠DBC = 90°

⇒ (8x - 28) + (4x + 10) = 90

⇒ 8x - 28 + 4x + 10 = 90

⇒ 8x + 4x - 28 + 10 = 90

⇒ 12x - 18 = 90

⇒ 12x - 18 + 18 = 90 + 18

⇒ 12x = 108

⇒ 12x ÷ 12 = 108 ÷ 12

⇒ x = 9

Substitute the found value of x into the expression for m∠DBC:

⇒ m∠DBC = 4x + 10

⇒ m∠DBC = 4(9) + 10

⇒ m∠DBC = 36 + 10

⇒ m∠DBC = 46°

Answer:

His estimate is reasonable

Step-by-step explanation:

1/10 + 6/10 = 7/10, which can be rounded to 1

1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 1

As you can see, 7/10 is very close to 1.

Hope this helps!

If a scatter plot displays data that shows a positive correlation, then the correlation coefficient will be closest to +1.

The correlation coefficient is a numerical measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.

Since the scatter plot displays data that shows a positive correlation, the correlation coefficient will be positive and closer to +1 than to 0 or -1. The exact value will depend on the strength of the correlation. If the data points are tightly clustered around a straight line, the correlation coefficient will be closer to +1, indicating a strong positive correlation. If the data points are more spread out, the correlation coefficient will be smaller, but still positive, indicating a weaker positive correlation.

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Answer:

x=6

Explanation:

Given the equation:

First, cross multiply:

Next, open the brackets:

Subtract 3x from both sides of the equation:

Add 6 to both sides of the equation:

Finally, divide both sides by 5:

The value of x is 6.

Answer:

B . 980 just trust me

Step-by-step explanation:

You set up proportions

Answer:

g(10)=-33, x=3

Step-by-step explanation:

g(x)=-4x+7. --------(1)

a) g(10)=?

since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x

g(10)=-4(10)+7

g(10)=-40+7

g(10)= -33

b.)find x if g(x)=-5. ---------(ii)

g(x)=-4x+7. we will place (I) in (ii)

g(x)=-5

-4x+7=-5

-4x=-5-7

-4x=-12

cancel the minus(-) sign in both sides

4x=12

x=12/4

x=3

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Answer:

I think C

Step-by-step explanation:

oh god sorry if you get this wrong im so sorry.

Answer:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

x  =  − 6

Step-by-step explanation:

I hope this helps! Have a nice day!

The answer is A: x = 22√3 / 2 and y = 11. We can simplify x by multiplying both the numerator and denominator by 2 to get x = 22√3.

A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed where the two shorter sides of the triangle meet. The side opposite to the right angle is called the hypotenuse, while the other two sides are called the legs.

The Pythagorean theorem is a fundamental relationship that applies to right-angle triangles. It states that the sum of the squares of the two shorter sides (legs) of a right-angle triangle is equal to the square of the hypotenuse. In other words, a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right-angle triangles are commonly used in mathematics, physics, engineering, and many other fields. They can be used to solve problems related to distances, heights, and angles, and are a fundamental building block in many geometric constructions.

The special properties of right-angle triangles also make them useful in practical applications, such as in construction, where they can be used to measure angles and distances accurately, and in navigation, where they can be used to calculate distances between two points using trigonometric functions.

In triangle ABC, we know that angle BAC is 30 degrees, and angle ABC is a right angle. Therefore, angle ACB is 60 degrees (since the angles in a triangle add up to 180 degrees).

We can use the sine and cosine ratios to find the values of x and y. Using the definition of sine and cosine:

sin(30) = opposite / hypotenuse

cos(30) = adjacent / hypotenuse

In this case, AB is the adjacent side to angle BAC, and AC is the hypotenuse. Therefore:

cos(30) = AB / AC

Substituting the given values, we get:

cos(30) = x / y

Solving for x, we get:

x = y cos(30)

Plugging in y = 11, we get:

x = 11 cos(30)

Using a calculator, we can find that cos(30) = √3 / 2, so:

x = 11 × √3 / 2

x = 11√3 / 2

Therefore, the answer is A: x = 22√3 / 2 and y = 11. We can simplify x by multiplying both the numerator and denominator by 2 to get x = 22√3.

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Answer:

Step-by-step explanation:

The visitor might be exactly 54 inches or above 54 inches.

Answer:

Step-by-step explanation:

Exponents are powers or indices. An exponential expression consists of two parts, namely the base, denoted as b and the exponent, denoted as n. The general form of an exponential expression is b n.

How to Subtract Exponents?

The operation of subtracting exponents is quite easy if you have a good understanding of exponents. In this article, you will learn the rules and how to apply them when you need to subtract with exponents.

But before we can embark on subtracting with exponents, let us remind ourselves some of the basic terms about exponents.What is an exponent?

Well, an exponent or power denotes the number of times a number is repeatedly multiplied by itself. For example, when we encounter a number written as, 53, it simply implies that 5 is multiplied by itself three times. In other words, 53 = 5 x 5 x 5 = 125The same format of writing exponents applies with variables.  Variables are represented by letters and symbols. For instance, when x is multiplied repeated by itself 3 times, then we write this as; x3. Variables are usually accompanied by coefficients. A coefficient is therefore an integer that is multiplied by variable.

For instance, in 2x3, the coefficient is the number 2 and x is the variable. When a variable has no number before it, the coefficient is always 1. This is also true when a number has no exponent. The coefficient of 1 is normally negligible, and therefore cannot be written with a variable.

Subtraction of exponents really does not involve any a rule. If a number is raised to a power. You simply compute the result and then perform the normal subtraction. If both the exponents and the bases are the same, you can subtract them like any other like terms in algebra. For example, 3y – 2xy = x y.

Subtracting exponents with the same base

Let’s explain this concept with the help of a few examples.

Example 1

23– 22 = 8 – 4 = 4

53 – 52 = 75 – 25 = 50

Subtract x 3 y 3 from 10 x 3 y 3

In this case the coefficients of exponents are 10 and 1

The variables are like terms and hence can be subtracted

Subtract the coefficients = 10 – 1

= 9

Thus, 10x 3y 3– x 3y 3 = 9 (xy)3

You can notice that, the subtraction of exponents with like terms is done by finding the difference of their coefficients.

Subtract 8x2 – 4x2

In this case, the variables 4x2 and 8x2 are like terms and their coefficients are 4 and 8 respectively.

= 8x2 – 4x2

= (8-4) x2.

= 4 x2

Work out (-7x) – (-3x)

Here, -7x and -3x are like terms

= -7x – (-3x)

= -7x + 3x,

= -4x.

15x – 4x – 12y – 3y

Subtract like terms

15x – 4x = 11x

12y – 3y = 9y

Thus, the answer is 11x – 9y.

Subtract (4x + 3y + z) – (2x + 3y – z).

These variables are like terms

(2x + 3y – z) – (4x + 3y + z)

Open the parenthesis;

= 2x + 3y – z – 4x – 3y – z,

Rearrange the like terms, and perform the subtraction

= 2x – 4x + 3y – 3y – z – z

= -2x + 0 – 2z,

= -2x – 2z

Subtracting exponents with different base

Exponents with different bases are computed separated and the results subtracted. On the other hand, variable with unlike bases can not be subtracted at all.  For, example subtraction of a and b can not be performed and the result is just a -b.

To subtract a positive exponents m and negative exponents n, we just connect both the terms by changing the subtraction sign to a positive sign and write the result in the form of m + n.

Therefore, subtraction of a positive and a negative unlike exponents m and -n = m + n.

Example 2

42 – 32 = 16 – 9 =7

Subtract: 11x – 7y -2x – 3x.

= 11x – 2x – 3x – 7y.

= 6x – 7y

Evaluate 3x2 – 7y2

In this case, the two exponents 3x 2 and 7y2 are unlike terms and so it will remain as it is.

Here 3x and 7y both are unlike terms so it will remain as it is.

Therefore, the answer is 3x2 – 7y2

Evaluate 15x – 12y – 11x

= 15x5 – 11x5 – 12y5

= 4x5 – 12y5

a) The line of symmetry for function f is x = 2, and the line of symmetry for function g is x= 1

b) The y-intercept of function f is is greater than the y-intercept of function g

c) Over the interval [2,4], the average rate of change of function f is less than the average rate of change of the function g

Here, we want to compare some important properties for both functions

We have it as the folllowing;

a) Line of Symmetery

The line of symmetery is that line that divides the quadratic graph into two equal parts of right and left

For the function f, the line of symmetry is x = 2 while the line of symmetry for function g is also x = 1

b) y-intercept

The y-intercept of the function refers to the point at which the graph/plot touches the y-axis

It is the point at which x is 0

For function f, the y-intercept is y = -5

For function g, the y-intercept is y = -6

c) Average rate of change

The average rate of change of a function over an interval [a,b] can be calculated using the formula;

According to thisn question, a is 2 while b is 4

For the function f; f(2) is -9 while f(4) is -5

For the function g; g(2) is -6 while g(4) is 2

So the average rate of change for the function f on the interval is;

For the function g, the average rate of change on the interval is;