Properties of real numbers -8+0=-8
What properties is that equation?

The number of bacteria  in an egg salad that is left out at room temperature is 256 option D.

The bacteria would double 4 times in 2 hours, so the total number of bacteria in the egg salad would be 256.

So we have 4 bacteria after 2 hours we have,

4 x 4 x 4 x 4 = 256 bacteria.

Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring.

Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilised in probability distribution, in which you will learn about the possible results of a random experiment. To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

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Complete question:

There are four bacteria in an egg salad that is left out at room temperature. After two hours, how many bacteria will be in the egg salad?

- 32

- 2048

- 8

- 256

Answer:

Deepika Deepika use 32% of his salary ^ housed and which is the amount of this is Monica is in driving on the monthly on the this is profit or loss we know don't don't know that we are what we do if x x is value of you don't know why I don't know it's your mistake I don't care

Answer:

x = 15

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

( leg of large Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse )

x² = 9 × 25 = 225 ( take the square root of both sides )

x = \(\sqrt{225}\) = 15

The age that she must work till she is qualified to receive Social Security benefits when she retires is: 56 years

Social Security benefits provide partial replacement income for retired beneficiaries and disabled persons, as well as their spouses, children and survivors.

To be eligible for Social Security benefits, you must be enrolled in the Social Security program and accumulate 40 credits while employed.

Benefits are based on your income history, year of birth, and age at which you began applying for Social Security.

If your spouse is unemployed or has not reached the required number of credits, you can receive benefits according to your spouse's work performance.

Benefits may likely be taxed based on the specific income and tax return status.

She will be required to earn a total of 40 credits in order to qualify to be able to receive social security benefits, due to the fact that she earns the maximum number of 4 credits per year, she therefore has to work for at least a minimum of ten years or until at least she is 56.

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Answer:

y= -1/3x + 1

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y= -1/3x + 1

The bride and groom can form 252 different groups of five people from the total of 10 people at the rehearsal dinner, as they need to assign them to two tables of five people each.

To determine the number of different groups of five people that can be formed, we can use the concept of combinations. In this scenario, we have 10 people who need to be divided into two groups of five people each.

The number of ways to choose five people out of 10 can be calculated using the combination formula. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where n represents the total number of people and r represents the number of people to be chosen. In this case, n = 10 and r = 5.

Plugging these values into the formula, we get:

C(10, 5) = 10! / (5! * (10 - 5)!)

= (10 * 9 * 8 * 7 * 6 * 5!) / (5! * 5 * 4 * 3 * 2 * 1)

= (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)

= 252

Therefore, the bride and groom can form 252 different groups of five people from the total of 10 people at the rehearsal dinner. This means that there are 252 distinct ways to divide the 10 people into two tables of five people each, providing flexibility in creating diverse groups for the dinner.

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The value of x in the interval [1, 1.5] for which f(x) = 1 is approximately 1.408.

To find the value of x in the interval [1, 1.5] for which the function f(x) = 4x³ - x - 7 takes the value 1, we can use a numerical method like the bisection method or Newton's method.

Let's use the bisection method to solve this problem.

The bisection method works by repeatedly bisecting the interval and narrowing it down until we find a solution within a desired tolerance.

In this case, we want to find a value of x such that f(x) = 1. We'll start with the interval [a, b] = [1, 1.5] and iteratively narrow it down.

Let's perform the iterations using the bisection method:

Iteration 1:

a = 1, b = 1.5

c = (a + b) / 2 = (1 + 1.5) / 2 = 1.25

f(c) = 4(1.25)³ - 1.25 - 7 ≈ -1.422

Since f(c) is negative, the solution lies in the right half of the interval [1.25, 1.5].

Iteration 2:

a = 1.25, b = 1.5

c = (a + b) / 2 = (1.25 + 1.5) / 2 = 1.375

f(c) = 4(1.375)³ - 1.375 - 7 ≈ -0.287

Since f(c) is still negative, the solution still lies in the right half of the interval [1.375, 1.5].

Iteration 3:

a = 1.375, b = 1.5

c = (a + b) / 2 = (1.375 + 1.5) / 2 = 1.4375

f(c) = 4(1.4375)³ - 1.4375 - 7 ≈ 0.360

Since f(c) is now positive, the solution lies in the left half of the interval [1.375, 1.4375].

Iteration 4:

a = 1.375, b = 1.4375

c = (a + b) / 2 = (1.375 + 1.4375) / 2 = 1.40625

f(c) = 4(1.40625)³ - 1.40625 - 7 ≈ -0.467

Since f(c) is still negative, the solution still lies in the right half of the interval [1.40625, 1.4375].

Continuing this process, we can narrow down the interval further until we reach the desired tolerance.

After performing several more iterations, we find that the value of x in the interval [1, 1.5] for which f(x) = 1 is approximately 1.408.

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Using system of linear equations he will require 20kg of 15% copper and 30kg of 70% copper to produce an alloy of 48% in 50kg

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

To solve this problem, we need to write a system of linear equations and find the equivalent amount of the metal required to make the desired amount of the alloy.

0.15x + 0.7y = 0.48(50) ..eq(i)

0.15x + 0.7y = 24 ...eq(i)

x + y = 50 ...eq(ii)

solving equation (i) and (ii)

x = 20, y = 30

He needs 20kg of 15% copper and 30kg of 70% copper to get 48% of 50kg of alloy.

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Answer:

Interval Notation:  ( − ∞ , 3 ) ∪ ( 3 , ∞ )

Set-Builder Notation:  { x | x ≠ 3 }

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

54 m squared

Step-by-step explanation:

If you look at it from a birds eye view, the post being in the middle, it's just a 9m*6m rectangle of feeding area.

To find the area that the sheep can feed on, we need to find the area of circle. The area that the sheep can feed on is  254.57 square meters.

We can approach this problem by drawing a diagram:

                 fence

    o------------|------------o

                  |

                  |

                  |

                  |

                  |

                  | 9m

                  |

                  |

                  |

                  |

                  |

                  |

                  |

                  o sheep

               post (6m)

The sheep is tethered to the post, and the rope has a length of 9 meters. The post is 6 meters away from the fence. The sheep can move around in a circle whose center is at the post, and whose radius is the length of the rope.

To find the area that the sheep can feed on, we need to find the area of this circle. The formula for the area of a circle is:

A = πr^2

where A is the area, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius.

In this case, the radius is 9 meters, so we have:

A = π(9)^2

 = π(81)

 ≈ 254.57 square meters

Therefore, the area that the sheep can feed on is approximately 254.47 square meters.

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The value of a is 50, the value of b is 7, and the value of c is 1. Hence, the unknown constants a, b, and c such that aA+bB+cC=k^m are a=50, b=7, and c=1.

Given that:A = 2i^+3j^+k^m, B = i^+4j^−2k^m, and C = −3i^−j^m

We are to find the unknown constants a, b, and c such that aA+bB+cC=k^m.

So we can write the equation as (a, b, c) = k^m (2i^+3j^+k^m) + k^m (i^+4j^−2k^m) + k^m (−3i^−j^m)

Let us solve the equation (a, b, c) = k^m (2i^+3j^+k^m) + k^m (i^+4j^−2k^m) + k^m (−3i^−j^m)

Given expression can be written as (2k^m)i^ + (3k^m+4k^m-1)i^ + (-2k^m-3k^m) i^ = k^m i^ Now we know that k^m i^ = ai.

Thus, a= 2k^mIn the same way, we can get the values of b and c as follows: (3k^m+4k^m-1)j^ = bj.

Thus, b = 7k^m/25And, (-2k^m-3k^m) k^m j^ = cj^m.

Thus, c = k^m/25

Therefore, the value of a is 2k^m, the value of b is 7k^m/25, and the value of c is k^m/25.

Now, given k^m as the coefficient of the vectors, we can equate it to 1 to get the value of k^m.

Let k^m = 25. Now, putting this value in a, b, and c, we get:

a = 2k^m = 2 * 25

= 50, b

= 7k^m/25

= 7 * 25/25 = 7, and c = k^m/25

= 25/25

= 1

Therefore, the value of a is 50, the value of b is 7, and the value of c is 1.Hence, the unknown constants a, b, and c such that aA+bB+cC=k^m are a=50, b=7, and c=1.

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Answer:

23/24

Step-by-step explanation:

I don't have an explanation take it or leave it.

By using the concept of confidence interval, it can be concluded that-

Confidence interval = (0.1954, 0.2286)

We are 95 % confident that the true proportion of working adult who

were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years falls within this interval

Second option is correct

What is confidence interval?

Suppose there is a parameter which is unknown. Confidence interval will give the range of this unknown parameter.

Let the unknown  parameter be θ,  A confidence interval for the parameter θ is an interval (u, v)

where P(u < θ  < v) = 1 - α, where P is the probability

α is called level of significance

Total number of working adults = 2305

Number of working adults surveyed = 489

Proportion of sample surveyed = \(\frac{289}{2305}=\) 0.212

Standard error = \(\sqrt{\frac{0.212 \times ( 1- 0.212)}{2305}} = 0.0085\)

At 95% confidence interval, z value = 1.96

Margin of error = 1.96 \(\times\) 0.0085 = 0.0166

Lower bound for the confidence interval = 0.212 - 0.0166 = 0.1954

Upper bound for the confidence interval = 0.212 + 0.0166 = 0.2286

Confidence interval = (0.1954, 0.2286)

Now since this is a problem on confidence interval, so a concept of confidence will come into question.

So, we are 95 % confident that the true proportion of working adult who

were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years falls within this interval

Second option is correct

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Complete Question

The complete question has been attached

Answer:

-7x + 7y - 14

Step-by-step explanation:

To draw the net of a regular triangular prism with a base edge of 4 cm and a height of 5 cm, follow these steps:

1. Draw the base: Draw an equilateral triangle with all sides measuring 4 cm each. This will be the base of your triangular prism.

2. Draw the lateral faces: From each vertex of the equilateral triangle, draw a rectangle with one side being the height of the prism (5 cm) and the other side equal to the base edge (4 cm).

You should have three rectangles, each connected to one side of the equilateral triangle.

3. Draw the second base: Connect the three free vertices of the rectangles to form another equilateral triangle with sides measuring 4 cm each.

This will be the top of your triangular prism.

4. Separate and flatten the shape: Finally, to create the network of the triangular prism, imagine unfolding the prism and laying it flat.

The net will consist of two equilateral triangles (the bases) and three rectangles (the lateral faces) connected to each other.

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Answer:

5

Step-by-step explanation:

slopes of the parallel lines are always same this line has slope five

because equation in y intercept form is y=mx+b

where m is the slope.

so the slope of the new line will be five

Answer:

√3 + 24/5 or 6.532

Step-by-step explanation:

I hope this helps.

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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The correct option for the demand requirement constraint in a production scheduling LP is option (c): beginning inventory + production - ending inventory = demand.

In a production scheduling LP, the demand requirement constraint represents the balance between the available inventory and the demand for the product. The constraint ensures that the production and inventory levels are sufficient to meet the specified demand.

Option (c) represents this relationship accurately by stating that the beginning inventory, production, and ending inventory, when subtracted from each other, should equal the demand. This equation reflects the concept of maintaining a balance between the production output and inventory changes to meet the demand

Option (a) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Option (b) is also incorrect because it uses the equality (=) symbol, which implies an exact balance between the inventory and demand, disregarding the changes in inventory.

Option (d) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Therefore, option (c) is the correct representation of the demand requirement constraint in a production scheduling LP.

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The statement ''A frequency polygon is a very useful graphic technique when comparing two or more distributions'' is true because a frequency polygon is a very useful graphic technique for comparing two or more distributions.

A frequency polygon is a line graph that shows the distribution of a dataset.

It is created by plotting the frequency of each data value or interval on the y-axis and the corresponding values or intervals on the x-axis, and then connecting the points with line segments.

By using frequency polygons, it becomes easy to compare the shapes and spread of two or more distributions. We can overlay different frequency polygons on the same graph and compare them.

This helps to identify similarities and differences between the data sets.

For instance, frequency polygons can help identify which data set has a higher mean or median, and which distribution has a greater variance.

In summary, frequency polygons are a useful visual tool for comparing distributions and identifying patterns in data.

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C. Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the median. Add "whiskers" extending to the low and high values.

Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the median. Add "whiskers" extending to the low and high values. Quartiles are three values ​​that divide the statistical data into four parts, each containing the same observation. A quarter is a type of quantity. First quartile: Also called Q1 or lower quartile. Second quartile: Also called Q2 or median. Third quarter: Also called Q3 or upper quarter.

Quartiles are values ​​that divide a list of numeric data into quarters. The three-quarter median measures the center of the distribution and shows the data near the center. The lower half of the quartile represents only half of the dataset below the median, and the upper half represents the remaining half above the median. In summary, quartiles describe the distribution or distribution of a data set.

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Answer:

50.24

Step-by-step explanation:

Area = pie * r^2

Radius = 4 (half a diameter)

3.14 * 4^2

3.14 * 16

50.24

Two students using the same piece of glassware may not have the exact same measurement.

While the same glassware provides a consistent measuring tool, variations in the students' measurement techniques, environmental conditions, and inherent limitations of the glassware can lead to differences in the obtained measurements.

Factors such as parallax errors, variations in reading techniques, and differences in the precision of the measuring instrument can all contribute to variations in measurements.

Additionally, small imperfections in the glassware, such as scratches or irregularities, can affect the accuracy of the measurement. These imperfections may cause slight variations in the volume or capacity being measured.

To minimize discrepancies, it is important for students to follow proper measurement techniques, ensure accurate calibration of the glassware, and consider potential sources of error.

By adhering to standardized procedures and using precise measurement techniques, students can aim to obtain measurements that are as consistent and reliable as possible.

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Answer:

try C=5B

Step-by-step explanation:

Step-by-step explanation:

(A) (In the fig. triangle represented by small triangle with angle of elevation 30° and height h1 ) ( Using this explanation since the figure is not marked)

\(tan30 = \frac{h1}{40} \)

\(h1 = \frac{40}{\sqrt{3} } m\)

(B) (In the fig. triangle represented by small triangle with angle of depression 58° and height h2 )

\(tan58 = \frac{h2}{40} \)

\(h2 = 64m\)

(C)

\(Height \: of \: Building \: A = h2 = 64m\)

\(Height \: of \: Building \: B = h1+h2 = (64 + \frac{40}{ \sqrt{3} } )= 87m\)

ii) Using laws of logic [(r ∧ ¬q) ∨ (p ∨ r)] = [(r ∨ p) ∨ (r ∨ ¬q)] (using distributive law)

i) Drawing a circuit that represents the given logical expression

We need to draw a circuit that represents the given logical expression.

Let's represent the variables p, q, and r with the help of NOT, AND and OR gates.

The given expression is [(r ∧ ¬q) ∨ (p ∨ r)].

The NOT gate negates the input, and it has one input. The output is equal to 1 when the input is 0, and the output is equal to 0 when the input is 1.

The AND gate has two inputs, and the output is equal to 1 if both inputs are 1.

If either or both of the inputs are 0, then the output is equal to 0.

The OR gate has two inputs, and the output is equal to 1 if either or both inputs are 1.

If both inputs are 0, then the output is equal to 0.

The circuit that represents the given expression is shown below:

ii) Using laws of logic to simplify the expression and stating the name of the laws used

To simplify the given expression, we will use the distributive law of Boolean algebra.

The distributive law states that a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c) and a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c).

Now, [(r ∧ ¬q) ∨ (p ∨ r)] = [(r ∨ p) ∨ (r ∨ ¬q)] (using distributive law)

We have simplified the given expression using the distributive law.

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Answer:

\( \sqrt{3} \)

Step-by-step explanation:

- since it's an isosceles triangle, the other two angle is the same, so 180-90÷2=45

- i use SOH, CAH, TOA rule and in this case, i use SOH.

Answer:

x = √3

Step-by-step explanation:

Let us use the Pythagoras theorem to find the value of x.

Accordingly,

x² + x² = (√6)²

2x² = 6

Divide both sides by 2.

x² = 3

Put square roots on both sides.

x = √3