Ada, Betty, Chris, and David have $45 in total. If Ada gets $2 from Betty, Chris triples his money, and David's money is cut by half, four of them have the same amount. Initially, Ada has??

Answer:

64 units³

Step-by-step explanation:

V =  S³

V =  4³

V = 64 Units³

Truth values (a) False                                                                                                           (b) False                                                                                                           (c) False                                                                                                            (d) True

Here is the translation of these quantifications into English and determine its truth value. a) ∀x∈R (x^2 = -1)
Translation: For all x belonging to the set of real numbers, x squared equals -1.
Truth value: False. No real number squared can equal a negative value.
b) ∃x∈Z (x^2 = 2)
Translation: There exists an x belonging to the set of integers such that x squared equals 2.
Truth value: False. No integer squared can equal 2.
c) ∀x∈Z (x^2 > 0)
Translation: For all x belonging to the set of integers, x squared is greater than 0.
Truth value: False. When x equals 0 (x=0), x squared equals 0, which is not greater than 0.
d) ∃x∈R (x^2 = x)
Translation: There exists an x belonging to the set of real numbers such that x squared equals x.
Truth value: True. There are two real numbers that satisfy this condition: x=0 and x=1.

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Answer:

\(x=7\)

Step-by-step explanation:

\(\sqrt{3x+8}=\sqrt{4x+1}\)

Square both sides:

\((\sqrt{3x+8})^{2} =(\sqrt{4x+1})^{2}\)

\(3x+8=4x+1\)

Subtract 8 from both sides:

\(3x+8-8=4x+1-8\)

\(3x=4x-7\)

Subtract 4x from both sides:

\(3x-4x=4x-7-4x\)

\(-x=-7\)

Divide both sides by -1:

\(\frac{-x}{-1}=\frac{-7}{-1}\)

\(x=7\)

The probability of the sum of the two recorded numbers being less than 4 is $\frac{3}{4}$.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4:

1) both numbers are 1 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$)

2) one number is 1 and the other is 2 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$).

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The probability of the sum of the two recorded numbers being less than 4 is \(\frac{3}{4}\).

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.

This is because there are three possible scenarios in which the sum of the two numbers can be less than 4.

1) both numbers are 1 (probability of \(\frac{1}{4}\) × \(\frac{1}{4} = \frac{1}{16}\))

2) one number is 1 and the other is 2 (probability of \(\frac{1}{4}\) × \(\frac{1}{4} =\) \(\frac{1}{16}\))

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Step-by-step explanation:

Find the rule:

2, -6, 18, ...

To get to -6, multiply by -3.

To get to 18, multiply by -3.

The rule is to multiply by -3.

Find the 7th term:

Multiply 18 by -3.

\(-18 \times 3 = -54\)

-54 is the 4th term.

Multiply -54 by-3.

\(-54 \times -3 = 162\)

162 is the 5th term.

Multiply 162 by -3.

\(162 \times -3 =-486\)

-486 is the 6th term.

Multiply -486 by -3.

\(-486 \times -3 = 1458\)

1458 is the 7th term.

Yes she is correct, because 810 km is approximately 500 miles

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

The distance between Cale and Johannesburg is 810 km.

1 mile is converted as 1.609km

There 1km = 1/1.609 miles

810 km = 1/1.609 × 810

= 503.4 miles

If this value is approximated to the nearest hundred,then it will be

500 miles

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Step-by-step explanation:

Notice that 1km = 1000m = 100000cm.

Therefore 21.7km = 2170000cm.

Answer:

2170000 cm

Step-by-step explanation:

21.7 k/m × 10³ × 10²

To determine the scores Jane needs to achieve on the Project and Final Exam in order to get an A in the class (with a total weighted score of 90).

We can calculate the weighted scores for each component of the course work based on the given weights and Jane's scores without the Project and Final Exam.

First, let's calculate the weighted scores for the components of the course work that Jane has already completed:

Homework weighted score = (0.2) * (92 + 90 + 88 + 80) = 0.2 * 350 = 70

Discussion Forum weighted score = (0.18) * (92 + 88 + 85 + 92 + 90) = 0.18 * 447 = 80.46

Midterm Exam weighted score = (0.22) * (88) = 0.22 * 88 = 19.36

Now, let's calculate the minimum scores Jane needs to achieve on the Project and Final Exam to reach a total weighted score of 90:

Total weighted score needed for an A = 90

Score needed for Project = (0.15 * Total weighted score) - (Homework weighted score + Discussion Forum weighted score + Midterm Exam weighted score)

Score needed for Project = (0.15 * 90) - (70 + 80.46 + 19.36) = 13.5 - 169.82 = -156.32

To get a positive score for the Project, Jane needs to score higher than -156.32. However, it is not realistic to score a negative value, so we will assume Jane needs to score 0 on the Project.

Score needed for Final Exam = (Total weighted score) - (Homework weighted score + Discussion Forum weighted score + Midterm Exam weighted score + Project score)

Score needed for Final Exam = 90 - (70 + 80.46 + 19.36 + 0) = 90 - 169.82 = -79.82

Similarly, to get a positive score for the Final Exam, Jane needs to score higher than -79.82. Again, it is not realistic to score a negative value, so we will assume Jane needs to score 0 on the Final Exam.

Therefore, Jane needs to score at least 0 on the Project and 0 on the Final Exam to get an A in the class with a total weighted score of 90.

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The electric field (E-field) associated with the given potential function V(x, z) = 4bx^2 + 4az^3 - 3cz^3 is E = -8bx i - (12az^2 - 9cz^2)j.

To find the electric field (E-field) associated with the given potential function, we need to calculate the negative gradient of the potential. The E-field is given by the following formula:

E = -∇V

Where ∇ is the gradient operator. In this case, the potential function V(x, z) is defined as:

V(x, z) = 4bx^2 + 4az^3 - 3cz^3

To calculate the E-field, we need to take the partial derivatives of V with respect to x and z and then apply the negative sign. Let's calculate each component separately:

Partial derivative with respect to x (dV/dx):

dV/dx = 8bx

Partial derivative with respect to z (dV/dz):

dV/dz = 12az^2 - 9cz^2

Now, we can write the E-field vector as:

E = -∇V = -(dV/dx)i - (dV/dz)j

Substituting the calculated partial derivatives, we have:

E = -8bx i - (12az^2 - 9cz^2)j

Therefore, the electric field (E-field) associated with the given potential function V(x, z) = 4bx^2 + 4az^3 - 3cz^3 is:

E = -8bx i - (12az^2 - 9cz^2)j

Note that the positive constants b and c are included in the E-field expression.

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Answer:

It should be -3

Step-by-step explanation:

Answer:

42°

Step-by-step explanation:

\(m\angle ABD + m\angle DBC = m\angle ABC\\

2x + 2x - 3 = 81\degree \\

4x - 3 = 81\degree \\

4x = (81+3)\degree \\

4x = 84\degree \\

x = \frac{84}{4}\\

x = 21\\\\

m\angle ABD = 2x = 2*21\degree = 42\degree \)

Answer:

∠AEC ≅ ∠BED by vertical angles theorem

Answer:

Answer:

∠AEC ≅ ∠BED by vertical angles theorem

Step-by-step explanation:

Answer:

Step-by-step explanation:

Marco is incorrect because a function is a relation for which each input has a different output. An example of a function is y=2x each input x has a different output y.

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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The given statement, "We can use the normal distribution to approximate the sampling distribution of the average (\(\bar X\)) for a small sample (n<30) even if our sample has clear outliers." is false.

Several random samples of a predetermined size are taken from the same population to generate a sampling distribution, which is a sort of probability distribution. You can better understand how a sample statistic fluctuates from sample to sample by using these distributions.

The given statement is false because when the sample size is small (n < 30) and the data have clear outliers, the normal distribution may not be a suitable approximation for the sampling distribution of the average (\(\bar X\)). In such cases, the presence of outliers can significantly affect the distribution, causing it to deviate from a normal distribution.

For small samples with outliers, it is generally recommended to use alternative methods or non-parametric tests that do not assume a specific distribution. These methods take into account the non-normal nature of the data and provide more robust and reliable results.

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1. L , M and N are collinear

2. Given

3. LM = MN

4. Bisector theorem

There were 2484 patrons in the theatre that night.

Let n represent the overall number of theatergoers that evening.

Let g represent the number of attendees in the gold seating, s represent the attendees in the silver seating, r represent the attendees in the red seating, and b represent the attendees in the black seating.

Consequently, n = g + s r b.

g = n because of the theatre goers are seated in the gold section.

r + b = n because of the customers are either in the red or the black seating.

The answer is obvious: b = 138.

As a result, r + b = n changes to

r + 138 = n, or r =  n - 138.

Since

n = n + 3(n - 138) + (n - 138) + 138

n = n + n - 414 + n - 138 + `138

n = n + n - 414

n = n - 414

n = 414

n = 2484

Therefore, there were 2484 patrons in the theatre that night.

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The solution to the equation is x = 105/14 and y = -27/2

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution.

We use different methods to solve simultaneous equations. Some of the common methods are:

By substitution method

-7x + -5y = 15 ----- 1

7x + 3y = 12 ----- 2

from equation 1

7x = -15 -5y ----- 3

substitute 7x in equation 2

-15 - 5y + 3y = 12

-2y = 12 + 15

-2y = 27

y = -27/2

To find x, substitute y in equation 3

7x = -15 - 5(-27/2)

7x = -15 + 135/2

Multiplying both sides by 2

14x = -30 + 135

14x = 105

x = 105/14

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The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

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The value x in the secant line using the Intersecting btheorem is 19.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the image;

External line segement of the first secant line = 8

First sectant line segment = ( x + 8 )

External line segement of the second secant line = 9

First sectant line segment = ( 15 + 9 )

Using the Intersecting secants theorem:

8 ×  ( x + 8 ) = 9 × ( 15 + 9 )

Solve for x:

8x + 64 = 135 + 81

8x + 64 = 216

8x = 216 - 64

8x = 152

x = 152/8

x = 19

Therefore, the value of x is 19.

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Answer:

Infinite

Step-by-step explanation:

Hope that this helps!

Answer:

Step-by-step explanation:

2 or 3 im not v sure tho

Answer:

X=5

Y=3

(5,3)

Step-by-step explanation:

Solve using substitution

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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The type of pay which is modeled in the image attached below is: D) piece rate.

Money or something paid for a purpose and especially as a salary or wage

The types of pay.

In Mathematics, there are four 5) different types of pay and these include:

The different types of compensation include:

Salary.

Hourly Wages.

Sales Commission.

Tips.

Stock Options.

Bonuses.

Incentive Pay.

Other Variable Pay.

Salary

Commission

Bonuses

Piece rate

Method of wage payment that remunerates the employees on the basis of quantity they produced is known as piece rate.

Plucking tea

The number of tee-shirts produced.

Pruning fruit trees

Sorting second-hand clothes (garments)

Hence the graph of a piece rate model is characterized by a straight line with the slope upwards as represented in the image attached.

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Answer:

5 shirts

Step-by-step explanation:

Y=12x+3 equation 1

y=8x+23 equation 2

12x+3=8x+23 substituting y value will cause equations to equal

4x=20

x=5 shirts

check answer

y=12x+3

y=12(5)+3

y=60+3

y=63

y=8x+23

y=8(5)+23

y=40+23

y=63

If the derivative of f' is bounded on interval i, then f satisfies a Lipschitz condition on i.

To prove this, let's consider two points x and y in interval i with x < y. By the mean value theorem, there exists a point c between x and y such that f'(c) = (f(y) - f(x))/(y - x). Since f' is bounded on i, we can say that |f'(c)| ≤ M, where M is the bound on f'. Therefore, |f(y) - f(x)| ≤ M|y - x|, which satisfies the Lipschitz condition with Lipschitz constant M.

Hence, if the derivative of f' is bounded on i, f satisfies a Lipschitz condition on i.

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Answer:

a. AD and DAB are not congruent

b. point E is 1.5 from point B

c. Yes, your friend is correct

Step-by-step explanation:

(a) tan(C) = opp/adj = 3/4 so C is 36.87 or roughly 37 degrees

so A = 90 - 37 = 53

tan(DAB) = opp/adj = (4/2)/3 = 2/3 so DAB is 33.7 or roughly 34 degrees

so CAD = 53 - 34 = 19

so CAD and DAB are not congruent

(b) angle bisector is the line or line segment that divides the angle into two equal parts. It intersects BC at E so CAE = EAB = 53/2 = 26.5

so tan(26.5) = BE/3

=> BE = 3 x tan(26.5) = 3(0.499) = 1.497 or roughly 1.5

(c) a line from E perpendicular to AC will intersect AC at F, which create angle EFA or EFC a 90 degree angle

Now we have 2 right triangles AEB and AEF with the same hypotenuse which is AE and the same angles at EAF and EAB which means EB and EF are congruent

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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