Evaluate: (7.88)(-1.5)​

Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

Answer:

The HCF of these polynomials is (p+2q).

Step-by-step explanation:

First of all, we need to factorize each polynomial:

a) \(p^{2}+4pq+4q^{2}\)

\(=p^{2}+4pq+(2q)^{2}\)

\(=(p+2q)^{2}\)

b) \(p^{4}+8pq^{3}\)  

\(=p(p^{3}+8q^{3})\)

\(=p(p^{3}+(2q)^{3})\)

\(=p(p+2q)(p^{2}-2pq+(2q)^{2})\)

c) \(3p^{4}-10p^{2}q^{2}+p^{3}q\)

\(=p^{2}(3p^{2}-10q^{2}+pq)\)

\(=p^{2}(3p-5q)(p+2q)\)

Therefore, the HCF of these polynomials is (p+2q).

I hope it helps you!

Answer:

Step-by-step explanation:number 12 is 210 to 150. Number 11 is 12 to 15. Number 13 is 20/28. Number 16 is 40 to 200. Number 15 is 30 to 54. Number 14 is 1/3 to 90.

Number 7 is 10/14. Number 8 is 5/4. Number 9 is 3/5 And number 10 is 9/24.

If the correlation between two variables was equal to 0, the scatterplot between these two variables would be represented as a graphical representation of the relationship between two variables

If the correlation between two variables is equal to 0, it means that there is no linear relationship between the two variables. In other words, as one variable changes, the other variable does not systematically change in any particular direction.

In a scatterplot, which is a graphical representation of the relationship between two variables, this would be represented by a random scattering of data points with no discernible pattern or trend. The points would be evenly distributed throughout the plot, without any apparent clustering in one direction or another.

Additionally, the line of best fit, which is used to describe the overall trend of the data, would be a horizontal line with a slope of zero, indicating that there is no relationship between the two variables.

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In general, different refrigerants should not be mixed or recovered into the same cylinder.

Different refrigerants have unique chemical compositions and properties that make them incompatible with one another. Mixing different refrigerants can lead to unpredictable reactions, loss of refrigerant performance, and potential safety hazards. Therefore, it is generally recommended to avoid recovering different refrigerants into the same cylinder.

When recovering refrigerants, it is important to use separate recovery cylinders or tanks for each specific refrigerant type. This ensures that the refrigerants can be properly identified, stored, and recycled or disposed of in accordance with regulations and environmental guidelines.

The refrigerant recovery process involves capturing and removing refrigerant from a system, storing it temporarily in dedicated containers, and then transferring it to a proper recovery or recycling facility. Proper identification and segregation of refrigerants during the recovery process help maintain the integrity of each refrigerant type and prevent contamination or cross-contamination.

To maintain the integrity and safety of different refrigerants, it is best practice to recover each refrigerant into separate cylinders. Mixing different refrigerants in the same cylinder can lead to complications and should be avoided. Following proper refrigerant recovery procedures and guidelines helps ensure the efficient and environmentally responsible management of refrigerants.

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The number of different refrigerants that may be recovered into the same cylinder is zero.

When it comes to refrigerants, it is important to understand that different refrigerants should not be mixed together. Each refrigerant has its own unique properties and should be handled and stored separately. mixing refrigerants can lead to chemical reactions and potential safety hazards.

The recovery process involves removing refrigerants from a system and storing them in a cylinder for proper disposal or reuse. During the recovery process, it is crucial to ensure that only one type of refrigerant is being recovered into a cylinder to avoid contamination or mixing.

Therefore, the number of different refrigerants that may be recovered into the same cylinder is zero. It is essential to keep different refrigerants separate to maintain their integrity and prevent any adverse reactions.

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The Domain of the function is : (−∞,∞).

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X .

Hence, The Domain of the function is : (−∞,∞).

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The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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To find the absolute maximum value of the function g(x)=−2x^2/x−1 over the closed interval [−3,5], we will use the Extreme Value Theorem (EVT).EVT states that if a function is continuous over a closed interval, then the function will have an absolute maximum and minimum over that interval.

So, for finding the absolute maximum value of the given function, we will follow these steps:Step 1: Check the function's domain.We know that the denominator of the function g(x) is x - 1, so the function is not defined at x = 1. However, the closed interval we are working with is [-3, 5], which does not include x = 1. Hence, the function is defined over this interval.Step 2: Find the critical points of the functionTo find the critical points, we need to differentiate the function g(x) and equate it to zero:g'(x) = (-4x(x-1) + 2x^2)/(x-1)^2= 2x(3-x)/(x-1)^2=0So, the critical points of g(x) are x = 0 and x = 3.Step 3: Find the end-point values of the functiong(-3) = -2/5, g(5) = -50/9.

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The specific numerical solution will depend on the number of firms in the market and their behavior.

In a Stackelberg version of monopolistic competition, there is a leader firm that sets its output first, and all the other firms in the market act as followers and choose their outputs simultaneously.

Suppose there are "n" firms in the market, with the first firm denoted as the leader. Let's assume that each firm has a constant marginal cost of $10 per unit. Then, the leader firm's profit-maximizing output level can be found by solving the following problem:

max (30-Q1-Q2-...-Qn)Q1 - 10Q1

subject to Q1 >= 0

where Q1 is the output level of the leader firm, and Q2, Q3, ..., Qn are the output levels of the follower firms.

Taking the first-order condition by differentiating with respect to Q1 and setting it equal to zero, we get:

d/dQ1 [(30-Q1-Q2-...-Qn)Q1 - 10Q1] = 0

Simplifying this expression, we get:

30 - Q1 - Q2 - ... - Qn - 2Q1 = 0

Solving for Q1, we get:

Q1 = (30 - Q2 - ... - Qn)/3

This equation gives us the leader firm's profit-maximizing output level as a function of the follower firms' output levels.

Now, let's consider the follower firms' profit-maximizing output levels. Since each follower firm is a price-taker, its profit-maximizing output level can be found by equating marginal cost to market price, which is equal to the market demand curve divided by the total quantity produced by all firms in the market. Therefore, the profit-maximizing output level of the jth follower firm can be expressed as:

Qj* = (1/n) * (30 - Q1 - Q2 - ... - Qj-1 - Qj+1 - ... - Qn - 10)

where Qj* is the follower firm's profit-maximizing output level, and j = 2, 3, ..., n.

Using these expressions for the leader and follower firms' profit-maximizing output levels, we can solve for the equilibrium outputs and profits in the Stackelberg version of monopolistic competition. However, the specific numerical solution will depend on the number of firms in the market and their behavior.

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Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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Answer:

Regular polygon of 10 sides or 10-gon

Explanation:

The angle of rotation symmetry is equal to

θ = 360/n

Where n is the order of rotation. In a regular polygon, the order of rotation for symmetry is the number of sides.

In this case, we can replace θ by 36 degrees and solve the equation for n

36 = 360/n

n = 360/36

n = 10

Therefore, the shape of rotation should be a regular polygon of 10 sides.

Answer:

2/9 times

Step-by-step explanation:

This is because 2/5 divided by 9/10 = 10/45 which if we simplify it we get 2/9  so that's why 2/9 is the right answer.  

Using the simplex method, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

To solve the linear program using the simplex method, we start by converting the problem into standard form with all constraints in the form of inequalities and non-negative variables. The initial tableau for the problem is as follows:

 |   x1  |   x2  |   s1   |   s2   |   b   |

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

z |  -3   |   6   |   0    |   0    |   0   |

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

s1|   5   |   7   |   1    |   0    |   35  |

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

s2|  -1   |   2   |   0    |   1    |   2   |

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

Next, we perform the simplex iterations to improve the objective function value. After performing the necessary row operations, we arrive at the final tableau:

 |   x1  |   x2  |   s1   |   s2   |   b   |

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

z |   0   |   1   |  3/2   |  -1/2  |   14  |

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

s1|   0   |   0   |   4    |   3    |   5   |

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

s2|   1   |   0   |  -1/2  |   5/2  |   3   |

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

From the final tableau, we can see that the optimal solution is z = 14, with x1 = 0 and x2 = 5. The decision variable x1 is at its lower bound, indicating that it is non-basic. Therefore, there are no alternative optimal solutions in this case.

In summary, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

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Answer:-0.2 or -0.16

Step-by-step explanation:

Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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Hi there!

\(\large\boxed{k> 6.125}\)

We can use discriminants to determine the value of k for which the equation would have complex solutions. (Those involving i)

If b² - 4ac < 0, then the equation will have complex solutions. Therefore:

Plug in the given values of b and a to solve:

7² - 4(2)(k) < 0

Simplify:

49 - 8k < 0

Solve the inequality:

49 < 8k

6.125 < k

k > 6.125. Anything greater than 6.125 would result in complex solutions.

The expected value for this game is $0.80.

The expected value for this game is calculated using  the formula below:

Data given:

If you pull a green candy you will have to pay them $1.00 and there is a 0.4 probability that you pull a green candy

If you pull a red candy you will have to pay them $2.00 and there is a 0.6 probability that you pull a red candy.

Expected value = (0.6 * $2.00) + (0.4 * -$1.00)

Expected value  = $1.20 - $0.40

Expected value = $0.80

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Answer:

(x + 1)(3x - 10)

Step-by-step explanation:

Given

3x² - 7x - 10

Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = - 7

The factors are + 3 and - 10

Use these factors to split the x- term

3x² + 3x - 10x - 10 ( factor the first/second and third/fourth terms )

3x(x + 1) - 10(x + 1) ← factor out (x + 1) from each term

(x + 1)(3x - 10), thus

y = (x + 1)(3x - 10) ← in factored form

a. The number of student surveyed is = 12 + 7 - 4 + 47 = 62

b. The number of student that are math major but not biology major = 7

c. The number of student that are neither math major nor biology major = 47

d. The number of student that are both math and biology major = 4

Answer:

24

Step-by-step explanation:

multiply base x height

Answer:

slope is 5, y intercept is -7

Step-by-step explanation:

In the form y=mx+c, m is the slope and c is the y-intercept.

Rearrange the formula to fit this form:

5x-y=7

-y=7-5x

y=5x-7

∴m(slope)=5

∴c(y-intercept)=-7

The other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

What is the quadrilateral?

A quadrilateral is a polygon with four sides and four angles. In other words, it is a closed figure that has four straight sides and four vertices (corners).

If <1 has a measure of 45 degrees, then the sum of the angle measures in the quadrilateral must be 360 degrees. Let's call the other three angles in the quadrilateral <2, <3, and <4.

Then we can use the fact that the opposite angles in a quadrilateral add up to 180 degrees to write two equations:

<1 + <3 = 180 (opposite angles)

<2 + <4 = 180 (opposite angles)

We also know that <1 = 45, so we can substitute that in the first equation:

45 + <3 = 180

Solving for <3, we get:

<3 = 135

Now we can substitute the values of <1 and <3 into the sum of angle measures equation:

45 + <2 + 135 + <4 = 360

Simplifying, we get:

<2 + <4 = 180

This is the same equation as the opposite angles equation, so we know that <2 and <4 are also opposite angles. Therefore, we can conclude that:

<2 = <3 = 135 degrees

<4 = 45 degrees

Hence, the other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

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The list A, N, A, L, Y, S, I, S can be sorted alphabetically as A, A, I, L, N, S, S, Y using Selection sort and Bubble sort. Comparing the growth of functions, logarithmic growth (log2(n)) is the slowest, followed by linear growth (4n, 6n), quadratic growth (100n^2, n^2), and exponential growth (2^n) being the fastest.

To sort the list A, N, A, L, Y, S, I, S in alphabetical order, let's first go through the steps for both Selection sort and Bubble sort:

Selection sort:

1. Start with the first element of the list.

2. Compare it with each element to its right.

3. If a smaller element is found, swap it with the current element.

4. Move to the next element and repeat steps 2 and 3 until the list is sorted.

Bubble sort:

1. Start at the beginning of the list.

2. Compare each pair of adjacent elements.

3. If they are out of order, swap them.

4. Repeat steps 2 and 3 until no more swaps are needed.

Using Selection sort, the sorted list would be A, A, I, L, N, S, S, Y.

Using Bubble sort, the sorted list would be A, A, I, L, N, S, S, Y.

Now, let's compare the order of growth of the given functions:

a) 4n and 6n:

Both functions have a linear growth rate (O(n)). However, the constant factor of 6 in 6n indicates that it would generally require more operations than 4n for the same input size.

b) log2(n) and n^2:

The function log2(n) has a logarithmic growth rate (O(log n)), while n^2 has a quadratic growth rate (O(n^2)). The logarithmic function grows much slower than the quadratic function.

As the input size increases, the difference in growth rates becomes more significant.

c) 100n^2 and log2(n):

Similar to the previous case, 100n^2 has a quadratic growth rate (O(n^2)), while log2(n) has a logarithmic growth rate (O(log n)). Again, the logarithmic function grows much slower than the quadratic function.

d) n^2 and 2^n:

The function n^2 has a quadratic growth rate (O(n^2)), while 2^n has an exponential growth rate (O(2^n)). The exponential function grows much faster than the quadratic function.

As the input size increases, the difference in growth rates becomes significantly larger.

In summary, the order of growth of the functions from slowest to fastest is: log2(n), 4n, 6n, 100n^2, n^2, log2(n), 2^n.

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a) The probability that the mean of the sample will fall between 50.5 and 52.3 is approximately 0.8623.

b) The probability that the sample standard deviation will exceed 10 is approximately 0.0244.

a) To find the probability that the mean of the sample falls between 50.5 and 52.3, we need to calculate the z-scores for these values and then use the z-table or a statistical calculator.

The formula to calculate the z-score is:

z = (x - μ) / (σ / √n)

Where:

x = the sample mean (in this case, the mean is between 50.5 and 52.3)

μ = the population mean (given as 51.4)

σ = the population standard deviation (given as 6.8)

n = the sample size (given as 64)

For 50.5:

z_1 = (50.5 - 51.4) / (6.8 / √64) = -0.15

For 52.3:

z_2 = (52.3 - 51.4) / (6.8 / √64) = 0.6625

Next, we use the z-table or a statistical calculator to find the probability associated with these z-scores. The probability of the mean falling between 50.5 and 52.3 is the difference between the cumulative probabilities at z_2 and z_1.

P(50.5 < x < 52.3) = P(z_1 < z < z_2)

Looking up the z-scores in the z-table or using a statistical calculator, we find that the probability associated with z_1 is approximately 0.4364 and the probability associated with z_2 is approximately 0.9454.

Therefore, the probability that the mean of the sample falls between 50.5 and 52.3 is approximately:

P(50.5 < x < 52.3) = 0.9454 - 0.4364 ≈ 0.8623

b) To find the probability that the sample standard deviation exceeds 10, we need to use the chi-square distribution.

The formula to calculate the chi-square statistic for sample standard deviation is:

χ² = (n - 1) * s² / σ²

Where:

n = sample size (given as 64)

s = sample standard deviation (in this case, we are interested in values exceeding 10)

σ = population standard deviation (given as 6.8)

To find the probability, we calculate the chi-square value and then use the chi-square distribution table or a statistical calculator.

χ² = (64 - 1) * 10² / 6.8² ≈ 121.5294

Using the chi-square distribution table or a statistical calculator, we find that the probability of the chi-square value exceeding 121.5294 is approximately 0.0244.

Therefore, the probability that the sample standard deviation exceeds 10 is approximately 0.0244.

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The interval that contains the central 80% of MCAT scores is 488.77 to 513.03, rounded to three decimal places.

To find the interval that contains the central 80% of MCAT scores, we need to find the standard deviation boundaries.

Using the standard normal distribution, we can find the Z-score that corresponds to the 80% interval. For a standard normal distribution, the Z-score for the lower boundary of the 80% interval is -1.282, and the Z-score for the upper boundary of the 80% interval is 1.282.

To find the MCAT score for each Z-score, we need to use the formula:

MCAT score = mean score + (Z-score * standard deviation)

For the lower boundary:

MCAT score = 500.9 + (-1.282 * 10.6) = 488.77 (rounded to two decimal places)

For the upper boundary:

MCAT score = 500.9 + (1.282 * 10.6) = 513.03 (rounded to two decimal places)

Therefore, the interval that contains the central 80% of MCAT scores is 488.77 to 513.03, rounded to three decimal places.

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Complete question is in the image attached

The average monthly salary of all the staff is going to be 19,333.34 ₹.

Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,

So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that

No. of males=10

No. of females=5

So, the total no. of figures = 15

Sum total of  set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be

=(20,000 × 10 + 18,000 × 5) ₹/15

=(200,000+90,000)/15₹

=290,000/15 ₹

=19,333.34 ₹

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