A group of students plotted the number of hours they worked weekly during the holidays and the number of hours they spent cycling. Graph shows 0 to 60 on x and y axes at increments of 10. The label on the x axis is Weekly Hours Worked, and the label on the y axis is Weekly Hours Cycling. Dots are made at the ordered pairs 10, 45 and 13, 35 and 16, 42 and 24, 32 and 26, 43 and 32, 29 and 37, 23 and 39, 27 and 42, 19 and 45, 21 and 49, 19 and 50, 12. Which statement best describes the relationship between the number of hours spent working and the number of hours spent cycling? Greater hours worked, fewer hours spent cycling. Fewer hours worked, fewer hours spent cycling. Greater hours worked, greater hours spent cycling. There is no relationship between hours spent working and hours spent cycling.

Answer: The equation in slope-intercept form: \(y=-5x+2\)

Step-by-step explanation:

The given equation of a line : \(y+3= -5(x-1)\)

The equation of a line in slope -intercept form: y=mx+c, where m= slope , c=y-intercept.

We first use distributive property(a(b+c)=ab+ac) to simplify the given equation, we get

\(y+3=-5x+5\)

Subtract 3 from both sides, we get

\(y=-5x-2\)

Hence, the equation in slope-intercept form: \(y=-5x+2\)

There are 720 possible horse combinations for the first 3 places in the race.

To solve this problem, let us break this down one by one.

There are 10 possible horses that could win in first place.

Therefore, this means that for each of these possibilities, there are now 9 horses that could come in second.

So there are 10 x 9 possible combinations for the first 2 places.

10 x 9 = 90.

And for each of those combinations, there are also 8 possible horses that could come in the third place. So

10 x 9 x 8 = 720

There are 720 possible horse combinations for the first 3 places in the race.

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The fraction of the box she puts in each bowl is, 1/10

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

To find the fraction of the box that Evangeline puts in each bowl, we need to divide the total amount of nuts in the box by the number of bowls.

The amount of nuts she has is 3/5 of a box.

To find the amount of nuts in each bowl, we need to divide 3/5 by 6:

(3/5) ÷ 6

To divide by a fraction, we can multiply by its reciprocal:

= (3/5) ÷ (6/1)

= (3/5) x (1/6)

Multiplying across, we get:

= (3/5) x (1/6)

= 3/30

= 1/10

Therefore, Evangeline puts 1/10 of the box in each bowl.

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The complete question:

Evangeline has 3/5 of a box of nuts. She uses it to fill 6 bowls. What fraction of the box does she put in each bowl.

Answer:

\(k<1, k>5\)

Step-by-step explanation:

\(3x+1=x^2+kx+2 \\ \\ x^2+x(k-3)+1=0 \\ \\ \Delta>0 \implies (k-3)^2-4(1)(1)>0 \\ \\ (k-3)^2-2^2>0 \\ \\ (k-1)(k-5)>0 \\ \\ k<1, k>5\)

The formula for the average height of the paraboloid over R is  1/8.

The formula for the average of a function f(x,y) over a rectangular region R with area A is as follows:

1/A ∫∫R f (x,y) dA

In this case, we want to find the average height of the paraboloid z = x^2y^2 over the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Therefore, we have:

A = ∫∫R dA = ∫0¹ ∫0¹ dx dy = 1

The formula for the average height of the paraboloid over R is:

1/A ∫∫R z dA = 1 ∫0¹ ∫0¹ x^2y^2dxdy

= 1/4 * [x^4y^2/2] from 0 to 1 and from 0 to 1

= 1/4 * [1(1/2) - 0(1/2)] * [1(1/2) - 0(1/2)]

= 1/8

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Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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The sampling distribution of difference between means approximates a normal curve whose mean is zero.

The sampling distribution means the probability distribution based on the large number of samples of size n from the given population

Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.

Here they used the normal curve, sot its mean value is zero

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Answer:

26 and 27

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW;

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?

Answers:

(–3, –0.90)

(–2.5, –0.75)

(4.5, 1.35)

(8, 2.40)

Answer

(8, 2.40)

Step by step Explanation

✓We can denote the number of days library book is late = X,

✓We can denote the the total fee = Y.

We were told $0.30 fee is charged at midnight.

Then for lateness for just 1day,the charged fees= 1day ×

$0.30

For X number of days the charged fees= Xday ×$0.30

Therefore, total charge for lateness for X number of days late = Y.

Then can be expressed as

Y= 0.30 * X...............eqn(1)

We can now test the option one after the other

FIRST OPTION (-3, -0.9)

Here we should know the number of days cannot be negative so there is no need of testing in the equation (1)

SECOND OPTION (-2.5, -0.75)

Here we should know the number of days cannot be negative so there is no need of testing in the equation (1)

THIRD OPTION(4.5, 1.35)

here the number of days will definitely be a whole number not 4.5, it's either

charge for 4 days or 5 days.

FORTH OPTION (8, 2.40)

this should be correct because the number of days is whole number and not negative, then if we test it from our equation it satisfy the equation too

Y= 0.30 * X...............eqn(1)

Y= 0.30 * X

2.40= 0.30 * 8

2.40 = 2.40.

Therefore, (8, 2.40) is the answer

The airplane will become balanced if we add a 100- pound weight to the baggage compartment.

An airplane is used to convey people and goods from one point to another by air. The airplane must be airlifted. This means that the airplane must be balanced while on air. If the airplane is not balanced, it may be difficult to control.

Looking at the situation of this airplane, the airplane will become balanced if we add a 100- pound weight to the baggage compartment.

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The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

(a) The graph given is a straight line that passes through (0, 40) and (10, 240).

The constant rate of change is equivalent to the the slope of the line given as,

⇒ (240 - 40)/(10 - 0) = 20

(b) The initial value of the graph is given as the y-intercept of the line.

Which is given as 40.

It might represent the fixed cost.

Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.

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The missing graph is attached here.

Answer:

\(\sqrt{85}\)

Step-by-step explanation:

Using the distance formula:

\(x=\sqrt{(5-(-2))^2+(3-(-3))^2}=\sqrt{7^2+6^2}=\sqrt{49+36}=\sqrt{85}\)

Hope this helps!

Answer:

$53.88

Step-by-step explanation:

27.38+5.3*5

5.3 x 5 = 26.5

27.38 + 26.5 = 53.88

The amount in the account after 18 years will be about $24,459.2.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Final amount in a compound interest can be calculated as,

A = P (1 + \(\frac{r}{n}\) ) ^ (n t)

Here, A is the final amount, P is the principal amount, n is the number times interest is compounded in a year, r is the rate of interest and t is the time in years.

Here, P = $10,000

r = 5% = 0.05

n = 4, since the compounding is quarterly

t = 18 years

Substituting,

A = 10,000 (1 + \(\frac{0.05}{4}\))^ (4 × 18)

  = 10,000 (1.0125)⁷²

  = 24,459.2

Hence there will be an amount of $24,459.2 in the account after 18 years.

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Answer:

Step-by-step explanation:

\( { ({6}^{2} )}^{x} = 1 \\ { ({6}^{2}) }^{x} = {6}^{0} \\ {6}^{2 \times x} = {6}^{0} \\ 2x = 0 \\ x = \frac{0}{2} \\ x = 0 \\ \)

\( {( {6}^{0} )}^{x} = 1 \\ { ({6}^{0} )}^{x} = {6}^{0} \\ {6}^{0 \times x} = {6}^{0} \\ 0 \times x = 0 \\ x = 0\)

As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).

In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.

The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.

The third set of data is 24, 25, 25, 25, 26, 26.

The median is the middle value, which is also (25+25)/2 = 25.

The mode is the value that appears most frequently, which is 25.

Therefore, the mode and median are the same, fulfilling Marjane's requirement.

Therefore, the correct option is (c).

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Option A. The statement is false. A sample statistic can change from sample to sample.

Values that are calculated from the sample data provided is referred to as a sample statistic. In simple terms, sample is the small group that is a part of large part. It is a measurement that is obtained from the samples that are taken to provide insight into the parameter of the population that is unknown. Although it is known for a specific sample, it is not a constant.

So basically yes, a sample statistic can change from sample to samples based on the data given each time.

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Answer:

16

Step-by-step explanation:

93:6=15.5 As the box can't be half so 16 boxes. In 15 she will pack in each 6 books and in other box 3 books

Answer:

She will need 16 boxes with space for 3 more books

Step-by-step explanation:

Answer:

x = 0.357143

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-1.6 - 2x = 5x + 0.9

Step 2: Solve for x

Answer:

d)the observations expressed in standard units

Step-by-step explanation:

The average will change and hence, consequently, so will the deviations from the average and also the standard deviation. so, the only option left is d)

1. To find two starting terms for a Diginacci sequence such that the 2021st term is 11, we can work backward from the 2021st term to determine the preceding terms.

Let's denote the first term as a and the second term as b. We need to find the values of a and b that will result in the 2021st term being 11.

Working backward, we know that the 2021st term (which is 11) is the sum of the digits of the previous two terms. Let's denote the (2020)th term as x and the (2019)th term as y. Therefore, we have:

11 = x + y

2. To find a suitable pair of x and y, we can iterate through possible values. Since the first two terms can be any positive whole numbers, we have some flexibility in choosing them.

For example, let's try a = 1 and b = 1:

Term 1: 1

Term 2: 1

Term 3: 2

Term 4: 1

Term 5: 3

Term 6: 4

Term 7: 7

Term 8: 11

The 8th term is 11, which matches our target. Therefore, if we start with a = 1 and b = 1, the 2021st term will indeed be 11.

To find a Diginacci sequence that has no term equal to 11, we need to ensure that none of the subsequent terms sum up to 11.

One way to achieve this is to start with two terms that are relatively large and have no digits summing up to 11. Let's try a = 99 and b = 100:

Term 1: 99

Term 2: 100

Term 3: 19 (9 + 9)

Term 4: 10 (1 + 0)

Term 5: 1

Term 6: 1

Term 7: 2

Term 8: 3

Term 9: 5

Term 10: 8

Term 11: 13

Term 12: 12

Term 13: 7

Term 14: 10

...

By starting with a = 99 and b = 100, the Diginacci sequence continues without reaching the value 11. The terms keep changing without summing up to 11, as seen in the subsequent terms above.

Thus, this particular Diginacci sequence starting with a = 99 and b = 100 does not have any term equal to 11.

While the importance of sub-scores may vary depending on the specific circumstances and goals of a multinational enterprise (MNE), one sub-score that is often considered crucial is the "Property Rights" sub-score.

Property rights provide the legal framework for protecting and enforcing ownership of assets, including intellectual property, real estate, and investments. Strong property rights ensure that MNEs have secure and enforceable rights over their assets, reducing the risk of expropriation, unauthorized use, or infringement.

For an MNE, secure property rights are essential for various reasons. They enable the MNE to confidently invest in and develop new assets, protect their intellectual property, and establish long-term contracts and business relationships. Secure property rights also foster a favorable investment climate, attracting foreign direct investment and facilitating economic growth.

Additionally, property rights contribute to a stable and predictable business environment, reducing uncertainty and facilitating planning and decision-making processes for MNEs. By considering the property rights sub-score, MNEs can assess the level of legal protection and security of their assets in a particular country, which is crucial for ensuring a favorable and stable business environment.

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Complete Question:

Look at the twelve sub-scores that make up a country's economic freedom score. Which sub-score do you think is most important for an MNE (multi-national enterprise) to consider? The sub-score groups are listed below in the bullet points.

Organizational culture is defined as the common beliefs, values, attitudes, customs, behaviors, and traditions that characterize a specific organization and determine the manner in which it functions. Organizational culture is set by the manager.

In a corporate or business environment, organizational culture can influence the daily operations of employees. It is the responsibility of managers to create a positive culture that emphasizes teamwork, respect, integrity, and accountability. The manager is an essential individual responsible for establishing and maintaining the organization's culture, which will ultimately define the employee's attitudes, behaviors, and productivity levels. He or she sets the tone for the workplace by creating an environment that fosters collaboration, innovation, and success. Employees need to feel connected to their workplace and colleagues to be motivated to do their best work. If a manager promotes a culture of fear, competition, or dishonesty, employees may become unmotivated or unproductive. An effective manager understands the importance of creating a positive workplace culture and works hard to establish and maintain it. Managers can establish a positive culture by encouraging open communication, providing regular feedback and recognition, fostering a sense of teamwork, creating opportunities for professional development, and setting high standards for performance. Managers must lead by example and demonstrate the behaviors and attitudes that they expect from their employees. They must hold themselves and others accountable for their actions, communicate expectations clearly, and provide support when needed. A positive organizational culture will enable an organization to attract and retain top talent, increase employee engagement, and promote collaboration and innovation.

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Answer:

option e

Step-by-step explanation:

It should be arranged in table form

Row ------> Classes

Column  -----> Courses

                     Sophomores           Juniors          Seniors

Biology                 110                        60                 20

Chemistry              50                        140               85

Physics                    17                         70                107

Answer:

  58.4°

Step-by-step explanation:

You have ∆FGH with f = 12 cm, g = 6 cm, and h = 14 cm, and you want to know the measure of angle F.

The law of cosines tells you ...

  f² = g² +h² -2gh·cos(F)

Solving for angle F gives ...

  F = arccos((g² +h² -f²)/(2gh))

  F = arccos(88/168) ≈ 58.412°

Angle HFG is about 58.4°.

The required length of altitude q in centimeters is 8 cm.

The geometric mean theorem for triangles states that if we draw an altitude from the vertex of the right angle of a right triangle, then the length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse that are adjacent to the altitude.

Here,
From the above definition,
q² = 4 × 16
q = √[4×16]
q = 8

Thus, the required length of altitude q in centimeters is 8 cm.

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Answer: 6 pounds is the mode

Step-by-step explanation: 6 is the most common number