Point $(x,y)$ is randomly picked from the rectangular region with vertices at $(0,0),(2008,0),(2008,2009),$ and $(0,2009)$. what is the probability that $x > 2y$? express your answer as a common fraction.

Probability of

=0.0403.

The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.

The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.

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In 84 ways 3 employees can be chosen from the set of 9.

What is combination?

Total 9 employees from that 3 employees can be chosen.

Total number of combination = ⁹C₃

= 9! / (9-3)! 3!

= 9 *8 *7/3*2

=3* 4* 7

= 12 * 7

= 84

Hence, in 84 ways 3 employees can be chosen from the set of 9.

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Answer:

It will decrease

Step-by-step explanation:

A lower number will lower the average of all the numbers.

We would expect that 4 of the next 9 children to enroll will be elementary school students.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

If 8 out of the last 18 children to enroll at the daycare center were elementary school students,

We can find the fraction of elementary school students in that group by dividing the number of elementary school students by the total number of children:

= 8/18

= 4/9

This means that 4 out of every 9 children enrolled were elementary school students.

If we want to predict how many of the next 9 children to enroll will be elementary school students,

We can use this ratio:

4/9 of 9 children

= (4/9) x 9

= 4

Therefore,

We would expect that 4 of the next 9 children to enroll will be elementary school students.

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Answer:

2 and 4 are Not a function

1 and 3 are a function

Step-by-step explanation:

Answer:

2nd and 3rd are functions and 1st and last are not functions

Step-by-step explanation:

Answer:

The square root of 2,100 is approximately 45.8257569495584 when rounded to 15 decimal places.

The solution to the elimination of the parameters is \(\mathbf{y = 27 \Bigg(\dfrac{\sqrt{x}}{3}, -\dfrac{\sqrt{x}}{3} \Bigg)^3}\)

In the scenario of two parametric equations, the parameter can be removed by first resolving it in equation 1 and then replacing it in equation 2.

Given that:

x = 9t² and y = 27t³

Set up the parametric equation for x(t) to solve the equation for t.

9t² = x

Divide both sides by 9

9t²/9 = x/9

t² = x/9

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

\(t = \pm \sqrt{\dfrac{x}{9}}\)

\(t = \pm {\dfrac{\sqrt{x}}{3}}\)

The complete solution is the result of both the positive and the negative portions of the solution.

\(t = {\dfrac{\sqrt{x}}{3}}\)

\(t = - {\dfrac{\sqrt{x}}{3}}\)

Replace t in the equation for y to get the equation in terms of x.

\(\mathbf{y = 27 \Bigg(\dfrac{\sqrt{x}}{3}, -\dfrac{\sqrt{x}}{3} \Bigg)^3}\)

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The magnitude of the force needed to supply 100 newton-meters of torque to the bolt is 250 newtons.  

Given,

Length of the wrench, l = 0.4 m

Direction of force, `F` = (0, 2, -3) Nm

Torque, `t` = 100 N-m

By definition,

Torque = Force × lever arm

Force = Torque / lever arm

Torque = Force × length of the wrench

Perpendicular distance between the line of action of the force and the axis of rotation is equal to the length of the wrench.

So, the distance between the line of action of the force and the origin of the coordinate system is `l = 0.4 m`.

The direction of the force is `F = (0, 2, -3) Nm` and it is perpendicular to the length of the wrench.

Thus, the lever arm is equal to the length of the wrench and it is pointing in the direction of the positive y-axis. Therefore, the direction of force is the direction of the lever arm.

Magnitude of the force, `F` is given by:

F = t / l

Magnitude of the force, `F` is

F = 100 N-m / 0.4 m

F = 250 N

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we have the following:

solving for x:

the missing denominator is 60

Answer: 12 cm

Step-by-step explanation:

If one of the legs of a right triangle measures 5 cm and its hypotenuse measures 10 cm. Then the measure of the other leg will be 8.66 cm.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

One of the legs of a right triangle measures 5 cm and its hypotenuse measures 10 cm.

Then the measure of the other leg will be

10² = 5² + B²

100 = 25 + B²

 B² = 75

  B = 8.66 cm

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For the given "regression-model", We get :

(a) The predicted delivery time is : 54.501,

(b) The adjusted R² is 95.64%, and overall model significance at 2.5% level is 264.

Part (a) : The multiple linear-regression model that was fitted is : Y' = 2.341 + 1.616×X₁ + 0.144×X₂,

Predict : We use the regression model by replacing X₁ with 10 and X₂ with 250,

So, Y' = 2.341 + 1.616(10) + 0.144(250),

Y' = 54.501,

So, the predicted delivery time is : 54.501,

Part (b) : The formula to calculate the adjusted R² is : 1 - (1 - R²)×(n - 1)/(n - k - 1),

where k is number of "independent-variables" which is : 2,

So, We get,

= 1 - (1 - 0.96)(25 - 1)/(25 - 2 - 1),

= 1 - 0.0436 ≈ 0.9564

So, the adjusted R² is 95.64%,

The "Overall-Significance" : F-Test statistics is = (R²/k)/{(1 - R²)/(n - k - 1)},

Substituting the values,

we get,

= (0.96/2)/{(1 - 0.96)/(25 - 2 - 14)},

= 264.

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The given question is incomplete, the complete question is

A soft drink bottler is interested in predicting the amount of time required by the route driver to service the vending machines in an outlet. The industrial engineer responsible for the study has suggested that the two most important variables affecting the delivery time (Y) are the number of cases of product stocked (X₁) and the distance walked by the route driver (X₂).

The engineer has collected 25 observations on delivery time and multiple linear regression model was fitted Y' = 2.341 + 1.616×X₁ + 0.144×X₂. and R² = 96%

(a) Write down the model and then predict the delivery time when number of cases of product stocked = 10 and the distance walked by the route driver = 250.

(b) Find the adjusted R² and test for the overall model significance at 2.5% level.

Answer:

11x+11

Step-by-step explanation:

4x+8+7x-3=11x+11

Hope this helps :D

Answer:

11x + 11

Step-by-step explanation:

( 4x + 8 ) + ( 7x + 3 )

Remove parenthesis;

Note: Remember, the associate property states that if an equation is either all multiplication or addition, then it can be done in any order, hence the parenthesis holds no weight in this case.

4x + 8 + 7x + 3

Combine like terms;

11x + 11

High-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

A scatter plot is a graphical representation of data points, with the x-axis representing the independent variable (such as the level of production) and the y-axis representing the dependent variable (such as the cost). Linear cost behavior means that the relationship between the independent and dependent variables can be approximated by a straight line. In other words, as the independent variable increases or decreases, the dependent variable changes proportionally.

To determine if a scatter plot depicts linear cost behavior, you need to visually examine the data points. If the points appear to align closely along a straight line, it indicates a linear relationship. However, if the points are scattered and do not follow a clear pattern, it suggests non-linear cost behavior.

High-low or least squares regression analysis are statistical techniques used to estimate and quantify the linear relationship between variables. These methods help determine the equation of the line that best fits the data points and can be used to predict future values. Therefore, performing these analyses is only meaningful when the scatter plot indicates linear cost behavior.

In summary, high-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

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The test score is 91.5.

z-score:

A z-score is the number of standard deviations from the mean value of the reference population.

Here we have to find the test score.

Mean(μ) = 90

Standard deviation(б) = 15

z-score = 0.1

Formula for z-score:

z = X - μ / б

Now putting the values in the equation:

0.1 = X - 90 / 15

1.5 = X - 90

X = 91.5

Therefore the test score is 91.5.

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Answer:

3. w=P/2-L

Step-by-step explanation:

Given formula:

Solving for w:

Correct answer choice is:

Answer: 300 sq. ft

Step-by-step explanation:

1/5x - 25 = 35

1/5 x = 35+25

x = 60 * 5 = 300 sq. ft.

Answer:

300

Step-by-step explanation:

I did it on edge

a). Between April 1 and September 30, there are no days with 17 hours of daylight.

b). Between April 1 and September 30, there is only one day with 14 hours of daylight, which takes place around August 10.

A quadratic equation is a second-degree polynomial equation, meaning it has one variable that has been raised to the power of two or squared. A quadratic equation has the following general form:  ax² + bx + c = 0

a). We need to calculate the following equation to see if there are any days between April 1 and September 30 with 17 hours of daylight:

-0.0002x² + 0.0381x + 12.482 = 17

The quadratic formula can be used to solve the following quadratic equation:

\(x=-b \pm\sqrt{\frac{b^2-4ac}{2a} }\)

where a = -0.0002, b = 0.0381, and c = 12.482 - 17 = -4.518.

Plugging in these values, we get:

x = (-0.0381 ± √(0.0381² - 4(-0.0002)(-4.518))) / 2(-0.0002)

x = 214.8 or x = 121.2

Day 1 being April 1, the first solution, which falls outside the specified range, corresponds to roughly November 1. Therefore, there are no days with 17 hours of daylight between April 1 and September 30.

b. We need to solve the following equation to see if there are any days between April 1 and September 30 that have 14 hours of daylight.

0.0002x² + 0.0381x + 12.482 = 14

The same quadratic formula that we previously used yields:

x = (-0.0381 ± √(0.0381² - 4(-0.0002)(-2.518))) / 2(-0.0002)

x = 131.1 or x = 182.9

Day 1 being on April 1, the first answer falls within the range since it roughly corresponds to August 10. The second answer falls outside the specified range and roughly matches to October 1.

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The present worth of all costs for a newly acquired machine with an initial cost of $34,000, annual operating costs of $17,000 for the first 4 years, increasing by 10% per year thereafter, a life of 13 years, and an interest rate of 10% per year is $222,543.

To calculate the present worth of all costs, we need to consider the initial cost, operating costs, and the time value of money. The initial cost of $34,000 is already in the present, so it remains unchanged. For the annual operating costs, we calculate the present worth for each year using the shifted gradient formula. The present worth of the operating costs for the first four years is $52,032, considering the increasing rate of 10% per year.

For the remaining nine years, we calculate the present worth of the increased operating costs and sum them up, resulting in $136,511. Adding the initial cost and the present worth of operating costs, we obtain the final answer of $222,543. This represents the total present worth of all costs for the newly acquired machine over its 13-year life span, taking into account the 10% interest rate per year.

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The day of the week with the most crime is [insert the day with the highest crime rate]. The day of the week does have an effect on the crime rate, as certain days may exhibit higher crime rates compared to others.

The analysis of crime data reveals patterns and trends that can help identify the day of the week when crime incidents are most prevalent. Law enforcement agencies and researchers often analyze crime statistics to understand the dynamics of criminal activity. By examining crime rates across different days of the week, they can identify any correlations or trends.

Factors such as social behaviors, economic conditions, and routine activities can influence crime rates on specific days. For example, weekends might see higher crime rates due to increased social gatherings and leisure activities, while weekdays may experience different patterns driven by work schedules and routines.

Additionally, factors like alcohol consumption, events, or cultural practices can also contribute to variations in crime rates on specific days.

Understanding the relationship between the day of the week and crime rate can inform law enforcement strategies, resource allocation, and community safety initiatives. By focusing resources and efforts during periods of heightened crime rates, authorities can work towards crime prevention and reduction.

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The slope of the line = change in y / change in x = 4/3.

The slope of a line is the rise over the run, which is the change in y/change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\)

To calculate the slope of the line that is given, chose any two points on the line as plotted in the given graph, say:

(30, 20) = \((x_1, y_1)\)

(60, 60) = \((x_2, y_2)\)

Substitute each of these values into the slope formula, \(\frac{y_2 - y_1}{x_2 - x_1}\):

Slope for the given line (m) = (60 - 20)/(60 - 30)

Slope for the given line (m) = 40/30

Slope for the given line (m) = 4/3.

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Answer:

85

Step-by-step explanation:

Complement = 90

Since 5 is given:

90 - 5 = 85

Answer: 17.8

Step-by-step explanation:

The solution to the proportion would be x = 17.8 which is the correct option (B).

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been the given proportion as:

⇒ 52 : x = 9.5 : 3.25

⇒ 52/x = 9.5/3.25

⇒ 52/x = 2.923

Cross multiplication, and we get

⇒ x = 52/2.923

Apply the division operation,

⇒ x = 17.8

Therefore, the solution to the proportion would be x = 17.8.

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from the picture we know that :

m∠HBD + m∠BDH + m∠DHB = 180°

so if

the value of x is

46° + 33° + (180 - x)° = 180°

79° + 180° - x = 180°

x = 79°

Answer:

Yes it is.

Step-by-step explanation:

Just multiply everything by 2.

Answer:

x=17

Step-by-step explanation:

we know the sum of angles in atriangle is 180°

x +17 + 4x -34 +6x +10 = 180

x+4x+6x +17 -34 +10 = 180

11x -7 =180

11x = 180 +7

x = 187/11 = 17

Answer: m-105= or > 1,000

Answer:

15

Step-by-step explanation:

2 + 13 = 15

15( 3 ) = 45

45-35= 15

The grocer used 10 lbs of $3.00 per pound trail mix and 5 lbs of $1.50 per pound trail mix.

Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations.

As per the given data:

Cost of one trail mix = $3.00 per pound

Cost of another trail mix = $1. 50 per pound

The grocer makes 15 lb of trail mix that costs $2.50 per pound.

Let's assume the grocer used 'A' pounds of $3.00 per pound trail mix and 'B' pounds of  $1. 50 per pound trail mix.

Total quantity of $2.50 per pound trail mix = 15 lb

Now, from the given data,

A + B = 15 ...(i)

Also, the total cost is going to remain the same.

3A + 1.5B = 15 × 2.50

3A + 1.5B = 37.5 ...(ii)

Using eq(i) A = 15 - B

Substituting in (ii):

3(15 - B) + 1.5B = 37.5

45 - 3B + 1.5B = 37.5

B = 7.5/1.5

B = 5

and A = 10

The grocer used 10 lbs of $3.00 per pound trail mix and 5 lbs of $1.50 per pound trail mix.

Hence, The grocer used 10 lbs of $3.00 per pound trail mix and 5 lbs of $1.50 per pound trail mix.

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Answer:

sin θ = 22.62°

cos θ = 22.62°

tan θ = 22.62°

Step-by-step explanation:

From the diagram above

Opposite = 5

Adjacent = 12

Hypotenuse = 13

a) sin θ = Opp/Hypotenuse

sin θ = 5/13

sin θ = 0.3846153846

arc sin 0.3846153846

= 22.619864948°

Approximately = 22.62°

b) cos θ = Adjacent/ Hypotenuse

θ = 12/13

= arccos(0.9230769230769231)

22.619864948°

Approximately = 22.62°

c) tan θ = Opposite/Adjacent

θ = 5/12

= arctan(0.4166666666666667)

= 22.619864948°

= 22.62°

The percent of the total calories in each brownie comes from fat will be;

⇒ 35.84%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The wrapper said each brownie was 451 calories, and had 252 calories of fat.

Now,

Since, The wrapper said each brownie was 451 calories, and had 252

calories of fat.

Hence, Total calories = 451 + 252

                                 = 703 calories

And, The calories of fat = 252 calories

Thus, The percent of the total calories in each brownie comes from fat is find as;

⇒ Percent = 252/703 × 100

                = 35.84%

Therefore, The percent = 35.84%

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Answer:

37.5 miles per gallon

Step-by-step explanation:

450/12 =37.5

this is around about how much it is

Answer:

37.5mi/g

Step-by-step explanation:

So if she's going 950mi total with a 12g tank, and is almost empty at 450mi, you would do 450mi / 12g which would be 37.5mi/g