I would appreciate any help ​

After using the mean, the expected number of cups of coffee is 1.28. So the option a is correct.

In the given question, a sample of 2,500 people was asked how many cups of coffee they drink in the morning.

We have to find the expected number of cups of coffee.

x            Frequencyf(x)       x^2            x∙f(x)            x^2∙f(x)

0                600                    0                 0                  0

1                 800                    1                 800               800

2                900                    4                1800             3600

3                200                    9                600               1800

Total        2500                                     3200             6200

Mean = Sum of f.x/Sum of f

Mean = 3200/2500

Mean = 1.28

Mean = 1.28

The expected number of cups of coffee is 1.28.

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The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.

With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.

Diameter of the semi-circle = 84cm

Now,

the circumference of the semi-circle  =  πr + 2r

Substituting the value of r in the given formula:

the circumference of the semi-circle  =  πr + 2r

                                                              = πr + 2r

                                                               = 48π + 42

The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

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Answer:

x =  2 units

Step-by-step explanation:

Diagonals of rectangle are congruent and bisect each other

Therefore, OB = OA

   5x + 4 =  3x + 8

    5x = 3x + 8 -4

    5x = 3x + 4

5x - 3x = 4

      2x =  4

      x = 4/2

      x =2

In Fluid Mechanics, we describe the motion of fluids using two different frames of reference- the Eulerian( fixed frame of reference wrt fluid particles; describes the rate of change of fluid flow property at a fixed position in space) and the Lagrangian (follows individual fluid particles and describes the rate of change of fluid flow properties of the particle as it passes through space).

A Material derivative is basically a Lagrangian way of expressing the rate of change of fluid flow property. It expresses the rate of change of fluid property wrt time and also the rate of change wrt space because of its movement at some velocity. It is best explained by John D Anderson jr. in his book "Computational Fluid Dynamics". He explains that the material derivative can be best understood by considering an example of imagining oneself entering a cold cave. The material derivative is the change in temperature you would feel as if you would just enter into the cave from the outside and precisely at the same time if someone throws snowballs at you. The rate of change of temperature because of your movement into the cave is the rate of change wrt space and that due to the snowball effect would be the rate of change w.r.t time.

Coming to the Reynolds Transport theorem is a powerful tool in fluid mechanics that relates the change in properties of a system to change in properties in a control volume. Since laws of thermodynamics are applicable to a system, the Reynolds transport theorem allows it to be applied to a control volume (fixed or moving, or deformable).

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The sample size used in this study with a 95% confidence interval for a population mean reported to be 152 to 160 and a standard deviation (s) of 15 is approximately 35.

To find the sample size used in this study with a 95% confidence interval for a population mean reported to be 152 to 160 and a standard deviation (s) of 15, you can follow these steps:

1. Calculate the margin of error by taking the difference between the upper limit and the lower limit, and divide it by 2.
Margin of Error = (160 - 152) / 2 = 8 / 2 = 4

2. Use the z-score corresponding to the 95% confidence interval. In this case, the z-score is approximately 1.96.

3. Use the formula for the margin of error: Margin of Error = (z-score * s) / sqrt(n), where n is the sample size.

4. Rearrange the formula to solve for the sample size (n):
n = (z-score * s / Margin of Error)²

5. Substitute the values into the formula:
n = (1.96 * 15 / 4)²

6. Calculate the sample size (n):
n ≈ 34.57

Since the sample size must be a whole number, round up to the nearest whole number, which is 35.

The sample size used in this study with a 95% confidence interval for a population mean reported to be 152 to 160 and a standard deviation (s) of 15 is approximately 35.

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The ratio of students who cheer to those who participate in a sport is 13:82.

To determine the ratio of students who cheer to those who participate in a sport, we need to calculate the number of students who participate in a sport.

By summing up the values in the "Number of Students" column, we find that the total number of students participating in sports is 35 + 27 + 43 + 33 + 26 = 164.

Since students can only play one sport at a time, the number of students who cheer is 26.

Therefore, the ratio of students who cheer to those who participate in a sport is 26:164.

To simplify this ratio, we can divide both numbers by their greatest common divisor, which is 2.

Dividing 26 by 2 gives us 13, and dividing 164 by 2 gives us 82.

Thus, the simplified ratio is 13:82.

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False. The total shrink for a three- and four-bend saddle is equal to that of an offset.

The statement "total shrink for a three- and four-bend saddle is twice that of an offset" is true.

1. Shrink: Shrink refers to the amount of extra conduit length needed to account for bends in the conduit, so it maintains the required distance between two points after bending.

2. Offset: An offset is a two-bend conduit configuration used to navigate around obstacles while maintaining a straight path. The total shrink for an offset can be calculated using the formula: Shrink = offset height x (multiplier for the specific angle).

3. Saddle: A saddle is a conduit configuration with either three or four bends. It is used to navigate over or under obstructions while maintaining a straight path.

4. Comparison: For both three- and four-bend saddles, the total shrink is twice that of an offset. This is because a saddle consists of two sets of bends (either two offsets or an offset and a U-bend) and requires additional conduit length to accommodate these extra bends.

In conclusion, the statement is true, as the total shrink for a three- and four-bend saddle is indeed twice that of an offset.

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They are congruent by SAS as follows if I understand you correctly:

Since x is shared by both NR and AG, it must be at their intersection.

Because it lies in the middle of both, NX = XR and AX = XG.

We join point A to point N and point R to point G to complete the triangles (any 2 points define a line).

Due to the fact that there are two triangles on either side of the point X, angle AXN is perpendicular to angle RXG. Angle AXN is equal to angle RXG because the vertical (opposite) angles formed by two intersecting lines are equal.

The following is how the SAS evidence of congruency is established:

Angle RXG in triangle RXG and angle AXN in triangle AXN are congruent (vertical angles)

Triangles AX in AXN and XG in RXG are congruent (midpoint X of line AG created these).

Triangle RXG and triangle AXN's NX and XR are congruent.

By SAS, triangles are congruent. this means they have two corresponding sides that are congruent and the angle between those 2 corresponding sides is congruent also.

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Answer:

x=-125/24

Step-by-step explanation:

(6x+10)+(-10-30x)=(30x+135)+(-10-30x)

(6x+10)+(-30x-10)=(30x+135)+(-30x-10)

6x+10-30x-10=30x+135-30x-10

6x-30x+10-10=30x-30x+135-10

-24x=125

24x/24=-125/24

x=-125/24

Answer:

70feet

Step-by-step explanation:

during the

1st sec it travels 28 ft

2nd sec =28-7=21ft

3rd sec= 21-7=14ft

4th sec= 14-7= 7ft

last sec=7-7=0ft, at this point the car stops.

so altogether it travels 28+21+14+7+0= 70 feet

Step-by-step explanation:

Let n be the number of caterpillars.

Since each catepillar eats 7 leaves,

Wesley have 7n number of leaves.

In this case 7n = 42, so n = 6.

Answer: 7n = 42, n = 6.

Explanation:

Every caterpillar eats 7 milkweed leaves. That means \(n\) is the number of caterpillars Wesley feeds every day. Since we know 7n is equal to 42, n = 6 because 42 ÷ 7 = 6.

Answer:

W= -6

Step-by-step explanation:

-4w = -5 + 29

-4w = 24

Divide both sides by -4

=

W = -6

Answer:

you change w to the other side then proceed as you normally would

The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.

The distribution of data is shown using a boxplot, which is a standardised method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum").

For the case of -

A total of 100 distinct gummy vitamins that are offered worldwide were counted for their milligrammes of vitamin C content.

The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.

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The pounds of the Earl Grey tea and Orange Pekoe tea are required from selling the new blend versus selling the other types is 225 pounds and 75 pounds.

Let x = amount of Earl Grey tea to mix

so, 300-x = amount of Orange Pekoe tea to mix

After putting the equations together,

6x+4(300-x)=5.5*300

6x+1200-4x=1650

2x=450

x=225

So amount of Earl Grey tea to mix is 225 pounds

amount of Orange Pekoe tea to mix = 300-x

300-225 = 75

So the amount of Orange Pekoe tea to mix is 75 pounds.

Amount of Earl Grey tea to mix=225 pounds

Amount of Orange Pekoe tea to mix=75 pounds

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Answer:

x =  12.714

Step-by-step explanation:

Vertical angles sum to 180 degrees

8x-12     + 6x + 14 = 180

   solve for x = 12.714

Answer:

b = c(5 - a)

Step-by-step explanation:

Given

a + \(\frac{b}{c}\) = 5 ( subtract a from both sides )

\(\frac{b}{c}\) = 5 - a ( multiply both sides by c to clear the fraction )

b = c(5 - a)

The value of b form the equation a + b/c = 5  will be b = c(5 - a)

We can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

Given;

a + b/c = 5

subtract a from both sides;

b/c  = 5 - a

multiply both sides by c to clear the fraction;

b = c(5 - a)

Hence, The value of b form the equation a + b/c = 5  will be b = c(5 - a)

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Answer:

p = 6

Step-by-step explanation:

Define the variable

Let p be the number of people who go to the amusement park.

Given information:

Therefore, the equation that represents the given information and the defined variable is:

\(39.25p + 12 \leq 247.50\)

(We have used the inequality sign since the question states the maximum amount of money the group of friends have to spend).

To solve, subtract 12 from both sides:

\(\implies 39.25p + 12 - 12 \leq 247.50 - 12\)

\(\implies 39.25p \leq 235.50\)

Divide both sides by 39.25:

\(\implies \dfrac{39.25p}{39.25} \leq \dfrac{235.50}{39.25}\)

\(\implies p\leq 6\)

Therefore, the maximum number of people that can go to the amusement park is 6.

Answer:

25 grams

Step-by-step explanation:

Three half live

1/2 * 1/2 * 1/2 = (1/2)³ = 1/8

There would be 1/8 of the original amount left

185 * 1/8 = 23.125

Rounded

25 grams

The objective function is a linear combination of decision variables, and the goal is to find the values of the decision variables that optimize the objective function.

The objective function is a linear combination of decision variables, and the goal is to find the values of the decision variables that optimize the objective function. The constraints are linear inequalities or equalities that restrict the feasible region of the variables. The variables are typically non-negative, as negative values do not have meaningful interpretations in many practical applications of linear programming.

A standard linear programming problem consists of an objective function to be maximized or minimized, along with a set of constraints. In the given linear programming problem, the objective is to maximize the expression z = 2x1 - 3x2 + 6x3. The decision variables are x1, x2, and x3. The problem is subject to two constraints. The first constraint is a less-than-or-equal-to inequality constraint, stating that 3x1 - 4x2 - 6x3 should be less than or equal to 2. The second constraint is a greater-than-or-equal-to inequality constraint, indicating that 2x1 + x2 + 2x3 should be greater than or equal to 11.

To solve this linear programming problem, optimization techniques such as the simplex method or interior point methods can be employed. These methods iteratively adjust the values of the decision variables to find the optimal solution. By solving the problem, the values of x1, x2, and x3 can be determined, result in the maximum value of the objective function z.

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56.6 years  is the mean of the modes of the given set of numbers.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

The mean is calculated by adding together all the values

                 =  (54+54+54+55+56+57+57+58+58+60+60

                  = 623

                  =  56.6 years.

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Answer:

Rahul by 1

Step-by-step explanation:

Johan - 3/7

Rahul - 4/9

1. Convert fractions

3/7 -> 27/63

4/9 -> 28/63

28/63 > 27/63

Rahul took more by 1/63

The shape classification is a Quadrilateral and the area of the shape is 30 inch ²

The circumference of the circle is 37. 7 m

The area of the circle is 113. 1 m²

The shape given is known as a trapezium and the area of a trapezium can be found by the formula :

= ( Side A + Side B ) / 2 x Height

= ( 10 + 5 ) / 2 x 4

= 7. 5 x 4

= 30 inch ²

The circumference of a circle is;

=  Pi x Diameter

= 22 / 7 x 12

= 37. 7 m

The area of the circle is:

= Pi x radius ²

= 22/ 7 x 6 x 6

= 113. 1 m²

Note : Radius is half of diameter

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The ratios involved in the ROI formula are the net profit and the investment cost.

The ROI (Return on Investment) formula includes the following ratios:

Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.

Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.

The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.

ROI = (Net Profit / Investment Cost) * 100%

Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.

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Answer:

25 ft

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

15^2 + 20 ^2 = x^2

225+400= x^2

625 = x^2

Take the square root of each side

sqrt(625) = sqrt(x^2)

25 = x

Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

20 kg is approximately equal to 44.0925 pounds ( rounded to four decimal places )

The conversion factor to convert kg to pounds is 2.20462

1 kg = 2.20462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in pounds = The mass in kg × conversion factor

Substitute the values in the equation

1 kg = 2.20462 pounds

20 kg =  20 × 2.20462

Multiply the numbers

= 44.0925 pounds  ( rounded to four decimal places )

Therefore, 20 kg is 44.0925 pounds

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Step-by-step explanation:

kinetic energy=1/2mv^2

=1/2×0.2kg×36

=3.6

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Answer:

2

Step-by-step explanation:

Answer:

2 is the smallest number

The R code provided performs various data manipulation tasks, including creating variables, combining vectors into a dataframe, and summarizing data. It does not require any external visual representation.

Task 1:

1. The `str()` function is used to investigate the structure of the `my_mtcars` dataframe. It will display information about the variables and observations in the dataframe.

2. To calculate engine displacement per cylinder, you need to divide a variable (XXXX) by the `cyl` variable. Replace the two XXXX placeholders with the name of the variable representing engine displacement.

  For example, if the variable representing engine displacement is named `disp`, the code will be:

  `my_mtcars$UnitEngine <- my_mtcars$disp / my_mtcars$cyl`

3. Use the `summary()` function to summarize the newly created variable `UnitEngine` and display descriptive statistics.

Task 2:

4. Create a numeric vector named `Pets` with the numbers (1, 1, 1, 0, 0).

  `Pets <- c(1, 1, 1, 0, 0)`

5. Create a numeric vector named `Order` with the numbers (3, 1, 2, 3, 3).

  `Order <- c(3, 1, 2, 3, 3)`

  Note: The instructions for creating the 'Order' vector were not provided in the given code, so it is assumed that you need to create it here.

6. Create numeric vectors `Siblings` and `IDs` with the provided values.

7. Combine all four vectors (`Pets`, `Order`, `Siblings`, `IDs`) into a dataframe named `myFriends` using the `data.frame()` function.

8. Use `str()` to display the structure of the dataframe and `summary()` to summarize the dataframe.

9. To list all values of the 'Pets' variable, use `myFriends$Pets`.

10. To print the value in the fifth observation of the 'Pets' variable, use `myFriends$Pets[5]`.

11. Use `cbind()` to add a vector called 'age' to 'myFriends'.

12. Define a vector named `names` with the given names. Then use `cbind()` to add the 'names' vector to 'myFriends'. Print the structure of 'myFriends' to see the data type of the 'names' variable.

Note: Please make sure to replace the XXXX placeholders and follow the instructions carefully to obtain accurate results.

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