is "-6" a rational number, irrational number, an integer, a whole number, a natural number, or some combination?

The wheel having 3feet diameter and travelling a distance of 45 feet is rotated about 30.00 radians.

A circle's circumference is equivalent to π times its diameter.

We can use the circumference formula to determine the circumference of the wheel

C = πd= π(3) = 9.42 feet where d is the diameter.

The wheel has traveled a distance of 45 feet.

We can determine the number of full rotations made by dividing the distance traveled by the circumference of the wheel.

Number of full rotations = distance traveled / circumference of the wheel= 45 / 9.42 = 4.77 full rotations

It is said that the wheel rolled without slipping, therefore the wheel must have turned 4.77 full rotations. The angle in radians through which it rotated is therefore

Angle in radians = number of full rotations x 2π= 4.77 x 2π= 30.00 radians

Therefore, the wheel rotated through a radian angle of 30.00.

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Mu X is a statistical concept used to measure the difference between two means.

It is calculated by subtracting the mean of one group from the mean of another group. Mu X is often used to compare the means of two or more groups, or to compare the means of two subgroups within a group. It can also be used to measure the relative size of a group's mean compared to the grand mean or the size of a group's mean compared to the mean of another group. Mu X is a useful tool for distinguishing between true and false differences between two means. It is also useful for understanding the relative importance of different factors in a study. Mu X is sometimes referred to as the difference in means or the mean difference, and it is an important concept in inferential statistics.

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Step-by-step explanation:

Note that sum = (+) and greater than or equal to sign is ≥

x + 7 ≥ 15

Answer:

7x(3+2)=35x

add:

3+2=5

multiply:

7x(5)=35x

just using the distributive property, nothing more

Answer:

35x

Step-by-step explanation:

you just use the distributive property and the combine like terms and thats it.

Answer:

14.42inches

Step-by-step explanation:

Given the following

b = 5 in

c = 8in

we are to find the measure of the space diagonal line

Using the pythagoras theoreml

l^2 = b^2 + c^2

l^2 = 13^2 - 5^2

l^2 = 169 -25

l^2 = 144

l = 12in

To get the measure of the space diagonal line in the box, we will use the pythagoras theorem;

s^2 = l^2 + c^2

s^2 = 144 + 8^2

s^2 = 144 + 64

s^2 = 208

s= 14.42inches

Hence the required length ix 14.42inches

Answer:

Let the three numbers be x, y and z.

Sum of the numbers is 98.

x + y + z = 98………………(i)

The ratio of the first to the second is 2/3.

x/y = 2/3.

x = 2/3 × y.

x = 2y/3.

The ratio of the second to the third is 5/8.

y/z = 5/8.

z/y = 8/5.

z = 8/5 × y.

z = 8y/5.

Put the value of x = 2y/3 and z = 8y/5 in (i).

2y/3 + y + 8y/5 = 98

49y/15 = 98.

49y = 98 × 15.

49y = 1470.

y = 1470/49.

y = 30 .

Therefore, the second number is 30.

Answer: (c)

Step-by-step explanation:

Answer:

75 geese

Step-by-step explanation:

Lets first calculate how many birds and turkeys there are to subtract from the 180 chickens.

1/3 x 180 = 60

1/4 x 180 = 45

The amount of chickens and turkeys combined is:

60 + 45

105

180 - 105 = 75

75 remaining

The procedure for finding the area between two curves Find the intersection points, set up the integral using the difference between the curves, integrate, take the absolute value, and evaluate the result and the area between the two curve in excercise 1 is 40/3

The procedure for finding the area between two curves involves the following steps:

Identify the two curves: Determine the equations of the two curves that enclose the desired area.

Find the points of intersection: Set the two equations equal to each other and solve for the x-values where the curves intersect. These points will define the boundaries of the region.

Determine the limits of integration: Identify the x-values of the intersection points found in step 2. These values will be used as the limits of integration when setting up the definite integral.

Set up the integral: Depending on whether the curves intersect vertically or horizontally, choose the appropriate integration method (vertical slices or horizontal slices). The integral will involve the difference between the equations of the curves.

Integrate and evaluate: Evaluate the integral by integrating the difference between the two equations with respect to the appropriate variable (x or y), using the limits of integration determined in step 3.

Calculate the absolute value: Take the absolute value of the result obtained from the integration to ensure a positive area.

Round or approximate if necessary: Round the final result to the desired level of precision or use numerical methods if an exact solution is not required.

In summary, to find the area between two curves, determine the intersection points, set up the integral using the difference between the curves, integrate, take the absolute value, and evaluate the result.

Here's the procedure explained using the exercises:

Exercise 1:

Consider the functions F(x) = \(x^2 + 2x + 1\)and f(x) = 2x + 5. To find the area between these curves, follow these steps:

Set the two functions equal to each other and solve for x to find the points of intersection:

\(x^2 + 2x + 1 = 2x + 5\)

\(x^2 - 4 = 0\)

(x - 2)(x + 2) = 0

x = -2 and x = 2

The points of intersection, x = -2 and x = 2, give us the bounds for integration.

Now, determine which curve is above the other between these bounds. In this case, f(x) = 2x + 5 is above F(x) =\(x^2 + 2x + 1.\)

Set up the integral to find the area:

Area = ∫[a, b] (f(x) - F(x)) dx

Area = ∫\([-2, 2] ((2x + 5) - (x^2 + 2x + 1)) dx\)

Integrate the expression:

Area = ∫\([-2, 2] (-x^2 + x + 4) dx\)

Evaluate the definite integral to find the area:

Area = \([-x^3/3 + x^2/2 + 4x] [-2, 2]\)

Area = [(8/3 + 4) - (-8/3 + 4)]

Area = (20/3) + (20/3)

Area = 40/3

Therefore, the area between the curves F(x) = \(x^2 + 2x + 1\)and f(x) = 2x + 5 is 40/3 square units.

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Yes, all rational and irrational numbers have decimal expansions. Rational numbers can be expressed as terminating or repeating decimals, while irrational numbers have non-repeating, non-terminating decimal expansions.

In decimal form, rational numbers have a finite or repeating pattern of digits after the decimal point, while irrational numbers have an infinite, non-repeating pattern of digits after the decimal point. For example, the rational number 1/4 is expressed as 0.25, while the irrational number pi is expressed as 3.14159265358979323846... where the decimal goes on infinitely without repeating. In conclusion, every real number can be represented in decimal form, either as a terminating or repeating decimal, or as a non-repeating, non-terminating decimal.

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Answer:

Step-by-step explanation:

The probability of rolling a 1 is 0.85; then the probability of rolling not 1 is

1 - 0.85 = 0.15

Each box that states rolling a 1 gets 0.85. Each box that states not rolling 1 gets 0.15.

                                   second

                first              roll

                roll            

                             /     0.85   1

       1        0.85 /

                           \    0.15     not 1

                             /  0.85   1

not 1           0.15

                         \

                            \    0.15     not 1

Answer:

(13.5)/4 = 3.375

step-by-step explanation

Answer:

x = 2

Step-by-step explanation:

\( log_{3}x(x+ 30) = log_{3}64 \\ x(x + 30) = 64 \\ {x}^{2} + 30x - 64 = 0 \\ x = 2 \: or \: x = - 32\)

-32 is rejected because in logarithms you cannot use negative value so x=2

According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.

The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.

Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.

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Prove of expression tan² θ - sin² θ = tan² θ × sin² θ is shown below.

Given that;

Expression is,

⇒ tan² θ - sin² θ = tan² θ × sin² θ

Now, We can simplify as;

⇒ tan² θ - sin² θ

⇒ sin² θ / cos² θ - sin²θ

⇒ sin² θ (1 / cos² θ - 1)

⇒ sin² θ (sec² θ - 1)

⇒ sin² θ × tan² θ

Thus, Prove of expression tan² θ - sin² θ = tan² θ × sin² θ is shown.

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The first-order Taylor formula for f(x, y) at (0, 0) is:

f(x, y) ≈ f(0, 0) + ∂f/∂x(0, 0)x + ∂f/∂y(0, 0)y

The second-order Taylor formula for f(x, y) at (0, 0) is:

f(x, y) ≈ f(0, 0) + ∂f/∂x(0, 0)x + ∂f/∂y(0, 0)y + (1/2)∂²f/∂x²(0, 0)x² + ∂²f/∂x∂y(0, 0)xy + (1/2)∂²f/∂y²(0, 0)y²

The first-order Taylor formula is an approximation of a function using its first derivatives.

In this case, the function f(x, y) is approximated at the point (0, 0) using the first partial derivatives ∂f/∂x and ∂f/∂y evaluated at (0, 0).

The formula consists of the function value at (0, 0) plus the partial derivatives multiplied by the corresponding variables x and y.

The second-order Taylor formula extends the approximation to include second partial derivatives.

In addition to the terms in the first-order formula, it includes the second partial derivatives ∂²f/∂x², ∂²f/∂x∂y, and ∂²f/∂y².

These terms account for the curvature of the function and provide a more accurate approximation near the point (0, 0).

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Answer: Add 40 to both sides to collect like terms on each side of the equation

Step-by-step explanation: That's the first step

Answer:

5779 silver coins

Step-by-step explanation:

The probability of surviving such a quest is 99.9% with premium of 5,852 silver coins.

If the insured were to die, the insurance company would pay a death benefit(incur a loss) of 67,329 silver coins.

The probability that the insured would die = 100%-99.9% =0.1%

Therefore, the expected value of this insurance policy to the insurance company

\(=(5,852 X 99.9\%)+(-67,329 X 0.1\%)\\=(5,852 X 0.999)+(-67,329 X 0.001)\\=5778.82\\\approx 5779$ silver coins\)

The expected value of this insurance policy to the insurance company is  5779 silver coins.

The equation for the amount left after t years if half life is

and initial amount is A is,

Determine the amount left after 450 years.

Thus amount of samarium left after 450 years is 11850 grams.

50

Step-by-step explanation:

you just subtract the 29 from 79

There are 50 candies left in the jar.

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

There are 79 candies in the Jar.

Aaron remove 29 candies from the jar.

Now,

Total number of candies in the jar =n 79

And, Aaron remove 29 candies from the jar.

Thus, Left candies in the jar = 79 - 29

                                           = 50

Therefore, There are 50 candies left in the jar.

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Answer:

ax2 + bx + c

Step-by-step explanation:

   Draw and label a picture if necessary.

   Define all of the variables.

   Determine if there is a special formula needed. Substitute the given information into the equation.

   Write the equation in standard form.

   Factor.

   Set each factor equal to 0. ...

   Check your answers.

Answer:

The Quadratic Formula: For ax2 + bx + c = 0, the values of x which are the solutions of the equation are given by:

x =  −b + √(b2 − 4ac)2a

​

Answer:

12.68

Step-by-step explanation:

With reference angle 45°

perpendicular (p) = 9

hypotenuse (h) = c

Now

sin 45 ° = p/ h

0.71 = 9 / c

c = 9 / 0.71

c = 12.68

Hope it will help :)

Answer: m=2

Step-by-step explanation: First convert the equation to slope-intercept form; y=mx+b. This new equation would be 3y=6x-12. Because y must be singular, each side must be divided by 3, to isolate the variable y. After doing this, the equation is y=2x-4. In terms of y=mx+b, m is attached to x, making the slope of this equation 2.

The area of the triangle is 715.7 square units, rounded off to one decimal place.

The given triangle's side lengths and the angles are a = 52, B = 115°, and C = 29°. The area of the triangle can be determined by applying the formula:A = (1/2) a² sin B sin C, where a is the length of the side opposite to angle A.The area of the triangle is  (rounding off to one decimal place)Therefore, the area of the triangle is 715.7 square units, rounded off to one decimal place.

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The surface area of the given rectangular based pyramid would be =116.8in². That is option A.

To calculate the surface area of the pyramid, the formula that should be used is given as follows;

S.A = A + 1/2 PS

P = perimeter of base

A = Area of base

S = Slant height

A = L×w = 6×5 = 30in²

P = 2(L+W) = 2(6+5) = 2×11 = 22in

S.A = 30 + ½ × 22× 7.8

= 30+85.8

= 116.8in²

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If SSR = 47 and SSE = 12, the correlation coefficient R is approximately ±0.8925.

HTo find the coefficient of determination (R-squared or R²) using SSR (Sum of Squares Regression) and SSE (Sum of Squares Error), you'll first need to calculate the total sum of squares (SST), and then use the formula R² = SSR/SST. Here are the steps:

1. Calculate SST: SST = SSR + SSE
  In this case, SST = 47 + 12 = 59
2. Calculate R²: R² = SSR/SST
  For this problem, R² = 47/59 ≈ 0.7966

Since R (correlation coefficient) is the square root of R², you need to take the square root of 0.7966. Keep in mind, R can be either positive or negative depending on the direction of the relationship between the variables. However, since we do not have information about the direction, we'll just provide the absolute value of R:

3. Calculate R: R = √R²
  In this case, R = √0.7966 ≈ 0.8925

So, if SSR = 47 and SSE = 12, the correlation coefficient R is approximately ±0.8925.

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These elements, along with a well-defined project plan, accurate tracking of work progress and expenses, and regular monitoring and analysis of performance metrics, provide the foundation for effective project performance management using EVM.

In order to effectively use earned value management (EVM) technique to manage project performance, several key elements are required. These elements provide the necessary information and metrics to monitor and evaluate the progress of a project. The following are the key components needed for implementing EVM:

1. Planned Value (PV): Also known as the Budgeted Cost of Work Scheduled (BCWS), PV represents the authorized budget assigned to the scheduled work for a specific period or task. It is important to have a well-defined project plan with planned activities and associated budgets in order to calculate PV.

2. Actual Cost (AC): This refers to the actual expenses incurred in completing the work at a given point in time. AC is the actual cost of the work performed, often tracked through financial records and accounting systems. Accurate and up-to-date financial data is necessary to determine the AC.

3. Earned Value (EV): EV, also known as the Budgeted Cost of Work Performed (BCWP), represents the value of work that has been completed or earned at a given point in time. It is measured based on the completion status of project activities. Tracking the progress and completion of tasks is crucial to calculate EV.

4. Schedule Performance Index (SPI): SPI measures the efficiency of the project's schedule performance by comparing the earned value (EV) to the planned value (PV). It provides insights into whether the project is ahead of schedule, on schedule, or behind schedule. SPI is calculated by dividing EV by PV.

5. Cost Performance Index (CPI): CPI evaluates the efficiency of the project's cost performance by comparing the earned value (EV) to the actual cost (AC). It indicates whether the project is over budget, under budget, or on budget. CPI is calculated by dividing EV by AC.

6. Variance Analysis: Variance analysis involves comparing the planned value (PV), earned value (EV), and actual cost (AC) to identify any deviations or variances. Variance analysis helps in identifying areas where the project is deviating from the planned schedule or budget, enabling timely corrective actions.

These elements, along with a well-defined project plan, accurate tracking of work progress and expenses, and regular monitoring and analysis of performance metrics, provide the foundation for effective project performance management using EVM. They enable project managers to assess the project's health, identify potential issues, make informed decisions, and take corrective actions to ensure successful project delivery.

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The standard normal distribution that represents the variable in the question indicates that we get;

a. The probability is about 0.42858

b. The probability that the average mpg of 3 randomly selected passenger cars is more than 32 mpg is 0.35197

c. The probability that all the three cars get more than 32 mpg is about0.0788

A standard normal distribution, also known as the Gaussian distribution, and the z-distribution, has a mean of 0, and a standard deviation of one.

a. The standard score (z-score) of 32 mpg can be obtained as follows;

z = (32 - 31.2)/4.5 ≈ 0.178

The probability that a standard normal variable has a z-score, larger than 0.178, obtained from the z-score table is therefore;

P(Z > 0.178) ≈ 1 - 0.57142 = 0.42858

b. The of the sample is μ = 31.2

The standard deviation of the sample is, σ = 4.5/√(3)

z = (x - μ)/(σ/√n)

Therefore;

z = (32 - 31.2)/(4.5/√(3)) ≈ 0.308

The probability that a standard normal variable has a z-score larger than 0.308, from the z-score table, therefore is; p(z > 0.308) = 1 - 0.64803 = 0.35197

c. The mpg ratings are independent, therefore, we get;

P(the three cars get more than 32 mpg) = P(car 1 gets more than 32 mpg) × P(car 2 gets more than 32 mpg) × P(car 3 gets more than 32 mpg)

The probability that a car gets more than 32 mpg is about 0.42858

Therefore;

P(the three cars get more than 32 mpg) = 0.42858 × 0.42858 × 0.4288 ≈ 0.0788

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

x = {-5, -⅓}

Step-by-step explanation:

\(3 {x}^{2} + 16x + 5 = 0\)

\(3 {x}^{2} + 15x + x + 5 = 0\)

\(3x(x + 5) + 1(x + 5) = 0\)

\((x + 5)(3x + 1) = 0\)

\(x = - 5 \: or \: - \frac{1}{3} \)

\(x = \{ - 5 \: , - \frac{1}{3} \}\)