A farmer uses a storage container shaped like a right cylinder to store his corn. The container has a radius of 5 feet and a height of 20 feet. The farmer plans to paint only the side of the cylinder with red paint. If one gallon covers 325 square feet, how many gallons of paint will he need to buy to complete the job?

The estimated variance of B is 0.000014 and the estimated variance of a is 26.792.

To estimate the variances of the parameter estimates in the linear regression model, we can use the following formulas:

Var(B) = (1 / [n * EX² - (EX)²]) * (EY² - 2B * EXY₁ + B² * EX²)

Var(a) = (1 / n) * (Ey? - a * EY - B * EXY₁)

Given the following values:

EX = 228

EY = 3121

EXY₁ = 38297

EX² = 3204

Exy = 3347-60

Ex? = 604-80

Ey? = 19837

n = 20

We can substitute these values into the formulas to estimate the variances.

First, let's calculate the estimate for B:

B = (n * EXY₁ - EX * EY) / (n * EX² - (EX)²)

= (20 * 38297 - 228 * 3121) / (20 * 3204 - (228)²)

= 1.331

Next, let's calculate the variance of B:

Var(B) = (1 / [n * EX² - (EX)²]) * (EY² - 2B * EXY₁ + B² * EX²)

= (1 / [20 * 3204 - (228)²]) * (3121² - 2 * 1.331 * 38297 + 1.331² * 3204)

= 0.000014

Now, let's calculate the estimate for a:

a = (EY - B * EX) / n

= (3121 - 1.331 * 228) / 20

= 56.857

Next, let's calculate the variance of a:

Var(a) = (1 / n) * (Ey? - a * EY - B * EXY₁)

= (1 / 20) * (19837 - 56.857 * 3121 - 1.331 * 38297)

= 26.792

To know more about variance,

brainly.com/question/28426562

#SPJ11

The demand (in number of copies per day) for a city newspaper, x, has historically been 47,000, 59,000, 69,000, 87,000, or 99,000 with the respective probabilities .1, .16, .4, .3, and .04. The expected demand for the city newspaper is 71,800 copies per day.

The expected demand for a city newspaper can be calculated by multiplying the demand for each number of copies by its respective probability, and then summing the products.

The formula for expected demand is as follows:

Expected demand = ∑(Demand * Probability).

Here, the demand for the city newspaper, x, are:47,000, 59,000, 69,000, 87,000, or 99,000.

The respective probabilities are: 0.1, 0.16, 0.4, 0.3, and 0.04.

So, the expected demand can be calculated as follows:

Expected demand = (47,000 x 0.1) + (59,000 x 0.16) + (69,000 x 0.4) + (87,000 x 0.3) + (99,000 x 0.04)

Expected demand = 4,700 + 9,440 + 27,600 + 26,100 + 3,960

Expected demand = 71,800

Therefore, the expected demand for the city newspaper is 71,800 copies per day. Rounded to the nearest whole number, this is 71,800 copies per day.

To know more about expected demand, visit:

https://brainly.com/question/32229713

#SPJ11

Answer:

84

Step-by-step explanation:

The radius is half of the diameter. So in order to get the diameter you need to multiply the radius by 2.

Answer:

18

Step-by-step explanation:

Let the number be x.

1/3 of itself is 1/3 x or x/3.

x = x/3 + 12

3x/3 - x/3 = 12

2x/3 = 12

3/2 * 2x/3 = 3/2 * 12

x = 18

Answer: 18

The equation is formed as x - x/3 = 12. Then the solution of the equation will be 18.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The number is 12 more than 1/3 of itself.

Let the number be 'x'. Then the equation is written as,

x = x/3 + 12

Simplify the equation, then the value of 'x' will be calculated as,

x - x/3 = 12

3x - x = 36

2x = 36

x = 36/2

x = 18

The equation is formed as x - x/3 = 12. Then the solution of the equation will be 18.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ5

The slope of the line c is - 92.

The points via which the line b passes are:

(-20, 4) and (-21, 96).

The slope of the line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Slope of the line b passing through these points are:

m = (96 - 4) / (- 21 + 20)

m = (92) / (-1)

m = - 92

Since, line b is parallel to line c,

Slope of line b = slope of line c

So, the slope of line c is also:

m' = - 92

Therefore, we get that, the slope of the line c is - 92.

Learn more about slope here:

https://brainly.com/question/3493733

#SPJ4

Hours satellite will take  to reach a star that is three light years away is 1.039 * \(10^{9}\) hours.

Given :

satellite can move at 17,000 miles per hour.

let t be the number of hours

Convert the disance to miles

3 light years = 3 * 9.5 * \(10^{12}\) kilometers

= 3 * 9.5 * \(10^{12}\) * 0.62 miles

= 1.767 *  \(10^{13}\) miles

divide by the speed to get the time in hours

t = 1.767 *  \(10^{13}\) miles /17000 miles /hour

t = 1.039 * \(10^{9}\) hours

Hence hours satellite will take  to reach a star that is three light years away is 1.039 * \(10^{9}\) hours.

Learn more about the satellite and light here:

https://brainly.com/question/11742677

#SPJ1

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

To learn more about division, click on below link:

https://brainly.com/question/11781269

#SPJ4

The electric bill for the house for the month of June is ₹591.12.

To calculate the electric bill for the month of June, we need to determine the total energy consumption of each appliance and then calculate the total cost based on the cost per unit of electrical energy.

a. Refrigerator:

The refrigerator has a power rating of 400 watts and is used for 10 hours per day. Therefore, the energy consumption of the refrigerator per day can be calculated as follows:

Energy consumption = Power rating × Time

Energy consumption = 400 watts × 10 hours = 4,000 watt-hours or 4 kilowatt-hours (kWh)

b. Electric fans:

There are two electric fans, each with a power rating of 80 watts, and they are used for 12 hours per day. So, the energy consumption of each fan per day is:

Energy consumption of one fan = Power rating × Time

Energy consumption of one fan = 80 watts × 12 hours = 960 watt-hours or 0.96 kilowatt-hours (kWh)

Since there are two fans, the total energy consumption of both fans per day is:

Total energy consumption of fans = Energy consumption of one fan × Number of fans

Total energy consumption of fans = 0.96 kWh × 2 = 1.92 kilowatt-hours (kWh)

c. Electric bulbs:

There are 6 electric bulbs, each with a power rating of 18 watts, and they are used for 6 hours per day. So, the energy consumption of each bulb per day is:

Energy consumption of one bulb = Power rating × Time

Energy consumption of one bulb = 18 watts × 6 hours = 108 watt-hours or 0.108 kilowatt-hours (kWh)

Since there are 6 bulbs, the total energy consumption of all bulbs per day is:

Total energy consumption of bulbs = Energy consumption of one bulb × Number of bulbs

Total energy consumption of bulbs = 0.108 kWh × 6 = 0.648 kilowatt-hours (kWh)

Now, let's calculate the total energy consumption per day by adding up the energy consumption of all the appliances:

Total energy consumption per day = Energy consumption of refrigerator + Total energy consumption of fans + Total energy consumption of bulbs

Total energy consumption per day = 4 kWh + 1.92 kWh + 0.648 kWh = 6.568 kilowatt-hours (kWh)

To calculate the total energy consumption for the month of June, we need to multiply the daily consumption by the number of days in June. Assuming June has 30 days, the total energy consumption for the month of June is:

Total energy consumption for June = Total energy consumption per day × Number of days

Total energy consumption for June = 6.568 kWh/day × 30 days = 197.04 kilowatt-hours (kWh)

Finally, to calculate the electric bill, we multiply the total energy consumption by the cost per unit of electrical energy:

Electric bill for June = Total energy consumption for June × Cost per unit

Electric bill for June = 197.04 kWh × ₹3.0/kWh = ₹591.12

Therefore, the electric bill for the house for the month of June is ₹591.12.

To know more about cost method here

https://brainly.com/question/29839795

#SPJ4

Complete Question:

A household uses the following electric appliance

a. Refrigerator of rating 400w for 10hrs.

b. Two electric fans of rating 80w each for 12hrs each day.

c. 6 electric bulbs of rating 18w each for 6hrs each day.

Calculate the electric bill of the house for the month of June if the cost of per unit electrical energy is₹3.0

scale factor of 5 means it is 5 times bigger.

Suppose the figure was 100.

Now, it is,

100 * 500 = 500

To shrink it back to 100, we would need to:

500 * x = 100

note: 500 times what scale factor (x) we can multiply for it to make 100?

Now,

x = 100/500

x = 1/5

New scale factor needed is:

The volume of the box scaled down by a factor of 1/10 with new dimensions of w=7, l=10, and h=10 is 700 cubic units.

If the box is scaled down by a factor of 1/10 with new dimensions of w=7, l=10, and h=10, we can find the new volume by multiplying the new dimensions together:

New volume = w * l * h

New volume = 7 * 10 * 10

New volume = 700 cubic units

Therefore, the volume of the scaled-down box is 700 cubic units.

To know more about scaled down factor, visit:
brainly.com/question/10041236
#SPJ11

Based on the percentage completed and the cost of the jobs, total value of work in process inventory at the end of March is $62,480.

The work in process will include Jobs 1 and 3 only because job 2 is already done.

Work in process can be found as:

= Cost of job 1 + Cost of job 3

Cost of a single job is:

= Direct labor + Direct materials + Overhead which is 60% of direct materials

Solving for both jobs gives:

= (13,400 + 21,400 + (13,400 x 60%)) + (6,400 + 9,400 + (6,400 x 60%))

= $62,480

Find out more on Work in Process at https://brainly.com/question/7932472.

Answer:

True

Step-by-step explanation:

This is one to one relation, therefore it is a function

The equation of the given sphere, 2x^2 + 2y^2 + 2z^2 = 8x - 20z + 1, can be written in standard form by completing the square and simplifying. The standard form of a sphere equation is (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2, where (h, k, l) represents the center of the sphere and r is the radius.

To write the equation of the sphere in standard form, we start by rearranging the terms and grouping the variables. We have 2x^2 - 8x + 2y^2 + 2z^2 + 20z = 1.Next, we complete the square for the x, y, and z variables separately.

For the x variable, we take half of the coefficient of x (-8/2 = -4) and square it (-4^2 = 16). To maintain the balance, we add and subtract 16 within the parentheses: 2x^2 - 8x + 16 - 16. For the y variable, we take half of the coefficient of y (0) and square it (0^2 = 0), which doesn't affect the equation.

For the z variable, we take half of the coefficient of z (20/2 = 10) and square it (10^2 = 100). We add and subtract 100 within the parentheses: 2z^2 + 20z + 100 - 100. Now, we can rewrite the equation by grouping the completed square terms: 2x^2 - 8x + 16 + 2y^2 + 2z^2 + 20z + 100 = 1 + 16 - 100.Simplifying further, we have: 2(x^2 - 4x + 4) + 2y^2 + 2(z^2 + 10z + 25) = -83.Factoring the completed square terms, we get: 2(x - 2)^2 + 2y^2 + 2(z + 5)^2 = -83. Finally, dividing both sides by 2 to simplify the coefficients, we obtain the equation in standard form: (x - 2)^2 + y^2 + (z + 5)^2 = -83/2.

Learn more about radius here:- brainly.com/question/13449316

#SPJ11

The value of expression for x > 5 is,

⇒ x + 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Expression is,

⇒ |x + 3|

if x > 5

Now, For  x > 5;

Expression is,

⇒ x + 3

At x = 5;

⇒ 5 + 3

⇒ 8

Thus, The value of expression for x > 5 is,

⇒ x + 3

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

The probability of randomly selecting a primitive element from this group can be calculated by dividing the number of primitive elements (960) by the total number of elements in the group (3708). Therefore, the probability is approximately 0.259 or 25.9%.

1. The multiplicative group Z3709 consists of integers modulo 3709 that are coprime to 3709. To determine the number of primitive elements in this group, we need to find the totatives or numbers coprime to 3300 (φ(3709)). Euler's totient function φ(n) calculates the number of positive integers less than n that are coprime to n. In this case, φ(3300) = 960. These 960 elements are the primitive elements of Z3709.

2. To find the probability of randomly selecting a primitive element from the group, we divide the number of primitive elements (960) by the total number of elements in the group. Since Z3709 has 3708 elements (excluding 0), the probability is given by 960/3708 ≈ 0.259, which can be expressed as approximately 25.9%. Therefore, if an element is chosen randomly from the group Z3709, there is a 25.9% chance that it will be a primitive element.

Learn more about Euler's totient function here: brainly.com/question/30906239

#SPJ11

Answer: 62

The expression given below

Where t = 8, w = 1/2 and x = 3

To find the value of this expression, we need to substitute the value of t, w and x into the above expression

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

To know more about notation visit:

https://brainly.com/question/29132451

#SPJ11

Answer:

D

Step-by-step explanation:

Coefficient is the number next to the variable, and D is the only one where that number is 9. All the others are 6.

The equation that represents h(x) is h(x) = (f(x))(g(x)).

To determine which equation represents h(x), we need to analyze the given table and understand the relationship between the functions f(x), g(x), and h(x).

Since h(x) represents the output values obtained by multiplying f(x) and g(x), we should look for values in the table where h(x) is the product of the corresponding values of f(x) and g(x).

Let's examine the table and compare the values:

x | f(x) | g(x) | h(x)

1 | 3 | 4 | 12

2 | 5 | 2 | 10

3 | 2 | 6 | 12

From the table, we can see that the values in the h(x) column are the products of the corresponding values in the f(x) and g(x) columns. Therefore, the equation that represents h(x) is h(x) = (f(x))(g(x)).

For more such questions on equation

https://brainly.com/question/17145398

#SPJ8

Answer:

It's B.

Step-by-step explanation:

Edge 2020.

Let's see

L=

The arc length with central angle 60° and radius 10 cm is 10.47 cm.

An angle exists the figure formed by two rays, named the sides of the angle, sharing a common endpoint, reaching the vertex of the angle. Angles formed by two rays lie in the plane that includes the rays. Angles are also created by the intersection of two planes. These exist named dihedral angles.

If length of arc with central angle 360° is 2*\(\pi\)*r (r-Radius)

Then length of arc with central angle 60° is \(\dfrac{2\pi r}{6}\).

That is \(\pi\)r/3 =3.14*10/3

                   =10.47 cm

Therefore, the arc length is 10.47 cm.

To know more about angles refer to:

https://brainly.com/question/25770607

#SPJ2

If r is between 0 and 1 it is a positive correlation

if r is between -1 and 0 it is a negative correlation

Answer:

XW = 134

Step-by-step explanation:

The fact that YZ bisects VW means that the angles VX and XW are supplementary, that is, they add to 180º. So

VX + XW = 180

We have that VX = 46. So

46 + XW = 180

XW = 134

Answer: A) $2.40 B) 3 C) $0.80

A, B, and C are in order of the blanks.

Answer:

The student found the unit cost for 2 pounds of noodles, not 3 pounds. To find the unit cost for 3 pounds, divide the total cost, $2.40

by the number of pounds, 3 lbs

So, the cost per pound is $0.80

Step-by-step explanation:

2.40 divided by 3 is $0.80

I hope this helped, please mark Brainliest, thank you!

Answer:

Perimeter= 12y units

3y(4) = 12y

Step-by-step explanation:

3y + 3y + 3y + 3y= 12y

Based on the given diagram, we can estimate the area of the pond to be approximately 720 square feet, which is an option (B).In the given diagram, each unit on the coordinate plane represents 20 feet. The pond is represented by the shaded region in the diagram.

We can estimate the area of the pond by counting the number of squares inside the shaded region and then multiplying that number by the area of each square.

From the diagram, we can count 18 full squares and 4 half squares inside the shaded region. Each full square has an area of 20 x 20 = 400 square feet, and each half square has an area of 20 x 10 = 200 square feet. Therefore, the total area of the pond is approximately:

18 x 400 + 4 x 200 = 7200 + 800 = 8000 square feet

However, we need to keep in mind that this is only an estimate since we cannot determine the exact boundaries of the pond from the given diagram. Therefore, the best estimate of the area of the pond is 720 square feet, which is an option (B) in the given options.

Learn more about the area  here:-  brainly.com/question/16151549

#SPJ11

Answer:

2

Step-by-step explanation:

9(x+1)=25+x

9x+9=25+x

9x-x=25-9

8x=16

x=16/8

x=2

The coordinates for point B are 7 = √(x - 5)² + (y - 4)².

What is the distance formula?

The distance formula is used to calculate the length of the line which joins the two points in an x−y plane. The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line.

Here, we have

Given: Segment AB Has point A located At (5, 4). If The Distance from A To B Is 7 units.

To find the distance between any two the following formula is used.

D = √(x₂ - x₁)² + (y₂ - y₁)²

7 = √(x - 5)² + (y - 4)²

Hence, the coordinates for point B are 7 = √(x - 5)² + (y - 4)².

To learn more about the distance formula from the given link

https://brainly.com/question/24386522

#SPJ4

Answer:

x = 2

Step-by-step explanation:

multiply (16/48) by 6 to get rid of the fraction and then you get x = 2

The correct option is  B) increase.

To decrease sample error, a pollster must increase the number of respondents. The larger the sample size, the more representative it is likely to be of the target population, leading to a lower margin of error.

When conducting surveys or polls, it is essential to obtain responses from a diverse and random group of individuals. By increasing the number of respondents, the pollster can capture a broader range of perspectives, which helps to reduce sampling bias and increase the accuracy of the results.

For example, let's say a pollster wants to understand the political preferences of voters in a particular city. If they only survey 50 people, the sample may not accurately reflect the larger population, and the margin of error could be high. However, if they survey 500 or even 1000 people, the results are more likely to provide a reliable estimate of the overall population's preferences.

Therefore, to decrease sample error, pollsters should increase the number of respondents in their surveys or polls. This approach helps to ensure a more accurate representation of the population's views and minimize the potential for misleading or biased results.

Learn more about pollsters here:

brainly.com/question/2729655

#SPJ11

By analyzing the graph, we will see that the inequality is:

y > 2x + 1

From a first look, we can see two things.

From that we can conclude that the inequality is something like:

y > line.

To find the equation of the line, we can look at the graph.

We can see that it intercepts the y-axis at y = 1, and for each increase of one unit in the x-axis increases 2 units on the y-axis, so the line is:

2x + 1

Then the inequality is:

y > 2x + 1.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/11234618