1. The manager of FrozonAir Refrigerator factory notices that on Monday it cost the company a total of $25,000 to build 30 refrigerators and on Tuesday it cost $30,000 to build 40 refrigerators. Find a linear cost function based on this information. What is the daily fixed cost, and what is the marginal cost?

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

Learn more about  balance from

https://brainly.com/question/28767731

#SPJ11

No solve this you have to multiply the cost per acre by the total are you want to plant:

It'll cost $73.3 to plant 2/3 of the acre.

Answer:

18:162

Step-by-step explanation:

1:9

1+9=10

(1×180)÷10= 18

(9×180)÷10=162

When shared in a ratio of 1:9,  £180 would be divided into the amounts, £18 and £162.

When dealing with ratios, you find the different shares in the following manner:

= Ratio / sum of ratios x Amount to be shared

When finding out the first amount, the amount is:

= 1 / (1 + 9) x 180

= 1 / 10 x 180

= £18

The second amount is:

= 180 - 18

= £162

In conclusion, the two amounts are £18 and £162.

Find out more at https://brainly.com/question/21299138.

Answer:

C. -2(-2)

Step-by-step explanation:

A. -2(-1/5) = 1

B. -2(1/2)=1

C. -2(-2)=4

D. -2(2)=-4

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

Learn more about constant term.

brainly.com/question/26099230

#SPJ11

Answer:

c for both

Step-by-step explanation:

This is because when there is no correlation, the variation in y cannot be explained by the variation in x, leaving a lot of room for error. the error variance for the linear model

a) If the correlation between x and y is 1, it means that the two variables have a perfect positive linear relationship. In this case, the error variance for the linear model would be 0. This is because when there is a perfect correlation, all the variation in y can be explained by the variation in x, leaving no room for error. Therefore, the error variance would be 0.

b) If the bet correlation ween x and y is 0, it means that the two variables have no linear relationship. In this case, the error variance for the linear model would be the sum of the variances of x and y. This is because when there is no correlation, the variation in y cannot be explained by the variation in x, leaving a lot of room for error. Therefore, the error variance would be the sum of the variances of x and y, which is 49+4=53.

a) If the correlation between x and y is 1, the value of the error variance for your linear model would be 0. This is because a correlation of 1 indicates a perfect positive linear relationship between x and y, meaning there is no error or deviation from the predicted values of y based on the linear model.

b) If the correlation between x and y is 0, the value of the error variance would be equal to the variance of y. This is because a correlation of 0 indicates that there is no linear relationship between x and y, meaning that the linear model provides no predictive value for y. In this case, the error variance is equal to the variance of y, which can be calculated by squaring the standard deviation of y (2^2 = 4).

learn more about  correlation here : https://brainly.com/question/22085260

#SPJ11

Answer:

\( \frac{BD}{AD} = \frac{5}{7} \)

Step-by-step explanation:

Coordinate of B = 1

Coordinate of D = 6

Coordinate of A = -1

BD = |1 - 6| = 5 units

AD = |-1 - 6| = |-7| = 7 units

\( \frac{BD}{AD} \)

Plug in the values

\( \frac{BD}{AD} = \frac{5}{7} \)

Answer:

x1 = 4/3, x2 = 1/2

Value to fill in the question mark: 3

Step-by-step explanation:

The vertical asymptotes occurs when the denominator of y are 0, so the value of y goes to infinity.

So, to find the asymptotes, we need to calculate:

\(6x^{2} - 11x + 4 = 0\)

Using Bhaskara's formula. we have:

\(\Delta = (-11)^2 - 4*6*4 = 25\)

\(\sqrt{\Delta} = 5\)

\(x_1 = (11 + 5)/12 = 4/3\)

\(x_2 = (11 - 5)/12 = 1/2\)

So the value we need to fill in the question mark is 3

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

Read more on inequality:

https://brainly.com/question/25275758

#SPJ1

Chuck originally tried to sell the "short coats" for $240 each.

How to find and what does discount mean?

Let's work backwards to find the original price of the "short coats." If the price after the 75% discount was $54, then the price before the discount was:

$54 / 0.25 = $216

Now we need to undo the 10% discount to find the original price. If $216 represents 90% of the original price, we can set up an equation:

$216 = 0.9x

where x is the original price. Solving for x:

x = $240

Therefore, Chuck originally tried to sell the "short coats" for $240 each.

A discount is a reduction in the price of a product or service. It is often used as a marketing strategy to attract customers and increase sales. A discount can be expressed as a percentage or an amount off the original price.

To know more about Discount related question visit:

https://brainly.com/question/3541148

#SPJ1

the pool can contain approximately 8,218 gallons of water.

A cylindrical swimming pool has a diameter of 20 feet and a height of 3.5 feet. We are required to find out how many gallons of water can the pool contain.

Converting diameter to radius: The diameter of the cylinder is given as 20 feet. Hence the radius of the cylinder can be obtained by dividing the diameter by 2.

r= 20/2 = 10 feet

Volume of cylinder:Volume of cylinder is given by πr2h where π is a mathematical constant whose value is approximately 3.14r is the radius of the cylinderh is the height of the cylinder.

Putting values into the formula, we get:

π(10)²(3.5)≈ 1,095.75 ft³

Converting ft³ to gallons: 1 ft³ = 7.5 gallons

Therefore, 1,095.75 ft³ ≈ 8,218.13 gallons

the pool can contain approximately 8,218 gallons of water.Hence, the pool can contain approximately 8,218 gallons of water.

To know more about diameter visit:

brainly.com/question/31445584

#SPJ11

The answer is,

\(x = \frac{13}{14} \)

And in decimal form it would be,

\(0.928571\)

Answer:

Step-by-step explanation:

\(\frac{5x-5}{x-2}=\frac{1}{3}\\ \\ 15x-15=x-2\\ \\ 14x=13\\ \\ x=\frac{13}{14}\)

Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

Learn more about Graphs and inequality here,

brainly.com/question/16608196

brainly.com/question/17448505

The expression which is the simplified form of the given expression as required to be determined is; Choice A; 1 / 3x²y³.

As evident from the task content; it follows that the expression which is the simplified form of the given expression is to be determined.

Since the given expression is; 5xy⁵ / 15x³y⁸.

Therefore, we have that;

= (5 / 15) × (x / x³) × (y⁵ / y⁸)

= (1 / 3) × (1 / x²) × (1 / y³)

= 1 / 3x²y³.

Ultimately, the answers choice A is the simplest form.

Read more on indices;

https://brainly.com/question/24291110

#SPJ1

Answer:

7

Step-by-step explanation:

Answer:

For x = 10:

\(x + 0y - 10 = 0\)

For y = - 3:

\(0x + y + 3 = 0\)

Step-by-step Explanation:

Before we start let's recall the formula for the linear equations.

\(ax + bx = c\)

So first let's solve for x=10:

\(x = 10\)

Move 10 to the other side.

\(x - 10 = 0\)

As there is no y given we will simply write 0y.

\(x + 0y - 10= 0\)

Now let's solve for y=-3:

\(y = - 3\)

Move -3 to the other side.

\(y + 3 = 0\)

As there is no x given we will simply write 0x.

\(0x + y + 3 = 0\)

If this answer helped you, give this answer a heart, rate it and if you could then please mark it brainliest. Thanks!

If it took 49 sec for 1.0L of helium to effuse through a pin hole, it would take 98 sec for 1.0L of methane, CH4, to effuse under identical conditions. So, correct option is e.

The rate of effusion of a gas is inversely proportional to the square root of its molar mass. Therefore, we can use Graham's law of effusion to compare the effusion rates of different gases.

The molar mass of helium (He) is approximately 4 g/mol, and the molar mass of methane (CH₄) is approximately 16 g/mol.

According to Graham's law, the ratio of the effusion rates of two gases is given by the square root of the ratio of their molar masses:

Effusion rate of helium / Effusion rate of methane = √(Molar mass of methane / Molar mass of helium)

Plugging in the values:

Effusion rate of helium / Effusion rate of methane = √(16 g/mol / 4 g/mol) = √4 = 2

Therefore, the effusion rate of methane is two times slower than the effusion rate of helium.

If it took 49 seconds for 1.0L of helium to effuse, it will take 49 seconds multiplied by 2, which is 98 seconds or 1 minute and 38 seconds, for 1.0L of methane to effuse under identical conditions.

So, correct option is e.

To learn more about Graham's law click on,

https://brainly.com/question/29450095

#SPJ4

Complete question is:

It took 49 sec for 1.0L of helium to effuse through a pin hole. How long will it take for 1.0L of methane, CH4, to effuse under identical conditions? a) 196 s

b) 75 s

c) 25 s

d)12 s

e) 98s

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

To learn more about Central tendency, refer:

https://brainly.com/question/1288901

#SPJ4

If there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

each slice of the 12-inch thin-crust cheese pizza would have an equal distribution of sauce and toppings. This means that each slice would have the same amount of sauce and toppings spread evenly across its surface.

Since the pizza is cut equally into eight slices, each slice would represent 1/8th of the total pizza. Therefore, each slice would have an equal portion of the sauce and toppings.

It's important to note that the exact amount of sauce and toppings on each slice would depend on the original distribution applied to the pizza before it was sliced. If the pizza was prepared with a uniform distribution of sauce and toppings across the entire pizza, then each slice would indeed have an equal amount. However, if there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

Learn more about exact amount here:

https://brainly.com/question/30069661

#SPJ11

The amount of the remittance from ABC is $1,960.

The given information states that merchandise is sold for $2,000 with terms of 2/10, n/30 to ABC. The terms 2/10, n/30 imply a 2% discount if payment is made within 10 days, with the full amount due within 30 days.

Since ABC sends a remittance on Dec. 26, it means the payment is made after the discount period but within the credit period. Therefore, ABC is not eligible for the discount of 2%.

To calculate the amount of the remittance, we simply subtract the discount from the total amount. In this case, the discount is $2,000 * 2% = $40. Thus, the remittance amount is $2,000 - $40 = $1,960.

In conclusion, the amount of the remittance from ABC is $1,960, as they did not qualify for the early payment discount.

Learn more about credit periods here:

brainly.com/question/2264363

#SPJ11

The type of survey that is utilized to determine the extent of problems in a certain area and then express the findings as rates affected within the population is known as an epidemiological survey.

What is an epidemiological survey?

An epidemiological survey is a type of survey used to understand the prevalence and incidence of particular health problems in a particular population. In addition, epidemiological surveys are utilized to determine the causes, transmission, and treatment of these problems.

Epidemiological studies are classified according to the types of questions that they are designed to answer. They are as follows:

Descriptive studies: These studies describe the incidence, prevalence, and distribution of diseases in populations.

Analytical studies: These studies are concerned with determining the causative factors of diseases in populations.

Experimental studies: These studies determine the efficacy and safety of new treatments for diseases.

Learn more about epidemiological survey here:

https://brainly.com/question/13497485

#SPJ11

Answer: Angles that have different sums .

Step-by-step explanation: Complementary angles are two angles with a sum of 90º. Supplementary angles are two angles with a sum of 180º. Vertical angles are two angles whose sides form two pairs of opposite rays.

Answer:

To work out the pressure that the car exerts on the road, we need to divide the force by the area of contact between the car and the road.

Since each of the car's 4 tyres has an area of 0.03 m² in contact with the road, the total area of contact is:

Total area of contact = 4 × 0.03 m² = 0.12 m²

So, the pressure that the car exerts on the road can be calculated as:

Pressure = Force / Area of contact

Pressure = 15,600 N / 0.12 m²

Pressure = 130,000 N/m²

Therefore, the pressure that the car exerts on the road is 130,000 N/m².

Answer:

Corresponding angles

Step-by-step explanation:

The name of these angels lying in the same position are called corresponding angle.

These angles are equal. When we talk of parallel lines, they are sets of lines that travel in the same direction but never meet. The third line that cuts through the two sets of parallel lines is referred to as the transversal line.

So the positions of these angles on each of the set of the parallel lines are equal in each of the cases and they are equal and are referred to as being corresponding to each other

Answer:

Step-by-step explanation: