The sum of their 3 prime numbers is 24.
What is the sum of their 3 prime numbers?
Let's start by finding the prime numbers that Jimmy, Kimmy, and Timmy are thinking of.
We know that the product of Jimmy's and Kimmy's prime is 34. Since 34 is not a prime number, it must be the product of two prime factors.
The only way to factor 34 as a product of two primes is 2 x 17.
So we know that Jimmy's prime is either 2 or 17, and Kimmy's prime is the other one. We also know that Kimmy's and Timmy's primes multiply to 85. Again, 85 is not a prime number, so it must be the product of two prime factors.
The only way to factor 85 as a product of two primes is 5 x 17.
Therefore, we know that Timmy's prime is 5.
So the three primes are 2, 17, and 5.
The sum of these three primes is 2 + 17 + 5 = 24.
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7. According to new research in 2021, Puerto Rican Reggaeton star Bad Bunny again took the title of
most-streamed artist in the world on Spotify. He received over 9.1 billion streams (9, 100, 000, 000)
without releasing a new album last year.
Use this number of streams with your equation to calculate how much money Bad Bunny may have
made via Spotify. (Worlds Most Streamed Songs (Spotify), 2021)
The requried, Bad Bunny may have made around $34.6 million from his 9.1 billion streams on Spotify in 2021.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As of 2021, Spotify's average payout per stream is about $0.0038, which means that an artist earns approximately 0.38 cents per stream.
So, to calculate Bad Bunny's potential earnings from 9.1 billion streams on Spotify, we can use the following equation:
Earnings = Number of Streams x Payout per Stream
Earnings = 9,100,000,000 x $0.0038
Earnings = $34,580,000
Therefore, based on this rough estimate, Bad Bunny may have made around $34.6 million from his 9.1 billion streams on Spotify in 2021. It's important to note that this is just an estimate and that the actual amount he earned could be higher or lower depending on the factors mentioned earlier.
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In a completely randomized experimental design involving six treatments, 11 observations were recorded for each of the six treatments. The following information is provided.
SSTR = 400 (Sum Square Between Treatments)
SST = 700 (Total Sum Square)
The mean square within treatments (MSE) is _____.
a. 5 b. 400 c. 80 d. 300
The mean square within treatments (MSE) is 5 when in a completely randomized experimental design involving six treatments, 11 observations were recorded for each of the six treatments.
What is mean?Mean is a measure of central tendency which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing the sum by the total number of values in the set.
Here,
To find the mean square within treatments (MSE), we need to use the formula:
MSE = SSE / df
where SSE is the sum of squares within treatments and df is the degrees of freedom within treatments.
Since we are given SSTR and SST, we can find SSE using the formula:
SSE = SST - SSTR
Substituting the given values, we get:
SSE = 700 - 400 = 300
The total number of observations is:
n = 6 treatments × 11 observations/treatment = 66 observations
The degrees of freedom within treatments is:
df = n - number of treatments = 66 - 6 = 60
Therefore, the mean square within treatments is:
MSE = SSE / df
= 300 / 60
= 5
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A regular pentagon has an area of 118.25 square meters, and each side of the pentagon measures 4.3 meters.
What is the length of an apothem of the pentagon?
Enter your answer in the box.
m
The length of the apothem of the pentagon is approximately 11 meters.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc.
Here, we have,
To solve this problem, we can use the formula for the area of a regular pentagon:
A = (5/2) × s × a
Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).
We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:
118.25 = (5/2) × 4.3 × a
Divide both sides by (5/2) x 4.3:
a = 118.25 / ((5/2) × 4.3)
= 118.25 / 10.75 ≈ 11 meters
Therefore, the length of the apothem of the pentagon is approximately 11 meters.
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Alex and his father took a taxi cab that charges $2.60 per mile plus $3.00 for the two passengers, and they paid a total of $18.60. Alex wrote the equation 18.60=2.60b+3.00 for this situation and found b=6, where b represents the number of miles the taxi traveled.
How could Alex correctly solve this problem without using the equation?
A He can find the total number of miles by dividing the total cost, $18.60, by $2.60.Then, he could subtract $3.00 from the quotient.
B He can find the total number of miles by dividing the total cost, $18.60,by $2.60.Then, he could add $3.00 to the quotient.
C He can find the total number of miles by adding $3.00 from the total cost, $18.60.Then, he could divide the sum by $2.60.
D He can find the total number of miles by subtracting $3.00 from the total cost, $18.60. Then, he could divide the difference by $2.60.
The answer here would be D. In choice A, this would be incorrect because he would divide the millage cost before the passenger fee. In choice B, this would be incorrect because he would add the passenger fee, when it is required to subtract it. Choice C would be incorrect, because yet again, you are not supposed to add the passenger fee. This leaves choice D, which is correct.
Mimi bought a sign in the shape of an arrow as shown. The base and height of the triangle are both 3 inches. What is the total area of the sign?
A. 11 1/4 square inches
B. 9 3/4 square inches
C. 15 3/4 square inches
D. 16 1/2 square inches
Answer:
the answer is A. 11 1/4
Step-by-step explanation:
the base times height for the triangle divided by 2 plus the bxh of the rectangle.
3x3/2 + 1 1/2 x 4 1/2
classify the following as point , line , and or plane ________1 Corner of a Vaccinatopn room ________2 Face mask ________3 Long chain of children for pediatric vaccination
1. Point - Corner of a Vaccination room
2. Plane - Face mask
3. Line - The long chain of children for pediatric vaccination
What are points, lines, and planes:Point:
A point is represented as a "dot" on paper. There will be no length, width, or height existing for a point. It simply identifies a certain position. Zero dimensions apply to it.
Line:
The line is a one-dimensional shape in geometry. A line, thus, has length but neither width nor height. In any direction, a line never stops. Two end points of lines act as the fundamental determinants of a line.
Plane:
The coordinate plane, which is used to plot points in algebra, is an example of a plane. The number lines on the coordinate plane stretch eternally from left to right and from up to down, respectively. The coordinate plane cannot be seen entirely.
Here we have
Corner of a Vaccination room, Face mask, The long chain of children for pediatric vaccination
Where
The corner of a Vaccination room represents a point.
Face mask represents a plane
The long chain of children for pediatric vaccination represents a line.
Therefore,
1. Point - Corner of a Vaccination room
2. Plane - Face mask
3. Line - The long chain of children for pediatric vaccination
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If f(1)=9f and f(n)=−2f(n−1)−1 then find the value of f(4)
Answer:
f(4)= 36
f(4) = 7n-7
Step-by-step explanation:
f(4)= 9(4)
36= f(4)
f(4) = - 2(4)(n-1)-1
8(n-1) - 1
7 (n-1)
7n-7 = f(4)
2. A client has approached a stockbroker with the following request: Invest $100,000 for maximum annual income under these conditions: • Spread the investment over no more than three different stocks • Put no more than 40 percent of the money into anyone stock • Put a minimum of $10,000 in to oil stock. The broker has identified three stocks for investing the funds. Their estimated annual returns and price per share are shown in the following table: Stock Price Per share Estimated annual return per share Oil $120 $11 Auto 52 4 Health 18 2 Required: Formulate an LPM for the problem. 1. Given this summarized linear programming model: Maximize: Subject to: 1. 2. 3. i) Graph the model ii) Find the optimal point on the graph using the extreme point approach iii) Use simultaneous equations to determine the optimal value of iv) Determine the amount of slack for each constraint
Answer:
Step-by-step explanation:
the optimal point is (40,000, 40,000, 20,000), which gives an annual income of $680,000. The slack for the first, second, and fourth constraints is 0, and the slack for the third constraint is also 0.
Assume that military aircraft use ejection seats designed for men weighing between 132. 4132. 4 lb and 217217 lb. If women's weights are normally distributed with a mean of 168. 7168. 7 lb and a standard deviation of 48. 848. 8 lb, what percentage of women have weights that are within those limits
The percentage of women with weights that are within the limits is:
60.93%
What percentage of women have weights that are within those limits?Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:
z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74
z-score for upper limit = (217 - 168.7) / 48.8 = 0.99
Next, we can use a z-table to find the corresponding probabilities for these z-scores:
Probability for lower limit = 0.2296
Probability for upper limit = 0.8389
Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093
Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.
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The population of a city increases by 0.5% per year. If this year's population is 201,000, what will next year's population be, to the nearest individual?
Next year's population is 202,005
How to calculate the quantity of next year's population?
The population of a city increases by 0.5% per year
This year's population is 201,000
Next year's population can be calculated as follows
201,000 × 0.5/100
= 201,000 × 0.005+1
= 201,000 × 1.005
= 202,005
Hence next year's population is 202,005
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A circular device has a diameter of 4.5 inches. What is the radius of the device?
Answer:
Hello there! If the circular device has a diameter of 4.5 inches, the radius of the device would be 2.25 inches.
Step-by-step explanation:
The diameter of the circle is a line segment that not only passes through the center of the circle, but also has endpoints that are on the circle and opposite sides to each other. The radius, on the other hand, is half the distance of the diameter, or the distance from any point on the circle to the center of the circle. I've attached a picture below to show you what that would look like, if you're a visual learner.
Since we know the diameter of the circular device is 4.5 inches, and we know that the radius of a circle is half the length of the diameter of that same circle, that means the radius of the circular device would be [tex]\frac{4.5}{2}[/tex] or 2.25 inches long.
Have a great day! Feel free to let me know if you have any more questions :)
Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 12 gallons of gasoline to travel 288 miles. How
many miles can the car travel if it has 9 gallons of gasoline?
Answer:
Step-by-step explanation:
225 miles because you have to divide 100 by 4 that would give me 25 MPG and be asked, how many miles can the car travel using? Nine gallons of gasoline? So that would be right here, And that's at 225 Miles that it can travel with nine gallons of gasoline.
NO LINKS!!! URGENT HELP PLEASE!!! NOT MULTIPLE CHOICE!!!!!
3. You are sitting on the edge of the pool and swim underwater to the other side. Your path through the water can be modeled by the equation d(p) = 1/4p^2 - 2p in feet per second. Use this scenario to answer questions a - c.
a. What is your deepest point underwater?
b. What is your depth when you have held your breath for 22 seconds? (Round your answer to the nearest foot)
c. How long do you hold your breath to make the swim?
Answer:
3.
a.4 feet
b.77 feet
c.8 seconds
Step-by-step explanation:
We can start by noting that the given equation, d(p) = 1/4p^2 - 2p, represents the depth (in feet) at a given point in time as you swim underwater, where p is the time in seconds since you started swimming.
a. To find the deepest point underwater, we need to find the maximum of the function d(p). We can do this by finding the vertex of the parabola. The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = 1/4 and b = -2, so the x-coordinate of the vertex is:
x = -b/2a = -(-2)/(2(1/4)) = 4
So the deepest point underwater occurs at p = 4 seconds. To find the depth at this point, we can substitute p = 4 into the equation:
d(4) = 1/4(4)^2 - 2(4) = -4 feet
Therefore, the deepest point underwater is 4 feet below the surface.
b. To find the depth when you have held your breath for 22 seconds, we need to evaluate the function d(p) at p = 22. We can round our answer to the nearest foot.
d(22) = 1/4(22)^2 - 2(22) = 77 feet
Therefore, the depth when you have held your breath for 22 seconds is approximately 77 feet below the surface.
c. To find how long you hold your breath to make the swim, we need to find the time it takes to swim from one side of the pool to the other. We can do this by finding the roots of the equation d(p) = 0, which represent the times when you reach the other side of the pool (i.e., when the depth is zero). We can use the quadratic formula to solve for p:
p = (-b ± sqrt(b^2 - 4ac))/2a
In this case, a = 1/4, b = -2, and c = 0, so the formula becomes:
p = (-(-2) ± sqrt((-2)^2 - 4(1/4)(0)))/(2(1/4)) = 8 or 0
The root p = 0 corresponds to the start of the swim, so the time it takes to make the swim is:
p = 8 - 0 = 8 seconds
Therefore, you hold your breath for 8 seconds to make the swim from one side of the pool to the other.
Completely factor the polynomial 2x³ + 54
Answer:
Step-by-step explanation:
2x³+54=2(x³+27)=2(x³+3³)
a³+b³=(a+b)(a²-ab+b²)
complete it
if you have to go to school 3 days from tuesday what day will you go back to school
Answer:
Three days from Tuesday is Friday.
What does the index value of 99.2 in 1980 mean? Explain your reasoning.
The index value of 99.2 in 1980 mean Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992, the correct option is D.
What is the ratio?
Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
Years, prices, prices as a percentage of 1990 price, price index 1990=100
Now,
The given table shows the average gasoline prices per gallon for various years, as well as the price index for each year, with 1990 being the reference year with a price index of 100. The price index measures the change in the price of gasoline relative to the price in 1990. Therefore, the price index value of 99.2 for 1980 means that the average gasoline price in 1980 was 0.992 times the price of gasoline in 1990.
It is important to note that the gas price index does not directly measure the cost per gallon of gas. Rather, it is a measure of the change in gasoline prices over time, with a reference year (in this case, 1990) used as a baseline.
Therefore, by ratio the answer will be Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992.
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You accidentally dial one number on your phone's keypad. Find the probability that the number you dialed is greater than 9.
Answer:
0
Step-by-step explanation:
What is probability?Probability (also known as chance) is the number that indicates how likely an event is to occur. If something has a low probability, it is unlikely to happen. If something has a high probability, it is likely to happen.
If we look at a phone keypad, you will see the numbers 0-9, but you will never see a number greater than 9.
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the numbers, but none are greater than 9.
Ocupó la respuesta de la página 153 del ejercicio 4?
On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].
What is algebraic expression?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
3x + y
Given is to find the equivalent value for the division as -
"153 ÷ 4"
On dividing 153 by 4, we can write the result as follows -
{x} = 153/4
{x} = 38.25
{x} = 38[tex]\frac{1}{4}[/tex]
Therefore, On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].
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{Question in english -
What is the remainder when 153 is divided by 4?}
Please help me. This is homework and I dont understand how to solve this...
The solution of the system x + y ≥ 75 and 2.5x + 10.5y ≤ 800 of the equation is
C. (250, 10)How to find the solution of the equationThe system of equation x + y ≥ 75 and 2.5x + 10.5y ≤ 800 will have a solution that is as written in the equation.
This is done by substituting each value
Using (250, 10)
250 + 10 ≥ 75
260 ≥ 75 correct
2.5x + 10.5y ≤ 800
2.5 * 250 + 10.5 * 10 ≤ 800
730 ≤ 800 correct
since the the values are correct for the equations, (250, 10) is the solution
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Can somebody please help me
find the value of x
Help me with number 7 please
Answer:
Are we supposed to give the answer in fractions?
If the value of XYZ Company stock drops from $25 per share to $21 per share, what is the percent of the decrease?
The percentage of the decrease in the value of the XYZ Company stock is 16%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
The decrease in the value of the stock is $25 - $21 = $4.
To find the percent decrease, we need to divide the decrease by the original value and then multiply by 100:
Percent decrease = (Decrease / Original value) x 100
In this case, the original value is $25, so:
Percent decrease = (4 / 25) x 100 = 16%
Therefore, the percentage of the decrease in the value of the XYZ Company stock is 16%.
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Please help me answer this question ASAP!!
The surface area of the rectangular prism, found by summing the surface areas of the six rectangular faces is about 2,600 square inches
What is a rectangular prism?A rectangular prism is a three dimensional solid with six rectangular faces, such that faces of the prism that face each other are parallel and congruent.
The surface area of the rectangular prism is the sum of the surface areas of the six rectangular faces of the prism
The area of the rectangles that make up the surface are;
A₁ = 8 inches × 36 inches = 288 square inches
A₂ = 23 inches × 8 inches = 184 square inches
A₃ = 23 inches × 36 inches = 828 square inches
A₄ = 23 inches × 8 inches = 184 square inches
A₅ = 8 inches × 36 inches = 288 square inches
A₆ = 23 inches × 36 inches = 828 square inches
The surface area of the rectangular prism, A, is therefore;
A = A₁ + A₂ + A₃ + A₄ + A₅ + A₆
Therefore;
A = 288 + 184 + 828 + 184 + 288 + 828 = 2600
The surface area of the rectangular prism is 2,600 square inches
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Find the number of years necessary for an investment to double at each of these rates of simple interest. Round to the nearest tenth if necessary.
Interest Rate: 11%
It would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
According to given information :To find the number of years necessary for an investment to double at a simple interest rate of 11%, we can use the following formula:
n = 72 / r
where n is the number of years required for the investment to double, and r is the interest rate.
Plugging in the values, we get:
n = 72 / 11
n ≈ 6.5 years (rounded to the nearest tenth)
Therefore, it would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.
What is simple interest ?Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested, and it is not compounded over time.
The formula for calculating simple interest is:
I = P * r * t
where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.
For example, if you borrow $1,000 for two years at a simple interest rate of 5%, the interest you would pay is calculated as follows:
I = 1,000 * 0.05 * 2
I = $100
So, you would have to pay back the $1,000 principal plus $100 in interest, for a total of $1,100.
Simple interest is commonly used in short-term loans or investments, and it is usually easier to calculate and understand than compound interest, which takes into account the effect of earning interest on previously earned interest.
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The sum of four times a number and seven is 27. Find the number.
Provide your answer below:
Answer:
Look at the screenshot.
Plot the following points in the Cartesian plane.
{(3,6),(−8,2),(−9,−4),(2,−8)}
What is cartesian plane ?
A Cartesian plane (also known as a coordinate plane or rectangular coordinate system) is a two-dimensional plane formed by two perpendicular number lines, referred to as the x-axis and the y-axis, that intersect at a point called the origin. The x-axis is a horizontal line, and the y-axis is a vertical line.
Explanation:
To plot the following points in the Cartesian plane:
{(3,6),(-8,2),(-9,-4),(2,-8)}
First, we draw the x and y axes to form a Cartesian plane.
Then, for each point, we plot the x and y coordinates on the graph. The x coordinate indicates the horizontal position of the point on the x-axis, while the y coordinate indicates the vertical position of the point on the y-axis.
The point (3,6) is plotted as a dot on the Cartesian plane located 3 units to the right of the origin on the x-axis and 6 units above the origin on the y-axis.
The point (-8,2) is plotted as a dot located 8 units to the left of the origin on the x-axis and 2 units above the origin on the y-axis.
The point (-9,-4) is plotted as a dot located 9 units to the left of the origin on the x-axis and 4 units below the origin on the y-axis.
The point (2,-8) is plotted as a dot located 2 units to the right of the origin on the x-axis and 8 units below the origin on the y-axis.
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An open cardboard box is 20 cm long, 12 cm
wide and 8 cm deep (Fig. 14.9). Calculate
the total area of cardboard in the box.
The Total Surface area of cardboard in the box is 992 cm².
What is Total Surface Area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.
Given:
length= 20 cm
width = 12 cm
height= 8 cm
So, the TSA of Cuboid
= 2(lw + wh + lh)
=2( 20 x 12 + 12 x 8 + 8 x 20)
=2( 240 + 96 + 160)
= 2(496)
= 992 cm²
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Solve the word problem for the portion, rate, or base. Suppose in a single month a certain baseball team won 21 games and lost 3. What percent of the games did they win? (Hint: Use total games played as the base.)
The baseball team won 87.5% of their games in that month.
Describe Algebraic Expression?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.
The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.
Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.
Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance
To find the percentage of games won, we need to divide the number of games won by the total number of games played and multiply by 100%:
percentage of games won = (number of games won / total games played) x 100%
total games played = number of games won + number of games lost = 21 + 3 = 24
percentage of games won = (21 / 24) x 100%
percentage of games won = 87.5%
Therefore, the baseball team won 87.5% of their games in that month.
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How would I complete the balance sheet?
The completed balance sheet is given below:
What is a Balance Sheet?A balance sheet is a financial statement that shows the financial position of a company at a specific point in time. It provides information about a company's assets, liabilities, and equity, and helps to illustrate the overall financial health of the company.
The Balance Sheet
Sheffield company
balance sheet (partial)
December 31, 2023
Plant Assets
Land $3,926,000
Building $28,650,000
Less: Accumulated Depreciation (14,396,250)
Net Building $14,253,750
Equipment $49,569,000
Less: Accumulated Depreciation (4,127,795)
Net Equipment $45,441,205
Total Plant Assets $63,620,955
Note that the buildings and equipment are shown at their net book value, which is the original cost less the accumulated depreciation.
The accumulated depreciation represents the portion of the cost that has been expensed over time due to wear and tear, obsolescence, or other factors.
The land is not depreciated, so its original cost is shown.
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The table values of two linear functions is given below.if they intersect at the point (a,b) what is the value of a+b
-2. - 1. 1. 2.
Answer:
Step-by-step explanation:
Here is a more detailed explanation:
We are given two linear functions, f(x) and g(x), and their values for x = 1 and x = 4:
x f(x) g(x)
1 3 5
4 9 20
To find the value of a + b at the point of intersection (a, b) of the two functions, we need to first find the equations of the two functions. To do this, we need to find the slope and y-intercept of each function.
For f(x), the slope is (9 - 3) / (4 - 1) = 2, and using the point (1, 3) we can find the y-intercept as:
y - 3 = 2(x - 1)
y - 3 = 2x - 2
y = 2x + 1
So the equation of f(x) is y = 2x + 1.
Similarly, for g(x), the slope is (20 - 5) / (4 - 1) = 5, and using the point (1, 5) we can find the y-intercept as:
y - 5 = 5(x - 1)
y - 5 = 5x - 5
y = 5x
So the equation of g(x) is y = 5x.
To find the point of intersection of the two functions, we can set their equations equal to each other and solve for x:
2x + 1 = 5x
3x = 1
x = 1/3
Substituting this value of x back into either equation, we can find the corresponding value of y:
y = 2(1/3) + 1 = 7/3
So the point of intersection is (1/3, 7/3).
Therefore, a + b = 1/3 + 7/3 = 8/3. This is approximately equal to 2.67. The answer closest to this value is -1, so the correct answer is (b) -1.
