If an object that has a volume of 30 cubic inches weighs 24 ouncess then the constant of variation is 0.8.
If the weight of an object varies directly with its volume, then we can write the following proportion
Weight / volume = constant of variation
Let's use w to represent the weight of the object and v to represent its volume. We are given that an object with a volume of 30 cubic inches weighs 24 ounces, so we can write
w / v = k
Where k is the constant of variation. We can solve for k by substituting the given values
24 / 30 = k
Simplifying this expression, we get
0.8 = k
Therefore, the constant of variation is 0.8.
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Question
Simplify.
(m + 13) - (p + 25)
The expression (m + 13) - (p + 25) after subtraction is simplified to m - p - 12.
The expression (m + 13) - (p + 25) can be simplified by subtracting each term inside the second set of parentheses by -1, which gives
(m + 13) + (-p - 25)
Then, we can group the like terms together
(m - p) + (13 - 25)
Simplifying further, we get
(m - p) - 12
Therefore, (m + 13) - (p + 25) simplifies to m - p - 12, which means that the difference between the sum of m and 13 and the sum of p and 25 is equal to m minus p minus 12.
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I need help now!!!! +10 points
The correct statement regarding the patterns is given as follows:
Every term in Pattern B is 1/4 the corresponding term in Pattern A.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The general term of an arithmetic sequence is given by the explicit formula presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
Each pattern has a first term of zero, while the first pattern has a common difference of 16 and the second pattern has a common difference of 4, hence the equations are given as follows:
A(n) = 16(n - 1).B(n) = 4(n - 1).The ratio is given as follows:
B(n)/A(n) = 4(n - 1)/16(n - 1) = 1/4.
Hence the correct option is given by the first option.
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Find the volume of this composite object!
(use 3 for pi)
Answer:
207 cubic cm
Step-by-step explanation:
3x3^2x11/3 = 99
4/3x3x3^3 = 108
108+99=207
An office manager paid $675.95 to build a web site. The office manager bought a software package for $68.50 and paid an employee $127.95 for each hour she worked on the website. What is x, the number of hours the employee worked on the website
An office manager paid $675.95 for computer equipment. The office manager bought one monitor for $127.95 and hard drives for $68.50 each. What is x, the number of hard drives the office manager bought?
A sales manager paid $675.95 for advertising. The sales manager paid $127.95 per hour for consulting and received a $68.50 discount. What is x, the number of hours the manager paid for consulting?
A business owner paid a total of $675.95 for two employees to work the same number of days. The business owner paid one employee $68.50. The business paid a second employee $127.95 per day. What is x, the number of days the employees worked?
Answer:
The situation best represented by the given information is option B: An office manager paid $675.95 for computer equipment. The office manager bought one monitor for $127.95 and hard drives for $68.50 each. What is x, the number of hard drives the office manager bought?
To represent this situation as an equation, let x be the number of hard drives. The total cost of the computer equipment is the cost of the monitor plus the cost of the hard drives:
675.95 = 127.95 + 68.50x
Now, we can solve for x to find the number of hard drives the office manager bought.
Identify the length of the missing section of each line. Assume that the lines are divided into equal parts.
A line segment, from 0 to 36, divided into 3 sections, with a bracket including the first 2 sections, labeled with a question mark.
The missing length are 24, 18 and 10.
We have,
1. There 36 labels having three division equally.
So. the length of missing section is
= 12 + 12
= 24
2. There 36 labels having 4 division equally.
So. the length of missing section is
= 9 + 9
= 18
3 There 16 labels having 8 division equally.
So. the length of missing section is
= 2 + 2 + 2 + 2 +2
= 10
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The two-way frequency table contains data about students' preferred exercise.
Enjoys swimming Enjoys cycling Row totals
Likes running 28 62 90
Does not like running 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who do not like to run but enjoy cycling?
64%
55%
32%
23%
Answer:
14%
Step-by-step explanation:
like running and summing=28
28/200=14
:in percent form it is 14%
A student was asked to sketch the graph below. Using the graph, determine whether each statement is true or false.
-1 is a zero of the function
0 is a zero of the function
1 is a zero of the function
2 is a zero of the function
True False
Find zw and Z/W.
(Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)
The product of the two expressions ZW, is 81( cos π²/132 + sinπ²/132 + i(cosπ/11sinπ/12 + sin π/11cos π/12).
The division of the expressions Z/W, is [ (cos π²/132 - sin π²/132) + i (sin π/11 cosπ/12 - sin π/12 cosπ/11) ] / (cos² π/12 - sin² π/12).
What is the simplification of the expression?The given expression is simplified as follows;
Z = 9(cos π/11 + i sin π/11)
W = 9(cos π/12 + i sin π/12)
The product of the two expressions is calculated as follows;
ZW = 9(cos π/11 + i sin π/11) x 9(cos π/12 + i sin π/12)
ZW = 81(cos π²/132 + i cosπ/11 sinπ/12 + i sin π/11 cos π/12 + sin π²/132)
ZW = 81( cos π²/132 + sinπ²/132 + i(cosπ/11sinπ/12 + sin π/11cos π/12)
The division of the expressions is calculated as follows;
Z/W = 9(cos π/11 + i sin π/11) / 9(cos π/12 + i sin π/12)
Z/W = (cos π/11 + i sin π/11) / (cos π/12 + i sin π/12)
Multiply the denominator and numerator with conjugate of (cos π/12 + i sin π/12) = cos π/12 - i sin π/12
Z/W = (cos π/11 + i sin π/11)/(cos π/12 + i sin π/12) x (cos π/12 - i sin π/12)/(cos π/12 - i sin π/12)
Z/W = [ (cos π²/132 - sin π²/132) + i (sin π/11 cosπ/12 - sin π/12 cosπ/11) ] / (cos² π/12 - sin² π/12)
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What is the mean of 5, 5, 4, 8, 10, and 10?
Answer: 7
Step-by-step explanation:
Mean means average. Add all the numbers and divide by how many there are.
(5+5+4+8+10+10)/6
=7
Answer:
7
Step-by-step explanation:
To solve this problem you simply, add 5+5+4+8+10+10 and divide it by the number of values present.
5+5+4+8+10+10 = 42/6 = 7, so you answer is 7
I need help mad fast
The probability of the events
1. The point is on QR = 44.44%
2. The point is on PQ = 22.22%
3. The point is on RS = 33.33%
4. The point is not on RS = 66.67%
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probability is expressed can be as ;
Probability = sample space / Total out come.
In percentage , the total probability is 100% it is equivalent to 1 in fraction.
The total length PS is calculated as ;
8+4+6 = 12 + 6
= 18
The probability of event (PQ) in percentage = 8/18 × 100
= 44.44%
The probability of event ( QR) = 4/18 × 100
= 22.22%
The probability of event ( RS) = 6/18 × 100
= 600/18 = 33.33%
The probability of the point not on RS = 100-33.33
= 66.67%
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suppose another dog weighs 25.7 pounds and consumes 70 ounces of food per week. what is the residual associate to this individual using the least squares estimate? provide your answer accurate to 1 digit past the decimal point.
The residual concerning this individual using the least squares estimate is 13.025 ounces under the given condition that another dog weighs 25.7 pounds and consumes 70 ounces of food per week.
Let's us consider x = weight of a dog in pounds
y = amount of food consumed by a dog in ounces per week.
Then the least squares estimate of y given x is
y = 2.75x - 17.5
Utilizing this equation, we can say that a dog weighing 25.7 pounds will consume
y = 2.75(25.7) - 17.5
= 56.975
To evaluate the residual concerning thr individual using the least squares estimate,
Residual = Observed value - Predicted value
= 70 - 56.975
= 13.025 ounces
The residual concerning this individual using the least squares estimate is 13.025 ounces under the given condition that another dog weighs 25.7 pounds and consumes 70 ounces of food per week.
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the experimental probability.
The table shows the outcomes of rolling two
number cubes at the same time and finding the
product of the two numbers.co
7. What is the theoretical probability, expressed as
a fraction, of rolling a product greater than 12?
1
1
2 2
3
3
4
5
6
Florida's B.E.S.T. Assessment Practice Workbook 2 of 2
لیا
4
5
6
2
2
4
6
800
10
12
3
3
6
9
12
15
12
16
20
24
15
20 25
30
18 24 30 36
4
4
8
80 2
5
5
10
8. If Alan rolls two number cubes 300 times, about how many times would he expect a
product greater than 10? Round to the nearest whole number.
6
6
12
18
Answer:
7. To find the theoretical probability of rolling a product greater than 12, we need to count the number of outcomes where the product is greater than 12 and divide by the total number of possible outcomes.
From the table, we can see that the outcomes with a product greater than 12 are: (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), and (6, 6). This gives us a total of 15 outcomes with a product greater than 12.
The total number of possible outcomes is 6 x 6 = 36, since there are 6 possible outcomes for each of the two number cubes.
Therefore, the theoretical probability of rolling a product greater than 12 is 15/36, which simplifies to 5/12.
8. To find the approximate number of times Alan would expect to roll a product greater than 10 in 300 rolls, we can multiply the total number of rolls by the probability of rolling a product greater than 10.
From the table, we can see that the outcomes with a product greater than 10 are: (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (3, 4), (4, 3), (5, 2), (6, 2), (4, 2), (5, 2), and (6, 2). This gives us a total of 21 outcomes with a product greater than 10.
The probability of rolling a product greater than 10 is 21/36, which simplifies to 7/12.
Multiplying the total number of rolls (300) by the probability (7/12), we get:
300 x 7/12 = 175
So Alan would expect to roll a product greater than 10 about 175 times in 300 rolls.
6010
Mary and Chance walk in the same direction along a straight path. For 0 ≤t≤ 20, Mary's velocity at time t is
given by M(t) = 72-30+50.5 and Chance's velocity at time t is given by C(t) = 8.5t³e-0.45t. Both M (t) and
C(t) are positive for 0 < t < 20 and are measured in meters per minute, and t is measured in minutes. Mary is
12 meters ahead of Chance at time t = 0, and Mary remains ahead of Chance for 0 < t ≤ 20.
6010 (2-36-30.5) (24-3)
-6010
(2643)
(a) Find the value of to M(t)dt. Using correct units, interpret the meaning of to
The average distance Mary travel
context of the problem.
Lt ²-3€+50:51
15
-15
M(t)dt in the
(b) At time t= 10, is Mary speeding up or slowing down? Give a reason for your answer. Mary is slowms.
49.17
M-7.03
m (16) = 6010 / 120.5
?
down because relowty is
Positin gaz allelere
(c) Is the distance between Mary and Chance at time t = 18 increasing or decreasing? Give a reason for your
answer.
MC18) - (C₁Y) = -1.021 It is decreams becaun Chance's unloch,
Mary's
(d) What is the maximum distance between Mary and Chance over the time interval 0 < t < 20 ? Justify your
answer.
a. The value of to M(t)dt based on the information is 544.09m/s.
b) Mary speed is increasing
c) The distance is increasing
d) The max Distance between Mary and Chance over the time interval is -443.553.
How to explain the informationWe need to find the maxima or minima, (-ve value of D(t) means Chance is ahead of Mary).
Solve for t OR (You can also plot d and get the max value of D).'
Either way at (t = 9.273) we get a minima of, -443.553 , which is the max distance difference between them.
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Clarence's office recycled a total of 27 kilograms of paper over 3 weeks. How many weeks will it take Clarence's office to recycle a total of 36 kilograms of paper? Solve using unit rates.
Answer: number of recycled paper in 1 week: 27/3= 9 kilograms
Clarence's office will recycle a total of 36 kilograms of paper in : 36/9= 4 weeks
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
12 weeks is your answer
Show that the product of two consecutive natural odd numbers is always an odd number. please answer it .....
Let the two consecutive odd numbers be (2n + 1) and (2n - 1)
There product is (2n - 1)(2n + 1)
4n² - 1
2(2n) - 1
let 2n² = x
2x - 1
Hence , we can say that product of two consecutive odd number is always odd.
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solve using elimination
9x-3y=24
7x-3y=20
Answer:
point form:(13/5, -3/5)
equation form: x=13/5
y=-3/5
Step-by-step explanation:
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ILLUSTRATIVE MATHEMATICS
Class B would be the one where pupils spend the least amount of time on their homework.
Class A has the least amount of variation in homework time.
The proportion of all students that prefer to use a metal pen would be 40 %.
The bookstore should not believe that the results represent the preferences accurately as the different is significant.
How to find the less variable class?The least amount of time was spent on homework by students in Class B, as seen by the fact that some of them only put in 10, 15, and 20 minutes, as opposed to 35 minutes for students in Class A.
Due to their smaller range, Class A also had less variability in the amount of time spent on homework:
Class A range :
= 100 - 35
= 65 minutes
Class B range :
= 80 - 10
= 70 minutes
How to find the proportion ?Proportion of students who prefer metal pens = (Number of students who prefer metal pens) / (Total number of students in the sample) = 4/10 = 0.40
= 40 %
Proportion of students who prefer metal pens on day 2 = 8/10 = 0.8
= 80%
The preferences of the student population are significantly different, according to these results.
The bookstore needs to collect more information in order to have a better knowledge of the preferences of the student population given the stark disparity in the results from the two days.
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Jessica pours herself a cup of boiling water, at 100°C, to make tea. After 312minutes, the temperature of her tea has decreased to 58°C. What was the average change in temperature each minute?
The required average change in temperature each minute is a decrease of 0.13°C.
What is average?The average of the values is the ratio of the total sum of values to the number of values.
We can use the formula:
average change = (final temperature - initial temperature) / time
Here, the initial temperature is 100°C, the final temperature is 58°C, and the time is 312 minutes.
So,
average change = (58 - 100) / 312
average change = -0.1346...
Rounding to two decimal places, we get:
average change = -0.13°C per minute.
So, the average change in temperature each minute is a decrease of 0.13°C.
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Factor each completely and show your work.
2n^2 + 5n + 2
HELP PLEASE ASAP 20 points
Answer:
55 degrees
Step-by-step explanation:
To solve this problem, all you have to do is 60 + 65 and subtract it from 180. We can do this because those 3 angles create a linear pair.
Answer: 55
Step-by-step explanation:
The 3 angles form a line, <4 60 and 65. since it is a line the 3 angles add up to 180
<4 +60 + 65 =180 solve for <4 by subtracting 60 and 65 from both sides
<4 = 55
Give the OTHER guy brainliest please. I liked his answer.
in a game, you have a spinner with 10 equal sections, numbered 1 to 10. what is the probability that you will spin the spinner three times and the sum of the numbers will be exactly 15?
If we spin a spinner with 10 equal-sections, then the probability that on spinning the spinner 3 times the sum becomes 15 is 0.011.
To find the probability of spinning the spinner "3-times" and getting a sum of exactly 15, we use a combination of probability and counting principles.
First, we find total number of possible outcomes when spinning the spinner 3-times.
Since there are 10 possible outcomes for each spin,
There are a total of 10 × 10 × 10 = 1000 possible outcomes,
Next, we count the number of ways to get a "sum-15" by listing out all the possible combinations of three numbers that add up to 15.
The Outcomes are : (1, 7, 7), (2, 6, 7), (2, 7, 6), (3, 5, 7), (3, 6, 6), (3, 7, 5), (4, 4, 7), (4, 5, 6), (4, 6, 5), (4, 7, 4), (5, 5, 5).
So there are 11 possible combinations of three numbers that add up to 15.
The probability of getting "sum-of-15" is found by dividing number of favorable outcomes (11) by total number of possible outcomes (1000);
⇒ P(sum of 15) = 11/1000,
Therefore, the required probability is 0.011.
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let be the smallest positive integer such that is a perfect th power of an integer for some , where . what is ?
Using the binomial theorem, we get the value of n to be 1.
The given expression can be simplified by factoring out (1 + x)² from each term, which gives
(1 + x)²[1 + (1 + x) + (1 + x)² + ... + (1 + x)⁴⁷ + (1 + x)⁴⁸]
We can then use the formula for the sum of a geometric series to simplify the expression inside the brackets
1 + (1 + x) + (1 + x)² + ... + (1 + x)⁴⁷ + (1 + x)⁴⁸ = (1 - (1 + x)⁴⁹)/(1 - (1 + x))
= ((1 - (1 + x)⁴⁹)/x)(1/x - 1)
Now, we can use the binomial theorem to expand (1 + x)⁴⁹ and simplify the resulting expression
(1 + x)⁴⁹ = ⁴⁹C₀ + ⁴⁹C₁x + ⁴⁹C₂x² + ... + ⁴⁹C₄₈x⁴⁸ + ⁴⁹C₄₉x⁴⁹
The coefficient of x² is ⁴⁹C₂ + ⁴⁹C₃, which simplifies to (3n + 1)⁵¹C₃. Therefore, we have
⁴⁹C₂ + ⁴⁹C₃ = (3n + 1)⁵¹C₃
We can solve for n by using the formula for binomial coefficients
ⁿCᵣ = n!/(r!(n-r)!)
Substituting this into the above equation and simplifying, we get
(49 × 48)/(2 × 1) + (49 × 48 × 47)/(3 × 2 × 1) = (3n + 1) × (3n) × (3n - 1) × ... × (3n - 50)
Simplifying the left-hand side and dividing both sides by (3n + 1), we get
(49 × 16) + (49 × 24 × 47)/(3 × 2) = (3n) × (3n - 1) × ... × (3n - 50)
784 + 2,352 = (3n) × (3n - 1) × ... × (3n - 50)
3,136 = (3n) × (3n - 1) × ... × (3n - 50)
Since 3n is a factor of the right-hand side, we can write
3n × k = 3,136
where k is a product of the remaining factors on the right-hand side. Since n is the smallest positive integer that satisfies this equation, we can start by letting n = 1 and finding the smallest factor k that is divisible by 3. We find that k = 16 × 31 × 32 × ... × 99. Therefore, the value of n is 1
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--The given question is incomplete, the complete question is given
" Let m be the smallest positive integer such that the coefficient of x²
in the expansion of (1 + x)² + (1 + x)³ + (1 + x)⁴ + ........... + (1 + x)⁴⁹ + (1 + x)⁵⁰
is (3n+1)⁵¹C₃
for some positive integer n. Then the value of n is-"--
The triangle above has the following measures.
a = 9 cm
b = 9√3cm
Use the 30-60-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
The length of the hypotenuse is given as follows:
c = 18.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The sides for this problem are given as follows:
[tex]a = 9, b = 9\sqrt{3}[/tex]
Then the hypotenuse is given as follows:
[tex]c^2 = 9^2 + (9\sqrt{3})^2[/tex]
c² = 324
c = 18.
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Giveing brainly to whoever helps And extra points:> Help pls im not caught up.
The data distribution is, skewed and the mean of the number of emails is equal to the median numbers of email.
Given that;
The dot plot shows the number of emails that Jade receive each day for the last 10 days.
Now, We can see that;
it has more data on one side rather than the other.
Hence, It shows the skewed.
And, Mean of dot plot is,
15, 16, 18, 19, 22, 22, 22, 22, 23, 23
Hence, Mean = (22 + 22) / 2
= 22
And, Median = 22
Thus, We get;
The data distribution is, skewed and the mean of the number of emails is equal to the median numbers of email.
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i need help ASAP LIKE ASAP PLEASE
Answer:
359.4 cubic feet
Step-by-step explanation:
The formula for the volume of a hemisphere is (2/3)πr^3, where r is the radius.
Substituting r=6.5 ft into the formula, we get:
V = (2/3)π(6.5 ft)^3
V ≈ 359.41 ft^3
Rounding to the nearest tenth of a cubic foot, we get:
V ≈ 359.4 ft^3
A new credit card holder must decide between two credit cards. The first card offers a current APR of 13.99%. The second card has a current daily periodic interest rate of 0.035%. Which card would be the better choice?
The second card is the better choice because the daily periodic interest on the first card is 0.038%, compared to 0.035% on the second card.
The second card is the better choice because the daily periodic interest on the first card is 0.035%, compared to 0.038% on the second card.
The first card is the better choice because the daily periodic interest on the first card is 0.035%, compared to 0.038% on the second card.
The first card is the better choice because the daily periodic interest on the first card is 0.038%, compared to 0.035% on the second card.
Based on the comparison of daily periodic interest rates, the second card with a 0.035% daily periodic interest rate is a better choice for a new credit card holder than the first card with a 0.03832% daily periodic interest rate.
You decide which credit card is a better choice by comparing their interest rates.
To make a fair comparison, let's first convert the Annual Percentage Rate (APR) of the first card into a daily periodic interest rate. The APR of the first card is 13.99%. To find the daily periodic interest rate, we divide the APR by 365 (the number of days in a year):
13.99% / 365 = 0.03832%
Now we can compare the daily periodic interest rates of both cards. The first card has a daily periodic interest rate of 0.03832%, and the second card has a daily periodic interest rate of 0.035%.
Since the daily periodic interest rate of the second card (0.035%) is lower than the first card (0.03832%), the second card would be the better choice for a new credit card holder. A lower daily periodic interest rate means that the cardholder will be charged less interest on their outstanding balance, which can save them money over time. Hence, The correct option is The second card is the better choice because the daily periodic interest on the first card is 0.035%, compared to 0.038% on the second card.
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18x+12 can you factor the expression completely
After considering the given data we conclude that the value generated after completely factorizing the given expression is 6(3x + 2).
To factor the expression completely, you need to find the greatest common factor (GCF) of the terms and then divide each term by the GCF. The GCF of 18x and 12 is 6, so we can write:
18x + 12 = 6(3x + 2)
This is the simplest form of the expression, so we are done. You can check your answer by expanding the parentheses and seeing if you get back the original expression.
The greatest common factor (GCF) is considered the largest positive integer that divides evenly into two or more given numbers.
In order to evaluate GCF of two numbers, we have to list the factors of each number and then identify the largest factor that is common to both numbers.
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TDC, Inc.s' net profits were -$2,000 each month last year. What was TDC's net profits for the year?
A. -$24,000
B. -$14,000
C. $10,000
D. $24,000
Answer:
A
Step-by-step explanation:
take the monthly net profits which is $2,000 and multiply with 12 which is the number of months in a year. the results is $24,000
culculation;
$2,000 X 12 = $24,000
what is the predicted time before the first engine overhaul for a particular truck driven 55,000 miles per year with an average load of 22 tons, an average driving speed of 55 mph, and 15,000 miles between oil changes. (do not round intermediate calculations. round final answer to 2 decimal places.)
The information provided is insufficient to determine the predicted time before the first engine overhaul.
To predict the time before an engine overhaul, we need to know the manufacturer's recommended mileage or hours of operation for an overhaul.
Factors such as miles per year, load, speed, and oil change intervals affect the engine's performance and wear but do not directly provide a specific time frame for an engine overhaul.
Summary: Without knowing the manufacturer's recommended mileage or hours for an engine overhaul, we cannot accurately predict the time before the first engine overhaul for the particular truck described.
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