Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 5 more days than the other?
A can build the room by himself in 10 days, and B can build the room by himself in 15 days.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's call the faster constructor "A" and the slower constructor "B".
We know that B takes 5 more days than A to complete the job.
Let's call the number of days it takes A to build the room "x".
Then the number of days it takes B to build the room is "x+5".
Now,
We also know that if they work together, they can finish the room in 6 days.
Let's call the fraction of the job that A can do in one day "a"
(which means that B can do "a - 1/6" of the job in one day).
We can use the following equation to solve for "a":
1 = (a + a - 1/6) x 6
Simplifying this equation, we get:
1 = (2a - 1/6) x 6
1 = 12a - 1
12a = 2
a = 1/6
So A can do 1/6 of the job in one day.
We can use this information to solve for "x" and "x+5":
1/x + (1/(x+5)) = 1/6
Multiplying both sides by the least common multiple of the denominators (6x (x+5) ), we get:
6 (x+5) + 6x = x (x+5)
Expanding and simplifying, we get:
x² - 7x - 30 = 0
Solving for x using the quadratic formula, we get:
x = 10 or x = -3
Since x has to be a positive number (because it represents the number of days it takes A to build the room), we can ignore the negative solution.
Now,
It takes A 10 days to build the room, and it takes B 15 days to build the room (since B takes 5 more days than A).
Therefore,
A can build the room by himself in 10 days, and B can build the room by himself in 15 days.
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Help please! Don’t understand!
Is how many countries are in North America a statistical question
The question, "How many countries are in North America" is not a statistical question.
What are statistical Questions?Statistical questions are defined as the questions which are answered by collecting data from many which will probably vary.
The given question is,
How many countries are in North America"How many countries are in North America.
Although the answers to this from the students may vary because they don't know, the answer to this question is a constant.
This is not something which varies.
Hence this is not a statistical question.
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write the function for the graph below
Richard and samantha are charting their monthly cash flow. They have some expenses like car repairs and vacations that are not paid each month. How can they account for these non-monthly expenses ?
Final answer:
Richard and Samantha should estimate yearly costs for non-monthly expenses, divide by 12, and save this amount each month, incorporating it as a fixed expense in their budget.
Explanation:
Richard and Samantha can account for non-monthly expenses in their monthly cash flow by setting aside money each month for these irregular expenses. To do this, they should estimate the total cost of these expenses for the year and divide that amount by 12. This will provide the monthly amount they need to save in order to cover costs such as car repairs and vacations without disrupting their budget. Each month, this amount should be treated like a fixed expense and set aside in a savings or separate account, ensuring that funds are available when these expenses occur.
Example:
Car Repairs: Estimated at $600 per year (divide by 12 = $50 per month)
Vacations: Estimated at $1200 per year (divide by 12 = $100 per month)
By including these estimated expenses in their monthly budget, they can create a more accurate and effective budget that accommodates all their financial activities throughout the year.
Frank wants to know how many people live in each household in his town. He conducts a random survey of 10 people and asks how many people live in their household. His results are shown in the table.
Number of People per Household
1 6 2 4 4 3 5 5 2 8
Calculate the mean absolute deviation of the number of people per household
The mean absolute deviation is 1.6.
Given that the number of People per Household
1 6 2 4 4 3 5 5 2 8
We have to determine the mean absolute deviation
What is the mean deviation?The mean absolute deviation is found by finding the mean, then finding how far each number is to the mean, then finding the mean of that.
The mean is: (1 + 6 + 2 + 4 + 4 + 3 + 5 + 5 + 2 + 8)/10 = 40/10 = 4
The distances of all of the numbers are
(absolute value of the difference between 3.5 and the number)
3,2, 2, 0, 0, 1, 1, 1, 2, 4
The mean of those is: 3+2+2+ 0+ 0+1+1+ 1+ 2+ 4 /10 = 16/10 = 1.6
Therefore the mean absolute deviation is 1.6.
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Find P(A or B) if the events are disjointed. P(A) = P(B) =
P(A) = 11/25
P(B) = 9/25
A. 4/25
B. 3/5
C. 2/25
D. 4/5
The google family built a rectangular swimming pool in their backyard.The floor of the pool has an area of 485 5/8 square feet.If the width of the pool is 18 1/2 feet,what is the length of the pool?
Your last five customer interactions lasted 2,3,6,8 and 4minutes how many minutes did i average across the 5
You average across 4.6 minutes per customer.
What is average?The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.
Given:
Your last five customer interactions lasted 2,3,6,8 and 4 minutes.
The total number of observation is 5.
The average = the sum of the observations / the number of observations.
The average = (2 + 3 + 4 + 6 + 8)/5
The average = 23/5
The average = 4.6 minutes.
Therefore, 4.6 minutes per customer is the average.
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The tip of a pendulum moves through an angle of 0.38 rad radians. If the radius of the pendulum is 25 centimeters then which of the following is the length of the arc the tip moves through
Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 3 ft, 6 ft, 9 ft B. 3 ft, 5 ft, 7 ft C. 3 ft, 6 ft, 12 ft D. 3 ft, 9 ft, 27 ft
what does the expression 0.30y represent ?
Simplify 5 √180 (show work)
To simplify 5√180, break down 180 into its prime factors, take out the square of the prime factors, and simplify.
Explanation:To simplify 5√180, we can break down 180 into its prime factors which are 2^2 * 3^2 * 5. Then, we can take out the square of the prime factors since we have a square root. This leaves us with 2 * 3 * 5√5. Simplifying further, we get 30√5.
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Is 35 over Pi (35 divided by pi):
Slightly less than 9
Slightly more than 9
Slightly less than 12
OR
Slightly more than 12
Please help and no wrong answers!
35/pi is a calculator question. A standard calculator has pi to about 10 digits stored in it's memory. As an educated guess before doing it (according to the bible is just under 12 since pi is recorded as 3 in Kings I think).
Our calculators record pi as 3.141592654
35/pi = 11.14084602 which is just under 12. <<<<< answer
1
A company says that the probability of finding an all-star card in a game pack is 12.5%. A student wants to determine the probability that, if he buys 6 game packs, 2 or more will have an all-star card.
To do this, he uses a random number table to pick 6 numbers from 1 to 8. He lets 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card. He repeats this for a total of 15 trials. The results are shown in the table.
561673 366468 314255 361362 838443 126285 257231 768551 652585 468113 123711 322764 487626 783134 384664
Select from the drop-down menus to correctly complete each statement.
To estimate the probability that 2 or more out of 6 packs will have an all-star card, the student must count the number of trials with BOX RIGHT HERE and divide by the number of trials.
This gives an estimated probability of about . BOX RIGHT HERE
PLEASE I NEED THIS ANSWERED I HOPE ITS CLEAR ENOUGH.
Answer:
the first box is "two or more 1s"
the second box is "0.13"
Step-by-step explanation: Im a K12 Student
The probability that 2 or more out of 6 packs will have an all-star card is given by the equation P = 0.1333
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that 2 or more out of 6 packs will have an all-star card be P
The probability of finding an all-star card in a game pack is 12.5 %
The student has pointed that 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card
The test results are given in set A = { 561673, 366468, 314255, 361362, 838443, 126285, 257231, 768551, 652585, 468113, 123711, 322764, 487626, 783134, 384664 }
The number of trials that represent that 2 or more out of 6 packs have an all-star are = { 468113 , 123711 }
Therefore , the probability is given as
Probability that 2 or more out of 6 packs will have an all-star card P = 2/15
On simplifying the equation , we get
Probability that 2 or more out of 6 packs will have an all-star card P = 0.133
Hence , the probability is 13.33 %
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What is the sum of 74.835 and 2.67
The area of a circular pool is 314 square feet. Write and solve an equation to find the diameter of the pool cover.
the fifth grade classes at sunshine School you six identical buses to go on the field trip there were a total of 30 seats on each bus all the seats on 5 buses were filled the 6 bus had 4/6 of the seats filled 1/5 of all the passengers were adults how many adults went on the field trip with the fifth grade class
the sum of three numbers is 161 the second number is six times the first and the third is 5 more than the second find the numbers
Sarah wants to hang a mirror in her room. The mirror and frame must have an area of 15 square feet. The mirror is 3 feet wide and 4 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? Square with an inner frame with height of 3ft on the left frame and width of 4ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. 3x2 + 14x − 2 = 0 4x2 + 14x − 3 = 0 x2 + 12x − 14 = 0 2x2 + 7x − 14 = 0
The length of a rectangle is 3 m longer then it’s width the area of the rectangle is 154 m^2 what is the width of the rectangle
i need alot of help in math
On a spinner: P(3) = ⅜ and p(4) = ⅓ What is the probability of getting 3 or 4?
Answer:
3/8. + 1/3
9/24 +8/24
17/24
Alternately, the gardener decides to choose the plants in the first row. What is the average number of tomatoes on these plants
m∠HGF = 16 x + 4, m∠EGF = 110°, and m∠HGE = 3 x + 11. Find x .
Teo has 4 2/3 pitchers of juice. One glass holds 1/6 of a pitcher. How many glasses can Teo fill?
Which group of numbers is ordered from least to greatest
Angle P measures 112 degrees, what are the measures of angle N and O?
The measures of angle N and O are: 34°
How to find the angle of the Isosceles triangle?We know that Isosceles triangle has two equal sides and we also know that the sum of angles in a triangle is equal to 180 degrees.
Since an Isosceles triangle has two equal sides, we know that the base angles are equal.
We are given the apex angle as 112 degrees. Thus:
2x + 112 = 180
2x = 180 - 112
2x = 68
x = 34
Thus:
The measures of angle N and O are 34°
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use the integer values of x from -3 to 13 to graph the equation y= -x
harry buys a sofa set that costs$2,000.he pays for it with 12 month installments. how much will he pay each month? if he has to pay5%in interest how much will he pay in all for the sofa set?
Harry's monthly payment for the sofa set is approximately $175, which includes principal and simple interest. The estimated total payment amount after 12 months is $2100.
Harry buys a sofa set that costs $2000 and chooses to pay for it in 12 monthly installments. First, to find out the monthly payment without interest, we divide the total cost by the number of installments. So, $2000 divided by 12 months equals to $166.67.
However, there is an interest of 5% on the outstanding amount. To calculate the total interest on an installment plan, we typically would need to calculate the interest on the reducing balance each month; however, for simplicity, let's assume it's 5% of 2000 for the year, which is $100 (5/100 * $2000). Divided by 12 months, that's about $8.33 in interest per month, giving a total monthly payment of $175 ($166.67 + $8.33).
This simplistic approach gives us a rough estimate, and the actual amount could be slightly different due to the reducing balance method used by most financing options. Assuming the simple interest calculation, Harry will pay $175 per month, and in all, he will pay an estimated total of $2100 ($175 * 12) for the sofa set.