The combined rate of the small and large pumps is 16/63 pools per hour, and it will take them approximately 3.94 hours to drain the pool when working together.
Explanation:To figure out how long it would take for both pumps to drain the pool simultaneously, we will use the concept of rates. Since the small pump can drain the pool in 9 hours, it has a rate of 1/9 pools per hour. Similarly, the large pump can drain the pool in 7 hours, so it has a rate of 1/7 pools per hour.
When we use both pumps together, we add their rates. So, the combined rate of the small and large pumps is (1/9 + 1/7) = 16/63 pools per hour.
To find the time it will take them to drain the pool together, we divide the size of the pool (1 pool) by their combined rate (16/63 pools per hour). Therefore, it will take the two pumps approximately 3.94 hours to drain the pool when working together.
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Tell whether the two ratios form a proportion. Explain. 25/80 and 5/16
-n^2+16n-63/n^2-2n-35
Find a whole number solution that makes the following true
a.) Divisible by 2 and 3 but not 6
b.) Divisible by 5 and 10 but not 2
The Martin family's truck gets an average of 25 miles per gallon. Predict how many miles they can drive using 7 gallons of gas.
Area model division 246÷3
Answer:
it is right
Step-by-step explanation:
solution for 5y+2y = -24
identify the decimal labeled with the letter A on the scale below
The decimal labeled with the letter A on the scale is 0.75.
What is number line?A number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
Here, the number starts with zero.
There are 8 division between 0 and 1.
So, first one represent 1/8= 0.125
second one =0.25
third one= 0.375
fourth one= 0.50
fifth one= 0.625
sixth one= 0.75
Hence, the decimal labeled with the letter A on the scale is 0.75.
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You weigh a gallon of 2% milk in science class and learn that it is approximately 8.4 pounds. You pass the milk to the next group, and then realize that you teacher wants it in kilograms, not pound. Explain how you can adjust your answer without weighing the milk again. Then give you the weight in kilograms.
1. In the on-line convex-hull problem, we are given the set Q of n points one point at a time. After receiving each point, we compute the convex hull of the points seen so far. Obviously, we could run Graham’s scan once for each point, with a total running time of O(n2lg n). Show how to solve the on-line convex-hull problem in a total of O(n2) time.
2. Show how to implement the incremental method for computing the convex hull of n points so that it runs in O(n lg n) time.
The weight of water is 62 1/2 lb per cubic foot. What is the weight of 1 1/9 cubic feet of water?
Final answer:
To determine the weight of 1 1/9 cubic feet of water, convert the mixed number to an improper fraction and multiply by the weight per cubic foot, resulting in approximately 77.16 pounds.
Explanation:
The student is asking to calculate the weight of 1 1/9 cubic feet of water given that the weight of water is 62 1/2 lb per cubic foot. To find the weight of the water, we multiply the volume by the weight per unit volume:
Convert 1 1/9 to an improper fraction: 1 1/9 = 10/9.
Multiply 10/9 cubic feet by 62.5 lb/ft³ (weight of water per cubic foot).
Calculate: (10/9) × 62.5 = 694.44/9 ≈ 77.16 lb.
Hence, the weight of 1 1/9 cubic feet of water is approximately 77.16 pounds.
what is 1.375 as a fraction
Final answer:
To convert 1.375 to a fraction, express it as 1,375/1,000 and simplify by dividing by the greatest common divisor, which is 125, to get 11/8.
Explanation:
To convert the decimal 1.375 to a fraction, we will follow a few steps. First, count the number of decimal places, which in this case is three. This tells us that the denominator of the fraction should be a power of 10; specifically, 1,000. So we write 1.375 as 1,375/1,000. Next, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 1,375 and 1,000 is 125. When we divide both the top and the bottom by 125, we get 11/8, which is the simplest form of the fraction.
Converting decimals to fractions involves aligning the decimal with the appropriate power of 10 in the denominator and simplifying by finding the greatest common divisor. This systematic approach ensures the representation of the decimal as a simplified fraction, such as 11/8 in the case of 1.375.
If u bring 10 empty bottles to the bottle shop, the bottle shop will change 10 empty bottles to 1 drink. If u bring 100 bottles to the shop. How many drinks will you get?
By bringing 100 bottles to the shop, you will receive 10 drinks.
The students question relates to a mathematical conversion problem, where empty bottles are exchanged for drinks at a bottle shop. If the conversion rate is 10 empty bottles for 1 drink, then by bringing 100 bottles, we can set up a simple division:
Number of bottles: 100
Conversion rate: 10 bottles per drink
To find out how many drinks you can get for 100 bottles, we divide the total number of bottles by the conversion rate:
Divide 100 (bottles) by 10 (bottles per drink).
100 / 10 = 10
Therefore, by bringing 100 bottles to the shop, you will receive 10 drinks.
if Q(x)=4x^2 -1, find Q (-7)
what is 694 divided by 41 and what is the remainder please help thank you
We can use long division in finding the remainder.
Place the divisor which is 41, outside the long division sign, and 694 under the long division sign as shown in the diagram.
41 goes into 694 16 times.
Write the 16 on top of the long division sign.
Multiply the 16 by 41, to obtain 656
Write the 656 below the 694 as in the diagram.
Subtract 656 from 694 to obtain 38.
Since 41 is more than 38 , we cannot proceed.
Hence,
[tex]\frac{694}{41}=16\:\:Remainder\:\:38[/tex]
Therefore the remainder is 38
The quotient is 16, and the remainder is 38.
We have,
To find the quotient and remainder when dividing 694 by 41, we can perform the division and observe the results.
Now,
41 x 16 = 656
And,
694 - 656 = 38
This means,
694 divided by 41 is equal to 16 with a remainder of 38.
Therefore,
The quotient is 16, and the remainder is 38.
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3 chairs and a table cost 149 4 chairs and a table cost 177 how much does each item cost?
Terry added 3 and 7 he got the sum of 9 his answer is is not correct described how Terry can find the correct sum
why is 50 + 7 x 5 = 85
"The answer is: 50 + 7 x 5 = 85 is correct due to the order of operations.
To understand why 50 + 7 x 5 equals 85, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). According to this rule, multiplication and division are performed before addition and subtraction.
Let's break down the expression step by step:
1. Identify the multiplication part of the expression: 7 x 5.
2. Perform the multiplication first: 7 x 5 = 35.
3. Now, we have 50 + 35, since we have already computed 7 x 5.
4. Finally, perform the addition: 50 + 35 = 85.
So, following the order of operations, we correctly get that 50 + 7 x 5 equals 85."
For a particular event, 845 tickets were sold for a total of $4162. If students paid $4 per ticket and non students paid $6 per ticket, how many student tickets were sold?
Final answer:
Using a system of equations, we found that 454 student tickets were sold at the event.
Explanation:
To determine how many student tickets were sold for the event, we need to set up a system of equations based on the information given. Let's define x as the number of student tickets sold at $4 each, and y as the number of non-student tickets sold at $6 each.
The total number of tickets sold (student plus non-student) is given as 845 tickets:
x + y = 845
The total amount of money made from selling these tickets is $4162:
4x + 6y = 4162
Now we have a system of two equations:
x + y = 845
4x + 6y = 4162
We can solve this system by multiplying the first equation by 4:
(4)(x + y) = (4)(845)
4x + 4y = 3380
Now, we subtract this new equation from the second equation given by the total amount made to eliminate y:
4x + 6y - (4x + 4y) = 4162 - 3380
2y = 782
Dividing both sides of this equation by 2 gives us:
y = 391
Now, substitute y back into the first equation to find x:
x + 391 = 845
x = 845 - 391
x = 454
So, 454 student tickets were sold.
4 options but only 3 have sea views what fraction has sea view
On Monday David travels m miles. On Tuesday he travels 35 more than he did on Monday. On Wednesday he travels a total of twice the distance he travelled Monday. Work out and expression of the total distance he travels during the three days
To find the total distance David travels during the three days, we add up the distances he travels on each day: m + (m + 35) + 2m = 4m + 35 miles.
Explanation:To find the total distance David travels during the three days, we need to add up the distances he travels on each day.
On Monday, David travels m miles.
On Tuesday, he travels 35 more than he did on Monday, so he travels m + 35 miles.
On Wednesday, he travels twice the distance he traveled on Monday, so he travels 2m miles.
To find the total distance, we add up the distances on all three days:
Total distance = m + (m + 35) + 2m = 4m + 35 miles.
If the diameter of the duct is 5.2 inches what's the area of the circular hole
what is 84 divide by 4
explain how you can determine if four points lie on a single parabola
Suppose that sin(θ)=6/10 and θ is in the second quadrant. Use trigonometric identities to find the following quantities exactly.
A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
a construction company is planning to bid on a building contract. the bid costs the company $1900. the probability that the bid is accepted is 1/10. if the bid is accepted, the company will make $94000 minus the cost of the bid.
a. what is the expected value in this situation?
The expected value for the construction company if they bid on the contract is $7,500, calculated by weighing the potential profit and loss with their respective probabilities.
Explanation:The question is asking us to calculate the expected value of the construction company's bid on a building contract. To find the expected value, we need to multiply each outcome by its probability and sum these amounts.
There are two possible outcomes:
The expected value (EV) is calculated as follows:
EV = (Probability of acceptance × Net profit when accepted) + (Probability of not being accepted × Loss when not accepted)
EV = (1/10 × $92,100) + (9/10 × -$1,900)
EV = $9,210 - $1,710
EV = $7,500
The expected value for the construction company if they bid on the contract is $7,500.
the sales tax rate for the state of washington was 5.1% . What is the sales tax on a $5900 car in Washington?
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 15 characters long, and that each character is either lowercase, an uppercase letter or a numerical digit. Assume that the hacker makes a random guess.
What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction.
The probability that the hacker guesses the password correctly on the first try is 1 / 62^15.
Explanation:To calculate the probability that the hacker guesses the password correctly on the first try, we need to determine the total number of possible passwords and divide it by the total number of possible guesses.
Since the password is 15 characters long and each character can be a lowercase letter, an uppercase letter, or a numerical digit, there are 26 + 26 + 10 = 62 possible options for each character.
Therefore, the total number of possible passwords is 62^15 (62 raised to the power of 15).
The probability of the hacker guessing the password correctly on the first try is 1 divided by the total number of possible passwords.
So, the probability is 1 / 62^15. This can be left as a fraction or converted to a decimal.
Danielle and David each have a job. Danielle earns $15 an hour. She also receives a $50 weekly bonus. Danielle wrote an equation to determine how much she earns in a given week. y=15x+50y=15x+50 David earns $12 an hour and receives an $80 weekly bonus. David made a graph to show how much he earns in a given week. How many hours will it take Danielle and David to earn the same amount of money? Enter your answer in the box below.
Answer:10
Step-by-step explanation:
Ron Co. sold sweatshirts ($20) and baseball caps ($10). If total sales were $2,860 and people bought 6 times as many sweatshirts as caps, how many of each were sold?
To find the number of baseball caps and sweatshirts sold, we can set up an equation using the given information and solve for the variables. The solution shows that 22 baseball caps and 132 sweatshirts were sold.
Explanation:Let's solve this problem step by step:
Let x represent the number of baseball caps sold.Since people bought 6 times as many sweatshirts as caps, the number of sweatshirts sold would be 6x.The total sales revenue can be calculated by multiplying the price of each item by the number of items sold. So, the equation becomes: 10x + 20(6x) = 2860.Simplifying the equation gives us 10x + 120x = 2860.Combining like terms, we get 130x = 2860.Dividing both sides of the equation by 130, we find that x = 22. So, 22 baseball caps were sold.Since people bought 6 times as many sweatshirts as caps, the number of sweatshirts sold would be 6 * 22 = 132.Therefore, 22 baseball caps and 132 sweatshirts were sold.
The problem is solved by setting up equations based on the given information. Ron Co. sold 132 sweatshirts at $20 each and 22 baseball caps at $10 each to make a total of $2,860 in sales.
Explanation:To solve the problem, let's define the variables representing the number of sweatshirts and caps sold. Let's say 's' equals the number of sweatshirts and 'c' equals the number of baseball caps.
We are given two pieces of information:
The price of a sweatshirt is $20, and the price of a cap is $10. The total sales can be expressed as the sum of the sales from sweatshirts and caps, which gives us the equation 20s + 10c = 2860.
Using the information that s = 6c, we can substitute 6c for s in the total sales equation to get 20(6c) + 10c = 2860. Simplifying this equation, we get 120c + 10c = 2860, which leads to 130c = 2860. Dividing both sides by 130 gives us c = 22.
Now, we can find the number of sweatshirts sold by substituting c into the equation s = 6c. So, s = 6(22) = 132.
Therefore, Ron Co. sold 132 sweatshirts and 22 baseball caps.