To solve this problem, you can use the principle of addition of rates since the work done (filling the tank) would be equal when the pipes are working together or separately. Therefore, adding the rate of pipe A and B should equal to the rate of them working together.
Explanation:To solve this problem, we'll use the principle that work done is equal to rate multiplied by time. In this case, the 'work' is filling the tank, and the 'rate' is how quickly each pipe can fill it.
Pipe A, we know, takes 18 hours to fill the tank. Therefore, its rate of work is 1/18 tanks per hour. For both pipes working together, it takes 9.9 hours, so their combined rate is 1/9.9 tanks per hour.
Assuming that the pipes work independently, we can add their rates together to get the combined rate. Let the rate of pipe B be 1/b, then:
(1/18) + (1/b) = 1/9.9
Solving this equation for b, which is the time taken by pipe B alone to fill the tank will give you the answer.
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plot on a number line 8 2/5 away from 2 3/4
What is the best estimate for 49% of 15
You want new picture frames that cost $12 each. Shipping is $8 per order. If you buy 15 frames, what is the cost of the order?
Answer:
$188
Step-by-step explanation:
Sally is trying to decide what to wear to school. She has 5 pairs of pants, 10 shirts, and 3 pairs of shoes. Assuming everything matches, how many outfits can she make?
Answer:
150
Step-by-step explanation:
Because, 5 x 3 x 10 = 150.
10 x 3
10 20 30
1 2 3
( add 10 every time )
30 60 90 120 150
1 2 3 4 5
( add 30 every time )
I tried to explain well.
Luke records Jesus' visit to Jerusalem when He was twelve years old for the Feast of the
Messi kicks a soccer ball from a position that is 3 meters from a sideline and 4 meters from a goal line. the ball lands at a position that is somwhere ... After watching the replay, the ratio between the distance of Messi and the ball is 3/2 meters to the distance between Suarez and the ball.
The actual answer to this problem is (4.8,7.6)
Using the internal division formula the coordinates of the ball are (4.8,7.6).
Let us assume the x-axis as the goal line and the y-axis as the sideline
So, coordinates Messi≡(3,4)
Similarly, coordinates Suarez≡(6,10)
Let us suppose the ball is somewhere in between Messi and Suarez
Suppose coordinates of the ball ≡(a,b)
Since the ratio between the distance between Messi and the ball to the distance between Suarez and the ball is 3/2.
This means ball is internally dividing Messi and Suarez in 3:2
So, applying the internal division formula for a straight line.
What is the internal division formula for a straight line?If a point (a,b) is internally dividing a line segment with coordinates of endpoints as (x₁,y₁) and (x₂,y₂) in the ratio m:n then
[tex]a= \frac{m_{1}x_2+m_2x_1 }{m+n}[/tex]
[tex]a= \frac{m_{1}y_2+m_2y_1 }{m+n}[/tex]
So, [tex]a = \frac{3*6 + 2*3}{3+2}[/tex]
[tex]a=4.8[/tex]
[tex]b= \frac{3*10+2*4}{3+2}[/tex]
[tex]b=7.6[/tex]
So, the coordinates of the ball≡(4.8,7.6)
Therefore, Using the internal division formula the coordinates of the ball are (4.8,7.6).
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Kiera wanted to find the approximate number of historical books at the library she works at. She used the computer to randomly take a sample of 80 books and found that 6 of them were considered historical books. There are 21,360 books at this library. What is the best estimate of the amount of historical books at this library
What are the coordinates of the vertex of the table? I X Y 0 1 -1 -2 -2 -3
The x-values in the table for f(x) were multiplied by -1 to create the table for g(x). What is the relationship between the graphs of the two function.
As g(x) is a function that is multiplied by - 1 with f(x) D. They are reflections of each other over x = y.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, g(x) is a function that is multiplied by - 1 with f(x).
∴ f(x) = - g(x).
So, They are reflections of each other over x = y.
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Find the general solution of the differential equation. (enter your solution as an equation.) (8 + x)y' = 3y
Final answer:
The general solution to the differential equation (8 + x)y' = 3y is y = C(8+x)³, where C is a constant and can be found by integrating and rearranging the separated variables.
Explanation:
To find the general solution of the differential equation (8 + x)y' = 3y, we can separate variables and integrate both sides. First, we divide both sides by (8 + x) and then by y to get [tex]\frac{ y'}{y} = \frac{3}{8 + x}[/tex]
Next, we integrate both sides:
Integrate LHS: [tex]\int \frac{dy}{y} = ln|y| + C_1[/tex]
Integrate RHS: [tex]\int \frac{3dx}{8 + x} = 3ln|8+x| + C_2[/tex]
Now, we can combine the two constants (C₁ and C₂) into a single constant C by writing C = C₂ - C₁. So our solution looks like ln|y| = 3ln|8+x| + C. We can exponentiate both sides to solve for y:
[tex]y = e^{3ln|8+x|+C}[/tex]
Remembering that [tex]e^{ln|a|} = a[/tex], we can simplify this to:
y = C(8+x)³ where C is a constant.
This is the general solution to the differential equation.
Find the cost of the following item. A table marked up $45.00, selling for $189.95 4.22 144.95 234.95 8,357.80
Answer:
Cost price of an item = $144.95
Step-by-step explanation:
Cost price is the price at which the article is purchased .
It includes all the expenses incurred on that item till the time it is owned by us .
Selling price is the price at which the item is sold to the customer .
Market price is the price marked on the product . It is basically the current price of the item .
We know that selling price - market price = cost price
Given :
Market price of an item = $45.00
Selling price of an item = $189.95
To find : cost price of an item
Solution :
Cost price = $189.95 - $45.00 = $144.95
what is the mad for 9,7,6,2,2,1
Answer:
9 + 7 + 6 + 2 + 2 + 1 = 27 ÷ 6 = 4.5
4.5 - 9 = 4.5
4.5 - 7 = 2.5
4.5 - 6 = 1.5
4.5 - 2 = 2.5
4.5 - 2 = 2.5
4.5 - 1 = 3.5
4.5 + 2.5 + 1.5 + 2.5 + 2.5 + 3.5 = 17 ÷ 6 = 2.83 or 2.8
so our MAD is 2.83 or 2.8!
Luis earns a base salary of $150 every week with an additional 14% commission on everything he sells. Luis sold $6050 worth of items last week. What was louis's total pay last week
Jeff said his City got 11/3 inches of snow.write this fraction as a mixed number
Cindy owns a rectangular lot that is 18 yards long and 45 feet wide. She is going to cover the lot with square pieces of sod. If the sod costs $12 per square yard, how much will Cindy pay to completely cover the lot with sod?
during a hike, 3 friends equally shared 1/2 pound of trail mix. what amount of trail mix, in pounds, did each friends recieve
3 friends equally shared 1/2 pound of trail mix, during the hike.
Total quantity of trail mix = 1/2 pound
Quantity shared by each friend is 1/3 rd of the trial mix
= 1/3 * 1/2 pound
= 1/6 pound
Therefore, during the hike, each friend shared 1/6 pound of the trail mix.
Hope this helps ..!!
Thank you :)
when 2 straight lines intersect a 15degrese angle is formed.what is the measure of the obtuse angle also formed?
the chapter in lost in outer space in 8 pages Long.Mrs.Ross read1/4 of the chapter to the class . Then Mrs.M read three pages to the class. How many pages have they read so far
Final answer:
To find the total number of pages they have read so far, add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class. The total number of pages they have read so far is 5 pages.
Explanation:
To find the total number of pages they have read so far, we need to add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class.
Mrs. Ross read 1/4 of the chapter, which is 8 x 1/4 = 2 pages.
Mrs. M read 3 pages to the class.
Therefore, the total number of pages they have read so far is 2 + 3 = 5 pages.
In the number 35.3816, the underlined three is __________ the other three.
What is the domain and range for 2x+3y=18? What is the domain and range of 3x-4y>16?
The domain of a function is the complete set of possible values of the independent variable.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
2x+3y=18
For this equation, domain and range both would be all real numbers.
3x-4y>16
Here domain and range both will be all real numbers.
what is the sum of the rational expressions below? x/x-2 + 7x/x+5
a. 8x/2x+3
b. 8x/x^2+3x-10
c. 8x^2-9x/x^2+3x-10
d. 8x^2-9x/2x+3
Final answer:
The sum of the rational expressions is found by obtaining a common denominator, combining the numerators, and simplifying the resulting expression. The correct answer is [tex](8x^2-9x)/(x^2+3x-10).[/tex]
Explanation:
The sum of the rational expressions [tex]x/(x-2) + 7x/(x+5)[/tex] requires finding a common denominator before the sum can be calculated.
The common denominator for these two fractions is the product of the individual denominators (x-2) and (x+5), which is [tex]x^2+3x-10.[/tex]
Once we have a common denominator, we can combine the numerators and simplify the expression as follows:
Multiply the first term by (x+5)/(x+5) and the second term by (x-2)/(x-2) to create a common denominator.
Combine the numerators: [tex]x*(x+5) + 7x*(x-2)[/tex]
[tex]= x^2+5x + 7x^2-14x[/tex]
[tex]= 8x^2-9x.[/tex]
Place the combined numerator over the common denominator: [tex](8x2-9x)/(x^2+3x-10).[/tex]
Therefore, the correct sum of the given rational expressions is option c. [tex](8x2-9x)/(x^2+3x-10).[/tex]
What is the measure of N to the nearest whole degree? 35° 45° 55° 65°
Answer:
55 degree
Step-by-step explanation:
By the Law of cosines: a2 = b2 + c2 – 2bccos(A)
That is the image. :-）
Jane is going to fence in her back yard. She has purchased 100 feet of fence she wants to fence in a rectangular area where one side will be the back of her house. She knows her house is 30 feet across the back. Which of the following is the equation that Jane can use to figure out how far back from the house she can fence in? A.30x=100 B.x+30=100 C.x+x+30=100 D.30(x+30)=100
A football is kicked off the ground. After traveling a horizontal distance of 24m, it just passes over a tree that is 3m tall before hitting the ground 28m from where it was kicked. a) Consider the ground to be the x-axis and assume the vertex lies on the y-axis. Determine the equation of the quadratic equation that models the path of the ball. b)Determine the maximum height of the ball. c)Suppose the football is kicked from a starting point at the origin. Develop a new equation of the quadratic function of the quadratic function that represents the football.
What is the remainder of x3 − 3x2 + 7x + 5 divided by (x + 4)?
A rectangular garden originally measured 5 feet by 10 feet as shown below. A path was created around the garden by increasing each side of the original rectangle by x-feet on both sides
an acute triangle has sides measuring 10 cm and 16 cm. the length of the third is unknown. which is best describes the range of the possible values for the third side of the triangle?
x<12.5'x>18.9
12.5
6
Answer:
B 12.5 < x < 18.9
Step-by-step explanation:
two jewlery stores buy silver chains from a manufacturer for c dollars each and then sell the chains at a 57% markup.store a has a sale and marks down all chains by 20% off retail.In addition customers can use a coupon worth 15% off the price of any item including sale items.Store b offers a coupon worth 35% off any one item.
At store a Aurelie used a 15% off coupon to buy a chain already marked down by 20%.write an expression for the price of this chain.
At store b Tucker’s used a 35% off coupon to buy a chain.write an expression for the price of this chain.
Which store offers a better price on chains?
Evan is wrapping a shipping box in brown paper the box in the shape of a right rectangular prism the box has a length of 2ft a width of 1 ft and a height of 4 ft how many square feet of brown paper will even need to wrap the entire box? HURRY 25 POINts
the surface area of a cone is 150 Pi square inches the radius of the base is 10in what is the slant height