Answer:
The faster pipe will take 16 hours to fill the pond alone
Step-by-step explanation:
* Lets explain how to solve the problem
- A sewage treatment plant has two inlet pipes to its settling pond
- One pipe can fill the pond 3 times as fast as the other pipe
∴ The rate of the faster pipe is 3 times the rate of the second pipe
- The rate and the time are inverse proportion because;
time = job/rate and the job here is constant (fill pool), then
time × rate = constant
∵ The rate of the faster pipe is 3 times the rate of the second pipe
∴ The time of the second pipe is 3 times the time of the faster pipe
- Assume that the time of the faster pipe is t
∵ The time of the faster pipe is t
∴ The time of the second pipe is 3t
- Together they can fill the pond in 12 hours
∴ [tex]\frac{1}{3t}+\frac{1}{t}=\frac{1}{12}[/tex]
- The L.C.M of 3t and t is 3t
∴ [tex]\frac{1}{3t}+\frac{3}{3t}=\frac{1}{12}[/tex]
∴ [tex]\frac{1+3}{3t}=\frac{1}{12}[/tex]
∴ [tex]\frac{4}{3t}=\frac{1}{12}[/tex]
- By using cross multiplication
∴ 48 = 3t
- Divide both sides by 3
∴ t = 16
∵ t represents the time of the faster pipe
∴ The time of the first pipe is 16 hours
* The faster pipe will take 16 hours to fill the pond alone
Final answer:
The faster pipe will take 6 hours to fill the sewage treatment pond by itself, calculated by setting up and solving a rate problem based on the information provided.
Explanation:
To determine how long it will take for the faster pipe to fill the sewage treatment pond alone, we can set up a rate problem where the pipes are filling the pond at their rates and a combined rate.
Let's define the rate of the slower pipe as 1/x ponds per hour (where x is the number of hours it takes the slower pipe alone to fill the pond). This means that the faster pipe works at a rate of 3/x (since it's three times as fast).
Combined, their rate is 1/12 ponds per hour (because together they fill the pond in 12 hours). Our equation will now look like this: 1/x + 3/x = 1/12.
Solving this equation, we find that x, the time it takes for the slower pipe to fill the pond alone, is 18 hours. Therefore, the faster pipe, being three times as fast, will take 18 hours divided by 3, which equals 6 hours to fill the pond alone.
What is .83 repeating expressed as a fraction in simplest form??? Plz help
Answer:
5/6
Step-by-step explanation:
Let x = 0.8333.....
Then 10x = 8.333...
Now we subtract x from 10x.
10x = 8.333...
- x = 0.833...
-----------------------------
9x = 7.5
9x = 7.5
9x/9 = 7.5/9
x = 7.5/9 = 15/18 = 5/6
Answer: 5/6
The repeating decimal .83 repeating is equal to the fraction 83/99 in simplest form. A repeating decimal can be expressed as a fraction using the method of setting up equations, exploiting the fact we know which digits are repeating.
Explanation:To express the repeating decimal .83 repeating as a fraction in simplest form, we first need to understand what a repeating decimal is. A repeating decimal is a decimal fraction in which a digit or group of digits repeats infinitely. In the case of .83 repeating, the group of digits that is repeating is '83'. This means that the decimal can be written out as .838383..., and so on, infinitely.
To represent this as a fraction, we can use the method of setting up a pair of equations. Let's define the repeating decimal like this: x = .8383... . Now, multiply x by 100 since there are two repeating digits, yielding the equation: 100x = 83.8383... . Subtract the first equation from this to give 99x = 83, or x = 83/99 when simplified. So, the decimal .83 repeating is equal to the fraction 83/99 in simplest form.
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Name each quadrant these points are in
1.(3,-1)
2.(-2,3)
3.(4.5,-3)
4.(-6,2.3)
Answer:
(3,1),(-2,3),(4.5,-3),(-6,2.3)
Translate the following phrase into an algebraic expression using the variable w. Do not simplify.
the perimeter of a rectangle if the width is w centimeters and the length is 8cm less than twice the width
Answer:
2 * ( [2w-8] + w)
Step-by-step explanation:
width = w
Length = 2w -8
Perimeter of Rectangle = 2 (l+b)
= 2 * ( [2w-8] + w)
A group of friends went to a hamburger bar 2\5 of them bought a hamburger 1\3 of them bought chips. The rest bought cola. What fraction of the group bought food? What fraction bought a drink?
Answer:
11/15 bought food and 4/15 bought a drink
Step-by-step explanation:
2/5 x 3 = 6/15 bought a hamburger
1/3 x 5 = 5/15 bought chips
6/15 + 5/15 = 11/15 bought food
11/15 - 15/15 = 4/15 bought a drink
20 POINTS!!! PLZ ANSWER!! On the moon, the time, in seconds, it takes for an object to fall a distance, d, in feet, is given by the function f(d) = 1.11√d. Part a: determine f(2) and explain what it represents. Part B: The imbrium basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by {d|0 ≤ d ≤ 3805774}. What does this tell you about the basin. Part C: how long would it take a rock to drop from the rim to the bottom of the basin?
Answer:
Part a) [tex]f(2)=1.57\ sec[/tex]
It takes 1.57 seconds for an object to fall a distance of 2 feet
Part b) see the explanation
Part c) [tex]2,165.43\ sec[/tex]
Step-by-step explanation:
Let
f(d) -----> the time in seconds it takes for an object to fall
d -----> distance in feet
we have
[tex]f(d)=1.11\sqrt{d}[/tex]
Part a): Determine f(2) and explain what it represents
we know that
f(2) represent the time in seconds it takes for an object to fall a distance of 2 feet
For [tex]d=2\ ft[/tex]
substitute in the function above and solve for f(2)
[tex]f(2)=1.11\sqrt{2}[/tex]
[tex]f(2)=1.57\ sec[/tex]
therefore
It takes 1.57 seconds for an object to fall a distance of 2 feet
Part b) The imbrium basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by {d|0 ≤ d ≤ 3805774}
What does this tell you about the basin?
The height of the basin is greater than or equal to 0 ft and less than or equal to 3,805,774 ft
so
The maximum height of the basin is 3,805,774 ft
Part c) How long would it take a rock to drop from the rim to the bottom of the basin?
we know that
The distance from the rim to the bottom of the basin is equal to the maximum height of the basin
so
[tex]d=3,805,774\ ft[/tex]
substitute the value of d in the function f(d)
[tex]f(d)=1.11\sqrt{3,805,774}[/tex]
[tex]f(d)=2,165.43\ sec[/tex]
The function f(d) = 1.11√d helps us find the time to fall a specific distance on the moon. It would take approximately 2 hours for a rock to fall from the highest point to the lowest point in the Imbrium Basin on the moon.
Explanation:The given function for time it takes for an object to fall on the moon is f(d) = 1.11√d. Here, d represents the distance the object falls.
Part A: To find f(2), we substitute d with 2 in the provided function, which gives us f(2) = 1.11√2 = 1.57 seconds (rounded to two decimal places). This represents the time it would take for an object to fall a distance of 2 feet on the moon.
Part B: The given domain {d|0 ≤ d ≤ 3805774} indicates the height variation in the Imbrium Basin on the moon, where 'd' represents the height in feet. The height could be any value between 0 feet (the lowest point) and 3805774 feet (the highest point), which is approximately 720 miles.
Part C: To find the time it would take for a rock to drop from the rim to the bottom of the basin in the given domain, we substitute the highest point, d = 3805774, into the function. So, f(3805774) = 1.11 √3805774 = 7317 seconds, which is approximately 2 hours.
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Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 sec . If the runners start at the same spot and run in opposite directions how long will it take the runners to cover 1/4 mi?
Answer:
67.5 seconds
Step-by-step explanation:
I can run faster :D
Find the mean of the runner's speeds as (72 + 63)/2 = 67.5
The runners take 67.5 seconds to cover 1/4 mi if Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.
The runners start at the same spot and run in opposite directions.
The runner's speeds = (72 + 63)
The time they take = 135/2
The time they take = 67.5 seconds
Thus, the runners take 67.5 seconds to cover 1/4 mi if Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.
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What is the simplest form of the ratio 11:16?
O A 1:6
OB. 5:8
Oc 11:16
OD 22:32
Answer:
11:16
Step-by-step explanation:
The ratio cannot be simplified any further.
Simplify the following expression.
(3x - 5)(4 – 9x) + (2x + 1)(6x2 + 5)
Answer: 12x3−21x2+67x−15
Step-by-step explanation:
(3x−5)(4−9x)+(2x+1)(6x2+5)
=12x+−27x2+−20+45x+12x3+10x+6x2+5
=12x+−27x2+−20+45x+12x3+10x+6x2+5
=(12x3)+(−27x2+6x2)+(12x+45x+10x)+(−20+5)
=12x3+−21x2+67x+−15
Answer:
12x^3 - 21x^2 + 67x - 15!
Step-by-step explanation:
what is the square root of 109
[tex] \sqrt{ 109 } [/tex]
which of these expressions is equal to 0?
a. -24/6 - 4
b. -24/-6 + 4
c. 24/6 + 4
d. -24/-6 - 4
Answer: B is the answer
Step-by-step explanation:
Why? It is equal to 0
Answer:
d. -24/-6 - 4
Step-by-step explanation:
Use order of operation (PEMDAS) to solve.
There are no parentheses.
There are no exponents.
There is multiplication and/or division. Do this first, from left to right.
There is addition and/or subtraction. Do this second, from left to right.
Solve. Remember that a negative times (or divided by) a negative makes a positive.
-24 / -6 = 4
4 - 4 = 0
Check your work. None of the other expressions are equal to 0.
a. -24 / 6 - 4 = -4 - 4 = -8
b. -24 / -6 + 4 = 4 + 4 = 8
c. 24/6 + 4 = 4 + 4 = 8
4.5)38.7
What is the answer
Answer:
If adding, 43.2.
If subtracting, -34.2.
If multiplying, 174.15.
If dividing, 8.6.
Step-by-step explanation:
Addition: Line up and add.
Subtraction: Add the first number and opposite of the second. 4.5+(-38.7)=-34.2.
Multiplication: Multiply as normal, count up how many decimal places are in the factors (2), and add that to your answer, 174.15.
Division: Turn both number into whole numbers by multiplying by 10. Then divide 387/45= 8.6.
CAN EXPLAIN FURTHER
Which shows the expression below in simplified form?
(8 × 10^6) × (4 × 10^-3)
A. 3.2 × 10^2
B. 3.2 × 10^5
C. 3.2 × 10^3
D. 3.2 × 10^4
Answer: C. 3.2 × 10^4
Step-by-step explanation:
for this case the multiplication of the values with exponent are summed, as the exponent are the 6 and -3
6 - 3 = 3
this will be the exponent of the common value which is the 10.
after you only need to multiply 8 and 4 by separate the
8 * 4 = 32.
then we only need to place the values one by one
32 × 10^3
3 is the result of the sum of the exponent.
10 is the common value.
32 is the result of the product.
if we add another zero to the multiplication we get 3.2 and exponent finish with one more zero, then we get this result
3.2 × 10^4
because of that the C is the correct answer, keep in mind that the other answers do not apply correctly the rule of the exponent, because the rest of answer give us wrong answer with final result of the exponent.
To simplify the expression (8 × 10^6) × (4 × 10^-^3) in scientific notation, we multiply the numbers (8 x 4) and add the exponents (6 + -3) resulting in 32 x 10^3. To represent the coefficient within the range of 1 and 10, we revise 32 as 3.2 x 10 yielding the answer 3.2 x 10^4.
Explanation:To answer the question, 'Which shows the expression below in simplified form? (8 × 10^6) × (4 × 10^-^3)', we need to understand the rules for multiplying numbers in scientific notation. To multiply two numbers in scientific notation, we multiply the coefficients (the numbers) first and separately add the powers of ten.
Here, the coefficients are 8 and 4 which multiply to give 32. The powers of ten are 10^6 and 10^-3. When multiplying powers of 10, we add the exponents, so 6 + -3 = 3. Therefore, the simplified form of the expression is 32 × 10^3. However, in scientific notation, we usually want the coefficient to be a number between 1 and 10. Therefore, we rewrite 32 as 3.2 x 10 to get the final answer: 3.2 x 10^4. So, the correct answer is option D. 3.2 x 10^4
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6x + 5 = 27 , if x = 4
Answer: 0.93
Explanation: write out the problem and sub in 4, for "x". So it would look like this; 6 (4) + 5=27
6 (4)= 24, then add 5, which equals 29. so your next step would look like this; 29=27. Once you get this you want to divide each side by 29. The 29 cancels and 27/29 is equal to 0.93
*PICTURE ATTACHED* please help
Answer:
Step-by-step explanation:
10^0=1
10^-3 = 1/10^3
4.0=4
so : 1.72×10^0/4.0×10^-3 = (1.72× 10^3)/4 =430
scientific notation is : 4.30× 10^2
Write an equation of the line that is parallel to the line whose equation is 3y+7=2x and passes through point (2,6).
Answer:
Step-by-step explanation:
To find the equation of a parallel line, we first need to find the slope of 3y + 7 = 2x.
We need to find it because, if two lines are parallel, then that means they have the same slope.
The best way to do this is solve for y:
[tex]3y+7=2x\\3y=2x-7\\y=\frac{2}{3}-\frac{7}{3}[/tex]
Due to the rule that in y = mx + b, m = the slope, we find that the slope is 2/3.
Now we use that slope in the same formula to find b of the line we're trying to find the equation for, and then we'll have our answer. We find b by plugging in (2, 6) for x and y:
[tex]y = mx+b\\y=\frac{2}{3}x+b\\6=\frac{2}{3}(2)+b\\18=4+3b\\ 14=3b\\\frac{14}{3} = b[/tex]
So our line is:
[tex]y=\frac{2}{3}x+\frac{14}{3}[/tex]
To find the equation of a line parallel to a given line and passing through a given point, first find the slope of the original line. Then, using the slope-intercept form of a line, substitute the given point's coordinates and the slope to find the equation of the parallel line.
Explanation:To find an equation of the line parallel to 3y+7=2x and passing through point (2,6), we need to find the slope of the original line and then use it to create the equation of the parallel line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
The given equation 3y+7=2x can be rearranged to y = (2/3)x + 7/3.
The slope of this line is 2/3. Since a line parallel to another line has the same slope, the slope of the parallel line is also 2/3.
Using the point (2,6) and the slope 2/3, we can use the slope-intercept form to find the equation of the parallel line: y = (2/3)x + b. Plugging in the coordinates of the given point, we get 6 = (2/3)(2) + b.
Solving for b, we find that b = 5/3. Therefore, the equation of the line parallel to 3y+7=2x and passing through (2,6) is y = (2/3)x + 5/3.
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12 The cost of a telephone call is $0.60 for the first three minutes plus $0.17 for each additional minute. What is the greatest number of whole minutes the telephone call can be if the cost cannot exceed $2.50?
F 8
G 11
H 14
j 18
Answer:
H
Step-by-step explanation:
The total cost of the call is $2.50
Since the first three minutes cost $0.60
x minutes = $2.50 - $0.60
x minutes = $1.9
Each additional minutes cost $0.17
So: $1.9 / $0.17 = 11
To find the total minutes
$0.60 + $1.9 = $2.50
3 + 11 = total minutes
14 = total minutes
Every Tuesday, a bake shop offers a $5 special for 5 items. A customer can get any combination of bagels and donuts, but no more than 5 items for $5.00. The bake shop found that donuts were selling out so they limited the number of donuts to no more than three. Which section of the graph should be shaded to represent the number of possible combinations a customer can get with this $5 deal?
Answer:
3
Step-by-step explanation:
1 Donut, 4 Bagels/2 donuts, 3 bagels/3 donuts, 2 bagels, 3 combinations that are possible
Rewrite using the
distributive property :
45 + 9
Answer: 9(5 + 1)
Step-by-step explanation:
Factor out the GCF (greatest common factor) of 45 and 9, which is 9.
[tex]9\bigg(\dfrac{45}{9}+\dfrac{9}{9}\bigg)\\\\\\=\large\boxed{9(5+1)}[/tex]
A student missed
15 problems on a Chemistry test and received a grade of
52 %. If all the problems were of equal value, how many problems were on the test? Round off your answer to the nearest integer.
Answer:
x = 31
Step-by-step explanation:
Let x: total amount of questions in the Chemistry test.
Then 52% represents the ratio of questions properly answered vs total questions:
[tex]\frac{Correct}{Total} = 52%[/tex]
The number of correct questions is the number of total questions take the number of missed questions.
[tex]Correct questions = Total questions - missed questions[/tex]
Since, missed questions = 15
[tex]\frac{x-15}{x} = 52%[/tex]
Also, 52% can be expressed as 0.52. Then, the expression can be rewritten as:
[tex]\frac{x-15}{x} = 0.52[/tex]
Then, rearranging:
[tex] x - 15 = 0.52x [/tex]
[tex] x - 0.52x = 15 [/tex]
[tex] 0.48x = 15 [/tex]
[tex] x = 15/0.48 [/tex]
[tex] x = 31.25 [/tex]
Rounding to the nearest unit: x = 31
Find −9/14 + 2/7. Write your answer as a fraction in simplest form.
Answer:
[tex]-\frac{5}{14}[/tex]
Step-by-step explanation:
When you add fractions, sometimes you have to raise a number to make it more easier for you.
As in this case, we have two fractions in which seem to not be the same, but note this.
7 is multiple of 14, meaning to make our life easier, we can do this method:
[tex]\frac{2 * 2}{7 * 2} = \frac{4}{14}[/tex]
Whoa! Now we have the same denominator for both fractions, now we made this problem way more easier than it was before.
Do the math:
[tex]\frac{-9 }{14} + \frac{4}{14}[/tex]
==> [tex]-\frac{5}{14}[/tex]
The fraction in the simplest form is -5/4.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators who let do a basic mathematical calculation.
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
We have been given that expression of fraction as
⇒ -9/14 + 2/7
We have to determine the fraction in the simplest form.
⇒ -9/14 + 2/7
Take the LCM,
⇒ (-9 + 2×2)/7
⇒ (-9 + 4)/7
⇒ -5/4
Therefore, the fraction in the simplest form is -5/4.
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Please answer quickly
The answer is choice A.
Answer:
the answer is A that stuff is real easy
if you deposit a check for $43.95 and $12.39 in cash, what is the total deposit amount?
Answer:
$56.34
Step-by-step explanation:
1. 3x + y = 11
5x - y = 21
Answer:
[4, -1]
Step-by-step explanation:
Using the Elimination Method:
3x + y = 11
5x - y = 21
__________
8x = 32
__ ___
8 8
x = 4 [Plug this back into both equations to get the y-coordinate of -1]; -1 = y
The y's are already additive inverses [result in 0], canceling each other out.
I am joyous to assist you anytime.
if x=π, what is x40000000000000000000
Answer:
1.256637061 x 10 (to the power of 20)
Step-by-step explanation:
Just apply these digits into your calculator.
What is 64x + 27 written as a sum of cubes?
Answer:
see explanation
Step-by-step explanation:
64x + 27 ← is not a sum of cubes. We would require
64x³ + 27 ← sum of cubes and factors as
64x³ + 27 = (4x + 3)(16x² - 12x + 9)
What is the number if 50% of 25% of a number is 48?
Answer:
384
Step-by-step explanation:
If 48 is 50% of something, that means
48 + 48 = 96. Now, what number is 96 25% of? well 96 • 4 = 384. Now let's do the math backwards!
25 % of 384 is 96. 50 % of 96 is 48! so your answer is 384! Hope this helps!!!
Answer:
384
Step-by-step explanation:
If 48 is 50% of something, that means
48 + 48 = 96. Now, what number is 96 25% of? well 96 • 4 = 384. Now let's do the math backwards!
25 % of 384 is 96. 50 % of 96 is 48! so your answer is 384! Hope this helps!!!
Step-by-step explanation:
What are the first two missing digits of this series 33772365
The missing digit in this numbers are 11
In the diagram, which angles are vertical angles? Select two options. AngleABE and AngleABC AngleABE and AngleCBD AngleABE and AngleEBD AngleABC and AngleEBD AngleABC and AngleCBD
Answer:
1. ABE and CBD
Notice that the vertex is B, so these two angles share the same vertex. Accordingly, these two angles are vertical angles.
2. ABC and EBD
The same reasoning is applied here. The vertex is also B. Notice that the angles CBD and ABD add up to 180 degrees.
Step-by-step explanation:
Vertical angles are a pair of opposite angles formed by intersecting lines. The pair of angles which are vertical angles are ∠ABE and ∠CBD.
What are vertical angles?Vertical angles are a pair of opposite angles formed by intersecting lines.
As we know about the vertical angles, it is formed by two intersecting lines as in the given figure below, therefore, the angles which are a pair of vertical angles are ∠ABE and ∠CBD.
Hence, the pair of angles which are vertical angles are ∠ABE and ∠CBD.
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To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
negative StartFraction 5 Over 2 EndFraction
negative StartFraction 2 Over 5 EndFraction
StartFraction 2 Over 5 EndFraction
StartFraction 5 Over 2 EndFraction
Final answer:
The slope of the line represented by the equation 2x + 5y = 10, passing through points (5, 0) and (0, 2), is calculated as -2/5, meaning the slope is negative two-fifths.
Explanation:
The slope of the line represented by the equation 2x + 5y = 10 can be calculated by using the coordinates of two points through which the line passes. In this case, the points are (5, 0) and (0, 2). According to the slope formula, slope (m) is defined as the change in y (the rise) over the change in x (the run). Therefore, the slope is:
m = (y2 - y1) / (x2 - x1)m = (0 - 2) / (5 - 0) = -2 / 5The slope of the line is negative two-fifths (-2/5). Since the slope is negative, this indicates that as the x-value increases, the line moves down the y-axis.
Jamie has a total of 40 coins that are all nickels and dimes. She has 12 more nickels than dimes. How many of
each type of coin does she have?
Answer:
Jamie has 14 dimes and 26 nickels
Step-by-step explanation:
nickels : x
dimes : y
[tex]x + y = 40 \\ x = y + 12 \\ \\ replace \: x \:in \: the \: first \: equation \\ y + 12 + y = 40 \\ 2y = 28 \\ y = 14[/tex]
Jamie has a total of 40 coins out of which there are 14 dimes and 26 nickels.
Let x represent the number of dimes. Since Jamie has 12 more nickels, the number of nickels is x + 12.
The total number of coins is 40, so x + x + 12 = 40.
Solve for x:
2x + 12 = 40, 2x = 28
x = 14.