If a pipe is leaking at a rate of 8 US fluid ounces per minute, then 3.75 US liquid gallons of the fluid will leak from the pipe in an hour.
As per the question statement, a pipe is leaking at a rate of 8 US fluid ounces per minute and we are required to calculate the amount of leak that will occur at the same rate of leakage, in an hour, in the units of US liquid gallons.
To solve this question, we need to know to know about two basic mathematical conversions, i.e.,
1 US Liquid Ounce = 0.00781 US Liquid Gallons, and
1 hour = 60 minutes.
Therefore, amount of leak that will occur at the rate of 8 US fluid ounces per minute, in an hour = [tex](8 * 60)=480[/tex] US fluid ounces.
And 480 US fluid ounces = [tex](0.00781 * 480)=3.75[/tex] US Liquid Gallons.
Hence, 3.75 US Liquid Gallons of fluid will leak from the pipe in an hour.
Fluid Ounce: It is an unit of volume, used for measuring liquids. "The British Imperial" and the "United States customary" fluid ounce are the only two that are still in use. The US Fluid ounce is an unit of capacity equal to one-sixteenth of a US pint (approximately 0.03 liter), while the British Imperial fluid ounce a unit of capacity equal to one twentieth of a pint (approximately 0.028 liter).Liquid Gallons: In the United States, Liquid Gallon is an unit of liquid capacity equal to four quarts or 231 cubic inches or 3.785 liters, while in the Great Britain, also known as the "Imperial Gallon", it is an unit of liquid and dry capacity equal to four quarts or 277.42 cubic inches or 4.544 liters.To learn more about Fluid Ounces and Liquid gallons, click on the klink below.
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Which of the following would represent three consecutive integers if X is the first integer? Check all that apply 
What is the equation of the tangent of f(x) 3 X at (1, 3)?
The Equation of the tangent line is y = 4x - 1.
According to the statement
We have to find that the equation of the tangent of the line.
So, For this purpose, we know that the
Equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.
From the given information:
f(x) = 3 X at (1, 3)
Then
The tangent line of a curve y = f(x) is a line that touches the curve at a point (x0, y0). Its slope (m) is found by substituting the point where it is drawn in the derivative f'(x) and its equation is found by using y - y0 = m (x - x0).
From the given it is clear that the slope of the equation is a 3.
Then m = 3
then
y – y1 = m (x – x1)
Substitute the points here
y - 3 = 4(x - 1)
Then
y = 4x - 4 +3
y = 4x - 1.
So, The Equation of the tangent line is y = 4x - 1.
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You have quarters, nickels,
and dimes that total $1.85. You have twice as many
nickels as dimes, and 2 more quarters than dimes.
How many of each coin do you have?
The number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.
Let the number of dimes be x.
So, we get that:
The number of quarters will be = x + 2
The number of nickels will be = 2 x
Now, 1 dime = $0.10.
1 nickel = $ 0.05
1 quarter = $ 0.25
Amount of dimes = 0.10 x
Amount of nickels = 0.10 x
Amount of quarters = 0.25 x + 0.5
Total amount of coins = $ 1.85
So, we get the equation as:
0.10 x + 0.10 x + 0.25 x + 0.5 = 1.85
0.45 x = 1.35
x = 135 / 45
x = 3
Dimes = 3
Nickels = 6
Quarters = 5
Therefore, we get that, the number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.
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500 values are normally distributed with a mean of 125 and a standard deviation of 10 which percent of the values lies between 115-125
The percent that the value is between 115 - 125 is 34.13%.
What is defined as the standard normal distribution?A standard normal distribution is a symmetric probability distribution with equal mean, mean, and mode values. The value of the probability of a standard normal distribution is achieved from a statistical table or computer software.For the given question;
The total number of the sample is 500.
The mean of the sample is; μ = 125.
The standard distribution is; σ = 10.
The percentage of the values must lie between 115-125.
Thus,
P(115 < X < 125) = P[(115 - 125)/10 < (x - μ)/ σ < (125 - 125)/10]
= P[-1 < Z < +0]
Z for +0 = 0.50000 and z for -1 = 0.15866 obtained from Z-score table.
P(115 < X < 125) = [0.50000 - 0.15866]
P(115 < X < 125) = 0.34134
P(115 < X < 125) = 34.13%
Therefore, the probability for percent of the values lies between 115-125 is 34.13%.
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Help fast please pamdas
I have an equation that I have an answer but no idea how it's solution works. This is an example for using the squeeze theorem, and the answer is 0:
[tex]f(x)=\frac{e\frac{-1}{13+\frac{1}{x^2}}\sin(1+cos\frac{\pi }{x^3})\sqrt{3x^4+5x^6}}{(x+x^\frac{1}{3})(3+arctan\sqrt{7+\frac{1}{x^8}})}[/tex]
The way the answer is arrived at is supremely confusing. Also the textbook used absolute values alongside inequalities when performing the algebraic manipulations (direct sub. doesn't work), which I also don't understand why. Please explain how this equations limit is zero in simple terms.
Step-by-step explanation:
You want to know how the squeeze theorem applies to help you find the limit of f(x) is zero as x approaches zero.
SummaryThe short of it is that you have ...
f(x) = [messy finite function] × [function that cleanly approaches 0 at x=0]
The zero product rule tells you that the product of any finite value and 0 is zero, so the limit of this product is 0 at x=0.
The graph in the attachment shows the "function that cleanly approaches 0" in red. When multiplied by the "messy finite function", the result is the blue curve. You can see that the result is a function that has a limit of 0 at x=0.
How to get thereHere, we'll decompose f(x) into two parts:
messy finite function (g(x))function that cleanly approaches zero at x=0 (h(x))Messy finite function
The numerator sine function factor of f(x) gets increasingly messy as x approaches zero, due to the cosine term it contains. We can define ...
[tex]g(x)=\sin(1+\cos(\pi x^{-3}))[/tex]
Because this is a sine function, its value is always in the range |g(x)| ≤ 1.
Function cleanly approaching zero
The remaining factors of f(x) need to be rearranged a bit to make a function that obviously approaches zero at x=0. We do that by factoring ∛x from the denominator and rearranging the leading fraction.
[tex]h(x)=\dfrac{e\dfrac{-1}{13+x^{-2}}\sqrt{3x^4+5x^6}}{(x+x^{1/3})(3+\arctan\sqrt{7+x^{-8}})}\\\\=-e\dfrac{x^2}{13x^2+1}\cdot\dfrac{x^2\sqrt{3+5x^2}}{x^{1/3}(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}\\\\h(x)=-e\dfrac{x^{11/3}\sqrt{3+5x^2}}{(13x^2+1)(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}[/tex]
Recognizing that the arctangent term will approach π/2 as x→0, this can be (more or less) directly evaluated at x=0 to give ...
[tex]h(0)=-e\dfrac{0\cdot\sqrt{3}}{1\cdot1\cdot(3+\dfrac{\pi}{2})}=0[/tex]
The sign of h(x) will be opposite the sign of x. The graph of h(x) is shown in red in the attachment.
The squeezeAs h(x) approaches zero, the product ...
f(x) = g(x)·h(x)
approaches zero. This is the essence of the squeeze.
Starting from our description of g(x) above, we can multiply both sides of the inequality by the positive value |h(x)| to get ...
|g(x)| ≤ 1 . . . . . . . . . . the range of the sine function
|h(x)|·|g(x)| ≤ |h(x)|·1 . . . . . . multiply by |h(x)|
Simplifying, this is ...
|f(x)| ≤ |h(x)| . . . . true for all x
So, the limit is ...
[tex]\displaystyle \lim_{x\to0}|f(x)|\le\lim_{x\to 0}|h(x)|\\\\\lim_{x\to0}|f(x)|=0[/tex]
The attachment illustrates this nicely, showing that the oscillating f(x) has its amplitude limited by h(x), which approaches zero.
__
Additional comments
The limit of x^-8 is positive infinity as x approaches zero. This means the arctangent function argument is positive infinity as x approaches zero, so the function value is π/2. The sign of x is irrelevant.
We cannot tell if the fraction following "e" in this function is supposed to be an exponent. The two typeset versions of f(x) seem to show "e" as a multiplier, not the base of an exponential term. Even if an exponential term is what is intended, that term would approach 1 at x=0, so the conclusion here remains unchanged.
-10x—16=14
-16x -6 = 14
Answer: No solution
Step-by-step explanation:
-10x-16=14
-16x-6=14
-10x-16=-16x-6
-10x+16x-16=-16x+16x-6
6x-16=-6
6x-16+16=-6+16
6x=10
x=10/6
x=5/3
-16(5/3)-6=
-80/3-6*3/3=
-80/3-18/3=
(-80-18)/3=-98/3 [tex]\neq[/tex] 14
Hence, there is no solution
Un centro recreacional cuenta con dos piscinas
temperadas, una para adultos que tiene una
capacidad de 240 000 litros de agua y una para
niños cuya capacidad es 2/3 de la de adultos. Cada
una de estas piscinas cuentan con un desagüe que
permite desalojar 2 500 litros de agua cada 5 min.
Si se requiere vaciar el agua de ambas piscinas y los
desagües se abren a las 8:10 am.
1. ¿A qué hora se terminará de vaciar cada piscina?
2. ¿cuánto más tardará en vaciarse una piscina que la otra que la otra?
1) La piscina grande tardó 8 horas en ser vaciado, culminando a las 4: 10 PM, y la piscina pequeña tardó 5 horas y 20 minutos en ser vaciado, culminando a las 1: 30 PM.
2) La piscina grande tardará 2 horas y 40 minutos más en vaciarse que la piscina pequeña.
¿Cómo determinar y estimar tiempos de vaciado de una piscina?
En este problema tenemos el caso de dos piscinas de diferente capacidad, la primera piscina tiene una capacidad de 240 000 litros de agua y la segunda piscina tiene una capacidad de 160 000 litros de agua. Ambas cuenta con un desagüe que desaloja a una tasa de 500 litros de agua por cada minuto de operación.
El tiempo total de vaciado es igual a volumen de la piscina dividido por la tasa de vaciado, entonces:
Piscina grande (V = 240 000 L, Q = 500 L / min)
t = V / Q
t = (240 000 L) / (500 L / min)
t = 480 min
Piscina pequeño (V = 160 000 L, Q = 500 L / min)
t = V / Q
t = (160 000 L) / (500 L / min)
t = 320 min
1) La piscina grande tardó 8 horas en ser vaciado, culminando a las 4: 10 PM, y la piscina pequeña tardó 5 horas y 20 minutos en ser vaciado, culminando a las 1: 30 PM.
2) La piscina grande tardará 2 horas y 40 minutos más en vaciarse que la piscina pequeña.
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answer for
D=
E=
F=
Bill weighs 240 pounds and is losing two pounds each month . Phil weighs 290 pounds and is losing 4 pounds each month . How many months , m, will it take Bill to weigh the same as Phil
They will weigh the same at twenty-five months.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Let the number of months when they will weigh the same would be m
Given that Bill is losing two pounds per month and is currently 240 pounds.
So his model expression of weight would be: 240 - 2m
And Bill is losing four pounds per month and is currently 290 pounds.
So his model expression of weight would be: 290 - 4m
As per the condition, they will weigh the same
⇒ 240 - 2m = 290 - 4m
⇒ 4m - 2m = 290 - 240
⇒ 2m = 50
⇒ m = 25
Therefore, they will weigh the same at twenty-five months.
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1/18 as a decimal equivalent to a rational number
The representation of 1 / 8 in decimal form will be 0.125 and it is a rational number as it is a terminating decimal.
We are given a fraction:
1 / 8.
We have to represent it as a decimal and tell that it is a rational number.
To write it as a decimal, First we will make the denominator a multiple of 10:
1 / 8 × 125 / 125 = 125 / 1000.
Now writing it in the decimal form, we get that:
= 0.125.
Now, we can see that it is a non repeating terminating number.
So, we can say that it is a rational number.
Therefore, the representation of 1 / 8 in decimal form will be 0.125 and it is a rational number as it is a terminating decimal.
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Solve AGHI. Round the answers to the nearest hundredth.
A. m/Gs 61.93°, m1s 28.07°, HI = 15
B. m/Gs 28.07°, m/1 61.93°, HI = 18.79
C. m/Gs 61.930, m1 28.07°, H/= 18.79
D. m/G 28.07°, m/1 61.93°, HI = 15
Jason has $200 Karen has 7/8 as much money as him how much money does Karen have
Answer:
175
Step-by-step explanation:
because 7/8 of 200 is 175
Watch help video
Find the distance between the two points in simplest radical form.
Answer:
(4, 3) and (-2, 0)
3√5
The distance between two points on an XY plane is calculated using the distance formula, which is employed in coordinate geometry or Euclidean geometry. The x-coordinate, often known as the abscissa, is a point's separation from the y-axis. The y-coordinate, often known as the ordinate, refers to a point's separation from the x-axis. A point on the x-axis has coordinates of the form (x, 0), and a point on the y-axis has coordinates of the form (0, y). We utilize the Pythagoras theorem in this case to determine the separation between any two points in a plane.
Distance formula = √ ( x₁ - x₂)² + ( y₁ - y₂)²
= √ 6² + 3²
=3√5
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is it correct ?
the question is :
(2/5 ÷ 3/8) ÷ (-3/5)
solution : =
2/5 × 8/3 = 16/15. 16/15 × -3/5 = -39 / 80
if its not correct please tell how to do it.
Answer:
Step-by-step explanation:
It is correct till 16/15
But after that it is 16/15 × 5/-3 = 80/-45
simplify it to 16/-9
please refer to the image
Is 604,892 divisible by 4?
Answer:
yes it is 604892÷4=151,223
In the two functions fand g, fog and go fare both equivalent to x. Which of the following statements must be TRUE?
2 and 3 50 points and Brainlyest
AAnswer:
AB (-1, 4) = 34^ and B = (3,-1) 249*32 = 20
Step-by-step explanation:
Answer:
[tex]AB=\sqrt{53}\:\sf units[/tex]
[tex]EF=\sqrt{349}\:\sf units[/tex]
Step-by-step explanation:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}.[/tex]
Given:
A = (-4, 1)B = (3, -1)Substitute the given points into the distance formula and solve for AB:
[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-4))^2+(-1-1)^2}\\& =\sqrt{(7)^2+(-2)^2}\\& =\sqrt{49+4}\\& = \sqrt{53}\end{aligned}[/tex]
Given:
E = (-7, -2)F = (11, 3)Substitute the given points into the distance formula and solve for EF:
[tex]\begin{aligned}\implies EF & =\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\& =\sqrt{(11-(-7))^2+(3-(-2))^2}\\& =\sqrt{18^2+5^2}\\& =\sqrt{324+25}\\& =\sqrt{349}\end{aligned}[/tex]
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“Back home, my tíos and tías, and primas, Mami and Papi, and mis hermanas had a party for me with sancocho and a store-bought pudín, inscribed with Happy Graduation, Julie.”
—“Names/Nombres,”
Julia Alvarez
Which inference would this passage best support?
The people at the store do not share Julia’s heritage.
Julia is very upset about her party.
Julia’s family does not speak Spanish.
Pudín is not a Dominican dessert.
An inference which this passage would best support is that: A. the people at the store do not share Julia’s heritage.
What is deductive reasoning?Deductive reasoning can be defined as a type of logical reasoning that typically involves drawing conclusions based on a given set of rules and conditions, or from one or more premises (factual statements) that are assumed to be generally (universally) true.
What is an inference?An inference can be defined as a process through which a reader can logically deduce the meaning or message (information) that is associated with a literary work, especially through induction.
Since "Happy Graduation, Julie." and "Names/Nombres," were inscribed on the gift, it ultimately implies that the people at the store were obviously of English speaking heritage, rather than Spanish (Julia’s heritage).
In conclusion, we can reasonably infer and logically deduce that an inference which this passage would best support is that: A. the people at the store do not share Julia’s heritage.
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Answer: A
Step-by-step explanation:
Molly is making strawberry infused water. For each ounce of strawberry juice, she uses two times as many ounces of water. How many ounces of strawberry juice and how many ounces of water does she need to make 39 ounces of strawberry infused water?
Answer: 39 ounces of strawberry juice, 78 ounces of water.
Step-by-step explanation:
Since Molly uses "each ounce" meaning 1 per strawberry juice, 39 ounces of strawberry infused water would mean she uses 39 ounces of strawberry juice. Then, it says she uses two times as many as those 39 ounces of strawberry juice for water. This means you multiply 39 by 2 which means you get 78 ounces.
Molly uses 39 ounces of strawberry juice and 78 ounces of water to get 39 ounces of Strawberry Infused Water.
Write a rule to describe each transformation please I need help asp
Answer:
The figure is reflected over the line x = -2
Step-by-step explanation:
If you drew a vertical line at x = -2, you would see that each point is the same distance from x = -2 but on the right side. E and E' are the same point because they are on the line x + -2. Point D is 3 units to the left of x = -2 for D' is 3 units to the right of x = -2 and so one
Solve for x.
8x - 2 = 3x + 5x
Answer:
x=-8
Step-by-step explanation:
8x-2=3x+5x
1. Combine Like Terms
3x+5x=8x
Now your equation looks like this:
8x-2=8x
+8x +8x
2. Move Variables to one side
Now this is your equation:
-2=16x
3. Divide to isolate "x"
16/-2
x=-8
Let me know if this helped! :)
A woman deposits $12,000 at the end of each year for 12 years in an investment account with a guaranteed interest
rate of 5% compounded annually.
(a) Find the value in the account at the end of the 12 years.
(b) Her sister works for an investment firm that pays 4% compounded annually. If the woman deposits money with this
firm instead of the one in part (a), how much will she have in her account at the end of 12 years?
(c) How much would she lose or gain over 12 years by investing in her sister's firm?
Answer:
(a) $191,005.52
(b) $180,309.67
(c) lose $10,695.85
Step-by-step explanation:
You want the future values of an ordinary annuity of $12,000 over 12 years at interest rates of 5% and 4%. You also want the difference between the values.
(a) 5%The future value of an ordinary annuity with n annual deposits of P, at interest rate r compounded annually is given by ...
FV = P((1+r)^n -1)/r
The value of $12,000 deposited for 12 years at 5% is ...
FV = $12,000((1.05^12 -1)/0.05 = $191,005.52
At the end of 12 years, she will have $192,005.52 in her account.
(b) 4%The value of $12,000 deposited for 12 years at 4% is ...
FV = $12,000((1.04^12 -1)/0.04 = $180,309.67
At the end of 12 years, she will have $180,309.67 in her account.
(c) differenceThe amount at 5% is greater, so by investing in her sister's firm, the woman would lose ...
$192,005.52 -180,309.67 = $10,695.85 . . . . amount lost
0.007349 to three significant figures
Answer:
Step-by-step explanation:
From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.
0.007349 to 3 significant figure=0.00735
A car rental agency advertised renting a car for $26.95 per day and $0.33 per mile. If Greg rents this car for 3 days, how many whole miles can he drive on a $200 budget?
Answer: 361 miles
Step-by-step explanation: 26.95x3=80.85
200-80.85=119.15
119.15/0.33
=361.06
Given the function ()=−4‾‾‾‾‾‾√,
g
(
m
)
=
m
−
4
,
evaluate
The required solution is 1(one) as per the given functions.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the sphere of the function and the set Y is called the codomain of the function. Functions were firstly the idealization of how a varying volume depends on another volume, an expression, rule, or law that defines a relationship between one variable( the independent variable) and another variable( the dependent variable). Functions were firstly the idealization of how a varying volume depends on another volume. For illustration, the position of the earth is a function of time.Every function has a(one) domain and codomain or range. A function is generally(ax) denoted by f(x) where x(ax) is the input
Given :
The function(one)
g(m)= m-4(four).
By put m is equal to 5(five) we get,
g(5)=5-4(four)
=1(one)
Hence, the required solution is 1(one) as per the given functions.
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Lynn's track team practices for 3 weeks before their first meet. The coach wants them to get in a total of 720 minutes of practice time before the first meet. If the track team meets every Monday, Wednesday, and Friday for 70 minutes, will they have enough practice time before the first meet? Explain.
Answer:
No
Step-by-step explanation:
By the time they meet at their first meet, they would have practiced for 630 minutes total.
70*3=210
If they meet every three days each week for 70 mins each day then I would have to multiply the answer to learn how many minutes they gain each week.
210*3=630
If they have 210 mins per week and they only meet 3 times before the first meet, they will have only met for a total of 630 mins.
Question 15 (1 point)
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5]
B = {1, 3, 5, 7}
How many elements are in AUB?
Answer:
6
Step-by-step explanation:
The union is defined as the set of all elements in at least one of the sets.
[tex]A \cup B=\{1,2,3,4,5,7\}[/tex]
So, there are 6 elements.
Ninety-six golf balls were picked up at the
driving range and placed into two buckets.
One bucket has twenty-eight more balls
than the other bucket. How many golf
balls are in each bucket?
Answer: 34 in one bucket, 62 in the other
======================================================
Work Shown:
x = number of golf balls in bucket A
y = number of golf balls in bucket B
Let's say bucket B has more golf balls. More specifically it has 28 more golf balls, so,
y = x+28
The two quantities must add to 96 golf balls total.
x+y = 96
x+x+28 = 96
2x+28 = 96
2x = 96-28
2x = 68
x = 68/2
x = 34 is the number of golf balls in bucket A
y = x+28
y = 34+28
y = 62 is the number of golf balls in bucket B
-------------
Check:
x+y = 34+62 = 96
The answer is confirmed.