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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help i need answer to this math question???
The solution of the geometrical system is (x, y) = (2.5, 48.5).
What are the missing values associated with a geometrical system?In this question we have a picture representing two lines and a semirray that brings out two formulae for supplementary angles, these are shown below:
(x + 10) + 30 + (3 · y + 2) = 180
x + 3 · y = 148 (1)
30 + (3 · y + 2) + (5 · x - 10) = 180
5 · x + 3 · y = 158 (2)
And now we resolve the entire system of linear equations by substitution:
By (1):
x = 148 - 3 · y
(1) in (2):
5 · (148 - 3 · y) + 3 · y = 158
740 - 15 · y + 3 · y = 158
12 · y = 582
y = 48.5
By (1):
x = 148 - 3 · 48.5
x = 2.5
The solution of the geometrical system is (x, y) = (2.5, 48.5).
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Find the x- and y-intercepts of the graph of the equation. (If an
(a)
X^2-xy+4y=49
Answer:
x=±7; y=12.25.
Step-by-step explanation:
1) x-interception:
(y=0): x²=49, ⇒ x=±7;
2) y-interception:
(x=0): 4y=49; ⇒ y=12.25.
In a salad recipe, the ratio of carrots to broccoli must remain constant. The table below shows some possible combinations of carrots and broccoli.
Salad Ingredients
Carrots
Broccoli
3
9
4
12
6
18
7
21
If only whole vegetables can be used, what is the fewest number of vegetables that can be used to make this salad?
A.1
B.3
C.4
D.12
Using a proportional relationship, the fewest number of vegetables that can be used to make this salad is:
C. 4
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For this problem, looming at the table, we have that the number of Broccoli is triple the number of carrots, hence the proportional function is:
B = 3C.
When there is one carrot, the number of broccoli is given by:
B = 3 x 1 = 3.
Hence the fewest number of vegetables is of 4, as 1 carrot + 3 broccoli = 4 vegetables, hence option C is correct.
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use addition properties and strategies to find the sum 13 + 26 + 54=
Answer:
93
Step-by-step explanation:
13 + 26 = 39
39 + 54 = 93
Use the given domain to find the range of each function. F(x)=|x|, D={-4,0,-3}
Answer:
[tex]R=\{0,3,4\}[/tex]
Step-by-step explanation:
We can find the range by finding the set of values the function takes for each element in the domain.
[tex]F(-4)=|-4|=4 \\ \\ F(0)=|0|=0 \\ \\ F(3)=|3|=3 \\ \\ \therefore R=\{0,3,4\}[/tex]
The domain and the range of the function are
Domain, D = {-4,0,-3}Range, R = {4,0,3}Calculating the domain and range of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = |x|
The rule of a function is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain, D = {-4,0,-3}
Range, R = {4,0,3}
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Find the future value (in dollars) of an 18-month investment of $4,300 into a simple interest rate account that has an annual simple interest rate of 5.1%.
keeping in mind that a year has 12 months, thus 18 months is really 18/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4300\\ r=rate\to 5.1\%\to \frac{5.1}{100}\dotfill &0.051\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ A=4300[1+(0.051)(\frac{3}{2})] \implies A=4628.95[/tex]
5 is 1/2% of what number
I need help with math ngl
Answer:
Oldest to newest:
10^-35, 10 ^-10, 0
Step-by-step explanation:
Scientific notation
To figure out the power of 10 think "how many places do I move the decimal point?"
When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.
When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.
Suppose that 14 inches of wire costs 84 cents.
At the same rate, how much (in cents) will 11 inches of wire cost?
Answer:
11 inches of wire will cost 66 cents
Step-by-step explanation:
14 inches - 84 cents
find unit rate by dividing 84 by 14
84/14=6
so is is 6 cents per inch
so multiply 6 by 11
11 inches of wire will cost 66 cents
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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Point B is on line segment
AC
. Given AB=3x, BC=4x+8, and AC=5x+10, determine the numerical length of
AC
.
Answer:
The length of AC is 15 units
Step-by-step explanation:
An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was
then recorded. The frequency histogram to the right gives the results. Use the histogram to complete parts (a) through (f).
a. What was the most frequent outcome of the experiment?
b. What was the least frequent?
c. How many times did we observe a 5?
d. How many more 8's were observed than 11's?
e. Determine the percentage of time a 5 was observed.
f. Describe the shape of the distribution.
The answers to the questions are:
The most frequent outcome of the distribution that we have here is 7.The least frequent outcome is 12The number of times that we observed a 5 is 10 timesThe 8ths that were observed than 11 is 16 - 4 = 12 timesA 5 was attempted at 10 percent of the timeThe shape of the distribution is the bell shaped distribution.What is a frequency histogram?This is the term that is used to refer to the graphical representation of a frequency distribution. It helps to show us the frequency that the details in the class would have to fall under.
For example, the most frequent outcome can be seen as the one that has the highest point on the graph. We can see the highest point as 7 and its frequency is 20.
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Answer:
A. 7
B. 12
C. 15
D. 16
E. 15%
F. Bell-shaped
Solve the literal equation for x. State any
necessary restrictions on the letters
representing constants in the equation.
a (bx + c) = 0
Loan payments of $4000 due 200 days ago and $6000 due 63 days ago are to be replaced
by a payment of$5000 today and the balance 92 days from today. If money is worth 8.3%
and the agreed focal date is 92 days from today, what is the size of the final payment?
The size of the final payment is $5378.08
What is the size of the final payment?P1 = One loan payment = $4000
P2 = Second loan payment = $6000
P3 = Payment = $5000
Let P4 = Second payment
n1 = 200 days
n2 = 63 days
n3 = 92 days
r = Interest rate = 8.3%
[P1 * (1+ (r * n1 /365))] + [P2 * (1+ (r * n2 /365))] = P3 + [P4 / (1+(r*n3/365)]
[$4000 * (1+(8.3%*200/365)] + [$6000 * (1+(8.3%*63/365)] = $5000 + [P4 / (1+(8.3%*92/365))]
[$4000 * 1.04547945] + [$6000 * 1.01432603] = $5000 + [P4 / 1.02092055]
$4181.9178 + $6085.95618 = $5000 + [P4/1.02092055]
P4/1.02092055 = $5267.87398
P4 = $5378.080801
Therefore, the size of the final payment is $5378.08
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Find the area of the triangle. Show your reasoning. If you get stuck, carefully consider which side of the triangle to use as the base.
The area of the triangle is found as 12 unit².
What is defined as the triangle?A triangle is a three-sided polygon with three sides that closes a space.
The three sides are formed by lines, line segments, or rays (in just about any combination). Three vertices, or corners, are formed if three sides form or meet.A triangle's height or altitude is calculated by drawing a perpendicular line through one side to the opposite angle.The base is the side with which the altitude intersects wherever it is built.The formula for the area of the triangle is;
Area of triangle= ½ × base × height
The base is given as 6 units and the height is 4 units. (count 1 column of graph as 1 unit).
Put the values in formula.
Area of triangle = ½(6)(4)
Area of triangle = 12 unit.²
Therefore, the area of the triangle is found as 12 unit.²
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Drag the decimal values to match the corresponding fraction values.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1/3 =
1/2 =
1/4 =
3/4 =
2/3 =
to choose from: 0.50 0.75 0.25 0.66 0.33
please help
[tex]1/3 \longrightarrow 0.33 \\ \\ 1/2 \longrightarrow 0.50 \\ \\ 1/4 \longrightarrow 0.25 \\ \\ 3/4 \longrightarrow 0.75 \\ \\ 2/3 \longrightarrow 0.66[/tex]
Which polynomial represents the sum below?
+
2x² + 5x+4
5x2+
Answer:
????
Step-by-step explanation:
I don't get this
at all
Erin watches the price of an item advertised on the internet. The ad says the price will go down $3 each hour. Erin wants to know how much the
price will change in 6 hours. She writes this number sentence.
(-3) x 6=-18
What does the number sentence mean?
O The price will rise $6 in 18 hours.
O The price will rise $18 in 6 hours.
O The price will drop $6 in 18 hours.
O The price will drop $18 in 6 hours.
5(x+11)>-4(-x-12)
someone pls help this is due tmrw!
Answer:
work is shown and pictured
Identify the errors made in finding the inverse of
y = x- + 12x.
x = y2+ 12x
y?=x-12x
y2=-11x
y=V-11x, for x 2 0
Describe the three errors.
The following mistakes were made in the solution of the inverse function:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.What are inverse functions?The original value for which the function's output was provided is returned by the inverse function.F and G are inverse in terms of functions, with f(g(x)) = g(f(x)) = x.The initial value is returned by a function that is its inverse. The inverse of f is then g(y) = (y-5)/2 = x. (x).Therefore, the first error is caused by the incorrect variable swap.
The correct expression is:
x = y² + 12yThe following error is:
y = √-11xThe correct expression:
y = ± √-11xFinally, the domain is incorrect.
Because if x is 0 or positive, y = -11x has no true value.As a result, the following errors were made in the inverse function solution:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.Know more about inverse functions here:
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The correct question is given below:
Identify the errors made in finding the inverse of y = x2 + 12x.
Describe the three errors.
Which measurement is closest to the circumference of the circle in square centimeters
Answer:
the measurement of the circumference of a circle is 21
Please help i dont understand
Answer :
1) If x = 6
Substitute 6 for x in the expression.
a) 5x-9
5(6)-9
30-9
21
b) 2x-7
2(6) -7
12-7
5
c) 8x+5
8(6)+5
48+5
53
d) 4(x+3)
4(6+3)
4(9)
36
e) x²-(-4)
6²-(-4)
36+4
40
f) 3x²+1
3(6²)+1
3(36) +1
108+1
109
2) Solve
a) 54 = 3x
Divide both sides by 3.
54/3 = 3x/3
x = 18
b) x-9 = -3
Add 9 to both sides.
x-9+9 = -3+9
x = 6
c) x/7 = 140
Express the 140 over 1 and cross multiply.
x/7 = 140/1
x = 140×7
x = 980
d) x/8 = 72
Express the 72 over 1 and cross multiply.
x/8 =72/1
x = 72×8
x = 576
Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
Answer:
each takes 3 together 3x3=9
A rectangular field is eleven times as long as it is wide. If the perimeter of the field is 1680 feet, what are the dimensions of the field? A) Write an equation you can use to answer the given question. Let w be the width of the field.
Answer:
2(w+11w)=1680
Step-by-step explanation:
If the width is w, then the length is 11w.
Using the formula for the perimeter of the rectangle, the equation is 2(w+11w)=1680
Solve for y.
5. x = 1/3y +2
Answer: y=3x-6
Step-by-step explanation:
ANSWER:y=1/(3x-6)
Step-by-step explanation:
i think you are asking for the change of subject of formula(Transposition of subjects).
x=1/3y+2
multiply both sides by 3y
x × 3y=1/3y × 3y + 2 × 3y
3xy=1+6y
collect like terms
3xy-6y=1
fractionalize
y(3x-6)=1
divide both sides by (3x-6)
y=1/(3x-6)
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Which diagram shows two figures intersecting at exactly four points?
Answer:
The rightmost figure
Step-by-step explanation:
That is the only figure where there are 4 points of intersection. It is a rhombus inscribed in a square
Find the volume of the solid of revolution formed by rotating
about the x-axis each region bounded by the given curves.
f(x) =(1/3)x + 2, y = 0, x = 1, x = 3
The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .
Let us think of any region that is enclosed by a function g(x) and the x-axis between x=a and x=b. If this region is rotated about the x-axis, the solid of rotation that results can be thought of as consisting of thin cylindrical discs with a width of dx and a radius of g (x). Therefore, by integrating the volume of this disc, the whole volume of the solid will be revealed.
Volume=[tex]\int^{a}_{b}\pi [g(x)]^2dx[/tex]
The given function is g(x)=(1/3)x+2 ranging from x=1 to x=3
Therefore volume of the solid formed is:
[tex]\int^{3}_{1}\pi [\frac{1}{3}x]^2dx\\=\int^{3}_{1}\pi [\frac{1}{9}x^2]dx\\=\pi \int^{3}_{1} [\frac{1}{9}x^2]dx\\\\=\pi [\frac{1}{27}x^3 ]^3_1\\= \frac{26}{27} \pi[/tex]
The volume of the solid thus formed is [tex]\frac{26}{27} \pi[/tex] .
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A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 12 feet less than 3 times the height. Find the width and the height if the carpenter
expects to use 22 feet of lumber to make it.
Width:
feet
Height:
feet
Answer:
The width is 3 feet and the height is 6 feet.
Step-by-step explanation:
Calculator is showing a result of 78.987625. What is this to 2 decimal places
Answer:
78.99
Step-by-step explanation:
Rounding to the 2nd decimal place the number 78.987625
Write down everything upto and including the 2nd decimal: 78.98
Check out the next digit. If >= 5, then increase the 2nd decimal digit above by 1, if not leave it as is.
For 78.987625 the digit next to the 2 decimal digit is 7 so we increase 78.98 to 78.99
6.1 Define the term inflation.
Answer:
the action of inflating something or the condition of being inflated.
"the inflation of a balloon"
ASTRONOMY
(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.
2.
ECONOMICS
a general increase in prices and fall in the purchasing value of money.
"policies aimed at controlling inflation"
