Rain is flowing into 2 containers at different rates. The figure below shows the volume of water in each container what is the difference in rate of change between the two containers
Answers
With the help of Linear relationships The difference in the rate of change between the two containers is 1/5 gallon per minute.
what is Linear relationships?
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships. In everyday life, linear relationships are quite prevalent.
Given:
Volume of water in each container.
To find:
Difference in the rate of change.
Solution:
Take any two points on container 1.
Let the points are (10, 2) and (20, 4).
m = (y2 - y1) / ( x2 - x1 )
= ( 4 - 2 ) / ( 20 - 10 )
= 2/ 10
= 1/ 5
Rate of change for container 1 is .
Take any two points on container 2.
Let the points are (5, 2) and (10, 4).
m = (y2 - y1) / ( x2 - x1 )
= ( 4 - 2 ) / ( 10 - 5)
= 2 / 5
Rate of change for container 2 is 2/5
Difference = (2 /5 ) - ( 1/ 5 )
= 1 / 5
Hence, The difference in the rate of change between the two containers is 1/5 gallon per minute.
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Related Questions
If a firm has a production quota of 400=5x1^2+8x1x2+15x2^2, what combination of good x1 and x2 should the firm produce to minimize cost of C=x1^2+x2^2
Answers
The firm should produce good x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .
What is Lagrange multipliers ?
Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.
To minimize the cost C = x₁² + x₂²
We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:
L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)
Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:
∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0
∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0
∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0
Solving these equations simultaneously, we get:
x₁ = 4
x₂ = 8
λ = 1/20
Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.
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suppose a store decreases the price of laundry detergent from 4.10 to 3.50 as a result quantity demanded increases from 210 to 230 using the midpoint approach calculate the percentage change in price
Answers
The percentage change in the price is 15.78% decrease.
What is the percentage?
A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.
Here are some percentage examples:
10% is 1/10 of a fraction.20% is equal to a 1/5 portion.25% is equal to 1/4 fractions.Now,
Initial price=4.1
Final price=3.5
Change=3.5-4.1= -0.6 , minus means decrease in price
final value + initial value
then
percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100
=0.6/3.8*100
=0.1578*100
=15.78%
hence,
The percentage change in the price is 15.78% decrease.
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can someone help with this asap
Answers
Answer:
There are 5⁸ blades.
Step-by-step explanation:
Given that,
The area of land \(=5^{12}\ \text{acres}\)
Each acre has 5⁴ blades of grass
We need to find how many blades of grass have by the entire land. It can be calculated as follows :
\(n=\dfrac{5^{12}}{5^4}\\\\n=5^{12-4}\\\\n=5^8\)
Hence, there are 5⁸ blades.
Find the area of the circle A) 12.56 mm^2B) 25.12 mm^2C) 37.17 mm^2D) 50.24 mm^2
Answers
The formula in getting the area of the circle is:
\(A=\pi r^2\)where r = the radius of the circle and the value of π = 3.14
In the diagram, the radius of the circle is 4 mm. Let's replace the "r" in the formula with 4 mm and "π" with 3.14
\(A=(3.14)(4mm)^2\)Then, simplify.
\(\begin{gathered} A=(3.14)(16mm^2) \\ A=50.24\text{ }mm^2 \end{gathered}\)Therefore, the area of the circle is 50.24 mm². (Option D)
We have π = 3.14 and the radius is 4 mm. Therefore we apply the following formula:
A = π * r²Replacing values in the equation.
A = 3.14 * (4 mm)²We calculate potentiation.
A = 3.14 * 16 mm²We multiply
A = 50.24 mm²
Answer: The circle area is 50.24 mm^2 (option D)✅ .
To learn: https://brainly.com/question/23422024To learn: https://brainly.com/question/16612428To learn: https://brainly.com/question/28570984To learn: https://brainly.com/question/24048237Cole says the distance between points (-5,0) and (0,5) is 5 units. Is he correct? Explain why or
why not
I will give Brainly
Answers
Answer:
No, because the distance between the 2 points is \(5 \sqrt{2} \) units.
Step-by-step explanation:
\(\boxed{distance \: between \: 2 \: points = \sqrt{ {(y1 - y2)}^{2} + (x1 - x2)^{2} } }\)
Distance between (-5, 0) and (0, 5)
\( = \sqrt{ {(0 - 5)}^{2} + {( - 5 - 0)}^{2} } \)
\( = \sqrt{ {( - 5)}^{2} + ( - 5)^{2} } \)
\( = \sqrt{25 + 25} \)
\( = \sqrt{50} \)
\( = \sqrt{25(2)} \)
\( = ( \sqrt{25} )( \sqrt{2} )\)
\( = 5 \sqrt{2} \)
Thus, he is not correct.
Answer: Incorrect
Step-by-step explanation:
To calculate the distance (d) use the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, - 5)
d =
=
= = = = 5 ← exact value
Bookwork code: K45 not allowed
The number line below shows information about a variable, p.
Select all of the following values that p could take:
-4, 0, -6, 5, -1, -2.5
T
T
р
-5 -4 -3 -2 -1 0 1 2 3 4 5
✓ Scroll down
Answers
A number line is a simple graph with numerical increments spaced evenly. The numbers on the line determine how the number on the line can be answered. The number's application is determined by the question to which it corresponds, such as when plotting a point.
What is meant by number line?A number line is a horizontal line with evenly spaced numerical increments. The numbers on the line will determine how to answer the number on the line. The number's use is determined by the question that goes with it, such as plotting a point.
The number line is a straight line with divisions at equal intervals, similar to a scale. You can choose any point as "0," and all positive numbers will be to the right of the "0," and all negative numbers will be to the left of the "0." Q.
Therefore,
The third number line correctly provides the solution to the statement -5 + (-4).Plot 1's solution is (-5) + (-2) because both arrows point 4 units to the left.Plot 2's solution is (5 + 2) because both arrows point 4 units to the right.Plot 3's solution is (5) + (2) because one arrow points 4 units to the left and the other points 4 units to the right.The plot 4 solution is (5 + 2) because one arrow points 4 units to the left and the other points 8 units to the right.As a result, the third number line is the one that shows the solution 5 + (-4).To learn more about number line refer
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A ship is anchored off a long straight shoreline that runs north and south. From two observation points
miles apart on shore, the bearings of the ship are
and
. What is the distance from the ship to each of the observation points? Round each answer to the nearest tenth of a mile.
The distance from the north most ship to the observation is
miles.
The distance from the south most ship to the observation is
miles.
Answers
The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.
The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.
From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.
Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:
[asy]
unitsize(1cm);
pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);
draw(O--N--A,Arrow);
draw(O--S--B,Arrow);
\(label("$52^\circ$", N + 0.3*dir(52), NE);\)
\(label("$134^\circ$", S + 0.3*dir(134), SE);\)
draw(O--A--B--cycle,dashed);
\(label("$x$", (N+A)/2, W);\)
\(label("$y$", (S+B)/2, E);\)
[/asy]
We can use the tangent function to find x and y, since we have the angle and opposite side.
From the north observation point, we have:
\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)
From the south observation point, we have:
\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)
Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.
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Write the following numbers in order, putting the largest
first:
a)
31 009
31.53
31. 099
b)
0.007
0.03
0.009
Answers
Answer:
a)
31.53
31.099
31.009 ⬅ (I'm assuming this one is a decimal too)
b)
0.03
0.009
0.007
Explanation:
Here ya go.
Hope this helps :)
500.00
-319.45 = m
Solve for m
Answers
Answer:
STo solve for m in the equation -319.45 = m, we can isolate the variable m by adding 319.45 to both sides of the equation:
-319.45 + 319.45 = m + 319.45
This simplifies to:
0 = m + 319.45
Finally, we can subtract 319.45 from both sides to solve for m:
0 - 319.45 = m + 319.45 - 319.45
-319.45 = m
Therefore, the value of m is -319.45.tep-by-step explanation:
help! help! please help
Answers
Answer:
to answer this i am gonna need the rise and run or the y2 -x2/ y1-x1 and then i well come back and edit this to the right answer
Step-by-step explanation:
Is y=x^2 a fraction?
Answers
Answer:
Nope
Step-by-step explanation:
It's a exponent, x^2 means x*x so it's actually a function
.....
......
........
..........
Answers
Answer:
There is a answer to the question
Joseph and Molly each have coin collections. Joseph starts with 15 coins in his collection and adds 25 coins each month. Molly starts with 25 coins in her collection and adds 25 coins each month. How many coins would Joseph have after 3 months?
Answers
Answer:
Joseph has 90 coins after 3 months
Step-by-step explanation:
Joseph: 25x + 15
Molly: 25x + 25
x = 3
Joseph: 25(3) + 15 = 90
Seventy percent of the children went on the excursion. If 27 stayed at school, how many went?
Answers
By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.
We are given that,
No. of children who stayed at school is 27,
Also, 70% of the children went on an excursion.
Suppose, the total number of children in percentage is 100%
Out of which 70% went on an excursion
Thus, the children who stayed at school is 100% - 70% = 30%
By using the Unitary method, we can find out the number of 70% of children.
If 30% of the children are 27
Then 70% of the children are = 27 × 100
30
= 63
∴ the total no. of children in the school = 27 + 63
= 90
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please help me with this please i need the amswers for today,
Answers
The coordinates of each points are:
A = (-0.5, -5)
B = (0.8, -1.8)
C = (-2.6, -2.2)
D = (-1.5, -8.9)
E = (2.5, -6.5)
F = (-1.5, 3.1)
G = (-2.4, 4.1)
H = (1.5, 3)
I = (2.7, 1.5)
J = (-1.5, 0)
K = (-6.5, 0)
We have,
The coordinates of each point are in an ordered form.
i.e
(x, y)
x is the x-axis value.
y is the y-axis value.
Thus,
A = (-0.5, -5)
B = (0.8, -1.8)
C = (-2.6, -2.2)
D = (-1.5, -8.9)
E = (2.5, -6.5)
F = (-1.5, 3.1)
G = (-2.4, 4.1)
H = (1.5, 3)
I = (2.7, 1.5)
J = (-1.5, 0)
K = (-6.5, 0)
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How far is the sailboat from the lighthouse, to the nearest kilometer? Round your answer to the nearest tenth.
Answers
In the figure, we can see that the indicated distance of the sailboat from the lighthouse is the side of the triangle opposite the right angle. Therefore, we are looking for the length of the hypotenuse of the triangle.
To get the hypotenuse, we will use the Pythagorean Theorem.
\(c=\sqrt{a^2+b^2}\)where c = hypotenuse and "a" and "b" are the legs of the triangle.
Given in the figure are the legs of the triangle which are 50 km and 130 km. Let's plug these into the equation above.
\(c=\sqrt{(50km)^2+(130km)^2}\)Then, solve.
Square each leg of the triangle.
\(c=\sqrt{2,500km^2+16,900km^2}\)Add the numbers under the radical sign.
\(c=\sqrt{19,400km^2}\)Get the square root of 19, 400.
\(c=139.28388km\approx139.3km\)Therefore, the distance of the sailboat from the lighthouse is approximately 139.3 km.
-8 5/6 - 3 2/3 show work pls !
Answers
The answer to the problem 5/6 - 3 2/3 is -5/18.
The problem 5/6 - 3 2/3 can be solved using the following steps:
First, convert both fractions to have the same denominator. To do this, we need to find the least common denominator of both fractions. The least common denominator of 5/6 and 3 2/3 is 6.
Therefore, we can convert 5/6 to 10/6 and 3 2/3 to 20/6.
Now, we can subtract the fractions using the following formula:
(Numerator1/Denominator1) - (Numerator2/Denominator2) = (Numerator1*Denominator2 - Numerator2*Denominator1)/(Denominator1*Denominator2)
(10/6) - (20/6) = (10*6 - 20*6)/(6*6) = (-10)/(36) = -5/18
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Complete question
What is the answer to the problem 5/6 - 3 2/3?
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
Answers
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
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geratgertregd hifbuwegftyfvjhwdgfuyguawebbfigigaibahg87ehrbguv bhrbguyghu
Answers
Answer:
Whaaaa?
Step-by-step explanation:
lol ;)
2
factorize :- a²-46²
Answers
Answer:
a²-46²(a-46)(a+46)hope it helps
stay safe healthy and happy.
Riley is saving up to buy a new television. She needs a total of $1,397.68. Riley has saved $200.08 already and earns $79.84 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answers
1303.99 = 200.79 + 78.80(x)
1103.20 = 78.80(x)
x = 14 weeks
Answer:
14
Step-by-step explanation:
i uses a calculator and kept adding up
Which ordered pair solves this linear system?
Y= -x
Y= 2x
Answers
The ordered pair that solves the system of equation is (0, 0).
To solve this system, we can substitute the first equation into the second equation to eliminate y:
x = 2x
Solving for x, we get x = 0.
Substituting x = 0 into the first equation, we get y = 0.
Therefore, the ordered pair that solves the system is (0, 0).
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HELP!!!!!!!!!!!!!!!!!!
Answers
Answer:
D 0.89275
Step-by-step explanation:
Given function f(x)=x^2+5, determine the value of f(f(5))
Answers
Answer:
905
Step-by-step explanation:
So your original equation is f(x) = x² + 5
First lets work with the stuff inside the parentheses.
f(5) = 5² + 5 = 30
So now you are finding,
f(f(5)) => f(30)
f(30) = 30² + 5 = 900 + 5 = 905
A rectangle is 1/2 feet long and 3/4 feet wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form
Answers
Answer: 3/8
Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.
Numerators first- 1x3Denominators second 2x4Alligators perform a spinning maneuver, referred to as a "death roll," to subdue their prey. In a study of alligator death rolls, one of the variables measured was the degree of the angle between the body and head of the alligator while performing the roll. A sample of rolls yielded the data provided below, in degrees. At the % significance level, do the data provide sufficient evidence to conclude that, on average, the angle between the body and head of an alligator during a death roll is greater than ? (Note: and s. Preliminary data analyses indicate that you can reasonably use a t-test to conduct the hypothesis test.)
Answers
Complete question :
Alligators perform a spinning maneuver, referred to as a "death roll," to subdue their prey. In a study of alligator death rolls, one of the variables measured was the degree of the angle between the body and head of the alligator while performing the roll. A sample of 20 rolls yielded the data provided below, in degrees. At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, the angle between the body and head of an alligator during a death roll is greater than 45 ? Note: x =46.255° and s = 12.251° Preliminary data analyses indicate that you can reasonably use a t test to conduct the hypothesis test.
Answer:
H0 : μ = 45
H1 : μ > 45
T statistic = 0.4472
Pvalue = 0.3299
We fail to reject the Null
Step-by-step explanation:
H0 : μ = 45
H1 : μ > 45
Test statistic, T :
(xbar - μ) ÷ (s/√n)
(46.225 - 45) ÷ (12.251/√20)
1.225 ÷ 2.7394068
= 0.4472
Using the Pvalue calculator, the Pvalue can be obtained using the test statistic and degree of freedom
Degree of freedom, df = 20 - 1 = 19
Tscore = 0.4472
α = 0.01
Pvalue = 0.3299
Pvalue > α
0.3299 > 0.01 ; Hence, we fail to reject the Null
We fail to reject the Null; The data does not provide sufficient evidence to conclude that average angle between alligator's body and its head is greater than the 45
figure a is a right triangle, and two of its sides have a length of 1 foot. therefore, its third side is greater than 1 foot in length.
Answers
According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.
What do you mean by right angle triangle?A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
What is the Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
p=1 foot
b=1 foot
\(h^{2} = p ^{2} + b ^{2}\)
\(h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\\)
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When Vondel Bradshaw checked his credit card statement, he found that a sales
slip dated 3/2 for $12.49 was posted as $12.99. He also found that a purchase
for $56.29 dated 2/19 was unauthorized. If the new balance on the statement
was $491.23, what is the correct new balance?
Answers
Answer: $548.02
Step-by-step explanation:
Correct for inaccurate postings...
add the $0.50 overcharge and the $56.29 unauthorized charge from $491.23
491.23+.50+56.29=548.02
You are starting your first job as a salesperson at a clothing store. You receive a base salary of $10.00 per hour with time-and-a half for hours in excess of 40 hours per week. You also receive a 3% commission on your total sales.
Calculate your paycheck if you work 40 hours both weeks, plus you sell $3,000 worth of merchandise.
a
800
b
830
c
890
d
970
Answers
The paycheck of the salesperson at the clothing store for two weeks will amount to c. $890.
How is the paycheck calculated?The paycheck can be computed by working out the base salary, overtime pay if any, and the sales commission separately and adding up these.
Some deductions (withholding taxes and insurance) are made to the gross pay to arrive at the paycheck, which is known as the net pay.
Data and Calculations:Base salary = $10.00 per hour
Overtime pay = 1.5 of the base salary per hour
Work week = 40 hours
Commission on total sales = 3%
Sales for a month = $3,000
Commission on $3,000 sales = $900 ($3,000 x 3%)
Base salary for two weeks = $800 ($10 x 40 x 2)
Paycheck = $890 ($800 + $900)
Thus, the paycheck of the salesperson at the clothing store for two weeks will amount to c. $890.
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65 miles per hour = ? inches per hour
Answers
Answer: 4,118,400 inches / hour
Step-by-step explanation: