A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough. ft3/min
Answers
Given:
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
The volume of the trough will be as follows:
[tex]undefined[/tex]Related Questions
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Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7)? Responses The graph of g(x) is the graph of f(x) translated 7 units left. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 7 units left. The graph of g(x) is the graph of f(x) translated 7 units down. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 7 units down. The graph of g(x) is the graph of f(x) translated 7 units right. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 7 units right. The graph of g(x) is the graph of f(x) translated 7 units up.
Answers
The statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) is the graph of f(x) translated 7 units right.
What is Graph?The graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them.
According to the question we have
g(x)=f(x−7).
Given that f(x) then f(x + a) represents a horizontal translation of f(x).
If a > 0 then shift units left
If a < 0 then shift units right
Therefore, f(x - 7) represents a shift right of 7 units.
Hence, The statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) is the graph of f(x) translated 7 units right.
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A grocery store sells steak for $3.10 per pound. To feed a family, you need 2.14 lbs. of steak. How much do you pay in total
Answers
Set up a proportion for the situation and solve for the unknown quantity. Round to the hundredths place because we are dealing with money.
See details:
given f(x)=3x-1 and (f∘g)(x)=x^2, find g(x)
Answers
The value of g(x) is [tex]\frac{x^{2} }{3x-1}[/tex] of a function f(x)=3x-1 and (f∘g)(x)=[tex]x^{2}[/tex] .
As the composite equation is [tex]f(X)=3x^{}-1[/tex]
[tex](FOG)= x^{2}[/tex]
As [tex](FOG) =f(gx^{})\\[/tex]
∴ [tex]3x-1(gx)=x^{2}[/tex]
⇒ [tex]gx=\frac{x^{2} }{3x-1}[/tex]
How to solve the Equation of (fog)?(fog)(x) = f(g(x)) is pronounced "f of g of x" or "f constructed with g of x." Keep in mind that the letters in each expression for the composition remain in the same order.
A composite function is a fog. G(x) function is in f(x) function if (fog) is true. (Gof) indicates that f(x) function is in g(x) function.
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Every purchase of 30 boxes gets 1 extra Free box. Rizky
Sejahtera Bersama shop sells to its regular Warung Rp 38.000,-/box (without
giving extra). How much profit does Rizky Sejahtera Bersama's shop get for each
box?
Answers
On selling 38 boxes daily without giving extra box will profit him one box daily
What is Profit?Profit: A profit occurs when you sell something. for more than it cost. A business profit occurs when a business. makes more money than it spends.
Every purchase of 30 boxes gets 1 extra Free box. Rizky Sejahtera Bersama shop sells to its regular Warung Rp 38.000,-/box (without giving extra)
On selling 38 boxes daily without giving extra box will profit him one box daily
for two days if we add 38+38=76 boxes which profit him 2 boxes
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question is in the picture
Answers
Answer: x=3
Use your equation to complete the table. grams of fish 1500 number of calories 3000
Answers
Answer:
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
5+5=10
What’s is the total weight and pounds of the books in Duane’s backpack
Answers
Part A:
Add all the values:
Convert the oz into pounds:
1oz = 16 pounds
Divide each value by 16:
55 oz = 55/16 = 0.3125 pounds
11 oz = 11/16= 0.6875 pounds
14 oz = 14/16 = 0.875 pounds
1 pound = 1 lb
3 3/4lb= 3.75 lb
2 1/4 = 2.25 lb
2lb
Now add:
Total weight = 3.75 + 0.3125+ 2.25+0.6875+0.875 = 7.875 lb
The earth travels one full rotation around the sun in approximately 365.25 days.
How many minutes does it take for the earth to travel one full rotation around the sun?
Show your work. Make sure to include units in your answer.
Answers
The number of minutes it takes for the earth to travel one full rotation around the sun is 529, 960
What is proportion?A proportion can simply be described as an equation in which varying elements, or given numbers are set equal to each other.
It is seen as a mathematical method of comparing two elements or numbers.
It is also defined as a relation that entails comparison on the basis of size or magnitude of numbers, quantities or elements.
From the information given, we have that;
The earth travels for 365. 25 days round the sun.
If 24 × 60 minutes = 1 day
Then x minutes = 365. 25 days
cross multiply, we have;
x = 24 × 60 × 365. 25
Multiply the values
x = 529, 960 minutes
Hence, the value is 529, 960 minutes
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Solve for U.
-3 + 2u + 6 = -8u - 7
What does U equal?
Answers
Answer:
U = -1
Step-by-step explanation:
Answer:
u=-1
Step-by-step explanation:
-3 + 2u + 6 = -8u - 7
2u-3+6=-8u-7
2u+3=-8u-7
we will collect like terms
2u+8u=-7-3
10u=-10
u=-1
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at what point does the graph of the equation y = - 2/3 x + 6 intersect the x - axis
Answers
At (9, 0), the graph of the equation y = - 2/3 x + 6 intersect the x - axis.
How to create linear equation using two variables?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation. A specific point on the graph represents the solution of a linear equation in two variables, ax + by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.
The linear equations can be solved using substitution method.
Given, the equation of the graph is : y = (-2/3) x + 6 -(i)
Also, the equation of x-axis is: y = 0 -(ii)
Substituting (ii) in (i), we get,
0 = (-2/3)x + 6 ⇒ (-2/3)x = -6 ⇒ (2/3)x = 6 ⇒ x = 9
Thus, the point where the graph of the equation y = - 2/3 x + 6 intersect the x - axis is (9, 0).
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acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. to ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.
Answers
Let X represent the number of defects.
When n=20 and p = 0.01,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.01)^0 * (1-0.01)^(20) + 20C1 * (0.01)^1 * (1-0.01)^(20-1) = 0.9831
When n=20 and p = 0.02,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.02)^0 * (1-0.02)^(20) + 20C1 * (0.02)^1 * (1-0.02)^(20-1) = 0.9401
When n=20 and p = 0.05,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.05)^0 * (1-0.05)^(20) + 20C1 * (0.05)^1 * (1-0.05)^(20-1) = 0.7358
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A model rocket reaches a maximum height of 2000 feet above ground and begins to
descend at a rate of 75 feet per second. Which equation models the height above
ground, y, of the model rocket, x seconds after it reaches its maximum height?
Answers
The equation which is best representing the height above ground, y, of the model rocket and x seconds after it reaches the maximum height is 75x + y = 2000.
The height above ground, y, of the model rocket, x seconds after it reaches its maximum height can be represent by a linear equation,
The maximum height is 2000 feet, after this the rocket starts to descend with a rate of 75 feet per second.
Let us say that when the rocket starts descending, our time is started from zero,
So, on plotting these points of graph, we can one point, (0,2000).
The rate of descend is the slope m of the graph,
m = -75 ft/s
We are taking it negative because height is decreasing with time,
We can use the point slope form of equation of line,
It says, if a line passes through (a,b) and has slope m. Then the equation of line is,
(y-b) = m(x-a)
So, our line is passing through (0,2000) and has slope -75 ft/s.
So, equation of the line is,
(y-2000) = -75(x-0)
75x + y = 2000.
This above equation of line is representing the relation between the height above ground and time of the model rocket.
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At noon the temperature was 45°F. At
7 A.M. the temperature was 17°E.colder.
The temperature at 7 P.M. Was 4°F .
warmer than at 7 A.M. What was the.
temperature at 7 P.M.?
Answers
The temperature at 7 P.M is 32 °F.
What is a temperature in fahrenheit?Fahrenheit temperature scale, scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.
Given that,
Temperature at noon = 45 °F
At 7 A.M. the temperature was 17°F colder = 45-17
= 28 °F
The temperature at 7 P.M. Was 4°F warmer than at 7 A.M
= At 7 A.M. the temperature was 17°F colder + 4°F
= 28+4
= 32 4°F
Hence, The temperature at 7 P.M is 32 °F.
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Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
Answers
Distributive property
Addition property
3x=x+16
Subtraction property
2x=16
And then if you move further than what is shown in the photo it should be x=8 by the division property.
Answer this question for me
Answers
Answer:
R ≈ 3.97 %
Step-by-step explanation:
HELP STANDARD DEVIATION
(please show work too)
What is the standard deviation of these numbers:
1,1,2,2,3,3,3,4,4,4,5,5,6,6
Answers
Answer: 1.5923926292577
Step-by-step explanation: Count, N: 14
Sum, Σx: 49
Mean, μ: 3.5
Variance, σ2: 2.5357142857143
Steps
σ2 =
Σ(xi - μ)2
N
=
(1 - 3.5)2 + ... + (6 - 3.5)2
14
=
35.5
14
= 2.5357142857143
σ = √2.5357142857143
= 1.5923926292577
Tamika bought snacks for her team's practice. She bought a bag of oranges for $2.19 and a 12-pack of juice bottles. The total cost before tax was $8.31. Which tape diagram could be used to represent the context if xx represents how much each bottle of juice costs?
Answers
The cost of each bottle of juice is $0.51.
What is a tape diagram?The tape diagram can be used to illustrate the relationship between the numbers that are given.
Let the cost of each bottle of juice be x.
In this case, she bought a bag of oranges for $2.19 and a 12-pack of juice bottles and the total cost before tax was $8.31.
This will be:.
2.19 + 12x = 8.31
Collect like terms
12x = 8.31 - 2.19
12x = 6.12
Divide
x = 6.12 / 12
x = 0.51
The cost is solved. Note that the tape diagrams weren't given but the.coat is solved accordingly.
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a racing car consumes a mean of 103 gallons of gas per race with a variance of 36. if 38 racing cars are randomly selected, what is the probability that the sample mean would be greater than 101.5 gallons? round your answer to four decimal places.
Answers
The probability that the sample mean would be greater than 101.5 gallons
P(x>101.5)=0.9382
This is further explained below.
What is the probability?Generally, From this population, a sample with the size n=38 is taken and analyzed.
Let's say that x is the sample's mean value.
It may be concluded that the sample distribution of the x-bar is about normal with
Mean =103
Standard deviation=0.9733
Now, the expression for the probability looked for is P(x>101.5)
[tex]=&\mathrm{P}\left[\left(\bar{x}-\mu_{\bar{x}}\right) / \sigma_{\bar{x}} > \left(101.5-\mu_{\bar{x}}\right) / \sigma_{\bar{x}}\right][/tex]
Where
P=Probabilty
x=mean
[tex]\mu[/tex] is population mean
[tex]\sigma[/tex]= Standard deviation
[tex]\\&=\mathrm{P}\left[\left(\bar{x}-\mu_{\bar{x})} / \sigma_{\bar{x}} > (101.5-103) / 0.97332852678\right]\right.\end{aligned}[/tex]
= P[Z > -1.54]
P(x>101.5)=0.9382
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The daytime temperature in Montana yesterday was -4.5 degrees, and it was expected to drop 6.5 more degrees today. What is today’s expected daytime temperature?
Answers
-11 degrees is the expected daytime temperature for today
The daytime temperature yesterday in Montana = -4.5 degrees
Expected temperature drop today = 6.5 degrees
The term "temperature" describes how hot or cold the atmosphere is and is measured with a thermometer. Temperature is reported by meteorologists in both Celsius (C) and Fahrenheit (F).
Today's expected daytime temperature:
The daytime temperature yesterday in Montana + Expected temperature drop today
But since the temperature of yesterday is negative we will use a negative sign to add the expected temperature of today. A drop in temperature will lead to a more cold temperature
= -4.5 + (-6.5)
= -11 degrees
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5 men take 28 days to build a boat. Assuming the men work at the same rate, calculate the number of men needed to build a boat in 20 days.
Answers
? men - 20 days
Cross multiplication:
(20x5)/28=3.57…≈4
you have a sample of contaminated benzoic acid that weighs 2.014 g. after performing a proper recrystallization with proper drying, the mass of your purified benzoic acid is 1.611 g. what is your percent recovery rounded to the nearest tenths? do not include the percent symbol in your answer (e.g., if your answer is 10.5%, submit your answer as 10.5).
Answers
The percent recovery of benzoic acid is equal to 80.0 if the mass of purified benzoic acid after recrystallization is 1.611 g.
The percent recovery can be described as the amount of a product available after its production and purification.
The percent recovery of benzoic acid can be calculated by using the following formula:
percent recovery of sample = (Mass of purified sample ÷ Mass of contaminated sample) × 100
Substituting the given values of contaminated and purified benzoic acid in this equation;
percent recovery = (1.611 ÷ 2.014) × 100
percent recovery = 0.7999 × 100
percent recovery = 79.99
Rounding it to the nearest tenth;
percent recovery = 80.0
Hence the percent recovery of benzoic acid is calculated to be 80.0
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»How many lines of symmetry does this figure have? x
Answers
Answer:
15
Step-by-step explanation:
Given m|n, find the value of x.
(10x-2)°
(9x+5)°
Answers
Answer:
x = 7
Step-by-step explanation:
(10x - 2) and (9x + 5) are corresponding angles and are congruent , then
10x - 2 = 9x + 5 ( subtract 9x from both sides )
x - 2 = 5 ( add 2 to both sides )
x = 7
Lisa has a beige skirt, a black skirt, and a denim skirt. She has a red sweater and
a white sweater, and she has a white blouse, a blue blouse, and a green blouse.
How many different ways can she wear a skirt, sweater, and blouse together?
Answers
There are 18 combinations that Lisa can wear by shuffling skirts, sweaters, and blouses together.
Given,
Number of skirts = 3
Number of sweaters = 2
Number of Blouse = 3
By using permutation and combination formula nCr = n! ÷ (r! (n-r)!),
3C1 × 2C1 × 3C1
= (3!) ÷ ((3-1)! × 1!) × (2!) ÷ ((2-1)! × 1!) × (3!) ÷ ((3-1)! × 1!)
= (3!) ÷ ((2)! × 1!) × (2!) ÷ ((1)! × 1!) × (3!) ÷ ((2)! × 1!)
= ((3 × 2 × 1) ÷ (2 × 1 × 1)) × ((2 × 1) ÷ (2 × 1 × 1)) × ((3 × 2 × 1) ÷ (2 × 1 × 1))
= (6 ÷ 2) × (2 ÷ 1) × (6 ÷ 2)
= 3 × 3 × 2
= 18
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Question 5 (05.05)Based on the graph, what is the initial value of the linear relationship?
Answers
4
1) Examining that graph, we can see that this is a decreasing function, due to the line direction. And that the initial value is the y-intercept.
2) Hence, the initial value is 4. Notice that all values after that goes decreasing for y.
3 times 697 estimate then find the product
Answers
Answer:
Product: 2091
Estimate: 2100
Step-by-step explanation:
Estimate 697 as 700
700 x 3 = 2100
Find Product
697 x 3 = 2091
21. Evaluate when a= 5, b= -9 and c= -32.
a. -b-c
Answers
[tex] a \times - b - c \\ =(5) \times - ( - 9) - ( - 32) \\ = 5 \times 9 + 32 \\ = 45 + 32 \\ = 77[/tex]
ATTACHED IS THE SOLUTION
Answer:
-77
Step-by-step explanation:
we replace a=5, b=-9, c=-32
5 * -9 - 32
-45 - 32
- 77
if luna adds 1/2 cups of flour to a mixing bowl for a recipe 5 times, how much flour has she added?
Answers
Answer:
10 cups
I hope this helps, have a great day/night!
Suppose a batch of steel rods produced at a steel plant have a mean length of 187 millimeters, and a variance of 64.
If 416 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than
0.65 millimeters? Round your answer to four decimal places.
Answers
Evaluate. Write your answer as a whole number or as a simplified fraction.
4^-2 / 6^3
Answers
Answer:
Your answer is [tex]\frac{1}{864}[/tex]
Step-by-step explanation:
[tex]4^{-1}[/tex] ÷ [tex]6^{3}[/tex] [tex]= 0.0011574074[/tex] or [tex]\frac{1}{864}[/tex]