Water is being poured at the rate of 27 ft3/min. into an inverted conical tank that is 12 ft deep and having radius of 6 ft at the top. If the water level is rising at the rate of ft/min and there is
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Water is being poured into an inverted conical tank at a rate of 27 ft3/min. The tank is 12 ft deep and has a radius of 6 ft at the top. The water level is rising at a rate of 1/6 ft/min.
There is a leak at the bottom of the tank, and the rate of water leakage is unknown. The goal is to find the rate of water leakage. Let h be the height of the water in the tank and r be the radius of the water surface. We know that the volume of water in the tank is given by the formula:
V = (1/3)πr^2h
We also know that the rate of change of the volume of water in the tank is equal to the rate of water pouring in minus the rate of water leakage. This can be expressed in the following equation:
(1/3)πr^2h' = 27 - L
where L is the rate of water leakage.
We are given that h' = 1/6 and r = 6. Plugging these values into the equation above, we get:
(1/3)π(6^2)(1/6) = 27 - L
Simplifying, we get:
12π = 27 - L
Solving for L, we get:
L = 27 - 12π
The rate of water leakage is 27 - 12π ft3/min.
The value of π is approximately 3.14. Therefore, the rate of water leakage is approximately 27 - 37.68 = -10.68 ft3/min. This means that the water is leaking out of the tank at a rate of 10.68 ft3/min.
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Related Questions
do teenagers prefer yellow candy or pink candy? two different supplements, which have no effect on taste, are used on identical candies to produce a yellow or pink candy. volunteer teenagers are randomly assigned to either pink candy or yellow candy. the participants are then asked to rate the candy on a 1- to 10-point scale. is blinding demonstrated in this experiment? no, because the volunteers do not know the color candy they are getting no, because the volunteers know whether they are eating yellow candy or pink candy yes, by having the experimenter in a separate room pick one of the two containers at random and having a candy pulled from that container remotely yes, by having the statistician analyzing the results not know which volunteer sampled which candy yes, by having the volunteers wear a blindfold while they eat the candy out of the container so they don't know the color of the candy they are tasting
Answers
No, blinding was not demonstrated in the experiment because the volunteers knew whether they are drinking purple juice or yellow juice.
What is blinding in an experiment?Blinding is the process of hiding a participant's group assignment from one or more other participants in a clinical research study, most frequently a randomized controlled trial (RCT).
Although the candy has the same flavour as the drink, participants can tell the difference based on colour. No, because the participants are aware of whether they are consuming yellow or purple juice.
To create a yellow or pink candy, two separate additives that don't affect flavour are added to identical sweets.
In each experiment, group allocations are concealed from data analyzers by blinding or masking. This experiment is not a blinding demonstration since the subject is aware of the juice.
As a result, adolescent volunteers are at random allocated either pink candy or yellow candy, both of whom are aware of the juice.
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I need help with the question above. I took a pic.
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Answer:
\(S=\frac{12}{5}\)Step-by-step explanation:
The common ratio of the following sequence is:
\(\frac{\frac{9}{16}}{\frac{3}{2}}=\frac{3}{8}\)If the common ratio is less than 1 or greater than -1 but not 0, we can use the following expression to determine the sum of the infinite geometric series:
\(S=\frac{a_1}{1-r}\)Therefore, if we have a common ratio of 3/8 or 0.375 and the first term of the series is 3/2.
The sum would be:
\(\begin{gathered} S=\frac{\frac{3}{2}}{1-\frac{3}{8}} \\ S=\frac{\frac{3}{2}}{\frac{5}{8}} \\ S=\frac{24}{10}=\frac{12}{5} \end{gathered}\)Identify the following dilemmas as either constructive or destructive. Then suggest a refutation for each by escaping between the horns, grasping by the horns, or constructing a counterdilemma.
If the Mitchells get a divorce, they will live separately in poverty; but if they stay married, they will live together in misery. Since they must either get a divorce or stay married, they will either live separately in poverty or together in misery.
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This is a false dilemma, also known as a black-and-white fallacy, which presents only two extreme options and assumes that there are no other alternatives.
In this case, the dilemma suggests that the only two choices for the Mitchells are to get a divorce or to stay married, and both options have negative outcomes. However, there may be other alternatives that are not considered in this dilemma, such as counseling, financial planning, or other ways to improve their relationship and financial situation.
A possible refutation could be constructing a counterdilemma, such as:
Are there no other alternatives for the Mitchells to consider besides getting a divorce or staying married? What if they sought professional counseling or financial advice to address their issues?
Are poverty and misery the only possible outcomes for the Mitchells if they get a divorce or stay married? What if they found ways to improve their financial situation or relationship while living apart or together?
By questioning the premise of the dilemma and considering other options, we can escape between the horns or grasp the situation by the horns and find a better solution.
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A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
The average change in water volume is (answer here)iter(s) per day.
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The average change in the volume of water per day is obtained as 0.625 litres.
What is the rate change of volume?The rate change of volume is the change of volume with respect to time.
For instantaneous change the derivative of the expression of volume can be taken.
The average change in the volume of water can be obtained as follows,
Average change = Volume of water ÷ Number of days
= 2.5 ÷ 4 = 0.625
Hence, the average change in water volume is given as 0.625 liters per day.
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Which expression is equivalent to 4(23)?
Answers
Answer:
92
Step-by-step explanation:
Multiply 4 and 23:
4 * 23 = 92
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=3 feet and b=5 feet, what is the perimeter? If necessary, round to the nearest tenth.
Answers
Answer:
The perimeter of the triangle 12 cm.
Step-by-step explanation:
Given that,
In a right angled triangle, a and b are the length of the legs and c is length of the hypotenuse.
Pythagorean Theorem:
Sum of square of the legs is equal to square of hypotenuse.
∴\(a^2+b^2=c^2\)
\(a= ?\), \(a= 3\) cm and \(b=5\) cm
\(a^2+3^2=5^2\)
⇒ \(a^2+9=25\)
⇒ \(a^2=25-9\)
⇒ \(a^2=16\)
⇒ \(a = 4\) \(cm\)
The perimeter of the triangle = sum of all sides
\(=a+b+c\)
\(=(4+3+5)\) \(cm\)
\(=12\) \(cm\)
The ratio of teachers to students is 1 to 26. Find an equivalent ratio.
a. 52 to 2
b. 11 to 36
c. 26 to 1
d. 5 to 130
Answers
Answer:
d. 5 to 130
Step-by-step explanation:
1 = 26
2= 52
3 = 78
4 = 104
5 = 130
I'm not the best at explaining but basically the ratio needs to stay in order, so the answer needs to stay in the same formation as in the question that's why A is incorrect, because it flops the 26 with the 1 in the opposite order. The same applies with the third answer, so it's D.
if you divide 130 by 26, you get 5
if you divide 5 by 1 you get 5
if you multiply 26 by 5 you get 130
if you multiply 1 by 5 you get 5
therefore d is a equivalent ratio
If a study shows a result with a P value of 0.2, what does that mean? A)There is an 80 percent chance the relationship being studied is real. B)There is a 0.8 percent chance the relationship being studied is real. C)There is a 0.2 percent chance the relationship being studied is real. D)There is a 20 percent chance the relationship being studied is real.
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There is a 20 percent chance the relationship being studied is real. Option D
If a study shows a result with a P value of 0.2, it means that there is a 20 percent chance that the observed relationship being studied is due to random chance or sampling variability.
In other words, the P value represents the probability of obtaining a result as extreme as, or more extreme than, the observed result if the null hypothesis were true.
The null hypothesis assumes that there is no real relationship or effect in the population being studied. The alternative hypothesis, on the other hand, suggests that there is a real relationship or effect. The P value helps determine the strength of evidence against the null hypothesis.
A P value of 0.2 means that if the null hypothesis were true (i.e., there is no real relationship), there would be a 20 percent chance of obtaining a result as extreme as, or more extreme than, the observed result by random chance alone.
This implies that the observed result is not statistically significant at conventional levels of significance (typically set at 0.05 or 0.01), which means there is not enough evidence to reject the null hypothesis.
Therefore, the correct answer is (D) There is a 20 percent chance the relationship being studied is real. It's important to note that the P value does not directly indicate the probability of the relationship being true or real, but rather the probability of obtaining the observed result under the assumption of no relationship. Option D
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Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?
(–3, –0.90)
(–2.5, –0.75)
(4.5, 1.35)
(8, 2.40)
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Answer:
The last option is correct
Which number, when rounded to the nearest tenth, is 43.6?
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Answer:44
Step-by-step explanation:
Answer:
Is this multiple choice?
Step-by-step explanation:
Between 43.55 and 43.649
What is the slope of the line shown below?
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Answer:
4
Step-by-step explanation:
(9 - 1) / (3 - 1) = 8/2 = 4
Answer:
4
Step-by-step explanation:
To find the slope using two points
m= (y2-y1)/(x2-x1)
= (9-1)/(3-1)
= 8/2
= 4
The 22 students in a health class conducted an experiment in which they each recorded their pulse rates, in beats per minute, before and after completing a light exercise routine. The dot plots below display the results. Beats per minute before exercise Beats per minute after exercise Let and be the standard deviation and range, respectively, of the data before exercise, and let and r1 be the standard deviation and range, respectively, of the data after exercise. Which of the following is true?
A) s1 = s2 and r1 = r2
B) s1 < s2 and r1 < r2
C) s1 > s2 and r1 > r2 D) s1 ≠s2 and r1 = r2
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The correct Answer is D
s1 = s2 and r1 = r2
The two data sets have the same range. The first data set has a range of 88 − 56 = 32, and the second data set has a range of 112 − 80 = 32.
What does standard deviation say about range?This relationship is sometimes referred to as the range rule for standard deviation. The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s = (Maximum – Minimum)/4.
Which is better range or standard deviation?The standard deviation is a more effective measure of variation than the range. Range of the data is a measure of variation which gives the difference in the maximum and the minimum observation of the dataset. It is only based on two observations, the maximum and the minimum.
Alternatively, it can be seen visually that the ranges are the same because the two dot plots are aligned, the scales of the graphs are the same, and the graphs have the same width. The two data sets have different standard deviations. Both dot plots show distributions that have a mean near the center value of the dot plot. The first dot plot shows most values clustered near the mean, while the second dot plot shows most values farther from the mean. Therefore, the standard deviations of the two data sets are not equal—the data represented by the second dot plot has a greater standard deviation.
Choices A, B, and C are incorrect because they incorrectly assert either that the standard deviations are the same or that the ranges are different.
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Use the ordered pairs shown in the table.
Which equation represents the data in the
table?
Answers
Answer:
Option C y = 1.5x
Step-by-step explanation:
If you look closely you will notice that there is a pattern that follows all the time. And the pattern is...
y = 1.5x
A derivative is available with premium W(0)=1.34 when its underlying asset has value S(0)=36. This derivative will have expiry values W(1,↑)=0.64 and W(1,↓)=4.55, when the underlying asset has values S(1,↑)=57 and S(1,↓)=26, respectively. A writer sells 100 of these derivative and wants to set up a portfolio which will have zero cash flow, both at the time the derivative is sold and at the time the derivative expires. The portfolio will include 100 derivatives, borrowed or lent cash, and bought or short sold underlying assets. To ensure a zero cash flow, how many underlying assets should the writer have in the portfolio (with positive meaning bought assets and negative meaning short sold assets)? Give your answer to the nearest integer.
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To ensure a zero cash flow in the portfolio, the writer needs to set up a portfolio that offsets the cash flow from selling the derivatives. The writer should have -3 underlying assets in the portfolio (meaning short sold assets)
The cash flow from selling 100 derivatives can be calculated as:
Cash Flow from selling derivatives = 100 * (Premium at time 0 - Expiry value)
Cash Flow from selling derivatives = 100 * (1.34 - 0.64) = 70
To offset this cash flow, the writer needs to include an equal and opposite cash flow from the underlying assets. Let's assume the writer buys ""x"" underlying assets.
Cash Flow from underlying assets = x * (Value at time 0 - Value at time 1)
Cash Flow from underlying assets = x * (36 - 57) = -21x
To make the cash flow from underlying assets equal to the cash flow from selling derivatives, we set up the equation:
-21x = 70
Solving this equation, we find:
x ≈ -3.33
Since the number of underlying assets must be an integer, we round -3.33 to the nearest integer, which is -3.
Therefore, the writer should have -3 underlying assets in the portfolio (meaning short sold assets).
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Can someone help me with this circle geometry question ty
Answers
Answer:
Step-by-step explanation:
RT × TS = PT × TQ
Suppose that a school of 452 students is having a debate about gun control, and the students were asked to vote. The results show that 67 percent are in favor of banning guns, and 26 percent are against banning guns. The remaining students chose not to voice their opinions. How many students didn't voice their opinions? Round your answer to the nearest whole number?
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Answer: 32
Step-by-step explanation:
Total number of students = 452
Students in favor of banning guns = 67%
Students against banning guns = 26%
Students who didn't voice their opinions = 100% - (67% + 26%) = 100% - 93% = 7%
The number of students who didn't voice their opinions would be:
= 7% × 452
= 0.07 × 452
= 31.64
= 32 to nearest whole number
Jesse’s luggage weighs 55 pounds. The airline says that luggage cannot be more than 30 kilograms. Is her luggage under this limit? Explain.
Answers
Answer: yes, her luggage is under limit
Step-by-step explanation:
1 kg = 2.2 pounds
Take 55 divided by 2.2 = 25 kg
25 < 30
Her luggage is under the limit
write the following as a system of first-order equations (t 1)2 d 3 y dt3 d 2 y dt2 2 dy dt 6y(t)
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The system of first-order equations that is equivalent to the given second-order differential equation is dy/dt = z, dz/dt = w, and dw/dt = (-3z - 2w - 6y)/t².
To write the given second-order differential equation as a system of first-order equations, we need to introduce new variables.
Let z = dy/dt. Then, we can rewrite the given equation as
d³y/dt³ = dz/dt
d²y/dt² = dz/dt = z
Substituting these expressions into the original equation, we get
(t²) (d³y/dt³) + 3(d²y/dt²) + 2(dy/dt) + 6y = t² (dz/dt) + 3z + 2(dy/dt) + 6y
Simplifying and grouping the terms, we obtain
d/dt [y, z, w] = [z, w, (-3z - 2w - 6y)/t²]
where w = dt/dt = 1.
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f(4) if f(x) = 3x - 1
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Simply substitute the value of 3 given. In other words,
f(3) is the function of
f(x), however, in this case, x is 3
f(3)=3(3)−4
Distribute 3 through the parenthesis
f(3)=9−4
Simplify
f(3)=5
Subtract: 22²+8242²+122-16
O22²+122-12
4(x+4)(x-1)
O -x²+12x-12
4x(x+4)(x-1)
-2²+6x-6
о 22(x+4)(x-1)
H
-2x²+12-12
2(x+4)(x-1)
=
6-2(x-1)
6
2x(x+4)= 4(x+4)(x-1) = 2z(x+4)-2(x-1)
x.x
4(x+4)(x-1)-
Answers
Answer:
the correct answer is the second one
Step-by-step explanation:
I will add a photo of my solution, because there's a lot to type here
Make
x
the subject of the formula
a = bx + c
Answers
Answer: x = a/b - c
Step-by-step explanation:
First divide by b on each side to get the x by itself.
Then subtract c from both sides to make x the subject of the formula.
Step-by-step explanation:
a = bx + c
the goal is to get to a form with "x = ...".
a - c = bx
(a - c)/b = x
done.
This is 7th grade math just trying to see if I’m doing it right so I need this answer please hurry
Answers
Answer:
I assume you are trying to find the area of it, then it would be 182m.^2
PLEASE HELP !!! THIS IS ALGEBRA 1 <333
I'll give u brainliest (if possible) if its right !
PLEASE AND THANK YOU !!!!!!!!
Answers
1. b
2. c
3. b
4. a
5. c
Solve -8x + 3 + 2x = 5(x - 6) with steps
Answers
Answer:
Step-by-step explanation:
-8x+3+2x=5(x-6)
-6x+3=5x-30
-11x=-33
x=3
intersecting lines r, s, and t are shown below. s t 23° r 106° x° what is the value of x ?
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To find the value of x, we need to use the fact that when two lines intersect, the sum of the adjacent angles formed is equal to 180 degrees.
In this case, the angle formed between lines s and t is 23 degrees, and the angle formed between lines r and s is 106 degrees. Let's denote the angle between lines t and r as x.
Using the information given, we can set up the equation:
(106 degrees) + (23 degrees) + x = 180 degrees
Combine the known values:
129 degrees + x = 180 degrees
To isolate x, subtract 129 degrees from both sides of the equation:
x = 180 degrees - 129 degrees
x = 51 degrees
Therefore, the value of x is 51 degrees.
In conclusion, the value of x, the adjacent angles formed between intersecting lines t and r, is 51 degrees.
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If you vertically compress the absolute value parent function, f(x) = Ixl, by a
factor of 3, what is the equation of the new function?
OA. g(x) = 1x - 31
OB. g(x)=x
O C. g(x) = 31x1
O D. g(x) = 13x|
Answers
Answer:
The equation for new function is
Step-by-step explanation:
We have been given the absolute value parent function f(x) = |x| and this function is vertically compressed by a factor 3.
If we multiply the function with a constant (say a) then the parent function will get stretch/compressed vertically.
We have below conditions for vertical stretch and compression.
a > 1 => vertically stretch
0 < a < 1 => vertically compression
Hence, in order to vertical compression by a factor 3, we have to multiply the whole function by 1/3
Therefore, the equation for new function is
Step-by-step explanation:
g(x) = 1/3 |x| !
A regular pentagon is centere about the orgin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?.
Answers
A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.
The number of sides (n) of the pentagon is:
n =5
The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).
To draw the pentagon onto itself, the pentagon has to be rotated.
The angle of rotation is:
θ \(= \frac{360}{n}\)
θ \(=\frac{360}{5} = 72\)
Other possible angles of rotation must be multiple of 72. i.e.
θ= 72, 144, 216, 288...
Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.
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The complete question is:
A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?
a. A reflection across line m
b. A reflection across the x-axis
c) A clockwise rotation of 144 degrees about the origin
El costo de combustible por hora que un tren gasta en su recorrido es de \(V^2/5\) pesos donde v es la velocidad en kilómetros por hora Note que el costo depende del cuadrado de la velocidad Otros costos, incluyendo el de mano de obra, son de $400 por hora. Expresa el costo total de un viaje de 500 kilómetros como una función de la velocidad v
Answers
The total cost of the trip is a function of the velocity v is:
Cost (v) = 500v + 400/v
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Distance = 500 km
Velocity = v km/h
Now,
Velocity = Distance /Time
Time = distance/velocity
= 500 / v
The total cost of the trip.
Cost = fuel cost per hour x time + other costs per hour x time
= v² x 500/v + 400 x 500/v
= 500 v + 400/v
Thus,
The total cost of the trip is a function of the velocity v is:
Cost (v) = 500v + 400/v
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The complete question.
The cost of fuel per hour that a train spends on its journey is v^2 pesos, where v is the velocity in kilometers per hour. Note that the cost depends on the square of the velocity.
Other costs, including labor, are $400 per hour.
Express the total cost of a 500-kilometer trip as a function of the velocity v.
How in statistics the bayesian approach is different from the frequentist approach?.
Answers
In statistics, the bayesian approach treats parameters as random variables while in frequentist approach the parameters are fixed.
What is bayesian approach in statistics?There are different approaches in statistics that are used in data analysis they include the following:
Bayesian approach in statistics is defined as the approach that applies probabilities in a statistical procedure by treating the parameters under evaluation, randomly. The variables are being treated randomly but not fixed.
The frequentist approach is defined as the approach in statistics that deals with the frequency or proportion of the data and variables.
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An athlete runs 8 miles in 50 minutes on a treadmill at this rate how long will it take the athlete to run 9 miles
Answers
Answer:
56.25 minutes
Step-by-step explanation:
1 mile is 6.25 minutes
9 miles is _____?
6.25 minutes x 9 miles =
56.25 minutes
Find Unit Rate to help solve
Hope this helps :)