The rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
Explain the term rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.The rate of change of volume is-
dV/dt = 11 ft3/min.
Volume of cylindrical cone = (1/3)πr²h
As we're trying to find dh/dt, we need to calculate the volume within terms of just one variable, h.
Diameter = 22 ft
Thus, radius is 11 ft
By using height and radius of a water in the tank, we may calculate h using similar ratios.
11/44 = r/h
1/4 = r/h
r= h/4
Put into volume;
V = (1/3)π(h/4)h²
V = (1/3)(π)h³ / (16)
dV/dt = [(1/3)(3)(π)(h)² / 16](dh/dt)
V = [(π)(h)² / 16](dh/dt)
Solve for (dh/dt) ;
dh/dt = (dV/dt)(16) / [((π)(h)²]
Now, the change in volume is dV/dt = 11 ft³/min
dh/dt = (11 ft³/min)(16) / [((π)(h)²]
For h = 1 ft,
dh/dt = (11 ft³/min)(16) / [((π)(1 ft)²]
dh/dt ≈ 56.05 ft/min
Thus, the rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
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Azlyn had $25. She went to lunch and spent $15 what percentage of her money did Azlyn spend on lunch
Answer: 60%
Step-by-step explanation:
15 divided by 25 = 0.6
0.6 x 100 = 60%
:)
What is the common difference in the sequence 17, 21, 25, 29, 33
Answer: 4
Step-by-step explanation:
Every number you get is 4 higher than the previous number
a stone is tossed into a lake, sending out circular ripples whose area is increasing at the rate of 520 ft2/sec. how fast is the radius increasing when the radius is 30 feet?
The radius is increasing fastly at a rate of 2.75 feet per second when it is already 30 feet.
Here, it has been told that the rate of change of the area with respect to the time is = 520 ft²/sec - (i)
This can also be written as = dA/dt (ii)
We need to find the rate of change of radius with respect to the time at 30 feet. This can be written as = dr/dt (iii)
We already know that the area of a circle can be found out using the formula = πr² (iv)
Differentiating equation (ii) with respect to time, we get -
= d(πr² )/dt
= π*(dr²/dt)
= π*(dr²/dr)*(dr/dt)
= π*(2r)*(dr/dt)
= dr/dt = (dA/dt)*(1/ π*2r)
Using the given values, we get -
= (dr/dt) = 520 / π*2*30ft
= (dr/dt) = 2.75 ft/sec
Henceforth, we find that the rate of change of the radius with respect to time at 30 feet is going to be 2.75 ft/sec.
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Aaron separates 11 carrot sticks equally among 3 bags.
Drag carrots to show how many carrots will be in each bag and how many carrots will be left over.
Answer:
there will be 3 carrots in each bag and you will have 2 carrots left over
Step-by-step explanation:
hope this helps
Enter an equation of the line (in slope-intercept form) that passes through the point (20, −7) and is perpendicular to the line y = −5x + 9. Express any numeric values as integers or simplified fractions.
Answer:
y = 1/5x -11
Step-by-step explanation:
You want the slope-intercept equation of the line perpendicular to y=-5x+9 that goes through the point (20, -7).
Slope-intercept formThe slope-intercept form of the equation for a line is ...
y = mx +b . . . . . . . . where m is the slope and b is the y-intercept
This can be solved to find the y-intercept from a point on the line:
b = y -mx
Comparing this form to the given equation, you see the given line has a slope of m = -5.
Perpendicular lineThe perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line:
slope = -1/(-5) = 1/5
Y-interceptThe y-intercept of the desired line can be found using the equation for b above. The y-intercept of the line with slope 1/5 through point (x, y) = (20, -7) is ...
b = y -mx = (-7) -1/5(20) = -7 -4
b = -11
Now, we have the slope and intercept of the desired line, so we can write its equation:
y = 1/5x -11
ohnny is a sophomore in college and has a 1.5 cumulative grade point average (gpa). johnny's cumulative gpa will fall even further next semester if he performs worse than (i) his cumulative gpa. (ii) he ever performed before. (iii) he did last semester.
The value of the solution is B i.e., his cumulative gpa (i), he ever performed before (ii)
What do you mean by statistics?The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.
What are types of statistics?The two types of statistics are: Descriptive and inferential.
With the alternatives available, Johnny can only do worse if his performance falls short of both his lifetime GPA and his previous best performance. It's possible that the last scenario, in which Johnny performed worse than last semester, won't necessarily have an impact on his GPA. A cumulative GPA represents Johnny's overall GPA since he first began attending school. Considering that his most recent semester may have been one of his best and had a solid outcome, earning a result somewhat below that of his previous semester may not necessarily result in a drop in his cumulative GPA. Therefore, choice B is right.
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diego brought a box of 120 colored pencils to school. he gave 14 pencils to marcus and 32 pencils to anna. how many pencils did diego have left
Diego will have 74 pencils remaining after giving 14 pencils to Marcus and 32 pencils to Anna.
The question is about simple Subtraction. First, we know that the total number of colored pencils in the box is 120. Following is the step-by-step explanation for this question.
Let suppose,
Total Colored pencils = x = 120
Pencils given to Marcus = y = 14
Pencils are given to Anna = z = 34.
And, Total Pencil Remaining = R =?
We can show the given information in the equation as given below:
R = x - y - z
By putting the value in the above equation:
R = 120 - 14 -34
R = 74.
So, after giving the 14 and 32 pencils to Marcus and Anna, respectively. Marcus would remain with 74 Pencils.
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consider the process of throwing $m$ balls into $n$ bins, where each ball is thrown into a uniformly random bin, independent of other balls. what is the expected number of balls in a particular bin $b$?
The predicted quantity of balls in the first bin is (1/n)n.
Considering that,
There are the same number of balls and containers.
If so, then each container must always contain one ball. The probability of each ball landing in the first bin is (1/n)n.
For instance -
Three balls and three bins should be present. Next to each ball, place an A, B, and C. There are numbers 1, 2, and 3 on the containers. Ball A has a 1/3 chance of landing in bin 1. Although there is a 1/3 probability that ball B will drop in bin 1 and a 1/3 chance that ball C will do the same, both outcomes are possible. Therefore, bin 1 should be equal to 1/3 + 1/3 + 1/3. The rationale behind the projected values of bins 2 and 3 is identical.
According to the same logic, bins 2 and 3 should also have expected values of 1.
How probable is it that the first bin will receive all three balls?
In general, (1/n)n, which equals (1/3)3, or 1/3 x 1/3 x 1/3, equals 1/27.
Therefore, (1/n)n would be the expected number of balls in the first bin.
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the gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. a simple random sample of 81 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. construct a 95% confidence interval for the mean gas mileage for this car model.
The 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.
The confidence interval for a statistical data is written as-
(x+ zr/√n, x- zr/√n)
Here, we are given that-
Mean ⇒ x = 27.5 mi/gallon.
Standard deviation ⇒ r = 4 mi/gallon
Number of samples ⇒ n = 49
and Confidence interval = 95%
z-score at 95% confidence level = 2.17
Substituting the values we have;
= [27.5 - 2.17(4.0) /(√49), 27.5 + 2.17(4.0) /(√49)]
= (27.5 - 8.68 / 7, 27.5 + 8.68 / 7)
= (27.5 - 1.24, 27.5 + 1.24)
= ( 26.26, 28.74)
Therefore, the 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.
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to make sure that a few unusual responses don’t skew results or lead to inaccurate judgements, a data analyst focuses on what element of the data collection?
The component of the data that a data analyst is most interested in is sample size.
Given,
To prevent results from being skewed or causing incorrect conclusions, we must identify the data element on which the data analyst should concentrate;
The data analyst;
A data analyst looks at data to uncover useful consumer insights and possible applications for the knowledge. They also tell the management of the business as well as other stakeholders of this information.
Although it is advisable for data analysts to have a foundational knowledge of statistics and mathematics, many of their responsibilities can still be carried out without it. However, knowledge in statistics, linear algebra, and calculus is often required for data analysts.
Here,
A data analyst's primary interest in the data is sample size
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if a person is making the minimum salary for a construction worker, they are making more than what percentage of teachers?
If a person is making a minimum salary for a construction worker, in that case, they will make more than 75% of the teachers.
A salary is a form of periodic fee from a corporation to a worker, which can be laid out in an employment contract. it is contrasted with piece wages, in which every task, hour, or other unit is paid one after the other, in place of on a periodic foundation. From the factor of view of going for walks in a commercial enterprise, revenue can also be considered as the fee of obtaining and keeping human sources for jogging operations and is then termed personnel fee or salary cost. Payroll accounts are used in accounting to record.
Salary is a hard and fast amount of cash or compensation paid to a worker via an enterprise in return for work executed. salary is generally paid in fixed durations, for example, monthly bills of 1-twelfth of the annual salary.
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Please help me with this 2 problems
[9] Answer: x = 4
Step-by-step explanation:
Both of these problems use triangle's exterior angles. We will set up an equation and solve. The two opposite angles are equal to opposite exterior angle. After writing our equation, we will solve and isolate the variable using inverse operations.
17x + 1 + 18x + 3 = 144
35x + 4 = 144
35x = 140
x = 4
[10] Answer: x = 3
Step-by-step explanation:
Both of these problems use triangle's exterior angles. We will set up an equation and solve. The two opposite angles are equal to opposite exterior angle. After writing our equation, we will solve and isolate the variable using inverse operations.
20x + 23x + 1 = 130
43x + 1 = 130
43x = 129
x = 3
Choose the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.
1 divided by 5 raised to the twelfth power
negative 1 divided by 5 raised to the twelfth power
−5^12
5^26
5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.
What is Expression?An expression is combination of variables, numbers and operators.
Given,
5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.
This sentence can be written in the form below
(5⁻² × 5⁶)⁻³
According to laws of indices, we know that;
(a²)³ = a⁶
Thus;
(5⁻² × 5⁶)⁻³=(5⁻² )⁻³×(5⁶)⁻³
⇒ 5⁶ × 5⁻¹⁸
When bases are same then the powers will be added
⇒ 5⁶ × 5⁻¹⁸
⇒ 5⁻¹²
Hence, 5⁻¹² is the expression that is equivalent to the quantity 5 raised to the negative second power times 5 raised to the sixth power end quantity all raised to the negative third power.
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Answer:
1 divided by 5 raised to the twelfth power
Step-by-step explanation:
both of them equal the same thing
Suppose that 14 inches of wire costs 84 cents.
At the same rate, how much (in cents) will 37
inches of wire cost?
Answer: 222 cents
Step-by-step explanation: 84/14 = 6 This is the unit rate.
6 x 37 = 222
what is the answer to 2 (x + 14)=90
Answer:
x = 31
Step-by-step explanation:
Distribute 2 to x which equals 2x, and 2 times 14 which equals 28, which gets you to 2x + 28 = 90, then subtract 28 from 90, which leads you to
2x =62, and the final step is to divide 2 from 62 which gets you 31.
The interior angles formed by the sides of a hexagon have measures that sum to 720°.
What is the measure of angle F?
Enter your answer in the box.
m∠F=
Answer:
Step-by-step explanation:
(x-60)+(x-20)+(x-40)+130+120+110=720
3X -120 + 360=720
3x +240= 720
3x= 720-240
3x=480
x= 480/3 = 160
x=160
angle F = (x-20)
angle F = 160-20=140
angle F = 140
duke energy reported that the cost of electricity for an efficient home in a particular neighborhood of cincinnati, ohio, was $104 per month. a researcher believes that the cost of electricity for a comparable neighborhood in chicago, illinois, is higher. a sample of homes in this chicago neighborhood will be taken and the sample mean monthly cost of electricity will be used to test the following null and alternative hypotheses. h0: μ ≤ 104 ha: μ > 104 (a)assume the sample data lead to rejection of the null hypothesis. what would be your conclusion about the cost of electricity in the chicago neighborhood?
When the null hypothesis is rejected
The conclusion is that there is enough evidence to support the claim of the researcher
When a type I error occurs. The consequences is that the conclusion that there is enough evidence to support the claim of the researcher is actually incorrect
When a type II error occurs. The consequences is that the conclusion that there is enough evidence to support the claim of the researcher is actually correct
From the question we are told that,
Generally if the null hypothesis is rejected then the conclusion would be that there is enough evidence to support the claim of the researcher
Generally a Type I error is a an error that occurs when the null hypothesis is incorrectly rejected
So in the case of this question the consequence of making this type of error is that the conclusion that there is enough evidence to support the claim of the researcher is actually incorrect
Generally a Type II error is an error that occurs when the null hypothesis is incorrectly not rejected
So in the case of this question the consequence of making this type of
error is that the conclusion that there is enough evidence to support the claim of the researcher is actually correct.
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The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 59.1. O b. 7.688. O C. 7.018. O d. 49.25.
The point estimate of the population standard deviation is 5.91 (Option A)
Standard deviation refers to the spread of a data distribution and measures the distance between each data point and the mean. The sample standard deviation (s) is a point estimate of the population standard deviation σ.
The mean of the population ẋ = sum of all values/ total number of values = 97/6 ≈ 16
The point estimate of the population standard deviation S =√(∑(xi - ẋ)^2/n-1)
∑(xi - µ)^2 = (9 – 16)^2 + (13– 16)^2 + (15– 16)^2 + (15– 16)^2 + (21– 16)^2 + (24– 16)^2 = 79 + 9 + 1 + 1 + 25 + 64 = 179
s = √(179/5) = 5.98
Note: The question is incomplete. The complete question probably is: The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 5.91. O b. 7.688. O C. 7.018. O d. 4.925.
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Please help i’m so confused !!
Answer: 40.24
Step-by-step explanation: Use the Pythagorean Theorem
a^2 + b^2 = [tex]\sqrt[2]{c}[/tex]
36^2 + 18^2 = [tex]\sqrt[2]{1620}[/tex]
1296 + 324 = 1620
[tex]\sqrt[2]{1620}[/tex] = 40.24
HELPPP IT IS MATH AGIAN NOOO
Answer:
9 is 8 hours and 10 is 10 hours
Answer:
9. 8 Hours
10. 10 hours
Step-by-step explanation:
48 ÷ 4 = 12 The unit rate is 12 per hour
12x = 96 Divide both sides by 12
x = 8
54 ÷ 6 = 9 The unit rate is 9 per hour
9x = 90 Divide both sides by 9
x = 10
Write an inequality and use substitution to solve the following problem:
Janet plans on mowing lawns for 12 weeks in the summer. Her goal for the summer is to earn more than $500. Which of the following rates of weekly earning would allow her to reach her goal?
The rates of weekly earning would allow her to reach her goal will be 12x > 500.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Janet anticipates cutting yards for quite a long time in the late spring. Her objective for the late spring is to acquire more than $500.
Let 'x' be the weekly rate. Then the inequality is written as,
12x > 500
The rates of weekly earning would allow her to reach her goal will be 12x > 500.
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An airplane flies 370 miles from point A to point B with a bearing of 24" . It then flies 240 miles from point B to point € with a bearing 0f 37" Draw diagram of the information. Then find the distance from point A to point C and the bearing from point A to point C
229.5 miles separate point A from point C
What is the short definition of cosine law?
According to a trigonometrical rule, the square of a side in a plane triangle is equal to the sum of the squares of the other sides minus twice that amount plus the cosine of the angle between the other two sides.
Given:
Angle AB = 370 miles 24 degrees is A.
Angle BC = 240 miles 37 degrees is B.
Since we have two angles and two sides of a regular triangle, we can apply the cosine law to calculate the distance between points A and C.
Angle B, which is 37 degrees, is the angle opposite side AC.
(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)
solve for AC:
(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37)
229,48 miles equal AC.
Therefore, 229.5 miles separate point A from point C.
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a 28 year old man plays 165 for a one year life insurance policy with coverage of 140000 if the probability that he will live through the year is 0.9994 what is his expected value for the insurance polixy
The insurance policy's anticipated value is -$81 for the one year life insurance policy.
Explain the term insurance policy?Term insurance is a form of life insurance policy which offers protection for a certain "term" of years, or a set amount of time.A deceased person will be paid if the insured passes away while the term insurance is still in effect and the insurance is active.Consider the various factors and the man's potential benifits.
-$165 because he already paid that sum.
The beneficiary could earn as a potential profit.
140000-165 = $139835
The probability of surviving is 0.9994.
The likelihood of not living is 0.0006.
The expected value is given by;
E(v) = (-165)(0.9994) + (139835)(0.0006)
E(v) = -164.901 + 83.901
E(v) = -81.
Thus, the insurance policy's anticipated value is -$81.
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Sin y = 4xy + x^2. Find dy/dx
Answer:
dy/dx=(4y+2x)/(cos y-4x)Step-by-step explanation:
Siny= 4xy +x²
dy/dx(cos y) =4y+ 4x(dy/dx)+2x
making dy/dx the subject
dy/dx(cos y)-4x(dy/dx)=4y+2x
dy/dx(cos y -4x)=4y+2x
dy/dx=(4y+2x)/(cos y -4x)
The question is attached on the image below. Help is needed urgently please help!
What is the average rate of change of the functionf(x)=20(14)x from x = 1 to x = 2? enter your answer, as a decimal, in the box. do not round your answer.
The average rate of change of the function f(x) is found as -3.75.
Explain the term average rate of change?The rate about which one value in a function evolves in proportion to another is known as the average rate of change. The slope of a graphical representation function is typically calculated using the average rate of change.The formula for the average rate of change (A(x)) of f(x) over the interval [a,b] is:
A(x) = f(b) - f(a) / b - a
The function being:
f(x) = 20.(1/4)ˣ
Its average rate of change between x = 1 to x = 2 must be determined.
At x = 1
Then;
f(x) = 20.(1/4)¹
f(1) = 5
At x = 2
Then;
f(x) = 20.(1/4)²
f(2) = 1.25
Add these to the formula above to get;
A(x) = f(2) - f(1) / 2 - 1
A(x) = - 3.75
Consequently, the average rate of change of a function f(x) between x = 1 and x = 2 is -3.75.
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If 6s=24, does 6s÷6=24÷6?
Answer:
i need points
Step-by-step explanation:
Which angle is an adjacent interior angle to ∠jkm? ∠jkl ∠mkl ∠klm ∠lmk
∠mkj angle is an adjacent interior angle to ∠jkm
Adjacent interior angles are two angles that share a common vertex and a common side. In the given angle ∠jkm, the common vertex is at point "k" and the common side is the line segment joining points "j" and "m". Therefore, the adjacent interior angle to ∠jkm is ∠mkj.
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The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5), and (6, 4).
Find the length of the sides of the rectangle and its perimeter.
Check the picture below.
when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes,: group of answer choices the variance of both of the original populations must be known (as opposed to estimated) the scores from both samples are combined to form a single sample, and the estimated variance is figured in the usual way, but using this combined sample the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants the variance of at least one of the original populations must be known (as opposed to estimated), but the other can be estimated from sample scores
The estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.
What is population variance?
Each data point's distance from the population mean is quantified by the population variance, which is a measure of dispersion. The average of the squares of the deviations from the data's mean value is known as population variance.
Hence, when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes, the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.
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