a) The rate of people leaving the health club, L(t), can be calculated as:
L(11) = 0.013(11)^2 - 0.25(11) + 8
b) To find the number of people, we integrate the net rate of change over the time interval:
Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20
c) This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.
To determine whether the number of people in the facility is increasing or decreasing at time t=11, we need to compare the rates of people entering and leaving the health club at that time.
a) At time t=11 hours:
The rate of people entering the health club, E(t), can be calculated as:
E(11) = -0.018(11)^2 + 11
Similarly, the rate of people leaving the health club, L(t), can be calculated as:
L(11) = 0.013(11)^2 - 0.25(11) + 8
By comparing the rates of people entering and leaving, we can determine if the number of people in the facility is increasing or decreasing. If E(t) is greater than L(t), the number of people is increasing; otherwise, it is decreasing.
b) To find the number of people in the health club at time t=20, we need to integrate the net rate of change of people over the time interval 0≤t≤20 hours.
The net rate of change of people can be calculated as:
Net Rate = E(t) - L(t)
To find the number of people, we integrate the net rate of change over the time interval:
Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20
c) To determine the time t at which the number of people in the health club is a maximum, we need to find the maximum value of the number of people over the interval 0≤t≤20.
This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.
Let's calculate these values and solve the problem.
Note: Since the calculations involve a series of mathematical steps, it would be best to perform them offline or using appropriate computational tools.
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consider the polynomial function q(x)=-2x^8+5x^6-3x^5+50
What is the end behavior of the graph of q?
Choose 1 answer:
(Choice A) As x→∞, q(x)→∞, and as x→−∞, q(x)→∞
(Choice B) As x→∞, q(x)→-∞, and as x→−∞, q(x)→∞
(Choice C) As x→∞, q(x)→-∞, and as x→−∞, q(x)→-∞
(Choice D) As x→∞, q(x)→∞, and as x→−∞, q(x)→-∞
Answer:
C.
Step-by-step explanation:
Answer A and D are definitely incorrect. Hope this helps Zoey. #Zoeyiscute:)
Verify that Rolle's Theorem can be applied to the function f(x) = 3 - 102 +31-30 on the interval [2, 5]. Then find all values of c in the interval such that f' (c) = 0.
Enter the exact answers in increasing order.
To enter √a, type sqrt(a).
c =
C=
Show your work and explain, in your own words, how you arrived at your answers.
Equation Editor A- A T I
BIUS X₂ x²
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The exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3
To verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5], we need to check if the following conditions are satisfied:
f(x) is continuous on [2, 5].f(x) is differentiable on (2, 5).f(2) = f(5).Let's check each condition:
f(x) = x³ - 10x² + 31x - 30 is a polynomial function and is continuous for all real values of x. So, it is continuous on [2, 5].
To check the differentiability, we need to find f'(x):
f'(x) = 3x² - 20x + 31.
The derivative f'(x) exists and is continuous for all real values of x. So, f(x) is differentiable on (2, 5).
Now, let's evaluate f(2) and f(5):
f(2) = (2)³ - 10(2)² + 31(2) - 30 = -10
f(5) = (5)³ - 10(5)² + 31(5) - 30 = 95
Since f(2) = -10 is not equal to f(5) = 95, we can conclude that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5] after differentiable.
To find the values of c in the interval (2, 5) such that f'(c) = 0, we need to solve the equation f'(c) = 3c² - 20c + 31 = 0.
Using quadratic formula:
c = (-(-20) ± sqrt((-20)² - 4(3)(31))) / (2(3))
c = (20 ± sqrt(400 - 372)) / 6
c = (20 ± sqrt(28)) / 6
c = (20 ± 2sqrt(7)) / 6
c = (10 ± sqrt(7)) / 3
The values of c in the interval (2, 5) such that f'(c) = 0 are:
c = (10 + sqrt(7)) / 3
c = (10 - sqrt(7)) / 3
Therefore, the exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3.
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Incomplete question:
Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² +31x-30 on the interval [2, 5]. Then find all values of c in the interval such that f' (c) = 0.
Enter the exact answers in increasing order.
To enter √a, type sqrt(a)
c = ?
a local ice cream shop has a special deal on thursdays: buy a waffle cone for $3 and get each scoop of ice cream for $1.50. what would be the rate of change in this word problem?
In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.
That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.
We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.
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please help me with this i will give brainliest
Answer:
A and E, The first and the last
could someone help me solve 7h plus 3
One pump can fill a tank of water in 5 hours. A second tank can fill the same tank in 4 hours. If both pumps are used together, how long will it take to fill the tank?
4/5 hours
20/9 hours
9/20 hours
5/4 hours
Answer:
4/5 hours
Step-by-step explanation:
Answer:
20/9 hours
Step-by-step explanation:
I got it right on the quiz
(3)(0.2)+9 help please
Answer:
9.6
Step-by-step explanation:
Answer:
[tex]9.6[/tex]
Step-by-step explanation:
1) Simplify 3 × 0.2 to 0.6.
[tex]0.6 + 9[/tex]
2) Simplify.
[tex]9.6[/tex]
Hence, the answer is 9.6
Find the mean, median, and mode of the data set.
{0,9, 3, 6, 10, 10, 7,1
MEAN:
MEDIAN:
MODE:
5. How many mililiters of a 3.5 M iron (II) nitrite (Fe(NO2)2) solution are needed to provide a tot
of 0.13 kg of Fe(NO),?
need help plss
Answer:
try this link!
Step-by-step explanation:
https://www.wylieisd.net/cms/lib09/TX01918453/Centricity/Domain/783/Math%20Connections%20Key.pdf
PLS HELP ME QUICK I NEED THIS GOOD GRADE PLS HELPPPP! Tell whether each statement is true or false. If false, provide a counterexample. The set of whole numbers contains the set of rational numbers. Every terminating decimal is a rational number. Every square root is a rational number. The integers are closed under addition.
Answer:
1. The set of whole numbers contains the set of rational numbers. FALSE.
The set of integers contains the set of rational numbers
2. Every terminating decimal is a rational number. TRUE
3. Every square root is a rational number. FALSE
Many square roots are irrational numbers, meaning there is no rational number equivalent.
4. The integers are closed under addition. TRUE
Given the coordinates for the function below, which of the following are coordinates for its inverse?
The inverse of the given function is represented by Data Table B.
What is a Function?A function is a law that relates a dependent and an independent variable.
The Inverse of the function is determined by interchanging the values of a and y in an f(x,y) function and then express the equation of y in terms of x.
Th table of the function is
Miles to go Miles Travelled
0 0
100 310
200 450
340 550
650 650
The inverse of this data table will be
Miles Travelled Miles to go
650 650
340 550
200 450
100 310
0 0
This is represented by Data Table B.
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If A, B and M are three collinear points, such that M divides AB internally in the ratio of 7:5 and P is any point not on the line AB, show that PM = PA + PB (4 marks] = 12 12
Given collinear points A, B, and M, with M dividing AB internally in the ratio of 7:5, and a point P not on the line AB, it can be shown that PM is equal to the sum of PA and PB.
Let's consider the line segment AB, where M is a point that divides it internally in the ratio of 7:5. This means that the ratio of AM to MB is 7:5.
Now, let's consider the triangle PAB, where P is a point not on the line AB. We want to show that PM is equal to the sum of PA and PB.
Since M divides AB internally in the ratio of 7:5, we can express AM and MB in terms of their lengths. Let's assume the length of AM is 7x and the length of MB is 5x.
Using this information, we can express the lengths of PA and PB in terms of x as well. Let's denote the length of PA as y and the length of PB as z.
Since M divides AB internally in the ratio of 7:5, we can write:
AM/MB = 7x/5x = 7/5
Similarly, we can express the ratios of PM to PA and PM to PB:
PM/PA = 7x/y
PM/PB = 5x/z
We need to show that PM is equal to PA + PB:
PM = PA + PB
Substituting the ratios we derived earlier:
(7x/y) = (5x/z) + 1
To simplify the equation, we can multiply both sides by yz:
7xz = 5xy + yz
Next, we can factor out the common factor of y:
7xz = y(5x + z)
Now, we can divide both sides by (5x + z):
PM = y
Therefore, we have shown that PM is equal to PA + PB.
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Use the Singapore Bar Method, including drawings, to solve the following problem. Identify the unit value when appropriate, including labels. The sides of the triangle are in the ratio 5:7:8 and the longest side is 36 cm longer than the shortest side. Find the perimeter of the triangle.
When the sides of the triangle are in the ratio 5:7:8 and the longest side is 36 cm longer than the shortest side, the perimeter is 240cm.
How to calculate the perimeterLet's assume the shortest side of the triangle has a length of x cm. According to the given ratio, the sides of the triangle are in the ratio 5:7:8. Therefore, the lengths of the sides can be expressed as:
Shortest side: 5x
Second side: 7x
Longest side: 8x
We are also given that the longest side is 36 cm longer than the shortest side. So we can set up the following equation:
8x = 5x + 36
Now, let's solve this equation to find the value of x:
8x - 5x = 36
3x = 36
x = 36 / 3
x = 12
Now we can substitute this value back into the expressions for the side lengths to find their actual lengths:
Shortest side: 5x = 5 * 12 = 60 cm
Second side: 7x = 7 * 12 = 84 cm
Longest side: 8x = 8 * 12 = 96 cm
Finally, we can calculate the perimeter of the triangle by adding the lengths of all three sides:
Perimeter = Shortest side + Second side + Longest side
= 60 cm + 84 cm + 96 cm
= 240 cm
Therefore, the perimeter of the triangle is 240 cm.
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Need help as soon as possible pls help
1. The value of x is:
180° - 40° - 30° = 110°
2. The value of x is:
90°- 38° = 52°
Answer:
Step-by-step explanation:
180 = 40 + x + 30
110 = x
90 = 38 + x
52 = x
Find the radius of the button.
28 mm
radius:
mm
Answer:
14 mm
Step-by-step explanation:
Just write down the answer.
Answer:
28mm
Step-by-step explanation:
is the right answer
I asked some friends how old they think they will be when they get married. Here are their answers:
{42, 38, 27, 53, 39, 29, 52}
Put this data in order from least to greatest.
Answer:
27,29,38,39,42,52,53
Step-by-step explanation:
9. (10%) Consider a linear block code whose generator matrix G is. 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 (a) (2%) Find the parity check matrix H. (b) (3%) What is the minimum distance of the code?
(a) The parity check matrix H is:
1 1 1 0 1
0 1 0 1 1
0 1 1 0 0
To find the parity check matrix H, we can use the fact that H is the transpose of the generator matrix G with an identity matrix on the right side.
Given the generator matrix G:
1 0 0 1
1 1 1 0
1 0 1 1
0 1 0 0
1 1 0 1
We can rewrite G as:
1 0 0 1 1 1 0 0
1 1 1 0 0 1 1 0
1 0 1 1 1 0 1 1
0 1 0 0 1 1 0 0
1 1 0 1 0 1 1 1
Now, we can obtain the parity check matrix H by taking the transpose of G and removing the rightmost identity matrix:
H = Transpose(G without the rightmost identity matrix)
H =
1 1 1 0 1
0 1 0 1 1
0 1 1 0 0
Therefore, the matrix H is:
1 1 1 0 1
0 1 0 1 1
0 1 1 0 0
(b) The minimum distance of a linear block code is the smallest number of bit positions in which any two codewords differ. It determines the error detection and correction capability of the code.
To find the minimum distance of the code, we can examine the columns of the parity check matrix H. The number of non-zero entries in the smallest column gives us the minimum distance.
Looking at the parity check matrix H, we see that the smallest column has two non-zero entries in positions 1 and 2. Therefore, the minimum distance of the code is 2.
In conclusion, the minimum distance of the code is 2.
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Please help!!
A circle has a circumference of 1007 cm. What is the radius of the circle?
Answer:
3/2 I'm not sure I think it's that
A race was 993 meters. If 28 people ran in the marathon how many meters would they
have run total?
Answer:
27,804
Step-by-step explanation:
28x993= 27,804
OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
AND CAN ANYONE PLS DRAW ME THE ANSWERS I CANT UNDERSTAND ANYTHING PLS I BEG U ILL GIVE U BRAINLEST
Answer:
here, i can help you out!
Step-by-step explanation:
Answer:
For 1. 2/5 is less full then 1/2
A food safety guideline is that the mercury in fish should be below 1 part per million (ppm) Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city Construct a 10% confidence interval estate f too much marcury in una sush? 051 0.01 0.10 0.96 128 057 056 What is the confidence interval estimate of the population mean? pppp Round to three decimal places as needed) Does it appear that there is too much mercury in una sush? OA. Yes, because it is possible that the mean is greater than 1 ppm. Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury 1. No, because it is possible that the mean is not greater than 1 ppm Also, at least one of the sample values is less than 1 ppm, so at least some of the fish sale OC. Yes because it is possible that the mean is not greater than 1 ppm. Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury OD. No. because it is not possible that the mean is greater than 1 ppm Also at least one of the sample values is less than 1 ppm, so at least some of the fish are safe
The confidence interval estimate of the population mean is (0.37, 0.75). The correct option is B No. Based on the confidence interval, it is not possible to say that the mean mercury level in tuna sushi is greater than 1 ppm.
How to explain the informationThe confidence interval includes 1 ppm, so the true mean could be 1 ppm or less. Additionally, at least one of the sample values is less than 1 ppm, so at least some of the fish are safe.
The sample standard deviation is calculated by finding the square root of the sum of the squared deviations from the mean for each value in the sample. The sample size is the number of values in the sample.
Confidence interval = sample mean ± 1.645 * (sample standard deviation / ✓(sample size))
Confidence interval = 0.51 ± 1.645 * (0.24 / ✓(7))
= (0.37, 0.75)
As you can see, the confidence interval includes 1 ppm, so the true mean could be 1 ppm or less.
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2. A wooded area is in the shape of a a trapezoid whose bases measure 128 m and $2 m and its height is 40 m. A 4 m wide walkway is constructed which runs perpendicular from the two bases. Calculate the area of the wooded area after the addition of the watkway
Correction in the Question:
A wooded area is in the shape of a a trapezoid whose bases measure 128 m and 92 m and its height is 40 m. A 4 m wide walkway is constructed which runs perpendicular from the two bases. Calculate the area of the wooded area after the addition of the walkway.
Answer:
The wooded area after the addition of the walkway is 4240 [tex]m^2[/tex].
Step-by-step explanation:
we are given
length of the two bases = 128m and 92m
height of the trapezoid = 40m
the approximate figure of the given trapezoid is given as:
__ __ __ 92 __ __ _
/ | | | \
/ | 40 |4| \
/__ _| __ __ | |__ __ __ __ \
128
Area of a trapezoid = [(a + b)/2] * height, where a and b are representing the bases of the given trapezoid.
Area = [(92 + 128)/2] * 40
= [220/2] * 40
= 110 * 40
= 4400 [tex]m^2[/tex]
Now there is a 4m wide walkway is to be constructed in that trapezoid. The pathway will be a rectangle as it has 4m width and 40m height as it is perpendicular to both the bases.
Area of a rectangle = length * width
Area = 40 * 4
= 160
Since the walkway will reduce the area of the trapezoid as it is constructed upon it therefore the wooded area after the addition of the walkway is
4400 + (-160) = 4240 [tex]m^2[/tex].
Solve -72 = 8 (y - 3) pls
Step-by-step explanation:
Given
- 72 = 8 ( y - 3 )
or - 72 / 8 = y - 3
or, - 9 = y - 3
y = - 9 + 3
Therefore X = - 6
Hope it will help :)❤
Answer:
Step-by-step explanation:
-72=8y-24
-72+24=8y
-48=8y
-48/8=y
-6=y
Kai has 8 pints of buttermilk. He uses 4 ounces of buttermilk in
his receipe for a loaf of bread. How many loaves of bread can he make with the buttermilk that he has?
A. 2 loaves
B. 16 loaves
C. 24 loaves
D. 32 loaves
whata 10 divided by 100
Answer:
it 10000
Step-by-step explanation:
79ib dlndokveik dinfl. kwbfb
The distribution of white blood cell count per cubic millimeter of whole blood is approximately Normal with mean 7500 and standard deviation 1750 for healthy patients Include an appropriately labeled and shaded Normal curve for each part. There should be three separate curves. 4. What is the probability that a randomly selected person will have a white blood cell count of between 2000 and 10,000?
The probability that a randomly selected person will have a white blood cell count of between 2000 and 10,000 is 0.9223 approximately.
The given mean, standard deviation, and the range of values are as follows:
Mean = 7500
Standard deviation = 1750
Range of values = Between 2000 and 10000
We are required to calculate the probability of a random person having a white blood cell count between 2000 and 10000.
Let's find the Z values for 2000 and 10000.Z1 = (2000 - 7500) / 1750 = -3Z2 = (10000 - 7500) / 1750 = 1.43
The required probability is the sum of the probability of the given range of values.
The probability of the first value is:P(X < 2000) = P(Z < -3) = 0.00135
The probability of the second value is:P(X > 10000) = P(Z > 1.43) = 0.0764
To find the probability for the given range, we will subtract the probability of the second value from the probability of the first value.
P(2000 < X < 10000) = 1 - P(X < 2000) - P(X > 10000)P(2000 < X < 10000)
= 1 - 0.00135 - 0.0764P(2000 < X < 10000) = 0.9223
The probability that a randomly selected person will have a white blood cell count between 2000 and 10,000 is 0.9223, approximately.
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Please help me out you can just give me the answer! PLEASE AND THANK YOU!
Answer:
(Disclaimer: all digits in the answers are in the measuring unit degrees)
1) 15
2) 16
3) 46
4) 59.
Step-by-step explanation:
The first one is said to add up to 89, so you have to do 89 subtract 44 and 30 as they are told. That = 15
The second one is a right angle, meaning it adds up to 90. You do 90 - 74 as that is the value told. That = 16
Angles on a straight line = 180 so you have to do 180 - 134 as that is the value told. This = 46
This is 54 as opposing angles on two lines are =. That means this = 59 too.
how do I solve sin(4x)=sin(2x)?
Answer:
sin(4x) = sin(2x) is unsolvable.
Step-by-step explanation:
The two sides are not equal.
Use completing the square to find the equation of the following circle in standard form.
x2 + y2 - 4x + 12y - 16 = 0
Answer:
Here's a calculator that should help
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/algebra/completing-the-square-calculator.php
SOLVE THIS PLEASE I WILL GIVE BRAINLIEST AND 5 STAR RATING! AND GIVING 70 POINTS!!!!!
Answer:
[tex]L^{2} + W^{2} = d^{2}[/tex]
d = 31.6
Step-by-step explanation:
[tex]L^{2} + W^{2} = d^{2}[/tex]
[tex]30^{2} + 10^{2} = d^{2}[/tex]
[tex]d^{2}[/tex] = 900 + 100
= 1000
d = [tex]\sqrt{100}[/tex] = 31.6