A survey was sent out to re-evalute the proportion of people who play games on pc computers, as the last study on the topic had been gathered four years prior. This survey was done specifically to test the possibility that fewer people are playing games on pc computers. The previous study found that 81% of people were playing games on pc computers. The current study, with 861 participants, found that 53% of people who responded play on a pc computer.
Calculate the p-value and determine if we should accept or reject H0 under alpha = 0.05.
Answer:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
Step-by-step explanation:
Info given
n=861 represent the random sample
[tex]\hat p=0.53[/tex] estimated proportion of people who responded play on a pc computer
[tex]p_o=0.81[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion decreases from 81%, the system of hypothesis are.:
Null hypothesis:[tex]p\geq 0.81[/tex]
Alternative hypothesis:[tex]p < 0.81[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
A card is drawn at random from a standard 52-card deck. Find the following probabilities: (2 points) a. The probability the card is a diamond or a face card. (2 points) b. The probability that the card is neither an ace nor a heart. (2 points) c. The probability that the card is a face card or a 3
Answer:
(a)[tex]\dfrac{11}{26}[/tex]
(b)[tex]\dfrac{9}{13}[/tex]
(c)[tex]\dfrac{4}{13}[/tex]
Step-by-step explanation:
Number of cards in a Standard Deck=52
(a)
Number of Diamonds (D)=13
Number of Face Cards(F) = 12
Number of Diamonds that are face cards = 3
[tex]Pr($that the card is a diamond or a face card)=P(D)+P(F)-P(D \cap F)\\=\dfrac{13}{52} +\dfrac{12}{52} -\dfrac{3}{52} \\=\dfrac{22}{52} \\=\dfrac{11}{26}[/tex]
(b)The probability that the card is neither an ace nor a heart.
Number of Aces (A)=4
Number of Hearts(H) = 13
Number of Hearts that are Aces = 1
[tex]Pr($that the card is a Ace or a Heart), P(A \cup H)=P(A)+P(H)-P(A \cap H)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\$Therefore, probability that the card is neither an ace nor a heart.\\=1-P(A \cup H)\\=1-\dfrac{16}{52}\\=\dfrac{36}{52}\\=\dfrac{9}{13}[/tex]
(c)The probability that the card is a face card or a 3
Number of 3 cards(T)=4
Number of Face Cards(F) = 12
[tex]Pr($that the card is a three or a face card)=P(T)+P(F)\\=\dfrac{4}{52} +\dfrac{12}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]
The distance between (2, 3) and (1,7) is:
Answer:
[tex] \sqrt{17}\: units [/tex]
Step-by-step explanation:
[tex]d = \sqrt{ {(2 - 1)}^{2} + {(3 - 7)}^{2} } \\ \\ = \sqrt{ {(1)}^{2} + {( - 4)}^{2} } \\ \\ = \sqrt{ 1 + 16 } \\ \\ d= \sqrt{17} \\ [/tex]
Answer:
d=√17≈4.12310562561766
Step-by-step explanation:
Which is the graph of f(x) = 2(3)^x?
Answer: The graph is:
You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h = 130 and a square base with side s = 870
To impress your Egyptian subjects, find the volume of the pyramid.
Answer:
32799000 cubic units
Step-by-step Explanation:
Height if the Pyramid=130 Units
Side Length of square base=870 Units
Volume of a Pyramid=[tex]\frac{1}{3}[/tex]* Base Area*Height
Since the base is a square,
Area of a Square of side length s[tex]=s^2[/tex]
Therefore:
Volume[tex]=\frac{1}{3}*870^2*130[/tex]
=32799000 cubic units
The volume of your pyramid is 32799000 cubic units.
Answer:
V = 3.28x10⁷
Step-by-step explanation:
The volume of a pyramid is given by:
[tex] V = \frac{1}{3}bh [/tex]
Where:
b: is the base of the pyramid
h: is the height of the pyramid = 130
The base of the square base of the pyramid is given by:
[tex] b = s^{2} [/tex]
Where:
s: is the side of the square base = 870
Thus, the base of the square base of the pyramid is:
[tex] b = s^{2} = (870)^{2} = 7.56 \cdot 10^{5} [/tex]
Now, the volume of a pyramid is:
[tex] V = \frac{1}{3}bh = \frac{1}{3}(7.56 \cdot 10^{5})*130 = 3.28 \cdot 10^{7} [/tex]
Therefore, the volume of the pyramid is 3.28x10⁷.
I hope it helps you!
Which of the following is a geometric sequence?
Answer:
D. 1, 1/2, 1/4, 1/8, ...
Step-by-step explanation:
Only one of the listed is a geometric sequence:
D. 1, 1/2, 1/4, 1/8, ... with the common ratio 1/2A bag contains 1p,20 and 5p coins 3/8 of the bag are 1p coins There are as many 5p coins as 1p coins in the bag. There are 640 coins in total. Work out the number of 20 coins in the bag
Answer:
160 off 20p coins
Step-by-step explanation:
1 p, 20 p, 5 p coins1 p= 3/8 of the bag5 p= 1 p= 3/8 of the bagtotal coins= 64020 p coins= 640 - 640*(3/8+3/8)= 640*(1- 6/8)= 640 * 2/8= 640* 1/4= 160
What is the quotient if 3/8 of 30 is divided by 15/16 of 5/10?
Answer:
24
Step-by-step explanation:
That would be:
(3/8)(30)
---------------
(15/16)(1/2)
This can be reduced in various ways. First, divide that 30 by 15, obtaining:
6/8
-----------
1/32
Now invert the divisor (1/32) and multiply:
(6/8)(32/1)
This reduces to 6*4, or 24.
g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high
Answer:
0.3537 feet per minute.
Step-by-step explanation:
Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.
[tex]\dfrac{dV}{dt}=10$ ft^3/min[/tex]
[tex]\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h[/tex]
If the Base Diameter = Height of the Cone
The radius of the Cone = h/2
Therefore,
[tex]\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}[/tex]
[tex]\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}[/tex]
Therefore: [tex]\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10[/tex]
We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.
[tex]When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute[/tex]
When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.
y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a solution of the differential equation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter IMPOSSIBLE.) y(0) = 1, y'(π) = 9
Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
What is the answer to this question–1 × –5?
Answer:
5
Step-by-step explanation:
a minus times by another minus makes a positive, so it is basically 1 x 5
Answer:
5
Step-by-step explanation:
Since the you are multiplying 2 minuses together they will cancel each other out to form a positive number. However if you have an example like this
-6 × 7
Then the answer will be -42 because there is only one negative
please help!! Select the two reasons which fit best in lines 1 and 2 of the proof (given and details in photo)
A: 1.) Vertical Angles are congruent
2.) SSS Congruence Postulate
B: 1.) Definition of Angle Bisectors
2.) SAS Congruence Postulate
C: 1.) Vertical Angles are congruent
2.) AAS Congruence Postulate
D. 1.) Vertical Angles are congruent
2.) SAS Congruence Postulate
Answer:
D
Step-by-step explanation:
Line 1: Since these angles are vertical, they are congruent
Line 2: We have 2 sides and an angle in between them so it is SAS
This means the answer is D.
Answer: The correct answer is this set:
1.) Vertical Angles are congruent
2.) SAS Congruence Postulate
Write the quotient in simplest form. Type answer as integer or a fraction
Answer:
[tex]-\dfrac{1}{26}[/tex]
Step-by-step explanation:
[tex]-\dfrac{12}{13}\div 24=\\\\-\dfrac{12}{13} \times \dfrac{1}{24}=\\\\-\dfrac{12}{13\times 24}=\\\\-\dfrac{1}{26}[/tex]
Hope this helps!
How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 98% confidence that the sample mean is within 4 minutes of the population mean, and the population standard deviation is known to be 12 minutes. 25 35 49 60
Answer:
49
Step-by-step explanation:
Margin of error = critical value × standard error
ME = CV × SE
The critical value at 98% confidence is z = 2.326.
Standard error is SE = σ / √n.
4 = 2.326 × 12 / √n
n = 49
Any help would be great
Answer:
88/57
Step-by-step explanation:
Answer: 88:57
Step-by-step explanation:
Length is 88 and width is 57
So the ratio is 88:57
There are 225 students at March middle school. On Friday, 135 students wore spirit shirts. What percent of the students did Not wear spirit shirts on Friday?
Answer:
40%
Step-by-step explanation:
To find the answer to this, you first can find out what percentage of students did wear spirit shirts. To do this you can divide 135 by 225 to give you 0.6. To convert the decimal into a percentage you can simply multiply by 100, giving you 60%. Then to find the percentage of students that did not wear spirit shirts, you can subtract 60 from 100, giving you 40%.
Use the following equation to answer the questions below:
y − 2 = 1 /3 (x + 4)
Find the equation of the line that is passing through (8, 2) and is perpendicular to the given line.
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped you plz don't forget to thank me...
got another math problem.. please help
the correct answer is 59.
Answer:
59
Step-by-step explanation:
[2+ (4-2)+8²]-[2-(-1)][2+2+64]-[2-(-1)]²68-3²68-959Some cruise ship passengers are given magnetic bracelets, which they agree to wear in an attempt to eliminate or diminish the effects of motion sickness. Others are given similar bracelets that have no magnetism. What type of study is this? What are the variables of interest?
Choose the correct answer below.
A. Observational study. The variable of interest is whether the passenger experienced motion sickness.
B. Observational study. The variable of interest is whether a passenger's bracelet is magnetized or not.
C. Experiment. The variable of interest is whether the passenger experienced motion sickness.
D. Experiment. The variable of interest is whether a passenger's bracelet is magnetized or not.
Answer:
Option c
Step-by-step explanation:
This is an experiment because the researcher wants to test efficiency of the magnetic bracelets in the elimination of motion sickness i.e. whether they experienced motion sickness even after wearing the magnetic bracelets.
X 8.2.79
Question Help
A dietitian at a hospital wants a patient to have a meal that has 64 grams of protein, 29 grams of carbohydrates, and 72.5 milligrams of vitamin A The hospital food
service tells the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash. Each serving of salmon steak has 40 grams of protein, 10 grams
carbohydrates, and 1 milligram of vitamin A. Each serving of baked eggs contains 20 grams of protein, 2 grams of carbohydrates, and 20 miligrams of vitamin A
Each serving of acom squash contains 4 grams of protein, 20 grams of carbohydrates, and 32 milligrams of vitamin A How many servings of each food should the
dietitian provide for the patient?
Answer:
steak: 1/2baked eggs: 2acorn squash: 1Step-by-step explanation:
Let s, b, a represent the numbers of servings of steak, baked eggs, and acorn squash, respectively. Then the equations we want to solve are ...
40s +20b +4a = 64 . . . . grams of protein
10s +2b +20a = 29 . . . . grams of carbohydrate
1s +20b +32a = 72.5 . . . milligrams of vitamin A
There are any number of calculators or web sites that will solve this system of equations for you. The solution is ...
s = 0.5
b = 2
a = 1
The dietitian should provide 1/2 serving of steak, 2 servings of baked eggs, and 1 serving of acorn squash.
Identify which type of sampling is used random, systematic, convenience, stratified, or cluster To determine customer opinion of their inflight service, Continental Airlines randomly selects 30 flights during a certain week and surveys all passengers on the flights. Which type of sampling is used?
A. Stratified
B. Cluster
C. Systematic
D. Random
E. Convenience
Answer:
B. Cluster
Step-by-step explanation:
Samples may be classified as:
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Each Continental Airlines flight is a group.
30 of them are chosen, and in each group chosen, every passenger is surveyed.
So cluster sampling was used.
The sum of two consecutive integers is −19. Find the integers.
Answer:
-9 and -10
Step-by-step explanation:
x + x+1=-19
2x+1=-19
2x=-19-1
2x=-20
x=-10
x+1
-10+1=-9
Answer:
[tex]-9[/tex]
[tex]-10[/tex]
Step-by-step explanation:
[tex]x+x+1=-19[/tex]
[tex]2x+1=-19[/tex]
[tex]2x=-19-1[/tex]
[tex]2x=-20[/tex]
[tex]x=-20 \div 2[/tex]
[tex]x=-10[/tex]
[tex]x+x+1=-19[/tex]
[tex]x+1=-19-x[/tex]
[tex]-10+1=-19-(-10)[/tex]
[tex]-9=-19+10[/tex]
[tex]-9=-9[/tex]
The table below shows the number of e-mails received each day by a company employee for two separate weeks. If the data were represented with a comparative dot plot, which day would have more dots for week 2 than week 1
Answer:
C
Step-by-step explanation:
Hope this helps
Answer:
C
Step-by-step explanation:
Wednesday hope this helps!
For an exam given to a class, the students' scores ranged from 34 to 99 , with a mean of 78 . Which of the following is the most realistic value for the standard deviation: -14,3,0,56,15?
Clearly explain what's unrealistic about each of the other values.
Answer:
The most realistic value for the standard deviation is 15.
Step-by-step explanation:
The standard deviation of a distribution is a measure of dispersion. It is a measure of the spread of the distribution from the mean of the distribution. It expresses how far most of the distribution is from the mean.
Mathematically, the standard deviation is given as the square root of variance. And variance is an average of the squared deviations from the mean.
Mathematically,
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable (ranges from 34 to 99)
xbar = mean = 78
N = number of variables
Now taking the given possible values of the standard deviation one at a time,
-14
The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, it directly translates that the standard deviation cannot be negative.
3
A small standard deviation like 3 indicates that the distribution mostly centres about the mean, with very little variation. And the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence, 3 is too low to pass ad the standard deviation of this distribution described.
0
A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That is, the distribution only contains 1 number, probably multiple times. So, this cannot be the standard deviation for the distribution described.
56
This value represents a value that is too high to express the spread of the distribution described. The mean (78) is very close to the maximum value of the distribution, and far away from the lower value(s), indicating that most of the distribution is in and around the upper values with a few variables closer to the lower limit. A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of variables far from the mean, which isn't the case here.
Moreso, a simple add of the standard deviation to the mean or subtracting the standard deviation from the mean should give at least one of the results with values within the distribution.
(Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)
(Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution)
15
This is the most realistic value for the standard deviation as it represents what the distribution described above is.
The mean (78) being close to the maximum value of the distribution, and far away from the lower value(s) indicates that most of the distribution is in and around the upper values with a few variables closer to the lower limit.
So, 15 indicates a perfect blend of small deviations due to the high values close to the mean and the very high deviation from the evidently few lower values.
(Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution)
(Mean) + (Standard deviation) = 78 - 15 = 63 > 34 (also within the distribution)
Hope this Helps!!!
When The most realistic value for the standard deviation is 15.
Step-by-step explanation:
Standard deviation The standard deviation of a distribution is a measure of dispersion. also, It is a measure of the spread of the distribution from the mean of the distribution. when It expresses how far most of the distribution is from the mean. Then according to Mathematically, the standard deviation is given as the square root of variance. And also variance is an average of the squared deviations from the mean.mathematically,When Standard deviation is = σ = √[Σ(x - xbar)²/N]After that x = each variable (ranges from 34 to 99)then xbar is = mean = 78Now N is = number of variablesThen we take the given possible values of the standard deviation one at a time, -14 after that The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, also it directly translates that the standard deviation cannot be negative. After that 3 no when A small standard deviation like 3 indicates that the distribution mostly centers about the mean, with very little variation. And also the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence proof that is, 3 is too low to pass ad the standard deviation of this distribution described. Then 0 when A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That means is, the distribution only contains 1 number, probably multiple times. So that, this can't be the standard deviation for the distribution described. Now 56 This value represents a value that is too high to express the spread of the distribution described. when The mean (78) is very close to the maximum value of the distribution, and also far away from the lower value(s), indicating that most of the distribution is in and also around the upper values with a few variables closer to the lower limit. when A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of the variables far from the mean, which isn't the case here. More so, when a simple addition of the standard deviation to the mean or subtracting the standard deviation from the mean should have given at least one of the results with values within the distribution.After that (Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)Then (Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution) Now last digit 15 This is the most realistic and also a value for the standard deviation as it represents what the distribution described above is.When The mean (78) is close to the maximum value of the distribution, and also far away from the lower value(s) indicates that most of the distribution is in and also that around the upper values with a few variables closer to the lower limit.So that, 15 indicates a perfect blend of small deviations due to the high values close to the mean and also the very high deviation from the evidently few lower values.Then (Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution) After that (Mean) + (Standard deviation) =Thus, 78 - 15 = 63 > 34 (also within the distribution)
Find out more information about standard deviation here:
https://brainly.com/question/25309029
please see attachment
Answer:
a) The value of absolute minimum value = - 0.3536
b) which is attained at [tex]x = \frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation:
Step(i):-
Given function
[tex]f(x) = \frac{-x}{2x^{2} +1}[/tex] ...(i)
Differentiating equation (i) with respective to 'x'
[tex]f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2} }[/tex] ...(ii)
[tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} }[/tex]
Equating Zero
[tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]
[tex]\frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]
[tex]2 x^{2}-1 = 0[/tex]
[tex]2 x^{2} = 1[/tex]
[tex]x^{2} = \frac{1}{2}[/tex]
[tex]x = \frac{-1}{\sqrt{2} } , x = \frac{1}{\sqrt{2} }[/tex]
Step(ii):-
Again Differentiating equation (ii) with respective to 'x'
[tex]f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4} }[/tex]
put
[tex]x = \frac{1}{\sqrt{2} }[/tex]
[tex]f^{ll} (x) > 0[/tex]
The absolute minimum value at [tex]x = \frac{1}{\sqrt{2} }[/tex]
Step(iii):-
The value of absolute minimum value
[tex]f(x) = \frac{-x}{2x^{2} +1}[/tex]
[tex]f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}[/tex]
on calculation we get
The value of absolute minimum value = - 0.3536
Final answer:-
a) The value of absolute minimum value = - 0.3536
b) which is attained at [tex]x = \frac{1}{\sqrt{2} }[/tex]
A tank contains 5,000 L of brine with 13 kg of dissolved salt. Pure water enters the tank at a rate of 50 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
Required:
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 20 minutes?
Answer:
a) [tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
b) 10.643 kg
Step-by-step explanation:
Solution:-
- We will first denote the amount of salt in the solution as x ( t ) at any time t.
- We are given that the Pure water enters the tank ( contains zero salt ).
- The volumetric rate of flow in and out of tank is V(flow) = 50 L / min
- The rate of change of salt in the tank at time ( t ) can be expressed as a ODE considering the ( inflow ) and ( outflow ) of salt from the tank.
- The ODE is mathematically expressed as:
[tex]\frac{dx}{dt} =[/tex] ( salt flow in ) - ( salt flow out )
- Since the fresh water ( with zero salt ) flows in then ( salt flow in ) = 0
- The concentration of salt within the tank changes with time ( t ). The amount of salt in the tank at time ( t ) is denoted by x ( t ).
- The volume of water in the tank remains constant ( steady state conditions ). I.e 10 L volume leaves and 10 L is added at every second; hence, the total volume of solution in tank remains 5,000 L.
- So any time ( t ) the concentration of salt in the 5,000 L is:
[tex]conc = \frac{x(t)}{1000}\frac{kg}{L}[/tex]
- The amount of salt leaving the tank per unit time can be determined from:
salt flow-out = conc * V( flow-out )
salt flow-out = [tex]\frac{x(t)}{5000}\frac{kg}{L}*\frac{50 L}{min}\\[/tex]
salt flow-out = [tex]\frac{x(t)}{100}\frac{kg}{min}[/tex]
- The ODE becomes:
[tex]\frac{dx}{dt} = 0 - \frac{x}{100}[/tex]
- Separate the variables and integrate both sides:
[tex]\int {\frac{1}{x} } \, dx = -\int\limits^t_0 {\frac{1}{100} } \, dt + c\\\\Ln( x ) = -\frac{t}{100} + c\\\\x = C*e^(^-^\frac{t}{100}^)[/tex]
- We were given the initial conditions for the amount of salt in tank at time t = 0 as x ( 0 ) = 13 kg. Use the initial conditions to evaluate the constant of integration:
[tex]13 = C*e^0 = C[/tex]
- The solution to the ODE becomes:
[tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
- We will use the derived solution of the ODE to determine the amount amount of salt in the tank after t = 20 mins:
[tex]x(20) = 13*e^(^-^\frac{20}{100}^)\\\\x(20) = 13*e^(^-^\frac{1}{5}^)\\\\x(20) = 10.643 kg[/tex]
- The amount of salt left in the tank after t = 20 mins is x = 10.643 kg
Tameka can make 32 beads with 4 sheets of paper. Right now she only has 3 sheets of paper. How many beads can Tameka make?
Answer:
24 beads
Step-by-step explanation:
beads in 4 sheet=32
beads in 1 sheet=32/4=8
beads in 3 sheet=8*3=24
Answer:
Assuming that you can make the same number of beads with 1 sheet of paper, Tameka can make 24 beads with 3 sheets of paper.
Forty adult men in the United States are randomly selected and measured for their body mass index (BMI). Based on that sample, it is estimated that the average (mean) BMI for men is 25.5, with a margin of error of 3.3. Use the given statistic and margin of error to identify the range of values (confidence interval) likely to contain the true value of the population parameter
Answer:
[tex] 25.5 -3.3= 22.2[/tex]
[tex] 25.5 +3.3= 28.8[/tex]
And the confidence interval would be given by: [tex] 22.2\leq \mu \leq 28.8[/tex]
Step-by-step explanation:
[tex]\bar X=25.5[/tex] represent the sample mean for the sample
ME= 3.3 represent the margin of error
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The margin of error is given by;
[tex] ME =t_{\alpha/2}\frac{s}{\sqrt{n}}= 3.3[/tex]
And the confidence interval would be given by:
[tex] 25.5 -3.3= 22.2[/tex]
[tex] 25.5 +3.3= 28.8[/tex]
And the confidence interval would be given by: [tex] 22.2\leq \mu \leq 28.8[/tex]
Breakfast Bar’s scrambled egg recipe uses 8 eggs to feed 5 people. How many eggs are they going to need to serve 100 people on Saturday morning?
Explain the steps you would use to solve the problem.
Answer:
800 eggs
Step-by-step explanation:
You would first thing about the starting numbers, Then look at the number 100 and multiply by 8. This would give you 800. This means that you will need 800 eggs to serve 100 people.
Brainliest is greatly appreciated
Answered by: Skylar
6/8/2020
9:59 AM (Eastern Time)
Answer:
the answer is 12.5 i know because i divided 100 by 8 and got 12.5 then multiply then got 100
Step-by-step explanation:
got it right just did the test
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
(4,1)
Step-by-step explanation:
(1+7)/2 = 4
(9+(-7))/2 = 1
