Answer:
The quantity of salt at time t is [tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex], where t is measured in minutes.
Step-by-step explanation:
The law of mass conservation for control volume indicates that:
[tex]\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}[/tex]
Where mass flow is the product of salt concentration and water volume flow.
The model of the tank according to the statement is:
[tex](0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}[/tex]
Where:
[tex]c[/tex] - The salt concentration in the tank, as well at the exit of the tank, measured in [tex]\frac{pd}{gal}[/tex].
[tex]\frac{dc}{dt}[/tex] - Concentration rate of change in the tank, measured in [tex]\frac{pd}{min}[/tex].
[tex]V[/tex] - Volume of the tank, measured in gallons.
The following first-order linear non-homogeneous differential equation is found:
[tex]V \cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]60\cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]\frac{dc}{dt} + \frac{1}{10}\cdot c = 3[/tex]
This equation is solved as follows:
[tex]e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }[/tex]
[tex]\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C[/tex]
[tex]c = 30 + C\cdot e^{-\frac{t}{10} }[/tex]
The initial concentration in the tank is:
[tex]c_{o} = \frac{10\,pd}{60\,gal}[/tex]
[tex]c_{o} = 0.167\,\frac{pd}{gal}[/tex]
Now, the integration constant is:
[tex]0.167 = 30 + C[/tex]
[tex]C = -29.833[/tex]
The solution of the differential equation is:
[tex]c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }[/tex]
Now, the quantity of salt at time t is:
[tex]m_{salt} = V_{tank}\cdot c(t)[/tex]
[tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex]
Where t is measured in minutes.
Thirty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly three will end up being replaced under warranty
Answer:
26.68% probability that exactly three will end up being replaced under warranty
Step-by-step explanation:
For each telephone under warranty, there are only two possible outcomes. Either they need to be replaced, or they do not need to be replaced. Each telephone is independent of other telephones. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
30% must be replaced with new units
This means that [tex]p = 0.3[/tex]
If a company purchases ten of these telephones, what is the probability that exactly three will end up being replaced under warranty
This is [tex]P(X = 3)[/tex] when [tex]n = 10[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.2668[/tex]
26.68% probability that exactly three will end up being replaced under warranty
Find the area of the following square.
Write your answer in simplest form.
Be sure to include the correct unit in your answer.
4 1/2m
Answer:
[tex]20.25 \: m^2[/tex]
Step-by-step explanation:
Use the formula for the area of a square.
[tex]A=s^2[/tex]
Where [tex]s=4.5[/tex]
[tex]s^2\\(4.5)^2\\20.25[/tex]
The area of the square is 20.25 square meters as per the concept of the square.
To find the area of a square, we need to square the length of one of its sides. In this case, the side length is given as 4 1/2 meters.
First, we need to convert the mixed number 4 1/2 into an improper fraction. We can rewrite it as 9/2.
Next, we square the side length:
[tex]\frac{9}{2}^2 = \frac{81}{4}[/tex].
To simplify the fraction, we can divide the numerator by the denominator:
81 ÷ 4 = 20 remainders 1.
Therefore, the area of the square is 20 1/4 square meters.
However, we can simplify the mixed number further. Since 4 can be divided by 4 and 1 can be divided by 4, we have:
20 1/4
= 20 + 1/4
= 20 + 1/4
= 20 + 0.25
= 20.25.
Therefore, the area of the square is 20.25 square meters.
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A study of the effect of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained:
Smokers: 69.3 56.0 22.1 47.6 53.2 48.1 52.7 34.4 60.2 43.8 23.2 13.8
Non-Smokers: 28.6 25.1 26.4 34.9 28.8 28.4 38.5 30.2 30.6 31.8 41.6 21.1 36.0 37.9 13.9
Which group having greater value of relative dispersion and why?
Answer:
The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.
CV smokers: 0.387
CV non-smokers: 0.234
Step-by-step explanation:
We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).
Then, first we calculate the mean and standard deviation for the smokers data:
Mean: 43.7
Standard deviation: 286.5
[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]
The mean and standard deviation for the non-smokers is:
Mean: 30.3
Standard deviation: 50.9
[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]
Now, we can calculate the coefficient of variation:
CV smokers:
[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]
CV non-smokers:
[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]
A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off. Assuming both promotions can be applied at the same time how much more would you pay if you applied the coupon first?
Answer:
[tex]\$0.26[/tex] has to be paid more if the coupon is applied first
Step-by-step explanation:
Given: A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off.
To find: how much more would be paid if the coupon is applied first
Solution:
Let $ x denotes cost of hand soap
Case 1:
If the discount is given first,
cost of hand soap = [tex]x-\frac{13}{100} x=\$ \frac{87}{100}x[/tex]
If the coupon for $2.00 off is applied,
Final cost of the hand soap = [tex]\$\,(\frac{87}{100}x-2)[/tex]
Case 2:
If the coupon for $2.00 off is applied first,
cost of hand soap = [tex]\$(x-2)[/tex]
If the discount is given then,
final cost of the hand soap = [tex](x-2)-\frac{13}{100}(x-2)=\frac{87}{100}(x-2)[/tex] = [tex]\frac{87}{100}x-\frac{87}{50}[/tex]
Here,
[tex]\frac{87}{100}x-\frac{87}{50}-\frac{87}{100}x+2=\frac{13}{50}=\$0.26[/tex]
So, [tex]\$0.26[/tex] has to be paid more if the coupon is applied first.
Answer:
$0.26
Step-by-step explanation: I took the test
If 20 drops fall in 76 seconds, how long will 8 drops take?
Answer:
x =30.4 seconds
Step-by-step explanation:
We can use ratios to solve
20 drops 8 drops
--------------- = ----------------
76 seconds x seconds
Using cross products
20x = 8*76
20x =608
Divide each side by 20
20x/20 = 608/20
x =30.4 seconds
Answer:
30.4 secs = 30secs
Step-by-step explanation:
20 drops fall in 76s
Hence 1 drop is 76/20
Therefore 8 drops would be ;
76/20 × 8 = 30.4 secs
The people at the party ate 16 chocolate chip cookies and 26 sugar cookies. What percent of the cookies were sugar cookies?
Answer:
61%
Step-by-step explanation:
16/26 x 100 = 61.538461
You have to round it up if the question tells you to round it up.
hope it helps! :)
Answer:
62%
Step-by-step explanation:
42 x 62% = 26.04
I am sorry if you get this wrong. I really hope this helps.
If P(-2, 1) is rotated 90°, its image is
Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.
Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
solve for x
x/9=3
whats x
Answer:
x = 27
Step-by-step explanation:
x/9 = 3
Multiply each side by 9
x/9 * 9 = 3*9
x = 27
Answer:
27
Step-by-step explanation:
x/9= 3
Carry over the 9 and make x the subject.
x= 3*9
x= 27
Therefore x is 27.
To check if the answer is correct, replace the x with the value of what it is in brackets. The value of x is 27.
(27)/9= 3
= 27/9
= 3
We got back the 3 so that means the answer is correct
An amount of money earned #24 in 4 years at a rate of 5% per year simple intrest. what was the amount of money
Answer:
4.8
Step-by-step explanation:
simple interest=Principal ×time×rate ÷100
=24×4×5÷100
=4.8
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.
Which number is irrational
Answer:
Can you give the question. Can you post the picture. I can help solve. I will edit this answer once you have given the question/picture.
Want Brainliest? Get this Correct The x-values in the table for f(x) were multiplied by -1 to create the table for g(x) What is the relationship between the graphs of the two functions? A. They are reflections of each other across the y-axis B. They are reflections of each other across the x-axis C. The graphs are not related D. They are reflections of each other over the line x = y
Answer:
Option (A).
Step-by-step explanation:
We choose a point from table of f(x), that is (-2, -31)
1). If this point is reflected across x-axis, rule to be followed,
(x, y) → (x, -y)
That means y coordinate of the point gets changed with opposite notation.
If (-2, -31) is reflected over the x-axis,
(-2, -31) → (-2, 31) ----------(1)
2). When a point is reflected over the y-axis,
Rule to be followed,
(x, y) → (-x, y)
(-2, -31) → (2, -31) ----------(2)
3). When a point is reflected over the line y = x
Rule to be followed,
(x, y) → (y, x)
(-2, -31) → (-31, -2) -----------(3)
By comparing f(x) and g(x) we find the relation between the functions as,
f(-2, -31) → g(2, -31)
Rule between the functions f and g matches with the rule number (2).
Therefore, function 'f' has been reflected across y axis to get the function 'g'.
Option (A) will be the answer.
a cog company produces 20 cogs a day, 4 of which are defective. Find the probability of selecting 4 cogs from the 20 produced where all are defective?
Answer:
1/4845
Step-by-step explanation:
The probability of selecting a defective cog first is
1/5
The second cog is
3/19
The third cog is
1/9
And the fourth cog is
1/17
Multiplying these together we get
1/5 * 3/19* 1/9 * 1/17 = 1/4845
The probability of selecting 4 cogs from the 20 produced where all are defective is approximately 0.000206.
What is probability?Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.
The probability of selecting 4 defective cogs from the 20 produced can be calculated as follows:
P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20)
The number of ways to select 4 defective cogs can be found by selecting 4 defective cogs out of the 4 defective cogs produced, and 0 non-defective cogs out of the remaining 20-4=16 non-defective cogs. This can be expressed mathematically as:
Number of ways to select 4 defective cogs = (4 choose 4) * (16 choose 0) = 1
The total number of ways to select 4 cogs from 20 can be found by selecting 4 cogs out of the 20 produced. This can be expressed mathematically as:
Total number of ways to select 4 cogs from 20 = (20 choose 4) = 4845
Therefore, the probability of selecting 4 defective cogs from the 20 produced is:
P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20) = 1/4845
Thus, the probability of selecting defective cogs is approximately 0.000206.
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Please answer this correctly without making mistakes
Answer:
508
Step-by-step explanation:
use l x w
40x7
10x18
8x6
508
c. Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 4 feet. What is the area of the shade?
Answer:
A=12 feet²
Step-by-step explanation:
1/2*base*height=area
(1/2)*4*6=12
Nike sells 20,000 pairs of shoes for $200 each pair. How much revenue did Nike make?
Answer:
$4,000,000
Step-by-step explanation:
20,000*200=4,000,000
John averages 58 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose John's words per minute on a minute on a typing test. Then X~N(58,11)
Answer:
The z score when x =72 is:
[tex] z = \frac{72-58}{11}= 1.273[/tex]
The mean is 58
This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.
Step-by-step explanation:
Assuming the following info for the question: Suppose John's words per minute on a typing test are normally distributed. Let X -the number of words per minute on a typing test. Then X N(58, 11) If necessary, round to three decimal places.
Provide your answer below rds per minute in a typing test on Sunday. The z score when x =72 is
For this case we know that the variable of interest is modelled with the normal distribution:
[tex]X \sim N (\mu= 58, \sigma=11)[/tex]
And the z score is given by:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z = \frac{72-58}{11}= 1.273[/tex]
The mean is 58
This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.
Find tan x if sec x = sort 37/6 and sin x <0
Answer:
tan(x) = -1/6
Step-by-step explanation:
We can use the relation between tan and sec:
[tex]\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}[/tex]
The tangent of x is -1/6.
I need HELP PLEASE HELP ME
Answer:
Graph 2
Step-by-step explanation:
You can see that all the shaded numbers are above negative 25 in that graph. Hope this helped!
Let x = 8.99999 . (a) Is x < 9 or is x = 9? x < 9 It is neither; x > 9 x = 9 x < 9 and x = 9 It cannot be determined. (b) Sum a geometric series to find the value of x. x = (c) How many decimal representations does the number 9 have? decimal representations (d) Which numbers have more than one decimal representation? the integers the rational numbers except for 0 all rational numbers that have a terminating decimal representation except for 0 all integers except for 0 all real numbers
Answer: idk
Step-by-step explanation:
idk
George is given two circles 0 and circles X as shown if he wants to prove that two circles are similar what would be the correct second step in his proof
Answer: Option A.
Step-by-step explanation:
Here we have two equations for the circumference, one for each circle:
C = 2*pi*r
C' = 2*pi*r'
now, if we take the quotient of those two equations, the left side must still be equal to the left side, this means that:
C/C' = 2*pi*r/(2*pi*r') = r/r'
So we have the relation:
C/C' = r/r'
And this is obtained for the division property of equality.
IF A = B, then as both numbers are equal, if we divide both sides by the same thing, then the equality must remain true.
Then the correct option is A.
There are 1760 yards in one mile about how many miles will a runner have to run
Answer:
3
I used to be an olimpic runner and I ran the 400 all the time and I did cross country
What is the distance from point N to line LM in the figure below?
Answer:
The correct answer would be F. 7.8
Step-by-step explanation:
the line is more or less a reflection of segment ON
so they are more or less the same.
I hope this helped you!
Factorize (3x-2y)2 + 3(3x-2y)-10
Answer:
[tex]5(3x-2y-2)[/tex] i think. i am sorry if i am wrong
Step-by-step explanation:
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained. 0.10 0.13 0.16 0.15 0.14 0.08 0.15 (a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars. (b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a),
The question is incomplete. Here is the complete qeustion.
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.10 0.13 0.16 0.15 0.14 0.008 0.15
(a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars.
(b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a), can we safely conclude that this requirement is being met?
Answer: (a) 0.089 ≤ μ ≤ 0.171
(b) No
Step-by-step explanation:
(a) To determine the confidence interval, first calculate the mean (X) and standard deviation (s) of the sample
X = [tex]\frac{0.1+0.13+0.16+0.15+0.14+0.08+0.15}{7}[/tex]
X = 0.13
s = [tex]\sqrt{\frac{(0.1-0.13)^{2} + (0.13 - 0.13)^{2} + ... + (0.15 - 0.13)^{2}}{7-1} }[/tex]
s = 0.029
The degrees of freedom is
N - 1 = 7 - 1 = 6
And since the confidence is of 99%:
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
The t-test statistics for [tex]t_{6,0.005}[/tex] is 3.707
(Value found in the t-distribution table)
Now, calculate Error:
E = [tex]t_{6,0.005}[/tex] . [tex]\frac{s}{\sqrt{N} }[/tex]
E = 3.707. [tex]\frac{0.029}{\sqrt{7} }[/tex]
E = 0.041
The interval will be:
0.13 - 0.041 ≤ μ ≤ 0.13+0.041
0.089 ≤ μ ≤ 0.171
(b) No, because according to the interval, the nitrode-oxide emissions range from 0.089 to 0.171, which is greater than required by EPA.
The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width. What is the length and width in yards?
Answer:
160 yards
Step-by-step explanation:
P=2l+2w
P=2(3w-8)+2(w)
432=2(3w-8)+2(w)
432=6w-16+2w
432=8w-16
432+16=8w
448=8w
w=448/8
w=56yards
l=3(56)-8
l=168-8=160yards
Write the equation of a line that is perpendicular to y= -x - 6 and that passes through the point (-9, -4).
Answer:
y = x + 5
Step-by-step explanation:
Perpendicular slope is opposite inverse so the perpendicular slope to -1x would be 1x
Then find b in y=mx+b
Plug in all the number
y=-9
x=-4
m=1
So, -4=1(-9)+b
1×-9=-9
+9 to both sides
5=b
Therefore,
y=x+5
What is the value of the expression 1/7 ÷8 A 1/12 B 1/35 C 5/7 D 6/7
Pss. Its multiple choice okay dont get confused
Answer:
Looks like it's none.
Step-by-step explanation:
[tex]\frac{1}{7}*\frac{1}{8}=\frac{1}{56}[/tex]
Answer:
Step-by-step explanation:B and D I belive.
which of the following expressions is equal to -3x^2-12??!!! please help him
Answer:
-3 ( x+2i) (x-2i)
Step-by-step explanation:
-3x^2-12
Factor out a -3
-3(x^2 +4)
Rewrite
-3 ( x^2 - -4)
-3 ( x^2 - (-2i)^2) This is the difference of squares ( a^2 -b^2 ) = (a-b)(a+b)
-3 ( x- -2i) (x+2i)
-3( x+2i) (x-2i)