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.
In a group, 10 freshmen have mean GPA of 3.5; 20 sophomores have a mean GPA of 2.9; 25 juniors have a mean GPA of 3.2; and 15 seniors have a mean GPA of 3.4. What is the mean of the entire group
Answer:
[tex] T_1 = 10*3.5 = 35[/tex]
[tex] T_2 = 20*2.9 = 58[/tex]
[tex] T_3 = 25*3.2 = 80[/tex]
[tex] T_4 = 15*3.4 = 51[/tex]
[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n_1= 10 , \bar X_1 = 3.5[/tex] for freshmen
[tex] n_2= 20 , \bar X_2 = 2.9[/tex] for sophomores
[tex] n_3= 25 , \bar X_3 = 3.2[/tex] for juniors
[tex] n_4= 15 , \bar X_4 = 3.4[/tex] for seniors
For this case we can use the formula for the sample mean in order to find the total of each group:
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]T= \sum_{i=1}^n X_i = n *\bar X[/tex]
And replacing we got:
[tex] T_1 = 10*3.5 = 35[/tex]
[tex] T_2 = 20*2.9 = 58[/tex]
[tex] T_3 = 25*3.2 = 80[/tex]
[tex] T_4 = 15*3.4 = 51[/tex]
And the grand mean would be given by:
[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]
Skyler is out shopping and sees that striped shirts are on sale for
$19.00 each, and plaid pants are on sale for $19.50 each. He
buys 8 shirts and 6 pairs of pants. What is the total of his
purchase?
The total was $_______
Answer:
His total is $269
Step-by-step explanation:
8x19 = 152
6x19.50 = 117
152+117 = 269
Given that (- 2, 7) is on the graph of f(x) , find the corresponding point for the function f(x + 4).
Answer:
[tex]\boxed{\ the \ corresponding\ point\ is \ (-6,7)\ }[/tex]
Step-by-step explanation:
We know that f(-2)=7
x+4 = -2 <=> x = -6
so f(-6+4) = f(-2)=7
then the corresponding point is (-6,7)
Solve: x - 1 < 3 help me plssss
Answer:
x =2
Step-by-step explanation:
becaue 2-1 is smaller than 3
Answer:
Hello!
I believe your answer is:
x=2
If this is not correct, please let me know and I will try again!
Step-by-step explanation:
The mean height of women in a country (ages 20minus29) is 64.2 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume sigmaequals2.84. The probability that the mean height for the sample is greater than 65 inches is nothing.
Answer:
[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]
And we can find the probability using the complement rule and with the normal standard table like this:
[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]
The probability that the mean height for the sample is greater than 65 inches is 0.007
Step-by-step explanation:
Let X the random variable that represent the women heights of a population, and we know the following parameters
[tex]\mu=64.2[/tex] and [tex]\sigma=2.84[/tex]
We are interested on this probability
[tex]P(X>65)[/tex]
Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we find the z score for 65 inches we got:
[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]
And we can find the probability using the complement rule and with the normal standard table like this:
[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]
The probability that the mean height for the sample is greater than 65 inches is 0.007
Pamela is a college student. She pays tuition every semester and rent every month, and she uses cash daily for food. The expression 2x+12y+365z represents her yearly expenses. Which variable represents her rent?
Answer:
Variable y represent the rent of Pamela
Step-by-step explanation:
Given
Pamela pays tuition every semester and rent every month, and she uses cash daily for food.
lets understand what constitute semester , month and day in a year.
A semester consist of 6 months.
As a year has 12 months , a year will have 2 semester.
If one pays x for one semester then in a year one has to pay 2x .
As a year has two semester
Similarly
A year has 12 months .
If one pays y for one month then in a year one has to pay 12y .
As a A year has 12 months .
A year has 365 days
If one pays z for each month then in a year one has to pay 365z .
As a A year has 365 days.
__________________________________________
Based on above discussion , we can now safely assume that the we have to look at the coefficient of expression 2x+12y+365z to find the which variable represent which type of bill.
As we have to find variable for rent and rent is paid monthly.
so for a year total bill will have 12 months and hence going by expression variable y represent the rent of Pamela.
what is 2n+3n +1 +8n+4
Answer:
13n + 5
Step-by-step explanation:
2+3+8 = 13n
1+4 = 5
13n+5
Jodie Meeks's Free Throws During the 2015-16 NBA season, Jodie Meeks of the Detroit Pistons had a free throw shooting percentage of 0.906 . Assume that the probability Jodie Meeks makes any given free throw is fixed at 0.906 , and that free throws are independent.If Jodie Meeks shoots 6 free throws in a game, what is the probability that he makes at least 5 of them?
Answer:
0.8973
Step-by-step explanation:
Relevant data provided in the question as per the question below:
Free throw shooting percentage = 0.906
Free throws = 6
At least = 5
Based on the above information, the probability is
Let us assume the X signifies the number of free throws
So, Then X ≈ Bin (n = 6, p = 0.906)
[tex]P = (X = x) = $\sum\limits_{x}^6 (0.906)^x (1 - 0.906)^{6-x}, x = 0,1,2,3,.., 6[/tex]
Now
The Required probability = P(X ≥ 5) = P(X = 5) + P(X = 6)
[tex]= $\sum\limits_{5}^6 (0.906)^5 (1 - 0.906)^{6-5} + $\sum\limits_{6}^6 (0.906)^6 (1 - 0.906)^{6-6}[/tex]
= 0.8973
80 81 82 83 84 85 86 87 88 89 90
Anika's test scores are shown below.
Anika's Test Scores
80 81 82 83 84 85 86 87 88 89 90
Which statement compares the shape of the two dot plots?
There is a gap in both plots.
There is a gap in Anika's scores, but not in Lorenzo's scores.
The data is widely spread across both plots.
The data is more widely spread for Lorenzo's scores than for Anika's.
Mark this and return
Save and Exit
Answer:
D :)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Braily please
A sinusoid is any function whose values repeat in a periodic manner.
A. True
B. False
SUBMIT
Answer: short answer
Just checked it’s False
Hope this helps :))
Step-by-step explanation:
Answer:
B. False
Step-by-step explanation:
A P E X
Help asap giving branlist!!!
Answer:
D.
Step-by-step explanation:
So you know you have to have $62 as the base fee.
If you exceed 2 gigabytes, you subtract that by 2 because you want to find how many gigabytes you're going over. You then multiply it by 30 to find the cost.
You get C = 62 + 30(g - 2)
Answer:
anwser is d because it is write.
Step-by-step explanation:
uppose that the length of 20 years worth of baseball games has been investigated, and that it has been found that the average (mean) length of a game is 165 minutes and the standard deviation is 30 minutes. What is the probability that a randomly selected game will last between 120 and 210 minutes
Answer:
P(120< x < 210) = 0.8664
Step-by-step explanation:
given data
time length = 20 year
average mean time μ = 165 min
standard deviation σ = 30 min
randomly selected game between = 120 and 210 minute
solution
so here probability between 120 and 210 will be
P(120< x < 210) = [tex]P(\frac{120-165}{30}< \frac{x-\mu }{\sigma } <\frac{210-165}{30})[/tex]
P(120< x < 210) = [tex]P(\frac{-45}{30}< \frac{x-\mu }{\sigma } <\frac{45}{30})[/tex]
P(120< x < 210) = P(-1.5< Z < 1.5)
P(120< x < 210) = P(Z< 1.5) - P(Z< -1.5)
now we will use here this function in excel function
=NORMSDIST(z)
=NORMSDIST(-1.5)
P(120< x < 210) = 0.9332 - 0.0668
P(120< x < 210) = 0.8664
At the kennel, the ratio of cats to dogs is 4:5. There are 27 animals in all. How many cats are in the kennel?
Answer:
Step-by-step explanation:
4x+5x=27
9x=27
x=27/9
x=3
4x3=12
5x3=15
The total number of cats were 12.
Based on the ratio of dogs to cats in the shelter, we know that out of 27 animals, there are 12 cats.
The ratio of cats to dogs is 4:5 which means that there are 5 dogs for every 4 cats.
This means that out of 9 animals, 4 would be cats and 5 would be dogs. If there was 27 animals therefore:
= 4 / 9 x 27
= 108 / 9
= 12 cats
In conclusion, there are 12 cats.
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Find the length of side x in simplest radical form with a rational denominator
Answer:
[tex] x = 7 \sqrt{3} [/tex]
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{7}{x} \\ \\ \therefore \: \frac{1}{ \sqrt{3} } = \frac{7}{x} \\ \\ x = 7 \sqrt{3} \\ [/tex]
The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 5.8, 5.9, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. Is the process in control or out of control and why?
Answer:
Step-by-step explanation:
The mean of the reading points is
Mean = (5.8 + 5.9 + 4.9 + 5.2 + 5.0 + 4.9 + 6.2 + 5.1 + 5.7 + 6.1)/10 = 5.48
The process is out of control if the mean salt level of the readings is greater than 5.4
For the null hypothesis,
µ = 5.4
For the alternative hypothesis,
µ > 5.4
This is a right tailed test.
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 5.4
x = 5.48
σ = 0.3
n = 10
z = (5.48 - 5.4)/(0.3/√10) = 0.84
Looking at the normal distribution table, the probability corresponding to the z score is 0.7996
The probability value to the right of the z score is 1 - 0.7996 = 0.2
Assuming a significance level of 0.05
Since alpha, 0.05 < than the p value, 0.2, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the process is not out of control. If we had rejected the null hypothesis, then our conclusion would be that the process is out of control.
Which ordered pair is the solution of the system of equations? 3x+2y=4, -2+2y=24
Answer:
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
y = 13
Step-by-step explanation:
→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):
-2 + 2y = 24
2y = 26
y = 13
→Then, plug in 13 for y into the other equation:
3x + 2y = 4
3x + 2(13) = 4
3x + 26 = 4
3x = -22
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
Please answer this correctly
Answer:
3.14
Step-by-step explanation:
We find the total circumference of a circle with radius 2 to be
2 * pi * r
= 2 * 3.14 * 2
= 12.56
We divide by 4 to get the perimeter of the quarter circle
12.56/4 = 3.14
What is the value of log625^5 converted to a fraction
Answer:
1/4
Step-by-step explanation:
625^x = 5
x = 1/4
What is the difference of the polynomials? (–2x3y2 + 4x2y3 – 3xy4) – (6x4y – 5x2y3 – y5)
Answer:
-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵
Step-by-step explanation:
(–2x³y² + 4x²y³ – 3xy⁴) – (6x⁴y – 5x²y³ – y⁵)=
–2x³y² + 4x²y³ – 3xy⁴ – 6x⁴y + 5x²y³ + y⁵=
-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵
What is the image of (-4,12) after a dilation by a scale factor of 1/4 centered at the origin
Answer:
(-1,4)
Step-by-step explanation:
Divide each imput by 4
The required image of the given point (-4, 12) dilation by a scale factor of 1/4 and centered at the origin is (1, -3).
Given that,
To determine the image of (-4,12) after dilation by a scale factor of 1/4 centered at the origin.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph
Here,
For the point, we have a dilation factor of 1/4,
So dilated coordinate,
= (1/4 * - 4 , 1/4 * 12)
= (-1 , 3)
To form the image across the origin
= - (-1, 3)
= (1, -3)
Thus, the required image of the given point (-4, 12) with a scale factor of 1/4 and centered at the origin is (1, -3).
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what is the least common denominator of 4 7/9 and 2 2/3
Answer:
9
Equivalent Fractions with the LCD
4 7/9 = 43/9
2 2/3 = 24/9
For the denominators (9, 3) the least common multiple (LCM) is 9.
Therefore, the least common denominator (LCD) is 9.
4 7/9 = 43/9 × 1/1 = 43/9
2 2/3 = 8/3 × 3/3 = 24/9
Hope this helps :)
The least common denominator of 4 7/9 and 2 2/3 is 9.
Given data:
To find the least common denominator (LCD) of 4 7/9 and 2 2/3, we need to first convert both fractions to their equivalent forms with a common denominator.
The given fractions are:
4 7/9 = 4 + 7/9
2 2/3 = 2 + 2/3
To find a common denominator, we need to find the least common multiple (LCM) of the denominators 9 and 3, which is 9.
Now, let's convert the fractions to their equivalent forms with a denominator of 9:
4 7/9 = (4 * 9)/9 + (7/9) = 36/9 + 7/9 = 43/9
2 2/3 = (2 * 9)/9 + (2/3) = 18/9 + 2/3 = 20/9
The fractions 4 7/9 and 2 2/3 are now expressed with a common denominator of 9.
Hence, the least common denominator (LCD) of 4 7/9 and 2 2/3 is 9.
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A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $200. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905, the value reported for all college students with credit cards
Answer:
Yes. There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.
Step-by-step explanation:
We want to test the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.
To perform this test we have a sample of 500 students which have paid their balance in full each month. The sample mean is $825 and the estimated sample deviation is considered $200.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=905\\\\H_a:\mu< 905[/tex]
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=825.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{200}{\sqrt{500}}=8.94[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{825-905}{8.94}=\dfrac{-80}{8.94}=-8.94[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=500-1=499[/tex]
This test is a left-tailed test, with 499 degrees of freedom and t=-8.94, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-8.94)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.
Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?
Answer:one would get 12 one would get 20
Step-by-step explanation:just plug it in to the equation
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer: f(x)=2-x^2
Step-by-step explanation:
The quadratic equation is
y=ax^2+bx+c
and c is equal to the y-intercept.
in the twi graphs shown both have the same shape but different y-intervepts.
c(the y-intercept) in the first graph is 5 and in the second graph(F) is 2.
On the graphing calculator it says that f(x)=2-x^2 is the correct answer therefore it is correct.
Please answer this correctly I have to finish this today as this is my deadline
Answer:
r = 1.499619733762 m There is no such thing a quarter radius!
C = 9.4223886775301 m
A = 7.065 m^2
Step-by-step explanation:
Calculate r and C | Given A
Given the area of a circle calculate the radius and circumference
r = √(A / π)
C = 2πr
Agenda:
r = radius
C = circumference
A = area
π = pi = 3.1415926535898
√ = square root
Evaluate x - 2y when x = 5 and y = 5.
Determine whether the ordered pair satisfies the equation.
x - 2y = -5; (5,5)
Yes, the ordered pair satisfies the equation.
No, the ordered pair does not satisfy the equation.
Answer:
For the first question we just plug in the values so we get 5 - 2 * 5 = -5.
Again, for the second one we'll plug in the values and see if it's a true statement. 5 - 2 * 5 = -5 and -5 = -5 so the answer is yes.
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $ 500 500, 3 prizes of $ 200 200, 5 prizes of $ 10 10, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Answer:
-$0.75
Step-by-step explanation:
For calculation of expected value first we need to find out the probability distribution for this raffle which is shown below:-
Amount Probability
500 - 1 = $499 1 ÷ 5,000
200 - 1 = $199 3 ÷ 5,000
10 - 1 = $9 5 ÷ 5,000
5 - 1 = $4 20 ÷ 5,000
-$1 5,000 - 29 ÷ 5,000 = 4,971 ÷ 5,000
Now, the expected value of raffle will be
[tex]= \$499 \times (\frac{1}{5,000}) + \$199 \times (\frac{3}{5,000}) + \$9 \times (\frac{5}{5,000}) + \$4 \times (\frac{20}{5,000}) - \$1 \times (\frac{4,971}{5,000})[/tex]
= 0.0998 + 0.1194 + 0.009 + 0.016 - 0.9942
= -$0.75
The expected value of this raffle per ticket is $ 0.25.
Given that five thousand tickets are sold at $ 1 each for a charity raffle, and tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5, to determine what is the expected value of this raffle if you buy 1 ticket, the following calculation must be performed:
(500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X (500 + 600 + 50 + 100) / 5000 = X 1250/5000 = X 0.25 = X
Therefore, the expected value of this raffle per ticket is $ 0.25.
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Find the area of the triangle
Answer:
Step-by-step explanation:
The formula for the area of a triangle is base*height divided by 2. Remember this because itll be important for everything you do in math relating to geometry and calculus. Assuming you go that far
[tex]\frac{base*height}{2} =\frac{14*8}{2} =\frac{112}{2} = 56 units^2[/tex]
Answer:
A =56 units^2
Step-by-step explanation:
The area of a triangle is given by
A =1/2 bh where 14 is the base and 8 is the height
A = 1/2 (14)8
A =56 units^2
−2.73(m+4)=−6m−4.38.
Answer:
m=2
Step-by-step explanation:
-2.73m-10.92=-6m-4.38
3.27m=6.54
m=2
What is the missing side length?
Answer:
8 yds
Step-by-step explanation:
The sides have to have the same length
14 yd = 6yd + ?
Subtract 6 from each side
14-6 = 8
8 yds
