Answer:
7.15/65 = 0.11
A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.
Answer:
Step-by-step explanation:
From the given information:
[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]
Given that the solution is pumped at a slower rate of 4gal/min
Then:
[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]
[tex]R_{out}= \dfrac{2A}{50+t}[/tex]
The differential equation can be expressed as:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]
Integrating the linear differential equation; we have::
[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]
[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]
multiplying above integrating factor fields; we have:
[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]
[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]
[tex](50 + t)^2 A = (50 + t)^3+c[/tex]
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]
A(35) =69.6193 pounds
A(35) [tex]\simeq[/tex] 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
Your classmate tells you the details of the great deal he got on his mortgage: 30-year 1.1% fixed rate with a 20% down payment
If his new home costs $136,000, what is his down payment?
Answer:
27200
Step-by-step explanation:
is 16-7=4+5 true, false, or open?
Answer:
open
Step-by-step explanation:
Answer:
This is True.
Step-by-step explanation:
16-7=9
5+4=9
same ting
How do I solve problems like
5 + 2y = 1
Answer:
y=-2
Step-by-step explanation:
its like in the paper sorry it if crops out
A meat inspector has randomly selected 30 packs of 95% lean beef. The sample resulted in a mean of 96.2% with a sample standard deviation of 0.8%. Calculate an upper prediction bound for the leanness of a new pack using a prediction level of 99%. Assume normality. The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9.6 liters. Find a 95% confidence interval for the mean contents of all such containers, assuming an approximately normal distribution.
Answer:
a
The upper bound of the 99% prediction level is [tex] 98.2 [/tex]
b
The 95% confidence interval is [tex]9.7383 < \mu < 10.2617 [/tex]
Step-by-step explanation:
Considering first question
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\= x = 96.2\%[/tex]
The standard deviation is [tex]s = 0.8\%[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 30 - 1[/tex]
=> [tex]df = 29[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\alpha , 29} = 2.462[/tex]
Generally the 99% prediction level is mathematically represented as
[tex]\= x \pm [(t_{\alpha , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]
Generally the upper bound of the 99% prediction level is mathematically represented as
[tex]\= x + [(t_{\alpha , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]
=> [tex] 96.2 + (2.462 ) * 0.8 * (\sqrt{1 + \frac{1}{ 30} } )}] [/tex]
=> [tex] 98.2 [/tex]
Considering second question
Generally the sample is mathematically represented as
[tex]\= x = \frac{\sum x_i}{n}[/tex]
=> [tex]\= x = \frac{ 9.8 + 10.2 + \cdots +9.6 }{7}[/tex]
=> [tex]\= x = 10[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \frac{ \sum ( x_ i - \= x)}{n-1} }[/tex]
=> [tex]\sigma = \sqrt{ \frac{ ( 9.8 -10)^2 + ( 10.2 -10)^2 + \cdots + ( 9.6 -10)^2 }{7-1} }[/tex]
=> [tex]\sigma = 0.283[/tex]
Generally the degree of freedom is mathematically represented as
[tex] df = n- 1 [/tex]
=> [tex] df = 7- 1 [/tex]
=> [tex] df = 6 [/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\frac{\alpha }{2} , 6 } = 2.447[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 6 } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =2.447* \frac{0.283 }{\sqrt{7} }[/tex]
=> [tex]E =0.2617[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]10 -0.2617 < \mu < 10 + 0.2617[/tex]
=> [tex]9.7383 < \mu < 10.2617 [/tex]
Solve the equation formed when f ( x ) = g ( x ).
f ( x ) = 4 x − 4
g ( x ) = 1 2 x + 3
Group of answer choices
A. x = -4
B. x = 4
C. x = 2
D. x = -2
Answer:
The answer should be x = -7/8 but it doesn't say that for any of the choices
Step-by-step explanation:
Tina wants to buy a bouquet
of red roses. The original price
is $24. How much will Tina PAY
if she buys it during the sale
when it is 25% off?
Answer:
18
Step-by-step explanation:
If we know she will have a 25% discount, we know she will only pay 75%. So you divide by 4 and get 6. So now, If we subtract 25% (6), our 75% will be 18.
Answer:
It's 18
Step-by-step explanation:
25 percent of 24 is 6 dollars, subtract 6 from 24, you get 18, your welcome :D
an electrician has a 16-foot spool of wire and he needs to cut an 11-foot, 4-inch piece from the spool to make a repair. how many inches of wire will he have left on the spool after he makes the repair
The electrician will have 56 inches of wire left on the spool after he makes the repair.
First, we need to convert the length of the wire that the electrician needs to cut into inches. 11 feet is equal to 11 * 12 = 132 inches, and 4 inches is equal to 4, so the total length of the wire that the electrician needs to cut is 132 + 4 = 136 inches.
The electrician started with a spool of wire that was 16 feet long, or 16 * 12 = 192 inches long. If he needs to cut 136 inches of wire, he will have 192 - 136 = 56 inches of wire left on the spool.
Therefore, the electrician will have 56 inches of wire left on the spool after he makes the repair.
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HELPPPPPPP PLEASEEEEEEEEWEEE
Answer:C
Step-by-step explanation: slope of 0 will always be horizontal
An african elephant in rhe wils will eat for as long as 16 hours each day. For how many hours does an elephant eat in one year? There are 365 days in one year.
Answer:
5840
Step-by-step explanation:
16 x 365 is 5840
Answer:
5,840
Step-by-step explanation:
16x365=?
16x365=5,840
Write the letters of the expressions that are equivalent to the given expression.
5(2x + 3)
a. 10x + 15
b. 5x + 15x + 5x
c. 10x + 8
Answer: A.) 10x + 15
Step-by-step explanation:
You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.
Therefore, 10x + 15 is your answer.
It is assumed that the test results for a class follow a normal distribution with a mean of 78 and a standard deviation of 36. If you know that a student's grade is greater than 72, what is the probability that it is greater than 84? What do I know? What do I want to find out? What do we expect the answer to be? How do I go from what I know to what I want to find? Does this answer seem reasonable?
Answer:
0.7143
- You know the minimum possible grade of the student
- You want to find out the probability that that grade which is greater than 72 is also greater than 84
- Expect the answer to be 0.7143
- The explanation/steps is given below
- The answer seems (and is) reasonable. You only created a new lower limit.
Step-by-step explanation:
Distribution Type: Normal
Mean: 78
Standard deviation: 36
Range of marks: [78 - 36], [78 + 36] = [42 to 114]
If you know that a student's grade is greater than 72, what is the probability that it's greater than 84?
In this case, the full probability level is between 72 and the upper limit of 114 (instead of between 42 and 114). First, find the fraction of this probability.
[114 - 72] ÷ [114 - 42] = 42/72 = 0.5833
So, the probability of a student's mark falling between 72 and 114 is 0.5833.
Now making this a whole interval, 114 - 72 = 42
What fraction of this interval of 42 will bear marks between 84 and 114?
[114 - 84] = 30
30/42 = 0.7143
Because of the first part of the question "If you know (are sure) that a student's grade is greater than 72...", your answer stops at 0.7143, since 72 was used as the lower limit.
Which statement about residual plots is NOT true?
A. The vertical axis shows residuals.
B. If there is an obvious pattern, the model is probably reasonable.
C. The x-axis appears in the middle of the graph.
D. The sum of the residuals is 0.
Answer:
A is the correct answer
Step-by-step explanation:
The not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.
What is a residual plot?A residual plot shows the difference between the observed response and the fitted response values.
Given that, Which statement about residual plots is not true
In the given options,
If there is an obvious pattern, the model is probably reasonable, this option is not correct because, The pattern in the residual plot suggests that predictions based on the linear regression line will result in greater error as we move from left to right through the range of the explanatory variable.
So, it is not needed if there is an obvious pattern, then the model is probably reasonable,
Hence, the not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.
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A researcher wishes to estimate within $5 the average repair cost of for a refrigerator. If she wishes to be 90% confident, how large of a sample would be necessary if the population standard deviation is $15.50?
Answer:
The sample size 'n' = 26
Step-by-step explanation:
Explanation:-
Given a researcher wishes to estimate within $5 the average repair cost of for a refrigerator
Given estimate "E" = $5
The estimate within the average is determined by
[tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]
Level of significance ∝ = 90 % or 10%
= 0.90 or o.10
Z₀.₁₀ = 1.645
[tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]
[tex]5 = \frac{1.645 X15.50 }{\sqrt{n} }[/tex]
√n = [tex]\frac{25.49}{5} = 5.099[/tex]
Squaring on both sides , we get
n = 26
Conclusion:-
The sample size 'n' = 26
Graph the line with slope −1 and y-intercept 3.
Answer:
See Attachment.
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define variables
Slope m = -1
y-intercept b = 3
Step 2: Write linear equation
Substitute into general form.
Slope-Intercept Form: y = -x + 3
Step 3: Graph
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Answer:
lol
Step-by-step explanation:
Which weighs more a backpack that weighs 9.5 kg grams or a case of water that weighs 16 pounds
Answer:
The backpack weighs more
Step-by-step explanation:
9.5kg = 20.94391 lbs
Answer:
a backpack that weighs 9.5kg
Step-by-step explanation:
kilogram (kg) is stated to be 2.2 times heavier than a pound
The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7), what are the
coordinates of B?
Answer:
(8,1)
Step-by-step explanation:
(8,1) you have to add do to the same to B
Pont B is located at coordinates at the line AB (8, 1)
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7)
From the general formula of midpoints of a line
coordinates of midpoint = ((x₂ + x₁)/2, (y₂ + y₁)/2)
where,
(x₁, y₁) are the coordinates of A
(x₂, y₂) are the coordinates of B
And in our case Coordinates of the midpoint are (6, -3)
Thus,
6 = (4 + x₂)/2
x₂ = 8
-3 = (-7 + y₂)/2
y₂ = 1
therefore, the coordinates of Pont B at line AB are (8, 1)
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Which of the following is equivalent to 3/8
0.0025
3.75
25/100
375/1,000
Answer:
375/1,000
Step-by-step explanation:
3/8=0.375
375/1,000 =0.375
Can you help me please
The weight of eggs from a local farm are Normally distributed with mean of 2.1 ounces and a standard deviation of 0.25 ounces.
A graph titled Weight of Eggs has ounces on the x-axis going from 1.35 to 2.85 in increments of 0.25. The highest point of the curve is at 2.1. Everything to the left of that point and under the curve is labeled average, everything to the right is large.
An egg that weighs 2.0 ounces or more is labeled large and anything below is labeled average.
What percent of eggs from this farm are labeled as large? Round to the nearest tenth.
⇒ 65.5 IS THE ANSWER
Answer:
65.5
Step-by-step explanation:
Answer:
65.5
Step-by-step explanation:
A population grows exponentially at the rate of 1.35%. How long (in years) will it take the population to double?
Answer: Approximately 51 years.
Step-by-step explanation: A population grows by changing exponentially over time, which can be mathematically demonstrated as:
[tex]P=P_{0}e^{rt}[/tex]
where
P is the population after time
P₀ is initial population, when time = 0
r is a percentage rate of growth
t is time passed
In this case, we have to calculate the amount of time it has passed for a population to double, so [tex]P=2P_{0}[/tex]:
[tex]2P_{0}=P_{0}e^{0.0135t}[/tex]
[tex]e^{0.0135t}=2[/tex]
[tex]ln(e^{0.0135t})=ln2[/tex]
Using Logarithm Rule [tex]ln(e^{k})=k[/tex]:
[tex]0.0135t=0.693[/tex]
t = 51.34
For a population with rate of 1.35%, it will take approximately 51 years to double.
find the missing value of 6/9 = m/6
Answer: 4
Step-by-step explanation:
6/9 = m/6 We can multiply both sides of the equation by 6 to solve for m
so we get 36/9 = m. m = 4
For the following quadratic equation, find the discriminant.
-x^2 + 20x -126 =5
i need help please
Answer:
d=-124
Step-by-step explanation:
To find the discriminant use the equation b^2-4ac
So, 20^2-4(-131)(-1)
400-524= -124
d=-124
Solve the given system of equations utilizing either the substitution or addition method.
Answer:
Value of x=4 and y=-13/3
Step-by-step explanation:
We need to solve the systems of equations
[tex]5x+3y=7 \ and \ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}[/tex]
Solving using substitution method:
Let:
[tex]5x+3y=7---eq(1) \\ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}---eq(2)[/tex]
Find value of x from eq(1) and put in eq(2)
[tex]5x+3y=7\\5x=7-3y\\x=\frac{7-3y}{5}[/tex]
Put value of x in eq(2)
[tex]\frac{3}{2}(\frac{7-3y}{5}) -\frac{3}{4}y =\frac{37}{4}\\\frac{21-9y}{10} -\frac{3}{4}y =\frac{37}{4}\\Taking \ LCM\\\frac{21*2-9y*2-3y*5}{20} =\frac{37}{4}\\\frac{42-18y-15y}{20} =\frac{37}{4}\\42-33y=\frac{37}{4}*20\\42-33y=185\\-33y=185-42\\-33y=143\\y=\frac{143}{-33}\\y=-\frac{13}{3}[/tex]
Now, finding value of x by putting value of y in eq(1)
[tex]x=\frac{7-3y}{5}\\x= \frac{7-3(-\frac{13}{3}) }{5}\\x=\frac{7+13}{5}\\x=\frac{20}{5}\\x=4[/tex]
So, Value of x=4 and y=-13/3
what is 13x144 i don't know what it it im 2nd grade
Answer:
Step-by-step explanation: 1,872
Answer: 1,872
Step-by-step explanation:
For a sample, the 95% confidence interval is (0.202, 0.482). What is the point estimate, \hat{p}, of this sample?
Answer:
The Point estimate p = 0.342
Step-by-step explanation:
For the sample, 95% confidence interval (0.202,0.482) . The Confidence interval width = (0.482 - 0.202) = 0.28
The margin of error = 0.28/2
The margin of error = 0.14
So, Point estimate p = Lower bound + Margin of error
Point estimate p = 0.202 + 0.14
Point estimate p = 0.342
Therefore, the Point estimate p = 0.342
Brainliest be good peeps Calculate the missing term in each
proportion.
2/11= /55
36/42= /
9/ = 21/28
6/9= /15
Answer:
1) 10
2) (not enough info) I got 6/7
3) 12
4) 10
Step-by-step explanation:
Find a GCF and find the numerator.
Given that 3x – tan y = 4, what is dy/dx in terms of y?
Answer:
[tex]\frac{dy}{dx}[/tex] = 3 cos² y ⇒ B
Step-by-step explanation:
∵ 3x - tan(y) = 4
∵ The differentiation of tan(y) with respect to x is sec² y · dy/dx
∵ The differentiation of 3x with respect to x is 3
∵ the differentiation to 4 with respect to x is 0
∴ d/dx [3x - tan(y) = 4] is 3 - sec² y · dy/dx = 0
∵ 3 - sec²(y) · dy/dx = 0
→ Subtract 3 from both sides
∴ - sec² y · dy/dx = -3
→ Divide both sides by -1
∴ sec² y · dy/dx = 3
→ Divide both sides by sec²(x)
∴ [tex]\frac{dy}{dx}=\frac{3}{sec^{2}y}[/tex]
→ Remember [tex]\frac{1}{secy}[/tex] = cos y
∵ [tex]\frac{1}{sec^{2}y}[/tex] = cos² y
∴ [tex]\frac{3}{sec^{2}y}[/tex] = 3 cos² y
∴ [tex]\frac{dy}{dx}[/tex] = 3 cos² y
dy/dx of 3x – tan y = 4 in terms of y is;
dy/dx = 3cos²y
We are given;
3x - tan y = 4
Let's differentiate in terms of y to get;
3 - sec²y(dy/dx) = 0
This is because the derivative of tan y in terms of y is sec²y(dy/dx).
Thus, using addition property of equality, we have;
3 = sec²y(dy/dx)
Now, in trigonometric ratios;
sec y = 1/cos y
Thus;
sec²y = 1/cos²y
Therefore;
3 = (1/cos²y) (dy/dx)
Thus;
dy/dx = 3cos²y
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if the current ratio is 2:1 it is possible that
Answer:
is this question complete? there is nothing after the word “that”
Step-by-step explanation: