Answer:
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
Step-by-step explanation:
Given that:
A tank contains 180 liters of fluid in which 50 grams dissolved inside.
Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min
The salt pumped out[tex]= \dfrac{6 L}{180 L} = \dfrac{1}{30}[/tex] of initial amount added salt
At (t = 0) = 50
To determine the number A (t)
[tex]\dfrac{dA}{dt}=Rate_{in} - Rate _{out}[/tex]
[tex]A' = 6 - \dfrac{1}{30}A[/tex]
[tex]A' + \dfrac{1}{30}A = 6[/tex]
Integrating factor [tex]y = e^{\int\limits pdt[/tex]
[tex]y = e^{\int\limits \dfrac{1}{30}dt}[/tex]
[tex]y = e^{\dfrac{t}{30}}[/tex]
[tex](e^{ \frac{t}{30}}A)' =4 e ^{\dfrac{t}{30}}+c[/tex]
Taking integral on the both sides;
[tex]Ae ^{\dfrac{t}{30}}= 6 * 30 e^{\dfrac{t}{30}} + c[/tex]
[tex]A = 180+ ce^ {-\dfrac{t}{30}}[/tex]
At A(t = 0) = 50
50 = 180 + C (assuming C = [tex]ce ^{-\dfrac{t}{30}}[/tex])
C = 50 - 180
C = 130
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
What is the first step of the following division problem? (8x3 – x2 + 6x + 7) ÷ (2x – 1)
Answer:
The first step is to determine how many times 2x goes into 8x^3
Step-by-step explanation:
The first step is to determine how many times 2x goes into 8x^3
4x^2
--------------------------
2x-1 | (8x3 – x2 + 6x + 7
8x^3 -4x^2
Answer:
A
Step-by-step explanation:
i just took the test
An employee wants to invest $50,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.75% compounded continuously.
(a) Which investment will ear more interest in 5 yr?
(b) How much more will the better plan earn?
Answer:
a. 6% one is better
b. $12,285.95
Step-by-step explanation:
a. For determining which investment earn more first we have to calculate both the investment which are as follows
a. Based on compound quarterly, the amount is find out by using the following formula
[tex]Amount = {Present\ value\times (1 + interest\ rate)} ^{number\ of\ years}[/tex]
where,
Present value is $50,000
Interest rate is = [tex]\frac{0.06}{4}[/tex] = 0.015
And, the number of years is
= [tex]4\times4[/tex]
= 16
So, the amount is
[tex]= \$50,000 \times (1 + 0.015)^{16}[/tex]
= $63,449.28
And, based on compounded continuously, the amount is determined by using the following formula
[tex]Amount = Present\ value\times e^{rt}[/tex]
[tex]= \$50,000 \times e.^{0575(4)}[/tex]
= $51,163.33
Therefore, The the investment at 6% is better
b. Now the difference in earning is
= $63,449.28 - $51,163.33
= $12,285.95
It took jack 4 and half minutes to do 100 multiplication facts how long it takes him to do 150
Answer:
6.75 min
Step-by-step explanation:
100 facts/4.5 min = 150 facts/x min
x=(150*4.5)/100=6.75
What is the solution of the following linear system? y = 3x + 1 2y = 6x + 2
Answer:
y = 3x +1 (1)
2y = 6x +2 (2)
We can devide equation (2) by 2 and we got:
[tex] y =3x +1[/tex] (3)
And since equations (1) and (3) are equal we can do this:
[tex] 3x +1 = 3x+1[/tex]
And that implies:
[tex] 0=0[/tex]
And for this case we will have infinite solutions for the sytem given since we have two lines equal
Step-by-step explanation:
For this case we have the following system of equations given:
y = 3x +1 (1)
2y = 6x +2 (2)
We can devide equation (2) by 2 and we got:
[tex] y =3x +1[/tex] (3)
And since equations (1) and (3) are equal we can do this:
[tex] 3x +1 = 3x+1[/tex]
And that implies:
[tex] 0=0[/tex]
And for this case we will have infinite solutions for the sytem given since we have two lines equal
Me.perez drove a total of 40 miles in 5 days she drove the same number of miles each day.how many miles did me.perez drive each day?
Answer:
She drove 8 miles each day.
Step-by-step explanation:
Given that she drove equal number of miles in 5 days. So in order to find the number of miles in each days, you have to divide it by 5,
[tex]5days = 40miles[/tex]
[tex]1day = 40 \div 5[/tex]
[tex]1day = 8miles[/tex]
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
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
D (4,11)
Step-by-step explanation:
Answer: it’s d
x is just going up by 1 and y is going up by 2
If a number is added to the numerator of 7/9 and the same number is subtracted from the denominator, the result is 3. Find the number.
Answer:
5
Step-by-step explanation:
[tex]\frac{7+x}{9-x}=3\\ 7+x = 3(9-x)\\7+x=27-3x\\x+3x=27-7\\4x=20\\x=5[/tex]
how do I find the volume of a triangular prism?
Answer:
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h.
Step-by-step explanation:
At a local college, 138 of the male students are smokers and are non-smokers. Of the female students, are smokers and are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Answer:
The probability that both the male and female student are non-smokers is 0.72.
Step-by-step explanation:
The complete question is:
At a local college,178 of the male students are smokers and 712 are non-smokers. Of the female students,80 are smokers and 720 are nonsmokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Solution:
Let, X denote the number of non-smoker male students and Y denote the number of non-smoker female students.
It is provided that:
X' = 178
X = 712
Tx = 890
Y' = 80
Y = 720
Ty = 800
Compute the probability of selecting a non-smoker male student as follows:
[tex]P (\text{Non-smoker Male student})=\frac{712}{890}=0.80[/tex]
Compute the probability of selecting a non-smoker female student as follows:
[tex]P (\text{Non-smoker Female student})=\frac{720}{800}=0.90[/tex]
Compute the probability that both the male and female student are non-smokers as follows:[tex]P(\text{Non-smoker Male and Female})=P(\text{Non-smoker Male})\times P(\text{Non-smoker Female})[/tex]The event of any female student being a non-smoker is independent of the male students.
[tex]P(\text{Non-smoker Male and Female})=0.80\times 0.90[/tex]
[tex]=0.72[/tex]
Thus, the probability that both the male and female student are non-smokers is 0.72.
What is the square root of -1?
uhh there is no such thing because -1 isn't a perfect square.
plz answer this asap
Answer: 20
Step-by-step explanation: 5 times 4 is 20 times 2 is 40, but when you divide by 1/2 you drop down to 20.
Write the ratio 70:80 in its simplest form
Answer:
7/8!
Step-by-step explanation:
They both can be divided by 10, so do just that. Then you are left with 7/8 which cannot be simplified.
The ratio 70:80 in its simplest form is equal to 7:8.
To simplify the ratio 70:80, we need to find the greatest common divisor (GCD) of the two numbers and then divide both numbers by the GCD.
Step 1: Find the GCD of 70 and 80:
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
The common factors of 70 and 80 are 1, 2, 5, and 10. The greatest common divisor (GCD) is 10.
Step 2: Divide both numbers by the GCD (10):
70 ÷ 10 = 7,
80 ÷ 10 = 8.
In summary, the ratio 70:80 can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 10. After simplification, the ratio becomes 7:8. Simplifying ratios involves dividing both parts of the ratio by the greatest common factor to express the ratio in its simplest and most concise form.
This makes it easier to understand and work with the relationship between the quantities being compared. In this case, the simplified ratio tells us that for every 7 units of the first quantity, there are 8 units of the second quantity.
To learn more about ratio click on,
https://brainly.com/question/14636942
#SPJ2
Which ratio is less than StartFraction 7 Over 15 EndFraction? StartFraction 9 Over 15 EndFraction Two-fifths Three-fifths StartFraction 24 Over 45 EndFraction
Answer:
2/5
Step-by-step explanation:
First you want to find the least common denominator, which in this case would be 15. If you multiply 2/5 by 3, you get 6/15 which is less than 7/15
Answer:
2/5
Step-by-step explanation:
I need help with all three :(
Answer:
1: Glide
2: Reflection
3: Reflection
Step-by-step explanation:
1): The first one is glide because you are just moving the triangle and not changing anything to the angle and the size.
2): The second one is a reflection because you are reflecting across an invisable line. Basicly think of it as a mirror. In the picture below, you can see the line of reflection.
3): The third one is also a reflection for the same reason as the second, (view attached image below for line of reflection.
A college job placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five. What is the sample space for the chance experiment of selecting two students at random
Answer:
Step-by-step explanation:
The following is the information provided
number of students is 5
The number of math major = 3
The number of statistic major = 2
Label math students as A, B, C
And statistic students as D, E
The total number of ways to select two students from 5 students is 10
The sample space is S = {AB,AC,BC,AD,AE,BD,BE,CD,CE,DE}
Yes , in the sample space the events are equally alike
What is the probability that both selected students are statistics majors
The selected students of statistic major are DE
the probability that both selected students are statistics majors is [tex]\frac{1}{10}[/tex]
= 1/10
What is the probability that both students are math majors
The selected students of statistic major are AC,AB,BC
the probability that both selected students are math majors is [tex]\frac{3}{10}[/tex]
= 3/10
What is the probability that at least one of the students selected is a statistics major
Number of ways to select at least one of the students selected is a statistic major is {AD,AE,BD,BE,CD,CE,DE}
the probability that at least one of the students selected is a statistics major is [tex]\frac{7}{10}[/tex]
7/10
What is the probability that the selected students have different majors
Number of ways to select students with different major is {AD,AE,BD,BE,CD,CE,}
the probability that the selected students have different majors is [tex]\frac{6}{10}[/tex]
6/10
On the map, Seattle, Portland, and Boise form a triangle whose sides are shown in the figure below. If the actual distance from Seattle to Boise is 400 miles, find the distance from Seattle to Portland.
Answer:
150 miles
Step-by-step explanation:
If the distance between Seattle and Boise is 400 miles and the image illustrates 4", then there must be a proportionate between the two values. Therefore, if the distance between Seattle and Portland is 1.5", then the real distance must be 150 miles.
Solve for x using the quadratic formula x^2-6x +9=0
Answer:
3 both ways x = 3
EXPLANATION:
plug in inputs and do a little simplifying we get
x = 6 ± √(36-36) all of that over 2
So we simplify and we get 6±sqrt(0) / 2
Then we get 6/2 = 3
x-0 = x+0
thats why there is only one answer
Answer:
The value of X is 3
Step-by-step explanation:
x²-6x+9=0
x²- 3x - 3x + 9= 0
X(x-3) -3(x-3)=0
(x-3) (x-3)=0
(x-3)²=0
(x-3)=0
x-3 = 0
X= 3
What is the gcf of 96x5 and 64x2
Answer:
The GCF is going to be 32
Answer:
32x^2
Step-by-step explanation:
B on edge
Ben scores 56 out of 79 marks in a maths test.
what is his score as a percentage to one decimal place
What are the next two numbers in the pattern of numbers; 45, 15, 44, 17, 40, 20, 31, 25, ...
Answer:
15, 33
(if I'm not wrong, it should work this way)
Five people have just won a $100 prize, and are deciding how to divide the $100 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $50 to first person and $10 to the second is different from vice versa. (a) How many ways are there to divide up the $100, such that each gets at least $10?
Answer:
give $20 to each person
Step-by-step explanation:
What is equal to 5x when x is equal 50
Answer:
250
Step-by-step explanation:
if x=50
5(x)=5*50=250
Hope it helps..Pls mark as Brainliest!!
Please answer this correctly
Answer:
d = 4
Step-by-step explanation:
Using the formula
A=pq/2
Dont for get to click THANKS
John has grades of 82 and 98 on his first two history tests. What must he score on his third test so that his average is at least 88?
John's average on all three tests, assuming a score of S on the third test, would be
(82 + 98 + S)/3
He wants the average to be at least 88, so solve the inequality:
(82 + 98 + S)/3 ≥ 88
82 + 98 + S ≥ 264
180 + S ≥ 264
S ≥ 84
So John needs to obtain a grade of at least 84 on the third test to get the average he wants.
The score on his third test is 84 so that his average is at least 88 given first two grades 82 and 98. This can be obtained by using the formula to find average.
What is the formula to find average?Average of observations is the ratio of sum of observations to total number of observations.
How do we find the third grade using average formula?
Grade of first test=82
Grade of second test = 98
let grade of third test be x
Average of the grades = [tex]\frac{82+98+x}{3}[/tex] ≥ 88
[tex]\frac{180+x}{3}[/tex] ≥ 88 ⇒ x ≥ 246-180 ⇒ x ≥ 84
Hence we can say that the score on his third test is 84 so that his average is at least 88 given first two grades 82 and 98.
Learn more about averages here:
brainly.com/question/19004665
#SPJ2
A Realtor claims that no more than half of the homes he sells are sold for less than the asking price. When reviewing a random sample of 14 sales over the past year, he found that actually 10 were sold below the asking price.
Required:
a. The assumption of normality is justified.
b. Calculate a p-value for the observed sample outcome, using the normal distribution.
c. At the 0.05 level of significance in a right-tailed test, is the proportion of homes sold for less than the asking price greater than 50%?
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions. CHECK ALL THAT APPLY
Answer:
A. it would be shifted up
Step-by-step explanation:
Y=MX+B
B is the Y-intercept.
Answer:
a. it would be shifted up
Step-by-step explanation:
the difference between the original and the new function is that the b value is changed from -6 to +8, meaning the y-intercept value has increased. this would shift the graph up by 14.
4x+6y=-10 8x+10y=-26 solve the system of the linear equation
Now by using equation 1 in equation 2 we get,
[tex]4x + 5y = - 13 \\ \\ 4( \frac{ - 5 - 3y}{2} ) + 5y = - 13 \\ \\ \frac{ - 20 - 12y}{2} + 5y = - 13 \\ \\ \frac{ - 20 - 12y + 10y}{2} = - 13 \\ \\ - 20 - 2y = - 26 \\ \\ - 2y = - 26 + 20 \\ \\ - 2y = - 6 \\ \\ y = 3[/tex]Now upon using the value of y in equation 1, we get
[tex]x = \frac{ - 5 - 3y}{2} \\ \\ x = \frac{ - 5 - 3 \times 3}{2} \\ \\ x = \frac{ - 5 - 9}{2} \\ \\ x = \frac{ - 14}{2} = - 7[/tex]Ben bought 4 volleyballs and 5 footballs for $352.65 altogether. If Ben’s brother bought 2 volleyballs and 4 footballs for $249.12 altogether, what was the price of each football?
Answer:
$48.53
Step-by-step explanation:
The purchases can be written in equation form as ...
4v +5f = 352.65
2v +4f = 249.12
Doubling the second equation and subtracting the first gives ...
2(2v +4f) -(4v +5f) = 2(249.12) -(352.65)
3f = 145.59 . . . . simplify
f = 48.53 . . . . . . divide by 3
The price of each football was $48.53.
Identify which of the following is NOT equivalent to 2 3/4
Answer:
Step-by-step explanation:
mabey its c
The equation which is equivalent to [tex]2^{\frac{2}{3} }[/tex] will be equal to [tex]\sqrt[4]{2^3}[/tex]. Hence, option C is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
[tex]2^{\frac{2}{3} }[/tex] = 1.68
Now, let's check the options,
A.
[tex](2^{\frac{1}{4} } )^{\frac{1}{2} }[/tex] = 1.09 ≠ 1.68, hence this is incorrect.
B.
[tex]2\frac{1}{4}*2\frac{1}{2}[/tex] = 9/4 × 5/2 = 5.625 ≠ 1.68, hence, this is incorrect.
C.
[tex]\sqrt[4]{2^3}[/tex] = 1.68 = 1.68, hence, this is correct.
D.
√8 = 2.82 ≠ 1.68, hence, this is incorrect.
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ5
