[tex]L= (-2, 2, 8) \\
B= (-2, 1, 2, 4, 8) \\ L \: n \: B \: = \: ( - 2, 2, 8) \\ L \: u \: B = ( - 2, 2, 1, 4, 8)[/tex]
Can somebody help me with this question
Answer:
93 ft
Step-by-step explanation:
the area of a triangle is :
A = (b*h)/2 where b is the base and h the height(here t)
4092 = (88*t)/2
2*4092 = 88*t
t= (4092*2)/88 = 93 ft
20. The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of units over the ten-year span, (number of units sold, profit) for specific recorded years: (46,250), (48, 305), (50,350), (52, 390), (54, 410) a) Use linear regression to determine a function y, where profit in thousands of dollars depends on the number of units sold in hundreds. b) Predict when the profit will exceed one million dollars.
Answer:
20
Step-by-step explanation:
The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given pair of (number of units sold y, profit x)
Linear equation slope and y-intercept
A linear equation or function is given as ;
y = mx + c
Here, c is the y-intercept and m is the slope.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope m = (y₂ - y₁)/(x₂ - x₁)
Therefore slope of (46,250), (48, 305)
m = (305 - 250)/(48 - 46) = 27.5
Put, m = 27.5 and (46,250)
250 = 27.5(46) + c
c = -1015
y = 27.5x - 1015
Hence "The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015".
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Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity. Please see picture attached.
Answer:
see attached
Step-by-step explanation:
The limit as x gets large is the ratio of the highest-degree terms. In most cases, the limit can be found by evaluating that ratio. Where an absolute value is involved, the absolute value of the highest-degree term is used.
If the ratio gives x to a positive power, the limit does not exist. If the ratio gives x to a negative power, the limit is zero.
The arrangement of functions according to the given condition
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
[tex]h(x)=\frac{x^{3} -x^{2} +4}{1-3x^{2} }[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]i(x)=\frac{x-1}{|1-4x| }[/tex]
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
[tex]f(x)=\frac{x^{2} -1000}{x-5}[/tex]
[tex]j(x)=\frac{x^{2}-1 }{|7x-1|}[/tex]
What is limit?A limit is the value that a function approaches as the input approaches some value.
According to the given question
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
⇒[tex]\lim_{nx\to \infty} \frac{5x^{2} -1}{x^{2} +1}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} }{x^{2} } \frac{5-\frac{1}{x^{2} } }{1+\frac{1}{x^{2} } }[/tex]
= 5 ([tex]\frac{1}{x^{2} } = 0[/tex] ,as x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0)
[tex]i(x)=\frac{x-1}{|1-4x|}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x-1}{|1-4x|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{1-\frac{1}{x} }{|\frac{-1}{4}+\frac{1}{x} | }[/tex] =[tex]\frac{1}{\frac{1}{4} }[/tex] =[tex]\frac{1}{4}[/tex]
As x tends to infinity 1/x tends to 0, and |[tex]\frac{-1}{4}[/tex]| gives 1/4
[tex]f(x)= \frac{x^{2} -1000}{x--5}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} -1000}{x-5}[/tex]= [tex]\lim_{x \to \infty} \frac{x^{2} }{x} \frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex]= [tex]\lim_{x \to \infty} x\frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex] ⇒ limit doesn't exist.
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
⇒[tex]\lim_{x\to \infty} \frac{4x^{2} -6}{1-4x^{2} }[/tex]=[tex]\lim_{x\to \infty} \frac{x^{2} }{x^{2} } \frac{4-\frac{6}{x^{2} } }{\frac{1}{x^{2} } -4}[/tex] [tex]= \lim_{n \to \infty} \frac{4}{-4}[/tex] = -1
As x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0.
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
⇒[tex]\lim_{x\to \infty} \frac{|4x-1|}{x-4}[/tex] = [tex]\lim_{x \to \infty} \frac{|x|}{x} \frac{4-\frac{1}{x} }{1 -\frac{4}{x} } }[/tex] = 4
as x tends to infinity 1/x tends to 0
and |x|=x ⇒[tex]\frac{|x|}{x}=1[/tex]
[tex]h(x)=\frac{x^{3}-x^{2} +4 }{1-3x^{3} }[/tex][tex]\lim_{x \to \infty} \frac{x^{3} -x^{2} +4}{1-3x^{3} }[/tex][tex]= \lim_{x \to \infty} \frac{x^{3} }{x^{3} } \frac{1-\frac{1}{x}+\frac{4}{x^{3} } }{\frac{1}{x^{3} -3} }[/tex] = [tex]\frac{1}{-3}[/tex] =[tex]-\frac{1}{3}[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]\lim_{x \to \infty} \frac{5x+1000}{x^{2} }[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{5+\frac{1000}{x} }{x}[/tex] =0
As x tends to infinity 1/x tends to 0
[tex]j(x)= \frac{x^{2}-1 }{|7x-1|}[/tex]
[tex]\lim_{x \to \infty} \frac{x^{2}-1 }{|7x-1|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{|x|}\frac{x-\frac{1}{x} }{|7-\frac{1}{x}| }[/tex] = [tex]\lim_{x \to \infty} 7x[/tex] = limit doesn't exist.
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If f(x)=2x−1, show that f(f(x))=4x−3. Find f(f(f(x))).
Answer: f(f(f(x)))=8x-7
Step-by-step explanation:
Since we were given f(x) and f(f(x)), We plug that into f(x) again to get f(f(f(x))).
2(4x-3)-1 [distribute]
8x-6-1 [combine like terms]
8x-7
Find an equation of the tangent line to the curve at the given point.x2+2xy−y2+x=101, (7,9) (hyperbola)
Answer:
The equation of the tangent line of the given curve
[tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]
The tangent of the given curve at the point
[tex](\frac{dy}{dx})_{(7,9)} = \frac{33}{4}[/tex]
Step-by-step explanation:
Explanation :-
Step(i):-
Given equation of the parabola
x²+2xy−y²+x=101 ...(i)
apply derivative Formulas
a) [tex]\frac{dx^{n} }{dx} = n x ^{n-1}[/tex]
b) [tex]\frac{d U V }{dx} = U \frac{dV}{dx} + V \frac{dU}{dx}[/tex]
Step(ii):-
Differentiating equation (i) with respective to 'x' , we get
[tex]2 x + 2 ( x \frac{dy}{dx} + y) - 2 y \frac{dy}{dx} +1 = 0[/tex]
[tex]2 x + 2 x \frac{dy}{dx} +2 y - 2 y \frac{dy}{dx} +1 = 0[/tex]
on simplification , we get
[tex]( 2 x - 2 y) \frac{dy}{dx} = - (2x +2y +1)[/tex]
[tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]
The tangent of the given curve at the point ( 7,9)
[tex](\frac{dy}{dx})_{(7,9)} = \frac{- ((2(7) +2(9) +1))}{( 2 (7) - 2 (9)}[/tex]
[tex](\frac{dy}{dx})_{(7,9)} = \frac{- (33)}{( -4} = \frac{33}{4}[/tex]
Final answer :-
The equation of the tangent line of the given curve
[tex]\frac{dy}{dx} = \frac{- (2x +2y +1)}{( 2 x - 2 y)}[/tex]
The tangent of the given curve at the point
[tex](\frac{dy}{dx})_{(7,9)} = \frac{33}{4}[/tex]
Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection? Use the table of randomly generated outcomes to answer the question. Each letter represents the first letter of the bead color.
Step-by-step explanation:
Given that Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. We are to calculate the probability that Rita will need to pick atleast 5 beads before she picks a grey bead from her collection.
Prob for drawing atleast 5 beads before she picks a grey bead from her collection
= 1-Prob for drawing atleast one grey beed in the first 5 draws.
(Because these two are complementary events)
no of grey beeds drawn in first 5 trials is
Bi=(5,1/6)
Prob for drawing atleast one grey beed in the first 5 draws.
=1-Prob of no grey
Hence required prob=P(X=0 in first 5 draws)
= 0.4018
6th beeds onwards can be grey also.
Nearest answer is c)0.45
Answer:
o.45
Step-by-step explanation:
i just did the test
Now that we have our linear regression model, let’s try to make a prediction for the sales given a new set of advertising budgets as follows: new.dat <- data.frame(TV=200, Radio=10, Newspaper=20) You are required to report the predicted sales as well as the lower and upper bound for the 95% prediction interval. What will you report?
Answer:
The predicted sales for the new set of advertising budgets is 14.
Step-by-step explanation:
The linear regression model is:
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
Compute the value of sales for:
TV = 200,
Radio = 10,
Newspaper = 20
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
[tex]=2.9389+0.0458\cdot(200)+0.1885\cdot(10)-0.0010\cdot(20)\\=2.9389+9.16+1.885-0.0002\\=13.9837\\\approx 14[/tex]
Thus, the predicted sales for the new set of advertising budgets is 14.
Which side lengths form a right triangle?
Answer:
B) 1, 8, √65
Step-by-step explanation:
For 3 side lengths to form a triangle the sum of two random sides must be bigger than the third side and their differences must be smaller than the third side.
1+8 > √65 because √65 is approximately 8.1
8-1 < √65
Answer:
B. 1,8,(65)½
Step-by-step explanation:
For the side lengths to form a right triangle they have to obey the Phythagorean Theorem which when paraphrased says " the square of the longer side is equal to the sum of the squares of the other sides"
A . 2² + 15² = 4 + 225 = 229
17² = 289
Not a Phythagorean triple
B. 1² + 8² = 1 + 64 = 65
(65½)² = 65
A Phythagorean triple
C. 2² + (80½)² = 4 + 80 = 84
9² = 81
Not a Phythagorean triple.
Which of the following is a negation for "There exists a real number x such that for all real numbers y, xy > y."1) There exists a real number x such that for all real numbers y, xy ≤ y.2) There exists a real number y such that for all real numbers x, xy ≤ y.3) There exists real numbers x and y such that xy ≤ y.4) For all real numbers x there exists a real number y such that xy ≤ y.5) For all real numbers y there exists a real number x such that xy ≤ y.
Answer:
1) There exists a real number x such that for all real numbers y, xy ≤ y.
Step-by-step explanation:
Given the statement:
"There exists a real number x such that for all real numbers y, xy > y"
The negation of the statement is:
"There exists a real number x such that for all real numbers y, xy ≤ y"
The correct option is 1
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Rewrite the following equation in the form y = a(x - h)2 + k. Then, determine the x-coordinate of the minimum.
y = 2x2 - 32x + 56
The rewritten equation is y =
(x -
)2 +
.
The x-coordinate of the minimum is
.
Answer:
Therefore the x - coordinate of the minimum is x = -8
Step-by-step explanation:
[tex]y = 2x^2 + 32x + 56 = 2(x^2 + 16x ) + 56 = 2(x^2 + 16x +64 - 64) + 56 \\= 2(x^2 + 16x +64) - 128 + 56 = 2(x+8)^2 - 72[/tex]
Therefore the x - coordinate of the minimum is x = -8
According to a government commision, 70% of all the nation’s households have vcrs. In a random sample of 15 households, what is the probability that exactly 10 have vcrs
Answer: P(10,15,0.7)=3003*0.7^10*0.3^5=approx 0.2061
Step-by-step explanation:
The required probability P(10,15,0.7)= C15 10 *p^10*q^(15-10) where
C15 10= 15 !/10!/5!= 11*12*13*14*15/(2*3*4*5)=11*12*13*14/(2*4)=11*3*13*7=
=77*39=3003
p=0.7 q=1-p =1-0.7= 0.3 (probability of not having vcrs)
So P(10,15,0.7)=3003*0.7^10*0.3^5=approx 0.2061
1. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Berwick sample is________.
a. 60
b. 75
c. 80
d. 90
2. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Milton sample is________.
a. 60
b. 75
c. 80
d. 90
3. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Leesburg sample is________.
a. 60
b. 75
c. 80
d. 90
4. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square test statistic for these samples is_______.
a. 1.49
b. 2.44
c. 4.15
d. 5.33
5. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The degrees of freedom for the chi-square critical value is_______.
a. 1
b. 2
c. 3
d. 4
6. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square critical value using alpha = 0.05 is_______.
a. 2.706
b. 3.841
c. 5.991
d. 7.815
7. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
Using alpha = 0.05, the conclusion for this chi-square test would be that because the test statistic is
A. More than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
B. Less than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
C. More than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
D. Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Answer:
1) Option B is correct.
Expected frequency of satisfied customers from the Berwick sample = 75
2) Option D is correct.
Expected frequency of satisfied customers from the Milton sample = 90
3) Option A is correct.
Expected frequency of satisfied customers from the Leesburg sample = 60
4) Option B is correct.
The chi-square test statistic for these samples = 2.44
5) Option B is correct.
The degrees of freedom for the chi-square critical value = 2
6) Option C is correct.
The chi-square critical value using alpha = 0.05 is 5.991
7) Option D is correct.
The conclusion for this chi-square test would be that because the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Step-by-step explanation:
Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Since this is a chi test that aims to check if there are differences in the proportion of expected number of customers for each location, we state the null and alternative hypothesis first.
The null hypothesis usually counters the claim we hope to test and would be that there is no difference between the proportion of expected frequency of satisfied customers at the three locations.
The alternative hypothesis confirms the claim we want to test and is that there is a significant difference between the proportion of expected frequency of satisfied customers at the three locations.
So, the total proportion of satisfied customers is used to calculate the expected number of satisfied customers for each of the three locations.
80+85+60= 225
Total number of customers = 100 + 120 + 80 = 300
Proportion of satisfied customers = (225/300) = 0.75
1) Expected frequency of satisfied customers from the Berwick sample = np = 100 × 0.75 = 75
2) Expected frequency of satisfied customers from the Milton sample = np = 120 × 0.75 = 90
3) Expected frequency of satisfied customers from the Leesburg sample = np = 80 × 0.75 = 60
4) Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Proportion for unsatisfied ccustomers = 0.25
So, expected number of unsatisfied customers for the three branches are 25, 30 and 20 respectively.
Chi square test statistic is a sum of the square of deviations from the each expected value divided by the expected value.
χ² = [(X₁ - ε₁)²/ε₁] + [(X₂ - ε₂)²/ε₂] + [(X₃ - ε₃)²/ε₃] + [(X₄ - ε₄)²/ε₄] + [(X₅ - ε₅)²/ε₅] + [(X₆ - ε₆)²/ε₆]
X₁ = 80, ε₁ = 75
X₂ = 85, ε₂ = 90
X₃ = 60, ε₃ = 60
X₄ = 20, ε₄ = 25
X₅ = 35, ε₅ = 30
X₆ = 20, ε₆ = 20
χ² = [(80 - 75)²/75] + [(85 - 90)²/90] + [(60 - 60)²/60] + [(20 - 25)²/25] + [(35 - 30)²/30] + [(20 - 20)²/20]
χ² = 0.3333 + 0.2778 + 0 + 1 + 0.8333 + 0 = 2.4444 = 2.44
5) The degree of freedom for a chi-square test is
(number of rows - 1) × (number of columns - 1)
= (2 - 1) × (3 - 1) = 1 × 2 = 2
6) Using the Chi-square critical value calculator for a degree of freedom of 2 and a significance level of 0.05, the chi-square critical value is 5.991.
7) Interpretation of results.
If the Chi-square test statistic is less than the critical value, we fail to reject the null hypothesis.
If the Chi-square test statistic is unusually large and is greater than the critical value, we reject the null hypothesis.
For this question,
Chi-square test statistic = 2.44
Critical value = 5.991
2.44 < 5.991
test statistic < critical value
The test statistic is Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Hope this Helps!!!
[PLEASE HELP] Each of these statements describe a transformation of a graph of y = x, The which of the statements correctly describe the graph of y =x + 7???
Answer:
B
Step-by-step explanation:
Adding the 7 to the input (x) will increase the output (y) by 7. Therefore, the graph is translated 7 units up.
Answer:
The answer is B
Step-by-step explanation:
well the equation of a line is : y = mx + b
in this question the equation is y = x
so the line y = x +7 will be 7 units up than y = x
Please help me with this question!!
Answer:
rationalirrationalirrationalirrational√7, it is irrationalStep-by-step explanation:
A rational number is one that can be expressed as the ratio of two integers. All fractions that have integer numerators and (non-zero) denominators are rational numbers. Any finite decimal number, or any repeating decimal number, is a rational number. These can always be expressed as the ratio of two integers. For example, 0.4040... = 40/99, and 0.286 = 286/1000.
To make an irrational sum, at least one of the contributors must be irrational. You want an irrational 2-number sum that has 7/8 as one of the contributors. Since 7/8 is rational, the other contributor must be irrational.
__
Step 1. The number 7/8 is rational.
Step 2. The desired sum is irrational.
Step 3. The rule rational + irrational = irrational applies.
Step 4. An irrational number must be chosen.
Step 5. √7 will produce an irrational sum, because it is irrational.
Want Brainliest? Get this correct Which of the following is the product of the rational expressions shown below?
We multiply the numerators together to get x*2x = 2x^2 as the numerator for the answer.
The denominators pair up and multiply to get (x-5)(x+4) = x^2+4x-5x-20 = x^2-x-20. You can use the distributive property, FOIL, or the box method to expand out (x-5)(x+4)
So that's how we end up with (2x^2) all over (x^2-x-20) as the answer.
Work out the surface area of this sphere.
Give your answer to 1 decimal place.
Answer:
452.4
Step-by-step equation:
surface area of a sphere formula= 4πr²
plug 6 in for r
4π(6)² =452.389 rounded to 452.4
Which is a possible paycheck deduction? Select all that apply.
commission
federal income tax
health insurance premium
overtime hours
state income tax
Answer:
Federal income taxes, health insurance premium, state income tax
Step-by-step explanation:
Commission may be a bonus from a sale you made and overtime hours are extra hours over 40.00 that you worked during the week
2 things are certain in life death and taxes
A tank contains 4,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 40 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 30 minutes? (Round your answer to one decimal place.
Answer:
(a)[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]
(b)13.3 kg
Step-by-step explanation:
The volume of brine in the tank = 4000L
Initial Amount of salt, A(0)=18 kg
The rate of change in the amount of salt in the tank at any time t is represented by the equation:
[tex]\dfrac{dA}{dt}=$Rate In$-$Rate Out[/tex]
Rate In = (concentration of salt in inflow)(input rate of brine)
Since pure water enters the tank, concentration of salt in inflow =0
Rate In = 0
Rate Out=(concentration of salt in outflow)(output rate of brine)
[tex]=\frac{A(t)}{4000}\times 40\\ =\frac{A(t)}{100}[/tex]
Therefore:
[tex]\dfrac{dA}{dt}=-\dfrac{A(t)}{100}\\\dfrac{dA}{dt}+\dfrac{A(t)}{100}=0[/tex]
This is a linear D.E. which we can then solve for A(t).
Integrating Factor: [tex]e^{\int \frac{1}{100}d}t =e^{ \frac{t}{100}[/tex]
Multiplying all through by the I.F.
[tex]\dfrac{dA}{dt}e^{ \frac{t}{100}}+\dfrac{A(t)}{100}e^{ \frac{t}{100}}=0e^{ \frac{t}{100}}\\(Ae^{ \frac{t}{100}})'=0[/tex]
Taking integral of both sides
[tex]Ae^{ \frac{t}{100}}=C\\A(t)=Ce^{ -\frac{t}{100}}[/tex]
Recall our initial condition
A(0)=18 kg
[tex]18=Ce^{ -\frac{0}{100}}\\C=18[/tex]
Therefore, the amount of salt in the tank after t minutes is:
[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]
(b)When t=30 mins
[tex]A(30)=18e^{ -\frac{30}{100}}\\=18e^{ -0.3}\\=13.3 $kg(correct to 1 decimal place)[/tex]
The amount of salt in the tank after 30 minutes is 13.3kg
In this exercise we have to use the integral to calculate the salt concentration:
(a)[tex]A(t)=18e^{-\frac{t}{100} }[/tex]
(b)[tex]13.3 kg[/tex]
Knowing that the volume of brine in the tank = 4000L, the initial Amount of salt, A(0)=18 kg. The rate of change in the amount of salt in the tank at any time t is represented by the equation:
[tex]\frac{dA}{dt} = Rate \ in - Rate \ out[/tex]
Rate In = (concentration of salt in inflow)(input rate of brine). Since pure water enters the tank, concentration of salt in inflow =0.
Rate In = 0
Rate Out=(concentration of salt in outflow)(output rate of brine)
[tex]\frac{A(t)}{4000}*(40)[/tex]
[tex]= \frac{A(t)}{100}[/tex]
Therefore:
[tex]\frac{dA}{dt} = \frac{A(t)}{100}\\\frac{dA}{dt} + \frac{A(t)}{100} = 0[/tex]
This is a linear D.E. which we can then solve for A(t). Integrating Factor: [tex]e^{\int\limits {\frac{t}{100} } \, dt\\e^{t/100}[/tex] . Multiplying all through by the Integrating Factor:
[tex]\frac{dA}{dt} = e^{t/100}+\frac{A(t)}{100}e^{t/100}\\(Ae^{1/100})'=0[/tex]
Taking integral of both sides:
[tex]Ae^{t/100}=C\\A(t)=Ce^{-t/100}[/tex]
Recall our initial condition:
[tex]A(0)=18 kg\\18=Ce^{0}\\C=18[/tex]
Therefore, the amount of salt in the tank after t minutes is:
[tex]A(t)=18e^{-t/100}[/tex]
(b)When t=30 mins
[tex]A(30)=18e^{-30/100}\\=18e^{-0.3}\\=13.3[/tex]
The amount of salt in the tank after 30 minutes is 13.3kg.
See more about concentration at brainly.com/question/12970323
Number of non sqaure number are there between 36² and 37²
Answer:
A 1,296
B 1,369
36 answer
Assume that the profit generated by a product is given by where x is the number of units sold. If the profit keeps changing at a rate of per month, then how fast are the sales changing when the number of units sold is 1900
Answer:
21794.495 units/month
Step-by-step explanation:
Some data are missing which i can assume as per requirement of the Question.
Let us consider that profit generated by a product is given by
p(x) =4√x
Also, consider that the profit keeps changing at a rate of $1000 per month.
Now, Using the chain rule we can write
dp/dx=(dp/dt)÷(dx/dt).
So, we can calculate
dp/dx=2x^(-1/2)=2/√x.
As per question we have to find out dx/dt
Since, dx/dt= (dp/dt)/(dp/dx),
so plugging x=1900 we get 1000√1900/2=21794.495 units/month increase in sales.
Find the value of c such that the three points (5,5), (-3,1), and (6,c) lie on the same line. Note: Three points are on the same line if the slope of the line through any two points is always the same.
Answer:
c = 5.5
Step-by-step explanation:
We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:
-4/-8 = 1/2
Now, we can plug in the slope and a point into the equation y = mx + b to find b:
5 = 1/2(5) + b
5 = 2.5 + b
2.5 = b
Then, we can plug in 6 in the point (6,c) to find c:
y = (1/2)(6) + 2.5
y = 3 + 2.5
y = 5.5
c = 5.5
Answer:
c = 5.5
Step-by-step explanation:
Find the slope with two points
m = (y2-y1)/(x2-x1)
m = (1-5)/(-3-5)
= -4/-8
= 1/2
If all the points are on the same line, then they have the same slope
m = (y2-y1)/(x2-x1)
Using the first and third points
1/2 = (c-5)/(6-5)
1/2 = (c-5)/1
1/2 = c-5
Add 5 to each side
5+1/2 = c
5.5 =c
make d the subject of the formula; n=k/d^2
Answer:
[tex]n = \frac{k}{ {d}^{2} } [/tex]
[tex] {d}^{2} = \frac{k}{n} [/tex]
[tex]d = \sqrt{ \frac{k}{n} } [/tex]
Here is the required firmula....Answer:
d = √(k/n)
Step-by-step explanation:
n = k/d²
n/1 = k/d²
Cross multiply.
k = nd²
Divide both sides by n.
k/n = nd²/n
k/n = d²
Take the square root on both sides.
√(k/n) = √(d²)
√(k/n) = d
Which point is located at (Negative 3.5, Negative 4.5)? On a coordinate plane, point A is 3.5 units to the left and 4.5 units down. Point K is 3.5 units to the right and 4.5 units up. Point R is 3.5 units to the left and 4.5 units up. Point Y is 4.5 units to the left and 3.5 units down. point A point K point R point Y
Answer:
Point A
Step-by-step explanation:
We know that on a coordinate plane, negative numbers can be found by moving down or moving to the left. This point must be found by moving down and left. To establish whether it is point A or point Y, we can remember that x coordinates move left and right and y coordinates move up and down. So, we would need to move 3.5 units left for x and then 4.5 units down for y. This leads us to point A.
hope this helps!
Answer:
it is point A
Step-by-step explanation:
forex is the name of the U.S. stock exchange.
-true
-false
Answer:
false
Step-by-step explanation:
hello
this is false
FOREX means Foreign Exchange
it refers to the foreign exchange market
hope this helps
Answer:
true, forex trading is a profitable than staking cryptocurrency. forex trading is the best thing I will refer someone I love because learning never stops and no on is above blowing accounts when beginning Forex
is 0.790 greater than or equal to 0.79?
It's the same vallue. If they were different, i could argue that 2.000 is greater than 2.00. Impossible, because 2 is equal to 2.
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 12 cm. Find the area of the shaded region.
Use the value 3.14 for at, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
15.48 ft^2
Step-by-step explanation:
According to the image we have the following information:
the length of the rectangle = diameter of the semicircle, therefore it is 12 feet
, the radius of the semicircle (half the diameter) = width of the rectangle = 12/2 ft = 6 ft
We also know that the area of the shaded region would be equal to the area of the rectangle minus the area of the semicircle.
Therefore, we replace:
Area of the rectangle = width * length
Ar = 6 ft * 12 ft = 72 ft ^ 2
Area of the semicircle = [1/2] * π * (r ^ 2)
As = [1/2] * 3.14 * (6 feet) ^ 2 = 56.52 ft ^ 2
We replace in the area of the shaded region
shaded region area = 72 ft ^ 2 - 56.52 ft ^ 2 =
Shaded region area = 15.48 ft ^ 2
A rookie quarterback is negotiating his first NFL contract.His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:________.
1 2 3 4
Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000
Contract 2 $2,000,000 $3,000,000 $4,000,000 $5,000,000
Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000
As his advisor, which contract would you recommend that he accept?
Answer:
He should accept contract 2 because it has a higher present value.
Step-by-step explanation:
we need to find the present value of each contract:
Contract 1 = $3,000,000/1.1 + $3,000,000/1.1² + $3,000,000/1.1³ + $3,000,000/1.1⁴ = $2,727,273 + $2,479,339 + $2,253,944 + $2,049,040 = $9,509,596
Contract 2 $2,000,000/1.1 + $3,000,000/1.1² $4,000,000/1.1³ + $5,000,000 /1.1⁴ = $1,818,182 + $2,479,339 + $3,005,259 + $3,415,067 = $10,717,847
Contract 3 $7,000,000/1.1 + $1,000,000/1.1² + $1,000,000/1.1³ + $1,000,000/1.1⁴ = $6,363,636 + $826,446 + $751,315 + $683,013 = $8,624,410
Nine balls, each marked with a number from 1 to 9, are placed in a bag and one
Ball is taken out at random. What is the probability that the number on the ball is:
(a) odd, (b) a multiple of 3, (c) 5, (d) not a 7
Answer:
a =5/9 b=1/3 c=1/9 d=8/9
Step-by-step explanation:
there are total 9 numbers
in a
there are 5 odd numbers
in b
there are 3 multiplier of 3
in c
there is only one 5
in d
there are 8 numbers except 7
a) 5/9 b) 1/3 c) 1/9 d) 8/9
Step-by-step explanation:
a) odd numbers between 1 to 9 are 1,3,5,7,9. so there are 5 odd numbers.
total balls are 9
=> probability is 5/9
b) multiples of 3 = 3, 6,9 there are 3 numbers.
=> probability is = 3/9 = 1/3
c) 5. only one 5 is there between 1 to 9 numbers.
=> probability is 1/9
d) not a 7.
removing 7. there will 8 numbers.
=> probability is 8/9
Express the confidence interval (0.036, 0.086) in the form of p-e< p
Answer:
p-e< p < p+e
(0.061 - 0.025) < 0.061 < (0.061 + 0.025)
0.036 < 0.061 < 0.086
Step-by-step explanation:
Given;
Confidence interval CI = (a,b) = (0.036, 0.086)
Lower bound a = 0.036
Upper bound b = 0.086
To express in the form;
p-e< p < p+e
Where;
p = mean Proportion
and
e = margin of error
The mean p =( lower bound + higher bound)/2
p = (a+b)/2
Substituting the values;
p = (0.036+0.086)/2
Mean Proportion p = 0.061
The margin of error e = (b-a)/2
Substituting the given values;
e = (0.086-0.036)/2
e = 0.025
Re-writing in the stated form, with p = 0.061 and e = 0.025
p-e< p < p+e
(0.061 - 0.025) < 0.061 < (0.061 + 0.025)
0.036 < 0.061 < 0.086
Phil Nelson deposited $35,000 at Wachovia Bank at 3.5% interest
compounded quarterly. How much money will be in this account at
the end of the year?
Answer:
$36,241.20
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Since we are given P, r, n, and t, simply plug it into the formula:
A = 35000(1 + 0.035/4)⁴⁽¹⁾
A = 35000(1 + 0.00875)⁴
A = 35000(1.00875)⁴
A = 35000(1.03546)
A = 36241.2