Answer:
[tex]\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]
Step-by-step explanation:
Volume of water in the tank = 1000 L
Let y(t) denote the amount of salt in the tank at any time t.
Initially, the tank contains 60 kg of salt, therefore:
y(0)=60 kg
Rate In
A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.
[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of solution)
[tex]=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}[/tex]
Rate Out
The solution is mixed and drains from the tank at the same rate.
Concentration, [tex]C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}[/tex]
[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)
[tex]=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}[/tex]
Therefore, the differential equation for the amount of Salt in the Tank at any time t:
[tex]\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]
A cell phone company
charges a $20 fee every
month and $0.01 for ten
minutes spent talking on
the phone. Write an
equation to model the cost
of a monthly cell phone bill
for the linear function.
Answer:
C = 20 + 0.001x
C = $20 + $0.001x
Step-by-step explanation:
Let x represent the number of minutes spent talking on the phone.
Given;
Fixed monthly charge F = $20
Charge per 10 minutes V = $0.01
Charge per minute = V/10 = $0.01/10 = $0.001
The equation to model the cost of a monthly cell phone bill;
Total cost = fixed cost + variable cost
C = F + (V/10)x
Substituting the values;
C = 20 + 0.001x
how many legs totally do five horses, two people,three children and five dogs have
If a line crosses the y-axis at (0,1) and has a slope of 4/5 what is the equation of the line
Answer:
y = 4/5x + 1
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
y = 4/5x + 1
Answer:4y-5x=5
Step-by-step explanation:
Chen spent 7 hours at school on Friday he spent 30 minutes at lunch 50 minutes at a school assembly and the rest in class how much time did Chen spend in class
Answer:
5 hours and 40 minutes would be class
Step-by-step explanation:
We know that the total time is 7 hours, which in minutes would be:
7 * 60 = 420
420 minutes would be class, now, we subtract the other times that are not to be in class and it would be:
420 - 30 - 50 = 340
So we could say that in class it takes 340 minutes, and if we spend hours it would be:
340/60 = 5.67 hours or also 5 hours and 40 minutes would be class.
Find the population mean or sample mean as indicated.
Sample: 17, 11, 8, 12, 22
Answer:
mean:12
Step-by-step explanation:
The population mean or sample mean as indicated in the given samples is 14
What is mean?A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.
Mathematically,
Mean = Sum of the observations/number of observations
Now the given sample is,
17, 11, 8, 12, 22
So, Number of sample = 5
Thus, Mean = Sum of the sample /number of sample
Mean = (17 + 11 + 8 + 12 + 22) / 5
⇒ Mean = 70/5
⇒ Mean = 14
Thus, the population mean or sample mean as indicated in the given samples is 14
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Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 18 specimens of a particular species, 5 resprouted after fire. Estimate with 99.5% confidence the proportion of all shrubs of this species that will resprout after fire.
Answer:
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 18, \pi = \frac{5}{18} = 0.2778[/tex]
99.5% confidence level
So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 - 2.81\sqrt{\frac{0.2778*0.7222}{18}} = -0.01 = 0[/tex]
We cannot have a negative proportion, so we use 0.
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 + 2.81\sqrt{\frac{0.2778*0.7222}{18}} = 0.5745[/tex]
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
Please answer this correctly
Answer:
Cable: 10% Satellite: 40% Streaming Service: 50%
Step-by-step explanation:
There are 10 friends
1 has cable
4 have satellite
5 have streaming service
Which means:
Cable is 10%
Satellite is 40%
Streaming Service is 50%
Answer:
Cable Television: 10%
Satellite Television: 40%
Streaming Service: 50%
Step-by-step explanation:
Cable television: [tex]\frac{1}{1+4+5} =\frac{1}{10} =\frac{10}{100}[/tex] or 10%
Satellite television: [tex]\frac{4}{1+4+5} =\frac{4}{10} =\frac{40}{100}[/tex] or 40%
Streaming service: [tex]\frac{5}{1+4+5} =\frac{5}{10} =\frac{50}{100}[/tex] or 50%
To determine the density of grains, a student uses a 50ml beaker graded by 5ml increments and a scale with 1g absolute uncertainty. The measurement of the volume results in 3 full beakers and 1 beaker filled up to 30ml. Measured mass of a plastic container with all the grains is 185 grams; measured mass of the same container without grains is 65 grams. What is the mass of the grains
Answer:
The mass of the grains = 120 ± 1 g
Step-by-step explanation:
we are given the following:
Total mass of container + grains = 185 grams
Mass of container = 65 grams
Therefore, mass of grains is calculated as follows:
Mass of grains = ( Mass of container + grains) - mass of container
= 185 - 65 = 120 grams.
since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g
what expression are equivalent to 4(4x + 9)
Answer:
16x+36
Step-by-step explanation:
4(4x + 9)
16x+36
____________________________________
Solution,
4(4x+9)
=4*4x+4*9
=16x+36
So the answer is 16x+36
Hope it helps
Good luck on your assignment
___________________________________
CAN SOMEONE HELP ME IN THIS INTEGRAND QUESTION PLS PLS PLS PLS
''Find the surface area between the z = 1 and z = 4 planes of z = x ^ 2 + y ^ 2 paraboloid.''
Answer:
Step-by-step explanation:
Answer:
S = ⅙ π (65^³/₂ − 5^³/₂)
Step-by-step explanation:
z = x² + y², 1 < z < 4
Surface area is:
S = ∫∫√(1 + (fₓ)² + (fᵧ)²) dA
where fₓ and fᵧ are the partial derivatives of f(x,y) with respect to x and y, respectively.
fₓ = 2x, fᵧ = 2y
S = ∫∫√(1 + (2x)² + (2y)²) dA
S = ∫∫√(1 + 4x² + 4y²) dA
For ease, convert to polar coordinates.
S = ∫∫√(1 + 4r²) dA
S = ∫∫√(1 + 4r²) r dr dθ
At z = 1, r = 1. At z = 4, r = 4.
So 1 < r < 4, and 0 < θ < 2π. These are the limits of the integral.
S = ∫₀²ᵖⁱ∫₁⁴√(1 + 4r²) r dr dθ
To integrate, use u-substitution.
u = 1 + 4r²
du = 8r dr
⅛ du = r dr
When r = 1, u = 5. When r = 4, u = 65.
S = ∫₀²ᵖⁱ∫₅⁶⁵√u (⅛ du) dθ
S = ∫₀²ᵖⁱ (⅛ ∫₅⁶⁵√u du) dθ
S = ∫₀²ᵖⁱ (¹/₁₂ u^³/₂ |₅⁶⁵) dθ
S = ∫₀²ᵖⁱ (¹/₁₂ (65^³/₂ − 5^³/₂)) dθ
S = (¹/₁₂ (65^³/₂ − 5^³/₂)) θ |₀²ᵖⁱ
S = (¹/₁₂ (65^³/₂ − 5^³/₂)) (2π)
S = ⅙ π (65^³/₂ − 5^³/₂)
Determine the interest earned on a 3 and 1/4 year investment of $2880 at a rate of 4.5%
Answer:
The interest earned is $421.2.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
In this question:
[tex]P = 2880, I = 0.045, t = 3 + \frac{1}{4} = 3.25[/tex]
So
[tex]E = P*I*t[/tex]
[tex]E = 2880*0.045*3.25[/tex]
[tex]E = 421.2[/tex]
The interest earned is $421.2.
help pls take your time..
Answer:
As [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex] and as [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]
Step-by-step explanation:
Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards minus infinity).
As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)
Please help! Correct answer only, please! Jason has the following averages in his math class: homework avg: 80 quiz avg: 84 test avg: 74 final exam: 60 if the teacher weights homework at 20%, quizzes at 30%, tests at 40%, and the final exam at 10%, what is jason's class average? A. 74 B. 77 C. 79 D. 82
Answer:
77
Step-by-step explanation:
80*0.2 + 84*0.3 + 74*0.4 + 60*0.1 = 76.8 = 77
A certain car can travel on a highway for 350 miles on 15 gallons of gas and in a city for 280 miles on 18 gallons of gas. If the car uses twice as many gallons for city driving as for highway driving, what is the car's average number of miles per gallon? Express your answer to the nearest whole number.
Answer:
The car's average 18 number of miles per gallon
Step-by-step explanation:
The car has different efficiencies depending if its used on highway or city streets.
The efficiency on a highway is:
[tex]E_h=\dfrac{350}{15}\;\text{miles/gal}=23.33\;\text{miles/gal}[/tex]
The efficiency for city driving is:
[tex]E_c=\dfrac{280}{18}\;\text{miles/gal}=15.56\;\text{miles/gal}[/tex]
We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.
Then, we can calculate how many miles makes the car on average as:
[tex]E=\dfrac{1}{3}E_h+\dfrac{2}{3}E_c\\\\\\E=\dfrac{1}{3}\cdot 23.33+\dfrac{2}{3}\cdot15.56=7.78+10.37=18.15\;\text{miles/gal}[/tex]
1)Twelve years ago Jane was five times as old as Anne. In three years time,Anne will be half Jane's age How old is each girl at the moment
Answer:
Step-by-step explanation:
Twelve years ago Jane was five times as old as Anne.
J-12=5(A-12)
In three years time, Anne will be half of Jane's age.
A+3=1/2(J+3)
Simplify and solve this system of equations:
J-12=5(A-12)
A+3=1/2(J+3)
Find the 1000th term for the sequence
Answer:
D. 7017
Step-by-step explanation:
if 24 is the first term, find 7x999, or 7x1000-7 and add 24
however a better way would be to use the formula
value=a+(n-1)d
a = the first term in the sequence (24)
n = the amount of terms you need (1000)
d = the common difference between terms (7)
3. Which of the following values is not possible in probability?
A. P(x) = 1
B. x P(x) = 3 C. P(x) = 0.5
D. P(x) = -0.5
Answer:
D . P(x)=-0.5
Step-by-step explanation:
i think please mark my answer as a brainliest answer and follow me.
What should I buy? A study conducted by a research group in a recent year reported that of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of cell phone owners is studied. Round the answers to four decimal places.
Answer:
The probability that seven or more of them used their phones for guidance on purchasing decisions is 0.7886.
Step-by-step explanation:
The question is incomplete:
What should I buy? A study conducted by a research group in a recent year reported that 57% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 14 cell phone owners is studied. Round the answers to at least four decimal places. What is the probability that seven or more of them used their phones for guidance on purchasing decisions?
We can model this as a binomial random variable, with p=0.57 and n=14.
[tex]P(x=k)=\dbinom{n}{k} p^{k}q^{n-k}[/tex]
a) We have to calculate the probability that seven or more of them used their phones for guidance on purchasing decisions:
[tex]P(x\geq7)=\sum_{k=7}^{14}P(x=k)\\\\\\[/tex]
[tex]P(x=7)=\dbinom{14}{7} p^{7}q^{7}=3432*0.0195*0.0027=0.1824\\\\\\P(x=8) = \dbinom{14}{8} p^{8}q^{6}=3003*0.0111*0.0063=0.2115\\\\\\P(x=9) = \dbinom{14}{9} p^{9}q^{5}=2002*0.0064*0.0147=0.1869\\\\\\P(x=10) = \dbinom{14}{10} p^{10}q^{4}=1001*0.0036*0.0342=0.1239\\\\\\P(x=11) = \dbinom{14}{11} p^{11}q^{3}=364*0.0021*0.0795=0.0597\\\\\\P(x=12) = \dbinom{14}{12} p^{12}q^{2}=91*0.0012*0.1849=0.0198\\\\\\P(x=13) = \dbinom{14}{13} p^{13}q^{1}=14*0.0007*0.43=0.004\\\\\\[/tex]
[tex]P(x=14) = \dbinom{14}{14} p^{14}q^{0}=1*0.0004*1=0.0004\\\\\\[/tex]
[tex]P(x\geq7)=0.1824+0.2115+0.1869+0.1239+0.0597+0.0198+0.004+0.0004\\\\P(x\geq7)=0.7886[/tex]
please help :( really need answer
Answer:
Options (C) and (F)
Step-by-step explanation:
Polynomial function is,
f(x) = x³ - x² - 5x - 3
Possible rational roots of the given function will be = [tex]\frac{\pm1, \pm3}{\pm1}[/tex]
By putting x = -1
f(-1) = (-1)³ - (-1)² -5(-1) - 3
= -1 - 1 + 5 - 3
= 0
Therefore, x = -1 will a root of the given function.
Now we apply synthetic division to get the other roots,
-1 | 1 -1 -5 -3
↓ -1 2 3
1 -2 -3 0
Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).
Now we will find the roots of (x² -2x - 3).
x² - 2x - 3 = x² - 3x + x - 3
= x(x - 3) + 1(x - 3)
= (x + 1)(x - 3)
For roots of the function, f(x) = 0
(x + 1)(x - 3) = 0
x = -1, 3
Therefore, roots of the function are x = -1, 3
Options (C) and (F) are the answers.
Solve the inequality for x
Answer:
see below
Step-by-step explanation:
[tex]\frac{x-c}{d} > y[/tex]
x - c > dy
x > dy + c
Solve for in the diagram below.
Answer:
x = 20
Step-by-step explanation:
The sum of the three angles in the diagram is 180 degrees since they form a straight line
x + 100 + 3x = 180
Combine like terms
100 +4x = 180
Subtract 100 from each side
100+4x-100 =180-100
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
verify clairaut's theorem for u=e^xysiny
In △ ABC, ∠C = 57° and ∠A = 103°. Side CB= 6.5 cm. Draw △ A′B′C′ under the same condition as △ ABC. Leave all construction marks as evidence of your work, and label all side and angle measurements(use text box). What can you conclude about △ ABC and △ A′B′C′? Justify your response.
Answer:
ΔA'B'C' is congruent to ΔABC
Step-by-step explanation:
See attached for the construction of ΔA'B'C'. (The vertices are labeled ABC.)
We computed angle B to be ...
∠B = 180° -∠A -∠C
∠B = 180° -103° -57° = 20°
We constructed segment BC of length 6.5. Then we constructed angles of 20° and 57° from B and C, respectively. The location where the rays from those angles cross is point A', and the angle there is 103°, as required.
__
ΔA'B'C' is congruent to ΔABC by the ASA congruence postulate.
Which expression converts 100 inches per minute to feet per minute?
O
100 inches
1 minute
60 minutes
1 hour
O
100 inches
1 minute
X
1 hour
60 minutes
100 inches
1 minute
X
1 foot
12 inches
O
100 inches
1 minute
12 inches
1 foot
Another question lol take your time
Answer:
100 inches Over 1 minute times × 1 foot Over 12 inches
Step by Step explanation
Remember that
1ft=12in
The expression converts 100 inches per minute to feet per minute is
100 inch / min x 1 ft/ 12 inch.
What is unit conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. Time can be expressed in minutes rather than hours, and distance can be expressed in miles, kilometres, feet, or any other measurement unit.
We know
1 feet = 12 inch
We have to convert 100 inches per minute to feet per minute.
So, 100 inches
= 100 inch / min x 1 ft/ 12 inch
= 8.33 ft per minute
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Rachel owns as twice as many beanie babies as Kaye. Alexia owns 1/3 as many beanie babies as Rachel. If Kaye owns 63 beanie babies,how many does Alexia owns?
Answer:
42
Step-by-step explanation:
Let the number of beanie babies Kaye has be x
according to question
Rachel owns as twice as many beanie babies as Kaye
number of beanie babies Rachel has : 2*x = 2x
Also,
Alexia owns 1/3 as many beanie babies as Rachel
number of beanie babies Alexia has : 1/3(2x) = 2x/3
It is given that Kayes has 63 beanie babies
thus x = 63
Thus,
Number of beanie babies Alexia has = 2x/3 = 2*63/3 =2*21 = 42
A 17-inch candle is lit and burns at a constant rate of 1.3 inches per hour. Let t represent the number of hours since the candle was lit, and suppose f is a function such that f ( t ) represents the remaining length of the candle (in inches) t hours after it was lit. Write a function formula for f . f ( t )
Answer
Since the lyla deleted it actually for a good reason let me explain. But you dont just delete random answers, you can give a comment. I can report you for doing that.
So since it burns at 1.3 per hour. Notice that since it gets removed per hour. so it would be 1.3t so it multiplies per hour. Then we need to subtract. Thats because it lowers the length of the candle. So we get the original length - 17 and get the function
f(t) = 17-1.3t
solve sqrt 3-5x= sqrt x+2 what is the value of x
Answer:
[tex]x=\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{3-5x}=\sqrt{x+2}\\Square\:both\:sides\\\left(\sqrt{3-5x}\right)^2=\left(\sqrt{x+2}\right)^2\\\mathrm{Expand\:}\left(\sqrt{3-5x}\right)^2:\quad 3-5x\\\mathrm{Expand\:}\left(\sqrt{x+2}\right)^2:\quad x+2\\3-5x=x+2\\\mathrm{Solve\:}\:3-5x=x+2:\quad x=\frac{1}{6}\\x=\frac{1}{6}\\\mathrm{Verify\:Solutions}:\quad x=\frac{1}{6}\space\mathrm{True}\\\mathrm{The\:solution\:is}\\x=\frac{1}{6}[/tex]
Answer:
A- 1/6
Step-by-step explanation:
GOT IT RIGHT ON EDGE
Using a 40% solution, make 100 mL of a 10% solution?
Answer:
I don't know
Step-by-step explanation:
but that looks like chemistry not biology
Solve for X 10(x-1) = 8x-2
Answer:
X = 4 x
over 5 ( x − 1 ) − 1 5 ( x − 1 )
Answer:
x = 4
Step-by-step explanation:
10(x-1) = 8x-2
Distribute
10x-10 = 8x-2
Subtract 8 from each side
10x-10-8x = 8x-2-8x
2x-10 = -2
Add 10 to each side
2x-10+10 = -2+10
2x = 8
Divide each side by 2
2x/2 = 8/2
x = 4
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
Answer:
Step-by-step explanation:
The formula is y = mx + b
m being the slope, rise over run. And b being the y-intercept. Right off the bat we can visually see the y-intercept is -4.
To find slope, we need to take two sets of coords and apply the slope fomula. The slope fomula is change in y divided by the change in x. The function itself is straight, so that means the slope will be the exact same no matter which points you choose.
(4, -1) and (8, 2) are coords on the line. Do 2 - (-1) to get 3. then do 8 - 4 to get 4. Finally, we just gotta do 3/4 which is simply [tex]\frac{3}{4}[/tex].
We have the slope of 3/4 and we have the y-intercept of -4. Just plug it in the standard formula of y = mx + b to get:
[tex]y=\frac{3}{4} x-4[/tex]
