Answer:
[tex]P(t)=M+Ce^{-kt}[/tex]
Step-by-step explanation:
Given the differential model
[tex]\dfrac{dP}{dt}=k[M-P(t)][/tex]
We are required to solve the equation for P(t).
[tex]\dfrac{dP}{dt}=kM-kP(t)\\$Add kP(t) to both sides\\\dfrac{dP}{dt}+kP(t)=kM\\$Taking the integrating factor\\e^{\int k dt} =e^{kt}\\$Multiply all through by the integrating factor\\\dfrac{dP}{dt}e^{kt}+kP(t)e^{kt}=kMe^{kt}\\\dfrac{dP}{dt}e^{kt}=kMe^{kt}\\(Pe^{kt})'=kMe^{kt} dt\\$Take the integral of both sides with respect to t\\\int (Pe^{kt})'=\int kMe^{kt} dt\\Pe^{kt}=kM \int e^{kt} dt\\Pe^{kt}=\dfrac{kM}{k} e^{kt} + C_0, C_0$ a constant of integration[/tex]
[tex]Pe^{kt}=Me^{kt} + C\\$Divide both side by e^{kt}\\P(t)=M+Ce^{-kt}\\P(t)=M+Ce^{-kt}\\$Therefore:\\P(t)=M+Ce^{-kt}[/tex]
A middle school band is selling candy bars and nuts to raise money for a field trip. Each candy bar, b, costs $1.50 and each box of nuts, n, costs $4.00. If they raised $418, what expression shows the portion that came from candy bar sales?
Answer:
1.5b = 418 - 4n (all in dollars)
Step-by-step explanation:
Let b represent the number of candy bars sold and n the number of box of nuts sold.
Given that each;
Candy bar costs $1.50
box of nut $4.00
Amount raised from candy bars = $1.50 × b
Amount raised from box of nut = $4.00 × n
Total amount raised = $418
The equation for the total amount raised is;
1.50 × b + 4.00 × n = 418
1.5b + 4n = 418
The portion that came from candy bars is;
Making 1.5b the subject of formula;
1.5b = 418 - 4n
In Don Javier's milking, milk is collected in two containers, one with a 300-liter capacity and one with 180 liters, if they are filled with 15 and 20-liter jugs. Which of the pitchers exactly fill the containers without milk being left over or missing?
Answer:
Both Pitchers
Step-by-step explanation:
First, we determine how many of each pitcher it would take to fill the 300 liter and 180 liter containers.
300÷15=20 of the 15 liter pitcher
300÷20=15 of the 20 liter pitcher
Similarly
180÷15=12 of the 15 liter pitcher.
180÷20=9 of the 20 liter pitcher.
The two pitchers gives a whole number when their volumes divide the volumes of the containers.
Therefore, the two pitchers exactly fill the containers without milk being left over.
Solve for v
3v-9=45
Simplify your answer as much as possible.
Answer:
v = 18
Step-by-step explanation:
3v-9=45
Add 9 to each side
3v-9+9=45+9
3v = 54
Divide each side by 3
3v/3 = 54/3
v =18
Answer:
Step-by-step explanation:
7x-3y=4 2x-y=1 the solution to the system of equations is
Answer:
x = 1 and y = 1
Step-by-step explanation:
7(1) minus 3(1) = 4
and 2(1) minus 1 = 1
just try and guess a number and try to solve the problem with that number, if it isn't the answer then repeat.
Answer: Use the app: photomath
Step-by-step explanation:
Which phrase represents the algebraic expression 3d+7?
Answer:
3 multiplied by a variable d and add seven to it
Step-by-step explanation:
3 multiplied by a variable d and add seven to it.
Rayan Company has 420, 000 shares of $ 10 par. 3 value ordinary shares outstanding. During the year Rayan declared a 5% share dividend when the market price of the shares was $ 36 per share. Three months later Rayan declared a $. 60 per share cash dividend. As a result of the dividends declared during the year, retained earnings [* decreased by
Answer:
The retained earnings decreased by $1,020,600
Step-by-step explanation:
Given that Rayan Company has 420,000 shares of $ 10 par. Rayan then declared a 5% share dividend when the market price of the shares was $36 per share.
Let's calculate the shares issued as stock dividends below:
Issued shares = stock dividends * outstanding shares
= 5% * 420,000
= 21,000
21,000 shares were issued.
Let's calculate the stock dividends.
Stock dividends = issued shares * market price per share
= 21,000 * $36
= $756,000
Stock dividends is $756,000
Let's calculate the amount of cash dividends, since the company declared a $0.60 per share cash dividend after 3 months. We have:
Cash dividend = cash dividend per share * new number of shares.
= $0.60 * (420,000 + 21,000)
= $0.60 * 441,000
= $264,600
Cash dividends paid is $264,600
The find the decrease in retained earnings, we have:
Decrease in Retained earnings = cost of stock dividend + cash dividend.
= $756,000 + $264,600
= $1,020,600
Therefore, the retained earnings decreased by $1,020,600
A recent study reported that 28% of shoppers only review one page when searching online for product information. A random sample of 100 shoppers was randomly selected. What is the probability that between 20 and 30 of these shoppers only review one page when searching online?
Answer:
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.28[/tex]
So
[tex]\mu = E(X) = np = 100*0.28 = 28[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.28*0.72} = 4.49[/tex]
What is the probability that between 20 and 30 of these shoppers only review one page when searching online?
Using continuity correction, this is [tex]P(20 - 0.5 \leq X \leq 30 + 0.5) = P(19.5 \leq X \leq 30.5)[/tex], which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 19.5.
X = 30.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 28}{4.49}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a pvalue of 0.7123.
X = 19.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19.5 - 28}{4.49}[/tex]
[tex]Z = -1.89[/tex]
[tex]Z = -1.89[/tex] has a pvalue of 0.0294
0.7123 - 0.0294 = 0.6829
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
I've been stuck on this for a little while now. Could anybody help?
Answer:
7
Step-by-step explanation:
The arrows on the diagonal lines mean those lines are parallel. That means the triangles are similar, so corresponding sides have the same ratio.
There are many ways we can write the proportion expressing that fact. It is convenient to do so with the variable in the numerator:
(3x -6)/12 = 10/8
Multiplying by 4, we have ...
x -2 = 5
x = 7 . . . . . . add 2
The sum of three numbers is 81. The
Second
number is 7 more
ore than the first
number and the third number doubles the sum of the first two numbers find the range of the set of numbers
Answer:
I'm assuming that the range means the smallest number to largest number which will be 10 to 54
Step-by-step explanation:
Let x represent 1st number, y represent 2nd number and z represent 3rd number
rest of the working is in the picture attached. hope you understand it!
6. The cost price of a watch is Rs
4000. Find the marked price so
that there would be a profit of 10%
after allowing a discount of 20%.
Answer:I believe it's C
Step-by-step explanation:
Line m has no y intercept, and it’s x intercept is(3,0). Line n has no x intercept, and it’s y intercept is (0,-4) the equation of line m is____ , and the equation of line n is ______
Answer:
x = 3y = -4Step-by-step explanation:
In order for a line to have no y-intercept, it must be parallel to the y-axis. Its equation will be of the form ...
x = constant.
If the x-intercept is (3, 0), then we must have constant = 3.
__
In order for a line to have no x-intercept, it must be parallel to the x-axis. Its equation will be of the form ...
y = constant.
If the y-intercept is (0, -4), then we must have constant = -4.
__
The equation of line m is x = 3.
The equation of line n is y = -4.
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
1. Calculate and print the mean points scored by your team during the years you picked.
2. Identify the mean score under the null hypothesis. You only have to identify this value and do not have to print it.
3. Assuming that the population standard deviation is unknown, use Python methods to carry out the hypothesis test.
4. Calculate and print the test statistic rounded to two decimal places.
5. Calculate and print the P-value rounded to four decimal places.
Answer:
1. M=108
2. μ=110
3. In the explanation.
4. Test statistic t = -1.05
5. P-value = 0.1597
Step-by-step explanation:
The question is incomplete: to solve this problem, we need the sample information: size, mean and standard deviation.
We will assume a sample size of 10 matches, a sample mean of 108 points and a sample standard deviation of 6 points.
1. The mean points is the sample points and has a value of 108 points.
2. The null hypothesis is H0: μ=110, meaning that the mean score is not significantly less from 110 points.
3. This is a hypothesis test for the population mean.
The claim is that the mean score is significantly less than 110.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu< 110[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=108.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{10}}=1.9[/tex]
4. Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{108-110}{1.9}=\dfrac{-2}{1.9}=-1.05[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
5. This test is a left-tailed test, with 9 degrees of freedom and t=-1.05, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.05)=0.1597[/tex]
As the P-value (0.1597) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean score is significantly less than 110.
Express the ratio 16:9 as a ratio to 1.
Answer:
(16/9):1
Step-by-step explanation:
How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show thatthe sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the the average professional football fan spend on food at a single football game.
Answer:
$70.00 +/- $4.43
= ( $65.57, $74.43)
Therefore at 95% confidence interval (a,b) = ( $65.57, $74.43)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Sample Mean x = $70.00
Standard deviation r = $17.50
Number of samples n = 60
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
$70.00+/-1.96($17.50/√60)
$70.00+/-1.96($2.259240285287)
$70.00+/-$4.428110959163
$70.00+/-$4.43
= ( $65.57, $74.43)
Therefore at 95% confidence interval (a,b) = ( $65.57, $74.43)
Please answer this correctly I want helping hand people to answer this correctly
Answer:
w = 36
Step-by-step explanation:
You can make a ratio 98 : 84 = 42 : w
[tex]\frac{49}{42}=\frac{42}{w}[/tex]
49w = 1764
w = 36
A right triangle has sides of integer lengths a, 40, and 41. Find a.
b) 9
c) 141-140
d) -9
a) 1
e) none of these.
Answer:
b) 9
Step-by-step explanation:
9 squared + 40 squared = 41 squared, which follows Pythagorean theorem.
Please help, find angle R
Step-by-step explanation:
√(7^2) + (9^2)
=√(49) + (81)
=√(130)
=11.401754251
HOPE THIS HELP YOU !!! ;))))Find the slope of the line that contains the points named.
R(O, 4), S(5,0)
-4/5
4/5
-5/4
Answer:
[tex] - \frac{4}{5} [/tex]
Step-by-step explanation:
Line is passing through the points R (0, 4), S (5, 0)
[tex]Slope \: of \: RS \\ = \frac{4 - 0}{0 - 5} \\ \\ = \frac{4}{ - 5} \\ \\ = - \frac{4}{5} [/tex]
Bilal's favorite colors are red and green.
He has 1 red shirt, 1 green shirt, 1 red hat, 1 green scarf, 1 red pair of pants, and
1 green pair of pants.
Bilal selects one of these garments at random. Let A be the event that he selects a green garment and let
B be the event that he chooses a scarf.
Answer:
P(A∪B) = 1/3
Step-by-step explanation:
Red Garments = 1 red shirt + 1 red hat + 1 red pairs of pants
Total Red Garments = 3
Green Garments = 1 green shirt + 1 green scarf + 1 green pairs of pants
Total Green Garments = 3
The total number of garments = Total Red Garments + Total Green Garments:
3 + 3 = 6
Let A be the event that he selects a green garment
P(A) = Number of required outcomes/Total number of possible outcomes
P(A) = 3/6
Let B be the event that he chooses a scarf
P(B) = 1/6
The objective here is to determine P(A or B) = P(A∪B)
Using the probability set notation theory:
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∩B) = Probability that a green pair of pant is chosen = P(A) - P(B)
= 3/6-1/6
= 2/6
P(A∪B) = 1/2 + 1/6 - 2/6
P(A∪B) = 2/6
P(A∪B) = 1/3
Answer:
in the khan academy answer is both A and B are dependent on each other.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer: B
Step-by-step explanation:
To find the answer, you add the two equations together
Answer:
A. x - 3
Step-by-step explanation:
Set it up like this:
(3x - 2) - (2x + 1)
Combine like terms:
3x - 2 - 2x - 1
3x - 2x = x
-2 - 1 = -3
Put it together:
x - 3
Find the product or type
"impossible".
3 -5 4 2
Answer:
The product of [tex]\begin{pmatrix}3&-5\\ \:1&7\end{pmatrix}\begin{pmatrix}4&2\\ \:-4&2\end{pmatrix}[/tex] is [tex]\begin{pmatrix}32&-4\\ -24&16\end{pmatrix}[/tex].
Step-by-step explanation:
A matrix is a rectangular arrangement of numbers into rows and columns.
Matrix multiplication refers to the product of two matrices.
The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal to the number of rows of the 2nd one.
To find the product of [tex]\begin{pmatrix}3&-5\\ \:1&7\end{pmatrix}\begin{pmatrix}4&2\\ \:-4&2\end{pmatrix}[/tex]
[tex]\mathrm{Multiply\:the\:rows\:of\:the\:first\:matrix\:by\:the\:columns\:of\:the\:second\:matrix}\\\\\begin{pmatrix}3&-5\end{pmatrix}\begin{pmatrix}4\\ -4\end{pmatrix}=3\cdot \:4+\left(-5\right)\left(-4\right)\\\\\begin{pmatrix}3&-5\end{pmatrix}\begin{pmatrix}2\\ 2\end{pmatrix}=3\cdot \:2+\left(-5\right)\cdot \:2\\\\\begin{pmatrix}1&7\end{pmatrix}\begin{pmatrix}4\\ -4\end{pmatrix}=1\cdot \:4+7\left(-4\right)\\\\\begin{pmatrix}1&7\end{pmatrix}\begin{pmatrix}2\\ 2\end{pmatrix}=1\cdot \:2+7\cdot \:2[/tex]
[tex]\begin{pmatrix}3&-5\\ 1&7\end{pmatrix}\begin{pmatrix}4&2\\ -4&2\end{pmatrix}=\begin{pmatrix}3\cdot \:4+\left(-5\right)\left(-4\right)&3\cdot \:2+\left(-5\right)\cdot \:2\\ 1\cdot \:4+7\left(-4\right)&1\cdot \:2+7\cdot \:2\end{pmatrix}[/tex]
[tex]\mathrm{Simplify\:each\:element}\\\\\begin{pmatrix}3&-5\\ 1&7\end{pmatrix}\begin{pmatrix}4&2\\ -4&2\end{pmatrix}=\begin{pmatrix}32&-4\\ -24&16\end{pmatrix}[/tex]
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?
A. g(x) = f(x - 5)
B. g(x) = f(x) - 2
C. g(x) = f(x + 2)
D. g(x) = f(x) - 5
Answer:
D. g(x) = f(x) - 5
Step-by-step explanation:
To move the intercept to -2, one needs to translate the function down by 5 or left by 5. The first translation (down 5) would result in ...
g(x) = f(x) - 5 . . . . . . matches choice D
The second translation (left 5) would result in ...
g(x) = f(x+5) . . . . doesn't match any available choice
Answer: g(x) = f(x) - 5
Step-by-step explanation:
just took this
Pulse rates of adult females are listed in Data Set 1 "Body Data" in Appendix B. The lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is x = 74.0 beats per minute, and their standard deviation is s = 12.5 beats per minute. a. What is the difference between the pulse rate of 36 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 36 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 36 beats per minute significant?
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: pulse rate of a female adult. (beats/min)
Mean X[bar]= 74.0 beats/min
Standard deviation S= 12.5 beats/min
The lowest pulse rate is 36 beats/min
a)
The difference between the lowest pulse rate and the mean pulse for females is: 36 - 74= -38 beats/min
b)
To calculate how many standard deviations a value of the variable is from the mean, you have to subtract the mean from it and divide by the standard deviation:
(X-X[bar])/S= (36-74)/12.5= -3.04
The minimum pulse for female adults is -3.04 standard deviations away from the mean.
c)
The z score for 36 beats/min is -3.04
Considering the region of acceptance (-2; 2), the calculated value is below its lower limit, so you can conclude that the pulse rate 36 beats/min is significantly low.
I hope this helps!
Find the value of X in the triangle
An outside angle is equal to the sum of the two opposite inside angles.
122 = x + 24
X = 122 - 24
X = 98 degrees
What is the solution of the system shown?
(2, 2)
(2,3)
(3, 2)
Answer:
(3,2)
Step-by-step explanation:
The solution of lines on a coordinate plane is its intersection point. In this case its (3,2)
4. In an electrical circuit it is known that the voltage V varies as the current I
(ie. that V is directly proportional to 1). It is also known that V = 36
when I = 8.
a Find a formula for V in terms of I.
b Find V when I = 14.
с Find / when V = 27.
Step-by-step explanation:
V∝I
V=kI
36=k*8
k=36/8
k=4.5
a. V=4.5I
b. V=4.5*14
V= 63
c. 27=4.5I
I=27/4.5
I= 6
Find sin(α) and cos(β), tan(α) and cot(β), and sec(α) and csc(β). The hypotenuse is 7 and side is 4.
The triangle is missing, so i have attached it.
Answer:
1)sin(α) = 4/7
2)cos(β) = 4/7
3)tan(α) = 4/√33
4)cot(β) = 4/√33
5)sec(α) = 7/√33
6)csc(β) = 7/√33
Step-by-step explanation:
(1) sin(α)
From trigonometric ratios, we know that sine of an angle in a right angle triangle = opposite/hypotenuse.
Now, in this question, the opposite side to α is 4 and the hypotenuse is 7. Thus, sin(α) = 4/7
2) cos(β)
Cosine of an angle = adjacent side/hypotenuse.
In the question, the adjacent side to the angle β is 4 and the hypotenuse is 7. Thus, cos(β) = 4/7
3)tan(α)
tan of an angle = opposite/adjacent side. The opposite side to α is 4, but the adjacent side is unknown.
Using the pythagoras theorem,
Adjacent side = √(7² - 4²)
Adjacent side = √(49 - 16)
Adjacent side = √33.
Thus, tan(α) = 4/√33
4) cot(β)
cot of an angle is the reciprocal of tangent of same angle.
The adjacent side to β is 4 while the opposite is √33.
So, tan(β) = (√33)/4
cot(β) = 1/tan(β)
cot(β) = 1/[(√33)/4]
cot(β) = 4/√33
5)sec(α)
sec of an angle is equal to one divided by cosine of that same angle, so it equals hypotenuse divided by the adjacent. The hypotenuse is 7 and the adjacent side to α is √33.
Thus, sec(α) = 1/cosα = 7/√33.
6) csc(β)
Csc of an angle is equal to one divided by sine of same angle, so it equals hypotenuses divided by the opposite. The hypotenuse is 7 and the opposite side to β is √33.
Thus, csc(β) = 1/sin(β) = 7/√33
A boating company charges $10 equipment fee and $5.50 per hour to rent a canoe. Which is the correct linear equation for this situation?
Answer:
[tex] y =mx +b[/tex]
Where m is the slope and b the intercept.
Using the information given the variable cost 5.5 per hour represent the slope and the fixed cost 10 represent the value of b and then our model would be given by:
[tex] y =5.5 x+ 10[/tex]
Wher y is the total cost and x the hours rented
Step-by-step explanation:
For this case we want to model the situation with a general equation given by:
[tex] y =mx +b[/tex]
Where m is the slope and b the intercept.
Using the information given the variable cost 5.5 per hour represent the slope and the fixed cost 10 represent the value of b and then our model would be given by:
[tex] y =5.5 x+ 10[/tex]
Wher y is the total cost and x the hours rented
All else being equal, a study with which of the following error ranges would be
the most reliable?
A. +12 percentage points
B. 117 percentage points
C. +2 percentage points
D. 17 percentage points
Any help would be greatly appreciated
Answer:
the answer is letter B for ur question
Answer:
A. 44,130
B. 44,100
C. 44,000
Step-by-step explanation:
1-4 round down to 0 do not change the desired place value| 5-9 round the desired place value up by one.
Tens (10) Hundreds (100) Thousands (1000)
