Answer:What?
Step-by-step explanation:
A survey asked, "How many tattoos do you currently have on your body?" Of the 12311231 males surveyed, 190190 responded that they had at least one tattoo. Of the 10671067 females surveyed, 143143 responded that they had at least one tattoo. Construct a 9090% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. Let p 1p1 represent the proportion of males with tattoos and p 2p2 represent the proportion of females with tattoos. Find the 9090% confidence interval for p 1 minus p 2p1−p2.
Answer:
[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]
[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]
We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]
Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs
Step-by-step explanation:
Information given
[tex]p_1[/tex] represent the real population proportion of males with tattoos
[tex]\hat p_1 =\frac{190}{1231}=0.154[/tex] represent the estimated proportion of males with tattos
[tex]n_1=1231[/tex] is the sample size for males
[tex]p_2[/tex] represent the real population proportion of female with tatto
[tex]\hat p_2 =\frac{143}{1067}=0.134[/tex] represent the estimated proportion of females with tattos
[tex]n_2=1067[/tex] is the sample size of female
[tex]z[/tex] represent the critical value
Confidence intrval
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
For the 90% confidence interval the value of [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2=0.05[/tex], and the critical value for this case would be:
[tex]z_{\alpha/2}=1.64[/tex]
Replacing the info given we got:
[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]
[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]
We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]
Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs
A graph shows average temperature (degrees Fahrenheit) labeled 10 to 60 on the horizontal axis and total coat sales on the vertical axis. A line decreases from 10 to 65. Which temperature values would an interpolation be limited to? less than 3 between 3 and 60 between 20 and 80 greater than 55 ................... nvm i got it its B.between 3 and 60. but still answer to get points lol
Answer:
between 3 and 60
Step-by-step explanation:
just did it on ed.
Answer: Between 3 and 60
Step-by-step explanation: Glad you figured it out! :)
if £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after 2 years
Principal Balance: 2000
Compound Interest: 3%
Type: Yearly
2000 x 1.03 = 2060
Year 1 : £2060
2060 x 1.03 = 2121.8
Year 2: £2121.8
There will be £2,121.80 in the account after 2 years.
Answer:okStep-by-step explanation:
How many 4 digit numbers can be formed if no two digits are the same?
Consider the following function. f(x) = (x + 5)2/3 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = −5 (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing (−5,[infinity]) decreasing (−[infinity],−5) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = DNE relative minimum (x, y) = −[infinity],[infinity]
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for detailed and step by step solution of the given problem.
a. The critical number of f is -5
b. The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).
c. There is no relative extremum at x = -5.
d. Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).
How to find the critical numbers(a) To find the critical numbers of the function, find where the derivative is 0 or undefined.
To find the derivative of f(x):
[tex]f'(x) = (2/3)(x + 5)^(-1/3)[/tex]
The derivative is undefined at x = -5, since[tex](x + 5)^(1/3)[/tex] would be 0 in the denominator.
So -5 is a critical number of f.
(b) To find the intervals on which the function is increasing or decreasing, examine the sign of the derivative on each interval.
Since f'(x) is always positive (except at x = -5, where it is undefined),
The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).
(c) To apply the First Derivative Test, look at the sign of the derivative near the critical point x = -5.
The derivative is undefined at x = -5, so the test is not applicable
Therefore, there is no relative extremum at x = -5.
Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).
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A shipment to a warehouse consists of 500 PS4. The manager chooses a random sample of 50 PS4 and finds that 3 are defective. How many PS4 in the shipment are likely to be defective?
Answer:
30 PS4's
Step-by-step explanation:
The manager chose 50/500 PS4's to sample
3/50 were defective
To find how many were defective in all 500, we multiply the fraction by a number that makes the 50 (the sample), into a 500(the total).
That number is 10
Whatever multiplication you do to the bottom of a fraction, you do to the top
3*10 / 50*10
30 / 500 are likely to be defective
Answer:
30
Step-by-step explanation:
What number is 62.5% of 195?
Answer:
121.875 if calculated so 121.875 if it shows it or less
Answer:
121.875
Step-by-step explanation:
To find the number you multiple 195 by 0.625 (0.625 is equivalent to 62.5%) which gets you 121.875
Using the textbook data set nlschools.csv, perform a hypothesis test to determine whether the proportion of students with language test scores greater than 37 is different for students from families of social-economic status at most 25 and students from families of social-economic status greater than 25. Perform the test at the α = 0.05 significance level.
Answer:
p-value is greater than 0.05, hence we accept the null hypothesis.
Step-by-step explanation:
See attached images
Time (hours) Number of Bricks
2 100
4 200
6 300
8 400
The time it takes a brick layer to lay bricks varies directly with the number of bricks. The brick layer's data is shown in the table. If x = time, and y = the number of bricks, which equation models the brick layer's direct variation?
Answer:
y=50x
Step-by-step explanation:
For every additional 2 hours (x), there are 100 bricks laid.
This means the slope is 50 (100/2)(200/4)etc.
50*2=100
50*4=200
50*6=300
50*8=400
The is 2/3 of a pizza left. Wakami eats 1/4 of it. How much of the pizza did he eat?
Answer:
If you mean how much is left after he ate 1/4 from the 2/3 then 5/12 of the pizza is left.
Step-by-step explanation:
Final answer:
Wakami ate 1/6 of the entire pizza by consuming 1/4 of the 2/3 of the pizza that was left.
Explanation:
To find out how much of the pizza Wakami ate, we need to calculate 1/4 of the 2/3 of the pizza that was left. This requires multiplying the two fractions together:
2/3 of the pizza left times 1/4 that Wakami eats = 2/3 times 1/4
To multiply fractions, you simply multiply the numerators (top numbers) and then multiply the denominators (bottom numbers):
(2 times 1) / (3 times 4) = 2 / 12
Now we simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2:
2 / 12 = 1/6
So, Wakami ate 1/6 of the entire pizza.
La compañía XX usa cuatro empresas de transporte: A1, A2 , A3 y A4 . Se sabe que 15% de los embarques se asignan a la empresa A1 , 30% a la A2 , 35% a la A3 y 20% a la A4 . Los embarques llegan retrasados a sus clientes en 7% si los entrega A1 , 8% si es A2 , 5% si es A3 y 9% si es A4 . Si sabemos que el embarque de hoy fue entregado con retraso,
¿cuál es la probabilidad de que haya sido la empresa A1 la encargada de hacerlo?
Answer:
[tex]P(E1/R)= 0.15[/tex]
Step-by-step explanation:
Hola!
La comañía en cuestión usa 4 empresas de transporte para realizar envios. Llamemos "E" al evento de que la empresa haya sido seleccionada para un envío:
E1: La empresa A1 realiza el envío ⇒ P(E1)= 0.15
E2: La empresa A2 realiza en envío ⇒ P(E2)= 0.30
E3: La empresa A3 realiza el envío ⇒ P(E3)= 0.35
E4: La empresa A4 realiza el envío ⇒ P(E4)= 0.20
Y también conoces las probabilidades de que un envío llegue con retraso, sabiendo cual es la empresa que realizó el envío. Llamemos "R" al evento que el envío llegó con retraso. Las probabilidades mencionadas son condicionales y se simbolizan de la siguiente manera:
P(R/E1)= 0.07
P(R/E2)= 0.08
P(R/E3)= 0.05
P(R/E4)= 0.09
Tienes que calcular la probabilidad de que un embarque que ha sido entregado con retraso, haya sido enviado por la empresa A1.
Esta probabilidad también es condicional, queremos saber la probabilidad de E1 sabiendo que ya ha pasado R, se simboliza de la siguiente manera:
[tex]P(E1/R)= \frac{P(E1nR)}{P(R)}[/tex]
Para poder calcularla necesitas averiguar el valor de la probabilidad de intersección entre E1 y R, P(E1∩R), y el valor de la probabilidad de R, P(R).
La probabilidad de R es una probabilidad marginal y es igual a:
P(R)= P(E1∩R)+P(E2∩R)+P(E3∩R)+P(E4∩R)
Para calcular los valores de las intersecciones debes aplicar la definición de probabilidad condicional:
[tex]P(A/B) = \frac{P(AnB)}{P(B)}[/tex] entonces P(A∩B)= P(A/B)*P(B)
Entonces:
[tex]P(R/E1)= \frac{P(RnE1}{P(E1)}[/tex] ⇒ P(E1∩R)= P(R/E1)*P(E1)= 0.07*0.15= 0.0105
P(E2∩R)= P(R/E2)*P(E2)= 0.08*0.30= 0.024
P(E3∩R)= P(R/E3)*P(E3)=0.05*0.35= 0.0175
P(E4∩R)= P(R/E4)*P(E4)= 0.09*0.20= 0.018
Ahora puedes calcular la probabilidad de que el envío llegue con retraso:
P(R)= 0.0105+0.024+0.0175+0.018= 0.07
Por último queda calcular la probabilidad solicitada:
[tex]P(E1/R)= \frac{0.0105}{0.07}= 0.15[/tex]
Espero que tengas un buen día!
Linda wants to purchase a Leisure Heights Condominium apartment. She will
borrow $100,000 from the Duchess Savings Bank. The bank is presently
offering a 30-year fixed rate mortgage with an APR of 7.1%. Her monthly
maintenance fee will be $310.
A) What is the monthly mortgage payment?
B) What will be her combined monthly payment?
Linda's monthly mortgage payment will be approximately $664.14.
Linda's combined monthly payment, including the mortgage and maintenance fee, will be $974.14.
We have
A)
Monthly Mortgage Payment:
Loan Amount: $100,000
Interest Rate: 7.1% per annum (APR)
Loan Term: 30 years (360 months)
Monthly Interest Rate = Annual Interest Rate / 12
= 7.1% / 12
= 0.0059
Number of Payments = Loan Term in years * 12
= 30 * 12
= 360
Monthly Mortgage Payment
= (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
Plugging in the values:
[tex]= (100,000 * 0.0059) / (1 - (1 + 0.0059)^{-360})[/tex]
= $664.14
B) Combined Monthly Payment:
Combined Monthly Payment
= Monthly Mortgage Payment + Monthly Maintenance Fee
= $664.14 + $310
= $974.14
Therefore,
Linda's monthly mortgage payment will be approximately $664.14.
Linda's combined monthly payment, including the mortgage and maintenance fee, will be $974.14.
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A) Linda's monthly mortgage payment is approximately $672.03.
B) Linda's combined monthly payment is approximately $982.03.
To determine Linda's monthly mortgage payment and her combined monthly payment, we can use the following steps:
A) Calculating the Monthly Mortgage Payment:-
We use the formula for the monthly mortgage payment on a fixed-rate mortgage:
[tex]\[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \][/tex]
Where:
- ( M ) is the monthly mortgage payment.
- ( P ) is the loan principal (amount borrowed), which is $100,000.
- ( r ) is the monthly interest rate, which is the annual rate divided by 12.
- ( n ) is the total number of payments (loan term in years multiplied by 12 months per year).
Given:
- [tex]\( P = 100,000 \)[/tex]
- Annual interest rate (APR) = 7.1% or 0.071
- Monthly interest rate [tex]\( r = \frac{0.071}{12} \approx 0.0059167 \)[/tex]
- Loan term ( n = 30 ) years, which is [tex]\( 30 \times 12 = 360 \)[/tex] months.
Substitute these values into the formula:
[tex]\[ M = 100,000 \times \frac{0.0059167(1 + 0.0059167)^{360}}{(1 + 0.0059167)^{360} - 1} \][/tex] = $672.03.
B) Calculating the Combined Monthly Payment
The combined monthly payment is the sum of the monthly mortgage payment and the monthly maintenance fee.
Given:
- Monthly maintenance fee = $310
So, the combined monthly payment ( C ) will be:
[tex]\[ C = M + 310 \][/tex]
Let's compute these values.
A) Monthly Mortgage Payment
Linda's monthly mortgage payment is approximately $672.03.
B) Combined Monthly Payment
To find the combined monthly payment, we add the monthly mortgage payment and the monthly maintenance fee:
[tex]\[ \text{Combined Monthly Payment} = 672.03 + 310 = 982.03 \][/tex]
Therefore, Linda's combined monthly payment is approximately $982.03.
What is the absolute value of -5.5
Answer:
positive 5.5
Step-by-step explanation:
Determine what type of observational study is described. Explain. Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with osteoperosis and an equal number of women without osteoperosis. The two groups were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups.
Answer: The type is Retrospective.
Step-by-step explanation: Observational Study is a type of research which measures determined characteristics of a population by studying individuals in a sample, without interfering or influencing the variables. There are 3 types of observational study:
Cross-sectional studies: colecting data at a certain point of time;Case-control studies: comparing individuals with a particular characteristics with others without it;Cohort studies: is the one where a group of individuals is selected to participate in the study;According to the description given, the study above is a case-control study and the type is called Retrospective because it asks the individuals to tell about past habits, exposure to sunshine in this case. This type of study is not very reliable because it depends on the memory and the ability of the individuals to be honest and it can only prove association, not causation.
The type of observational study described in the question is a case-control study. The researcher selected women with and without osteoperosis, collected data on their exposure to sunshine, and compared the amount of exposure between the two groups.
Explanation:The type of observational study described in the question is a case-control study. In a case-control study, the researcher selects subjects based on their disease status (in this case, women with or without osteoperosis) and compares their exposure to a risk factor (in this case, lack of exposure to sunshine). The researcher collected data on the exposure to sunshine over the previous twenty years for both groups and compared the amount of exposure between the two groups.
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The pizza shown has a radius of 14 cm. What is the approximate area of the pizza? (Use 3.14 for
.)
A. 615.44 cm?
B. 43.96 cm?
87.92 cm
1.230.88 cm?
Answer:
A. 615.44 cm²
Step-by-step explanation:
A = pi(r²)
= 3.14(14²)
= 3.14(196)
= 615.44 cm²
Final answer:
To find the approximate area of the pizza with a radius of 14 cm, use the formula for the area of a circle and substitute the given value, resulting in 615.44 cm².
Explanation:
The approximate area of the pizza can be calculated using the formula for the area of a circle:
A = πr²
Given that the radius is 14 cm, we substitute this into the formula:
A ≈ 3.14 x (14 cm)² = 615.44 cm²
Therefore, the approximate area of the pizza is 615.44 cm², which corresponds to option A.
A project has four activities (A, B, C, and D) that must be performed sequentially. The probability distributions for the time required to complete each of the activities are as follows: Activity Activity Time (weeks) Probability A 5 0.25 6 0.35 7 0.25 8 0.15 B 3 0.20 5 0.55 7 0.25 C 10 0.10 12 0.25 14 0.40 16 0.20 18 0.05 D 8 0.60 10 0.40 (a) Construct a spreadsheet simulation model to estimate the average length of the project and the standard deviation of the project length. Round your answers to one decimal place. Average Project Length weeks Standard Deviation in Project Length weeks (b) What is the estimated probability that the project will be completed in 35 weeks or less
Answer:
(a)
The average length of the project is 33.9 weeks
The standard deviation of the project length is 2.8 weeks
(b)
The estimated probability that the project will be completed in 35 weeks or less is 0.65
Step-by-step explanation:
(a)
The average length of the project is;
E(P) = E(A+B+C+D)
= 6.3 + 5.1 + 13.7 + 8.8
= 33.9
The standard deviation of the project length;
SD(P) = √V(P)
= √V(A+B+C+D)
= √1.01 + 1.79 + 4.11 + 0.96
= √7.87
= 2.8
(b)
Normal distribution with mean 33.9 weeks and variance of 2.8² weeks.
The estimated probability that the project will be completed in 35 weeks or less is;
[tex]P(P \leq 35) = P( \frac{P-E(P)}{SD(P)} \leq \frac{35-33.9}{2.8} )[/tex]
[tex]P(P \leq 35) = P(z\leq0.3929)[/tex]
= 0.65 → Using Excel command (NORM.S.DIST(0.3929,TRUE))
To estimate the average length and standard deviation of a project, use a spreadsheet simulation model. Calculate the expected completion time and standard deviation for each activity. To find the probability of completing the project in a certain time frame, sum up the probabilities of activities that can be completed within that timeframe.
Explanation:To estimate the average length of the project and the standard deviation of the project length, you can use a spreadsheet simulation model. Here are the steps you can follow:
Create a column for each activity (A, B, C, D) and list the possible time values for each activity.Create another column for the probability for each time value.In a separate column, calculate the product of the time value and its probability for each activity.Sum up the values from step 3 for each activity to get the expected completion time.Calculate the standard deviation using the formula: sqrt(sum of (time value - expected completion time)^2 * probability) for each activity.For part (b), to find the estimated probability that the project will be completed in 35 weeks or less, you'll need to sum up the probabilities of all activities that can be completed within 35 weeks or less.
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A graph of 2 functions is shown below.
graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2
Which of the following is a solution for f(x) = g(x)? (2 points)
Group of answer choices
x = −2
x = 1
x = 0
x = −1
Answer:
x=0 i think
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I took the quiz
What is the hinge Theorem in Geomatry
Answer:
In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
Step-by-step explanation:
Answer:
In geometry, the theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
Step-by-step explanation:
Please help in finding the radians in degrees!
Answer:
225°
Step-by-step explanation:
Multiply radians by 180°/π to get degrees.
(5π/4)×(180°/π) = (5/4)(180°) = 225°
A household goods manufacturer wants to increase the absorption capacity of a dish washing sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge
Answer:
[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value using the alternative hypothesis is given by:
[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]
Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge
Step-by-step explanation:
Information provided
4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9
We can find the sample mean and deviation with the following formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=3.76[/tex] represent the sample mean
[tex]s=0.241[/tex] represent the sample standard deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =3.5[/tex] represent the value to check
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the new design increased the absorption amount of the sponge (3.5), the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 3.5[/tex]
Alternative hypothesis:[tex]\mu > 3.5[/tex]
Since we don't know the deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value using the alternative hypothesis is given by:
[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]
Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge
A card is selected at random from a deck of 52 playing cards, the probability that a card 2 is selected will be ______________.
a) 13/52
b) 4/52
c) 26/52
d) 20/52
Answer:
b) 4/52
Step-by-step explanation:
Since there are only 4 playing cards in a full deck that are labeled '2', and there are 52 cards in total - then there is a 4 out of 52 chance that a '2' card will be selected!
Answer:
b) 4/52
Step-by-step explanation:
There are only 4 "2" cards in a deck of 52, so you only have a 4/52 chance of pulling one, or about 8%.
hope this helps :)
If p is a true statement and q is false, what is the truth value of p ∨ q?
Answer: the value is true
Step-by-step explanation:
In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation dP dt = P(a − bP), where a and b are positive constants. Although we will come back to this equation and solve it by an alternative method in Section 3.2, solve the DE this first time using the fact that it is a Bernoulli equation.
Answer:
If [tex]K[/tex] is a constant of integration, then
[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]
Step-by-step explanation:
According to the information of the problem we know that
[tex]{\displaystyle \frac{dP}{dt} = P(a-bP) }[/tex]
Remember that in general a Bernoulli equation is an equation of the type
[tex]y' + p(x)y = q(x)y^n[/tex]
And the idea to solve the equation is to substitute
[tex]{ \displaystyle v = y^{1-n}}[/tex]
Now for this case
[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]
Then we substitute
[tex]v = P^{1-2} = P^{-1}[/tex]
Therefore
[tex]P = v^{-1}[/tex]
and if you compute the derivative of that you get that
[tex]{\displaystyle \frac{dP}{dt} = -v^{-2} \frac{dv}{dt}}[/tex]
Now you substitute that onto the original equation and get
[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]
[tex]{\displaystyle -v^{-2} \frac{dv}{dt} - v^{-1} = -bv^{-2}[/tex]
If you multiply everything by [tex]-v^2[/tex] you get that
[tex]{\displaystyle \frac{dv}{dt} + v = b }[/tex]
That's a linear differential equation and the solution would be
[tex]v = {\displaystyle \frac{b}{a} + Ke^{-at}} = P^{-1}[/tex]
Where [tex]K[/tex] is a constant of integration, then
[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]
The given logistic equation is a Bernoulli equation, which can be solved using a substitution of variables method.
Explanation:The given differential equation is a Bernoulli equation, which is a nonlinear first-order ordinary differential equation of the form dy/dx = P(x)y + Q(x)y^n, where n is a constant. To solve it, we can use a substitution of variables by setting y = u^(1-n). Applying this substitution to the logistic equation, we get du/dx = (1-n)a*u + (1-n)b*u^(2-n), which can be solved using separation of variables method.
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If a ladder leans against a house and is 25 meters long, and the base of the ladder is 7 meters from the house, how many meters is the window to the ground.
Answer:
24 meters
Step-by-step explanation:
The Pythagorean theorem can be used to find the missing leg of the right triangle.
AB² = BC² +AC²
25² = 7² +AC²
AC = √(625 -49) = √576
AC = 24
The height to the top of the ladder is 24 meters.
In 2007, a census counted 2814 of a certain animal. This was 302 fewer than the number counted in 2006. What was the population of the animal in 2006?
The population of the animal in 2006 was
nothing. (Simplify your answer.)
Brandon poured what he estimated to be 32 ounces of oil into his car’s engine. From the markings on the container, he later determined that he had actually poured 36 ounces. What was the percent error in his estimate
Answer:
percentage error = 11.11 %
Step-by-step explanation:
Brandon poured w hat he estimated to be 32 ounces of oil into his car's engine . He later determined that he has actually poured 36 ounces from the marking on the container . The percentage error is computed below.
percentage error = approximate value - exact value/exact value × 100
approximate value = 32 ounces
exact value = 36 ounces
percentage error = |32 - 36| / | 36 | × 100
note we used the absolute value to eliminate negative signs
percentage error = 4/36 × 100
percentage error = 400/36
percentage error = 11.11 %
Which statements about the ellipse are true? Check all that apply.
The center is located at (2, –1).
The major axis is 8 units long.
The minor axis is 3 units long.
The vertices are 4 units above and below the center.
The foci are units above and below the center.
The foci are located along a horizontal l
Answer:
The center is located at (2, –1).
The major axis is 8 units long.
The vertices are 4 units above and below the centre.
The foci are √7 units above and below the centre.
Step-by-step explanation:
Assume the ellipse looks like the one below.
The properties of a vertical ellipse are
[tex]\textbf{Vertical ellipse}\\\dfrac{ (x - h)^{2} }{b^{2}} + \dfrac{(y - k)^{2}}{a^{2}} = 1\begin{cases}\text{Centre} = (h,k)\\\text{Dist. between vertices} = 2a\\\text{Vertices} = (h, k\pm a)\\\text{Dist. between covertices} = 2b\\ \text{Covertices}= (h\pm b, k)\\c = \sqrt{a^{2} - b^{2}}\\\text{Dist. of foci from centre} = c\\\text{Foci} = (h, k\pm c)\\\end{cases}[/tex]
A. Centre
TRUE. The centre is at (2,-1).
B. Major axis
TRUE
Length of major axis = 3 - (-5) = 3 + 5 = 8
C. Minor axis
False
Length of minor axis = 5 - (-1) = 5 + 1 = 6
D. Vertices
TRUE
Distance between vertices = 8 = 2a
a - 8/2 = 4
Vertices at (h, k ± a) = (2, -1 ± 4)
E. Foci
TRUE
c² = a² - b² = 4² - 3² = 16 - 9 = 7
c = √7
The foci are √7 above and below the centre.
F. Foci
False.
The foci are on a vertical line.
f(x)=-3x+8, find f^-1(x) then state whether f^-1(x) is a function
Answer:
-3x + 8 = y
-3x = y - 8
3x = 8 - y
x = (8-y)/3
Now interchanging x and y:-
y = (8-x)/3
Here, y is inverse function i.e. f⁻¹(x)
Hence, f⁻¹(x) = (8-x)/3
Since f⁻¹(x) is a linear expression of x, therefore it is a function.
Step-by-step explanation:
Answer:
Look at the answer of the pic
Why are asymptotes in parenthesis and not brackets
Answer:
Asymptotes, in mathematics, refer to a restriction at the domain set or the range set. It's drawn as a not solid line to indicate, graphically, the values that are not defined to the function.
So, when we express the domain and range sets of a function, we use parenthesis or brackets. In case of having asymptotes we use parenthesis, because that sing indicates an exclusion of the undefined value. On the other hand, the brackets indicates inclusion.
That means, if we use brackets to indicate asymptotes in an interval, that means the value is well defined for the function, which is false.
Name the constant of proportionality for the equation below:
y = -2/3 x
Answer:
[tex]-\dfrac{2}{3}[/tex]
Step-by-step explanation:
When variable y is said to be proportional to another variable x, it is written as:
[tex]y \propto x[/tex]
To introduce the equality sign, we introduce what is called the constant of proportionality, say k and write the above as:
y=kx
Comparing the given equation:
[tex]y=-\frac{2}{3}x[/tex]
We can see that our constant of proportionality:
[tex]k=-\dfrac{2}{3}[/tex]