5. If 2log, x + log, y = 3 then A xy? = 8 В ху3 4 C x²y = 3 D x?y = 8

Q: m=4 , n=5 2 log, 641.B = <+3 = 4 10 1.c=* 2. LetA = 4 4 21 т -7 and D = -1 Find X, if ABT +…

A: Two matrices A=a1a2a3a4 and B=b1b2b3b4 can be multiplied using the rules of matrix multiplication.…

Q: 4 If y = x, then F z = log.y G y = log,z H x = logry z = log,x

A:

Q: Suppose that log, x = 5 and log, y = 4 compute %3| log, Vx²y³

A: Given

Q: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

A: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

Q: n Example 6 we used data from 1920 and projected to 2050 and found that the expected life span in…

A:

Q: Find if z = log2 y – 6 log5 y. dy dz dz In- dy y In 10 dy y ln 10 Option 1 Option 4 64 dz In- 64 dz…

A: We know, ddxlogax = 1x·ln a a·ln b = ln ba ln a - ln b = ln ab

Q: (5) log yz (6) log (7) log (ry) (8) log rvz

A: We will find the value of these problem using logarithm formula.  We know  , log(A/B) = log(A)  -…

Q: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: If k is a positive constant, show that x^2 e^-kx approaches 0 as x --&gt; ∞.

A: Given  The x2e-kx approaches 0 as x→∞.Where k is a positive constant .

Q: Find the Solution set of The followmg equations 2Lo937-310g3 9=7 and LogI3 x-21093 y= 4 and Logs…

A: The given equations are: 2log3x-3log3y=7            (1)log3x-2log3y=4              (2)

Q: 5. Find y' and y". f(x)= log,0 x Find y' if y=In(x²+y?) 6.

A: f(x) = log10x ∴ f'(x) = 1/x and f"(x) = -(1/x2)

Q: 19. If logx y + log, x = 2.9 and xy = 128, find x + y. 24 O 20V2 O 36 O 34V 2 O 66

A:

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A: Given that Nt represents the number of people who are exposed to a particular advertisement. The…

Q: 17. Without using a calculator, solve each of the following: |4*+3 V 16* log, (x+3)+ log, (x-3)=2 b.…

A:

Q: A relationship between (y – 2) and (x – 1) is given by (y – 2) = ab(x -1). . With a suitable linear…

A:

Q: 3. If 19.4 = log (ab) and 7 = log₂ (a), where > 1, then log, (b) equals H 12.4 26 2.8 135.8 ◄ Prev…

A: We want to find the value of logxb.

Q: 1 1 1 The value of log, n log,n SI- log,™ -+- t.

A:

Q: 6. If 16 and log,(x – y) = 2, calculate the values of x and y algebraically. 1/2

A: Given,12x+y=16and log8x-y=2

Q: 2. It is estimated that t months from now, the population of a certain town will be changing at the…

A:

Q: 7. If log, w = and log6x + log6 y = 1, then determine the value of log7 (4) + log6 (36x²y²) ?|

A: topic- logarithmic equations logaa=1log(ab)=log(a)+log(b)logab=log(a)=log(b)log(am)=mlog(a)

Q: Suppose that at time t 0, 10 thousand people in a city with population 100 thousand people have…

A: In this question, the concept of the logistic equation is applied. The Representation  of Logistic…

Q: According to one hypothesis, the growth rate dV/dt of a cell’s volume V is proportional to its…

A:

Q: Here is a new twist on the question. Suppose we want to cool our hot coffee to 100 °F as quickly as…

A: Given:T(t) = A + (To-A)e-ktA = 72°Fk = 0.125To=170°F HenceT(t) = 72 + 170-72e-0.125tT(t) = 72 +…

Q: The number of days a barrel of water lasts varies inversely with the people who consume it. If a…

A:

Q: 1. y = e9z-5 2. y = 2x ln(x +2) 3. y = (2x – 5) log(3x² – 6æ)

A:

Q: It is estimated that i months from now, the population of a certain town will be changing at the…

A:

Q: Suppose that consumers have utility function U(C) = log(C) where C is the consumption level and log…

A: Expected utility is, = 0.4*ln(90) + 0.6*ln(95) = 4.5322

Q: Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both…

A: (a)

Q: 4. The population of Lalaland is 600,000 currently and is expected to grow (continuously) at 3.5%…

A: The present population P =600,000 Growth rate r = 3.5 % per year To find population after time t =…

Q: 2. It is estimated that t months from now, the population of a certain town will be changing at the…

A: This question is related to population growth, We will solve it using integration.

Q: Consider two populations that can be modeled by the logistic equation with the same carrying…

A: We are given two population modeled by logistic equations having same carrying capacity but…

Q: A species of butterflies is calculated to triple the size of its population every year. Which of the…

A: Current number of butterflies=1500

Q: It is projected that t years from now the population of a certain country will be changing at the…

A: We can solve this question as below

Q: At time t = 0, there is one individual alive in a certain population. A pure birth process then…

A: A pure birth process gives the successive birth times as 25.8, 42, 52, 55.8, 59.2, 63.3. The process…

Q: Suppose a certain population is initially absent from a certain area but begins migrating there at a…

A:

Q: 5. Find y' and y". In x (1) f(x)= (2) f(x)= log,o * 6. Find y' if y=In(x²+y?)

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: in The solution of the equation Log(z² – 1) = 7 is %3D Select one: 1 in 1 157 - - 24e 4 and 24e 4 1…

A:

Q: Differentiate y = (9x- 11) log3 (1læ – 9). %3D A. y' = 9(11x-9)+11(9z-11) In(9r-11) (9x-11) In(3)…

A:

Q: 2 log(x+y) = 3log3 +logx + logy

A:

Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

A:

Q: Differentiate y = 3e +7 ln(2x) + log, x- 4" O y' = 15e5 ++ 1 - 4* In 4 %3D - I In 2 O y' = 15e5-1 1…

A: We have to differentiate  y = 3e5x + 7 ln(2x) + log2x - 4x.

Q: 8) Suppose that the number of bald eagles in the U.S. at any given time is given by P(t) = 50, 000 –…

A:

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A: The logistic equation is given as dNdt=Na-bN and its solution is given as N(t)=aN0bN0+a-bN0e-at…

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A: Given relation is: Qt=-t3+6t2+24t a). The worker's rate of production at 11 AM: So put t=3 in given…

Q: A certain hermit wants to design a reactor using radioactive material A that will be converted into…

A: Topic :- Differential equation

Q: 7. If the equation 3(5)“ =k is solved for x in terms of k, the result is 1 k (1) x=-log, 3 3 = 2…

A: Solving this expression we have

Q: 2 log, 64|,B = |** 6 [x +3 = 4 В 10 -4] 4 [m LetA = 4 21 3. 2 -7 5 4 and D =, *,. Find X, if AB" +…

A: To find the value of X.

Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.