Try This 1 Suppose that you begin with a single E. coli baderium at time 0, and the conditions arme appropriate for the bacteria to double in population every 20 min. This growth can be modelled using the equation P= P. (2)20. 1. a. Create a table that shows the number of bacteria at 20-min intervals for 5 n. Your table might start out like this one. Time (in min) Number of Bacteria 0 20 40 Di Use your table to ostmate when there would be 10 000 bacteria 2 a. Follow the steps in the following table to algebraically determine an approximate time when there would be 10 000 bacteria. Make the assumption that the equation P=P, (2)á can be used to find an approximate time where there would be 10 000 bactena Write the equation Substitute the known values for P and P 10 000-102 11235 10 000 = 220 --230 Take the logarithm of both sides of the equation, Hint: log10 000 = log 2 PRACTICE Use the power law of logarithms log, ("). n log, M. to bring down the exponent 20 Divide both sides of the equation by log 2 QUOTIUN Multiply both sides of the equation by 20. Determine a decimal approximation of t. b. How does the time you determined in 2.a. compare to your estimate from 1.b.?

Explicit rule for 10th element of  (-7, -6, -5, -4, -3, ...) is  -7 + (n-1) , for {5, 7, 9, 11, 13, ...} is 5 + 2(n-1), for {0, 7, 26, 63, 124, ...} is 7(n-1)^2.

The Explicit rule for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.

An explicit rule for the sequence (-7, -6, -5, -4, -3, ...) is given by the formula:

a(n) = -7 + (n-1)

This formula generates the terms of the sequence by starting with the first term, -7, and adding the value of n-1 to it for each subsequent term.

To find a10, we can plug in 10 for n in the formula:

a(10) = -7 + (10-1)

= -7 + 9

= 2

So, a10 = 2.

An explicit rule for the sequence {5, 7, 9, 11, 13, ...} is given by the formula:

a(n) = 5 + 2(n-1)

This formula generates the terms of the sequence by starting with the first term, 5, and adding 2(n-1) to it for each subsequent term.

To find a10, we can plug in 10 for n in the formula:

a(10) = 5 + 2(10-1)

= 5 + 18

= 23

So, a10 = 23.

An explicit rule for the sequence {0, 7, 26, 63, 124, ...} is given by the formula:

a(n) = 7(n-1)^2

This formula generates the terms of the sequence by starting with the first term, 0, and adding 7(n-1)^2 to it for each subsequent term.

To find a10, we can plug in 10 for n in the formula:

a(10) = 7(10-1)^2

= 7(9)^2

= 7(81)

= 56

So, a10 = 567.

An explicit rule for the sequence {1/3, 1/2, 3/5, 2/3, 5/7, ...} is given by the formula:

a(n) = (n-1)/(n+1)

This formula generates the terms of the sequence by starting with the first term, 1/3, and adding (n-1)/(n+1) to it for each subsequent term.

To find a10, we can plug in 10 for n in the formula:

a(10) = (10-1)/(10+1)

= 9/11

So, a10 = 9/11.

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The expression  aₙ > 0 and lim n → [∞] aₙ + 1 is true.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

And we need to check whether the given statement is true or not.

While we looking into the given question, we have identified the following expression,

=> lim n → [∞] aₙ + 1

Here we have also know that the value of aₙ > 0.

When we equate the given expression with zero, we have get the following expression,

=> lim n → [∞] aₙ + 1 = 0

=>  lim n → [∞] aₙ = -1

Here we have given the condition that,  aₙ >0, so

=> lim n → [∞] aₙ = 0

Therefore, the expression is zero.

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Answer:

= 1/c

Step-by-step explanation:

Apply the sum/Different Rule: ( f + g ) ' = f ' + g'

= d/dx (x/c) + d/dx (b)

d/dx (x/c) = 1/c

d / dx (B) = 0

= 1/c + 0

Simplify = 1/c

Answer:

Step-by-step explanation:

An easy way to do slope is to know the formula which is (y1-y2)/(x1-x2)

In this case you have two points (2,5) and (0,-1)

2 = x1 (cause it’s the first x)

5 = y1 (cause it’s the first y)

0 = x2 (second x)

-1 = y2 (second y)

So the slope would be

(5-(-1))/2-0= 6/2 = 3

Answer:

no solution

Step-by-step explanation:

4(-8x+5)=-32x-26

first thing to do would be distribution

-32x+20=-32x-26

then add 32 from the right side to the left (or switch it doesn’t matter)

0x+20=-26

subtract 20 from both sides

0x=-46

since there is no x value the answer would be no solution

hope this helps!!

Answer: No solution

Step-by-step explanation:

4(-8x+5) = -32x-26

1. Divide the 4 from both sides of the equation

-8x+5 = -32x/4 - 26/4

-8x+5 = -8x-24

2. Get variables on one side and constants on the other

0≠ -29

no solution

For the linear equations provided by the coordinates in the table;

The first equation of this system is y = -2x.

The second equation of this system is y = x - 3.

The solution to the system is (1, -2).

We have four points (-5,10), (-1,2), (0,0), and (11,-22) for first equation, and four points (-8,-11), (-2,-5), (1,-2), and (7,4) the second equation.

The slope (m) is given by the formula (y2 - y1) / (x2 - x1).

For the first line, we can use the points (-5,10) and (-1,2)

m1 = (2 - 10) / (-1 - (-5)) = -8/4 = -2.

the first equation is y = -2x

the second line, we can use the points (-8,-11) and (-2,-5)

m2 = (-5 - -11) / (-2 - -8) = 6/6 = 1.

the second line has a slope of 1,

the equation should have the form y = x + c.

To find c, we can use one of the points, for instance (-2,-5):

-5 = -2 + c => c = -5 + 2 = -3.

So, the second equation is y = x - 3.

the solution to the system, we need to find where the two lines intersect.

y = -2x

y = x - 3

Setting both equation equally

-2x = x - 3

=> 3x = 3

=> x = 1.

Substituting x = 1 into the first equation

y = -2(1) = -2.

the solution to the system of linear equation would be (1, -2).

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Answer:

The number is already in standard form: 13450000000

Step-by-step explanation:

This number isn't in scientific notation. It is written like a regular number, which is also standard form.

Answer:

13450000000

Step-by-step explanation:

The number is already in standard form.

The DC current gain (βdc) of the transistor is 73.

The DC current gain (βdc) of a transistor is the ratio of the collector current (IC) to the base current (IB) at DC conditions. Therefore, to determine the βdc of a transistor with IB = 50 µA and IC = 3.65 mA, we simply substitute these values into the equation:

βdc = IC / IB

βdc = 3.65 mA / 50 µA

βdc = 73

Therefore, the DC current gain (βdc) of the transistor is 73.

This result indicates that for every 1 µA of base current, the transistor can allow 73 µA of collector current to flow. A high βdc value indicates that the transistor can provide significant amplification in a circuit. In addition, the βdc value is essential in selecting the appropriate biasing resistors and determining the operating point of the transistor in amplifier circuits.

Thus, by determining the βdc value, we can gain valuable insights into the performance characteristics of a transistor and how it can be used in various circuit designs.

Therefore, The DC current gain (βdc) of the transistor is 73.

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Answer:

-12 < x < 18

Step-by-step explanation:

x-3 < 15

x < 18

and

-x + 3 < 15

-x < 12

x > -12

The real-world problem involving a related set of two equations is given below:

Problem: Cost of attending a concert  is made up of base price and variable price per ticket. You are planning to attend a concert with your friends and want to know the number of tickets to purchase for lowest overall cost.

The related set of two equations are:

Equation 1: The total cost (C) of attending the concert is given by:

The equation C = B + P x N,

where:

B  = the base price

P  = the price per ticket,

N = the number of tickets purchased.

Equation 2: The maximum budget (M) a person have for attending the concert is:

The  equation M = B + P*X

where:

X = the maximum number of tickets a person can afford.

So by using the values of B, P, and M, you can be able to find the optimal value of N that minimizes the cost C while staying within your own budget M. so, you can now determine ticket amount to minimize costs and stay within budget.

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Answer :A trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides. So a parallelogram is also a trapezoid. Carlos says, A trapezoid has at least one pair of parallel sides, but it can also have another.

Step-by-step explanation:

The correlation between temperature in Celsius and temperature in Fahrenheit is a perfect positive correlation.

The relationship between temperature in Celsius and temperature in Fahrenheit is a perfect positive correlation. This means that as one variable (temperature in Celsius) increases, the other variable (temperature in Fahrenheit) increases at the same rate.

The reason for this perfect positive correlation is that the two scales are directly proportional to each other, with the same slope and intercept. Specifically, the formula for converting Celsius to Fahrenheit is F = (9/5)C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.

Thus, any change in Celsius will result in an equivalent change in Fahrenheit. This correlation is observed among typical stat100 students, as well as in any other population where the two temperature scales are used.

Therefore, a perfect positive correlation exists between the temperature in Celsius and the temperature in Fahrenheit

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Hey there! :)

Answer:

y = 10/9x + 8/3

Step-by-step explanation:

A line that is perpendicular to y = -9/10x - 10 has a slope that is the negative reciprocal. Therefore:

-9/10 --> 10/9. This is the slope of line q.

Use the formula y = mx + b where:

m = slope

x = x coordinate of point

y = y coordinate of point.

-4 = 10/9(-6) + b

-4 = -60/9 + b

Create a common denominator:

-36/9 = -60/9 + b

24/9 = b

Simplify:

b = 8/3.

Rewrite the equation:

y = 10/9x + 8/3

Answer:

50:75

Step-by-step explanation:

let the ratio of 2:3 be x

now,

125=2+3x

or,5x=125

therefore,x=125/5

                x=25

now,

2x=25*2

   =50

3x=25*3

    =75

Answer:

B

Step-by-step explanation:

Answer:

The answer is 6 to 12

Step-by-step explanation:

There are 6 ducks, and 12 chickens so therefore the ratio of ducks to chickens is 6:12. Hope this helps! (Brainliest pleasee I need one more!!) <3

Answer:

The manager predicts that 3 less hats will be sold for every $1 increase in price. For what prices can the manager predict that at least 50

Step-by-step explanation:

The manager can predict $26 that at least 80 hats will be sold.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost of one hat = $16.

And number of hats sold by manager = 120.

Also, given that,

if $1 increases 4 fewer hats will be sold.

To find the price when 80 hats will be sold.

40 fewer hats should be sold.

4 fewer hats increases $1.

40 fewer hats will increase $1 x 10 = $10.

So the price of new price of hat = 16 + 10 = $26,

At $26 per hat the manager can sell at least 80 hats.

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The Taylor series expansion by plugging in the values f(z) = f(z0) + f'(z0)(z - z0) + f''(z0)(z - z0)²/2,f(z) = (ln(sqrt(2)) + i (-π/4)) + (-1/2 - (1/2)i)(z - (-1 + i)) + (i/2)(z - (-1 + i))²/2

The principal value of the logarithm, denoted as Log z, is defined as follows:

Log z = ln |z| + i Arg(z)

The function Log z is analytic in the complex plane except for the branch cut along the negative real axis, which is the set of points of the form x + 0i where x ≤ 0. This branch cut is necessary to define a consistent argument (Arg) for the complex logarithm.

To expand the principal value of the logarithm in a Taylor series with centre z0 = -1 + i, the following formula for a complex function:

f(z) = f(z0) + f'(z0)(z - z0) + f''(z0)(z - z0)²/2! + f'''(z0)(z - z0)³/3! +

Let's start by finding the values of the function and its derivatives at z0 = -1 + i:

f(z0) = Log z0 = ln |-1 + i| + i Arg(-1 + i)

To find the modulus |z0|,use the distance formula in the complex plane:

|-1 + i| = sqrt((-1)² + 1²) = sqrt(2)

To find the argument Arg(-1 + i),use the inverse tangent function:

Arg(-1 + i) = atan(1/-1) = atan(-1) = -π/4

Therefore, f(z0) = ln(sqrt(2)) + i (-π/4).

Now, let's calculate the first derivative:

f'(z) = d/dz (ln |z| + i Arg(z))

= 1/z

At z = z0,

f'(z0) = 1/(-1 + i)

To simplify the expression, multiply the numerator and denominator by the conjugate of -1 + i:

f'(z0) = (1/(-1 + i)) × ((-1 - i)/(-1 - i))

= (-1 - i)/((-1)² - (i)²)

= (-1 - i)/(1 + 1)

= (-1 - i)/2

= -1/2 - (1/2)i

Now, let's calculate the second derivative:

f''(z) = d/dz (1/z)

= -1/z²

At z = z0,:

f''(z0) = -1/(-1 + i)²

To simplify the expression, square the denominator:

f''(z0) = -1/((-1 + i)²)

= -1/((-1 + i)(-1 + i))

= -1/(1 - 2i + i²)

= -1/(1 - 2i - 1)

= -1/(-2i)

= (1/2i)

= (1/2i) × (i/i)

= i/2

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The multiplied form of the expression 5abc⁵⋅3a²b³ is 15 a³b⁴c⁵.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given expression is,

5abc⁵⋅3a²b³.

To multiply the given expression,

Use multiplication mathematical operation,

15abc⁵.a²b³

15 a³b⁴c⁵

The required expression is 15 a³b⁴c⁵.

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Interactions involving dummy variables can provide insights into the different effects of independent variables across categories.

1. Dummy variables are binary variables that represent categorical variables in a regression analysis. When interactions are included between dummy variables and other independent variables, it allows for differential effects of the independent variables based on the different levels of the categorical variable.

For example, let's consider a regression model to predict income based on education level and gender. We can include an interaction term between education level (represented by dummy variables for different levels) and gender. This interaction term allows us to examine whether the effect of education level on income differs between males and females. It helps capture any gender-specific differences in the relationship between education and income.

1.2 The linear probability model (LPM) is a common approach to estimate the probability of an event occurring using a linear regression framework. However, it has several problems:

1. The predicted probabilities from the LPM can fall outside the [0, 1] range: Since the LPM does not impose any restrictions on the predicted probabilities, they can sometimes exceed the valid probability range. This violates the assumption of probabilities being bounded between 0 and 1.

2. Heteroscedasticity: The LPM assumes constant error variance across the range of the predictors. However, in practice, the variability of the error term may change with different levels of the predictors, resulting in heteroscedasticity. This violates the assumption of homoscedasticity.

3. Non-linearity: The LPM assumes a linear relationship between the predictors and the probability of the event. However, this may not always be the case, and using a linear model can result in misspecification.

To remedy these problems, an alternative to the LPM is to use logistic regression or probit regression models. These models explicitly model the probability of an event occurring and address the issues mentioned above. They provide predicted probabilities that fall within the valid range of 0 to 1, account for heteroscedasticity, and allow for non-linear relationships between the predictors and the probability of the event.

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Answer:

y=1/4x+5

Step-by-step explanation:

1/4x is your slope you get from graphing

The time of depreciation is 3.3 year

From the question, we have the following parameters:

Initial value = $27,300

Final value = $22,100

Rate of depreciation = 6.1% per year

These parameters can be represented using the following exponential equation

A(n) = A *(1 - r)ⁿ

Where

n = number of years

A  = Initial value = 27300

A(n) = Final value = 22100

r = rate of decay = 6.1%

Substitute the known values in the above equation, so, we have the following representation

27300*(1 - 6.1%)ⁿ = 22100

Divide

(1 - 6.1%)ⁿ = 0.81

0.939ⁿ = 0.81

Take the logarithm

n = log(0.81)/log(0.939)

Evaluate

n = 3.3

Hence, the number of years is 3.3 year

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Answer:

Step-by-step explanation:

Multiple the numbers one by one and the answers you’ll get u can choose to divide multiple plus or minus and u will get the answer

Options :

A. g - 0.05

B. g - 0.05g

C. 0.95g

D. 0.058

E. (1 – 0.05)g

Answer:

B. g - 0.05g

C. 0.95g

E. (1 – 0.05)g

Step-by-step explanation:

Given that :

Amount of Rainfall last week = g inches

Percentage change in Rainfall amount this week = 5%

Rainfall amount this week:

Amount of Rainfall lastweek(100% - 5%)

g(1 - 0.05) = g - 0.05g

g(1 - 0.05)

g(0.95) = 0.95g

Thus the expression, Amount of Rainfall lastweek(100% - 5%) could be rewritten or simplified into any of the expressions above and still arrive at the same solution.

Answer:

The answer is letter B.

Step-by-step explanation:

go left 2

up 3

Answer:

.3x - x

Example

My item is $100

.3(100) - $100

$30 - $100 = $70

$70 is the new price

Answer:

two and eighty-one thousandths

Step-by-step explanation:

Answer: two and eighty-one thousandths

Step-by-step explanation:

      We will write this out in words. The one is in the thousandths place, so we read it as eighty-one thousandths.

2 ➜ two

. ➜ and

81 ➜ eighty-one

0.081 ➜ eighty-one thousandths

2.081 ➜  two and eighty-one thousandths

The question is incomplete:

The telephone company offers two billing plans for local calls. Plan 1 charges ​$38 per month for unlimited calls and Plan 2 charges ​$18 per month plus ​$0.04 per call.

Use an inequality to find the number of monthly calls for which plan 1 is more economical than plan 2.

Answer:

Plan 1 is more economical than plan 2 when you make more than 500 monthly calls.

Step-by-step explanation:

Plan 1 costs $38 per month for unlimited calls and plan 2 costs $18 per month plus ​$0.04 per call which is: 18+0.04x and you can infer that plan 1 would be cheaper when you have to pay more than $38 using plan 2 and you can express it with the inequality:

18+0.04x>38, where x is the amount of monthly calls

Now, you can solve for x:

0.04x>20

x>20/0.04

x>500

According to this, plan 1 is more economical than plan 2 when you make more than 500 monthly calls.

The following statements can be concluded if ∠ABC and ∠CBD are a linear pair:

B. ∠ABC and ∠CBD are supplementary.

D. ∠ABC and ∠CBD are adjacent angles.

In Mathematics, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.

According to the linear pair theorem, ∠ABC and ∠CBD are supplementary angles because BDC forms a line segment. Therefore, we have the following:

∠ABC + ∠CBD = 180° (supplementary angles)

m∠ABC ≅ m∠CBD (adjacent angles)

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The correct order for picking u in Integration by Parts is: Logarithmic Function - Inverse Trigonometry Function - Algebraic Function - Trigonometric Function - Exponential Function.

The formula for using Integration by Parts is: ∫f(x)g(x)dx = f(x)∫g(x)dx - ∫f'(x)∫g(x)dx.

The evaluation of ∫f(x)cos(x)dx gives the answer xsin(x) - cos(x) + C.

The evaluation of ∫ln(2x)dx gives the answer xln(2x) - x + C.

The evaluation of ∫f(x)²cos(x)dx gives the answer x²sin(x) - 2xcos(x) - 2sin(x) + C.

When using Integration by Parts, it is important to choose the correct order for picking u. The correct order is determined by the acronym "LIATE," which stands for Logarithmic Function, Inverse Trigonometry Function, Algebraic Function, Trigonometric Function, and Exponential Function. Among the given options, the correct order is (a) Logarithmic Function - Inverse Trigonometry Function - Trigonometric Function - Algebraic Function - Exponential Function.

Integration by Parts is a technique used to integrate the product of two functions. The formula for Integration by Parts is ∫f(x)g(x)dx = f(x)∫g(x)dx - ∫f'(x)∫g(x)dx. This formula allows us to split the integral into two parts and simplify the integration process.

To evaluate ∫f(x)cos(x)dx, we use Integration by Parts. By choosing f(x) = x and g'(x) = cos(x), we find f'(x) = 1 and g(x) = sin(x). Applying the formula, we get xsin(x) - ∫sin(x)dx, which simplifies to xsin(x) - cos(x) + C.

To evaluate ∫ln(2x)dx, we again use Integration by Parts. By choosing f(x) = ln(2x) and g'(x) = 1, we find f'(x) = 1/x and g(x) = x. Applying the formula, we get xln(2x) - ∫(1/x)x dx, which simplifies to xln(2x) - x + C.

To evaluate ∫f(x)²cos(x)dx, we once again apply Integration by Parts. By choosing f(x) = x² and g'(x) = cos(x), we find f'(x) = 2x and g(x) = sin(x). Applying the formula, we get x²sin(x) - ∫2xsin(x)dx. Integrating ∫2xsin(x)dx leads to -2xcos(x) - 2sin(x) + C. Thus, the final result is x²sin(x) - 2xcos(x) - 2sin(x) + C.

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