problem 6. a population of bacteria, growing according to the malthusian model, doubles itself in 10 days. if there are 1000 bacteria present initially, how long will it take the population to reach 10,000?

Answer:

c = 72/0.45

c = 160

So the value of c =160

well, let's call "c" the 100%, and we know that 45% of that is 72, hmmm so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} c & 100\\ 72& 45 \end{array} \implies \cfrac{c}{72}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{ c }{ 72 } ~~=~~ \cfrac{ 20 }{ 9 }\implies 9c=1440\implies c=\cfrac{1440}{9}\implies c=160[/tex]

Withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

The actions of withdrawing $ from your checking account and depositing it into a savings account will affect the measures of money supply, M1 and M2, as follows:

M1: M1 is a measure of the narrowest definition of the money supply, which includes all currency (including coins), checking accounts, and travelers' checks. Withdrawing money from your checking account will reduce the amount of money in M1. However, depositing the funds into a savings account will not have any impact on M1 since savings accounts are not included in this measure of the money supply.

M2: M2 is a measure of the broader definition of the money supply, which includes M1 and all-time deposits, savings accounts, and money market securities with a value of less than $100,000. Depositing money into a savings account will increase the amount of money in M2, as savings accounts are included in this measure of the money supply. However, withdrawing money from a checking account will not have any impact on M2 as the decrease in M1 will be offset by the increase in savings accounts.

Therefore, In conclusion, withdrawing money from a checking account and depositing it into a savings account will only affect M1 and reduce the amount of money in this measure of the money supply. M2 will remain unchanged.

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Question Correction: Suppose you withdraw $6,000 from your checking account and use the funds to invest in a savings account at the bank. How will these actions affect M1 and M2?

A. M1 wil decrease and M2 wil not change

B. M1 and M2 will increase

C. M1 and M2 will not change.

D. M1 wil decrease and M2 will increase

In a 10-player round-robin tennis tournament, each player must play 45 games, and a total of 90 games will be played in the tournament.

A round-robin tournament is a type of competition in which every participant plays against every other participant. In a 10-player tournament, the number of games needed can be calculated using the formula for combination.

The density of a tournament can be defined as the number of games each player must participate in to play against every other player.

To calculate the density of a 10-player round-robin tournament, we use the formula

=> n(n-1)/2,

where n is the number of players.

In this case, n = 10. So, the density of the tournament is

=> 10(10-1)/2 = 45.

This means that each player must play 45 games in total, and each game involves 2 players.

So, there will be a total of

=> 45*2 = 90

games played in the tournament.

To summarize, The density of the tournament, 45 games per player, is calculated using the formula n(n-1)/2.

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a) The number of poker hands with exactly 2 aces and 3 kings is 24.

b) The probability that the first king is dealt out on the 13th card is approximately 0.0045, or approximately 0.45%.

a) To find the number of poker hands with exactly 2 aces and 3 kings, we have to choose which 2 aces out of the 4 available and which 3 kings out of the 4 available to include in our hand. We can do this in C(4,2) * C(4,3) ways, where C(n, k) is the number of combinations of n things taken k at a time.

Therefore, the number of poker hands with exactly 2 aces and 3 kings is C(4,2) * C(4,3) = 6 * 4 = 24.

b) The probability that the first king is dealt on the 13th card is the number of combinations of 12 cards that do not include any kings divided by the total number of combinations of the first 12 cards. This can be calculated as (48 choose 12) / (52 choose 12), where C(n, k) is the number of combinations of n things taken k at a time.

The probability is (48 choose 12) / (52 choose 12) = (48! / (12! * (48-12)!) ) / (52! / (12! * (52-12)!)) = (48 * 47 * 46 * 45 * 44 * 43 * 42 * 41 * 40 * 39 * 38 * 37) / (52 * 51 * 50 * 49 * 48 * 47 * 46 * 45 * 44 * 43 * 42 * 41) = approximately 0.0045, or approximately 0.45%.

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The simplified dorm of the expression [tex]\frac{\sqrt{15}}{5\sqrt{48}}\times\frac{\sqrt{48}}{\sqrt{48}}[/tex] is √720/240.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, A radical expression [tex]\frac{\sqrt{15}}{5\sqrt{48}}[/tex].

Therefore,

[tex]\frac{\sqrt{15}}{5\sqrt{48}}\times\frac{\sqrt{48}}{\sqrt{48}}[/tex].

= (√15×√48)/(5×48).

= √720/240 or √720×(1/240).

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Answer:

5

Step-by-step explanation:

This is a classic example of a system of equations with two variables. We can set up two equations to represent the given information:

x = number of ducks

y = number of sheep

heads: x + y = 15

legs: 2x + 4y = 38

To solve for the number of ducks, we can use substitution. We can solve one of the equations for one of the variables and substitute it into the other equation.

For example, solving the first equation for y: y = 15 - x. Then substitute it into the second equation:

2x + 4(15 - x) = 38

Solving this equation will give you the value of x, which is the number of ducks.

x = 5

So, there are 5 ducks in the meadow.

Answer:

ofc 15 heads 15 ducks bro comman sense no logic in there

The Probability that a randomly selected student who performed in the spring play, but did not perform in the spring concert is chosen is 26/53.

Now let A be the event of the student performing in Spring play

Let B be the event of students performing i the spring concert

Now according to what we know,

n(A) = 68

n(B) = 54

n(A ∩ B) = 16

Now total no. of students will be n(A U B) = 68 + 54 - 16

= 106

We need to find the number of people who performed in the spring play and not in the concert

Hence we need to find the Probability

P(A ∩ not B)

Now we can say that (A ∩ not B) will clearly be

A - (A ∩ B) Hence we get it to be

68 - 16 = 52

Hence, P(A ∩ notB) = 52/106

= 26/53

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The investor is doing a two-stage sampling or a two-phase sampling. This type of sampling involves two steps: first, a simple random sampling is used to create a set of groups, and then individuals are selected from within the selected groups for analysis.

In this case, the investor created 10 groups through simple random sampling and then selected and analyzed all the individuals in two groups. Random sampling is a statistical sampling technique where a sample is selected from a larger population so that each member of the population has an equal chance of being selected. This means that the sample should be selected randomly and not based on systematic or predetermined criteria.

The goal of random sampling is to produce a sample representative of the population, allowing for more accurate inferences about the population as a whole. Random sampling helps to eliminate bias in the sample selection process, improving the accuracy and validity of the results obtained from the sample.

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The numerical form of the statement is 4n + 7 = 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement the sum of 4 times a number and 7 is equal to 2.

Let, The number be 'n'.

The numerical form of the statement will be,

4n + 7 = 2.

4n = 2 - 7.

4n = - 5.

n = - 5/4.

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The competition took 2 minutes.

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

Given that, the Turtle and Achilles compete. They start at the same time from the same place. Achilles runs at a speed of 13 mph while the Turtle moves at a speed of 1 mph. When Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him.

Let t be the time taken in competition and the distance covered by Achilles be x miles.

We have been given that when Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him. This means that the distance covered by turtle will be: x - 2/5

Since we know that, speed = distance / time

So, we can set two equations for time taken by Achilles and turtle as:

t = x / 13

x = 13t......(i)

t = (x-2/5)/1....(ii)

Substituting this value in equation (2) we will get,

t = 13t - 2/5

5t = 65t - 2

60t = 2

t = 2/60

t = 1/30

So, the competition took 1/30 hour, let us convert our given time in minutes.

1/30 × 60 minutes

= 2 minutes

Hence, the competition took 2 minutes.

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The nth value equals 1 more than twice the previous value.

This statement correctly describes the sequence {1, 3, 7, 15, ...}, as each value in the sequence is 1 more than twice the previous value.

Answer:

What equation

Step-by-step explanation:

The minimal degree of the Taylor Polynomial required to calculate to 4 decimal places depends on the smoothness of the function and the error term in the Taylor Series is 0.0001

Taylor Polynomial is a mathematical tool used to approximate a function near a point using a polynomial. The degree of the polynomial determines how accurate the approximation is.

To calculate a Taylor Polynomial to 4 decimal places, we need to use a minimal degree that provides us with the desired accuracy.

The minimal degree depends on the smoothness of the function we are trying to approximate. The smoother the function, the lower the degree we need.

However, if the function has many twists and turns, we may need a higher degree to get the desired accuracy.

To calculate a Taylor Polynomial to 4 decimal places, we need to consider the error term in the Taylor Series.

The error term represents the difference between the actual value of the function and its approximation.

If the error term is less than 0.0001, we can be confident that our approximation is accurate to 4 decimal places.

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The probability of the union of events a and b is 0.21. the sum of their individual probabilities : P(a ∪ b) = 0.01 + 0.2 = 0.21.  Events a and b are mutually exclusive, it means that they cannot both happen at the same time.

In the event that occasions an and b are totally unrelated, it implies that the two of them can't occur simultaneously. In this way, the likelihood of their association (that is, the likelihood that either occasion an or occasion b will happen) is the amount of their singular probabilities:

P(a ∪ b) = P(a) + P(b)

Considering that P(a) = 0.01 and P(b) = 0.2, we can ascertain the likelihood of their association:

P(a ∪ b) = 0.01 + 0.2 = 0.21

In this way, the likelihood of the association of occasions an and b is 0.21.

The likelihood of occasion An incident is 0.01 and the likelihood of occasion B happening is 0.2. Assuming that these occasions are fundamentally unrelated, it implies the two of them can't occur simultaneously. The complete opportunity of either occasion An or occasion B happening is found by including the singular probabilities. In this way, the likelihood of occasion An occurrence or occasion B happening is 0.01 + 0.2 = 0.21. In basic terms, the opportunity of either occasion happening is 0.21.

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Explanation:

Each term has an x attached to it. We add the numbers in front

4x+7x+x = 4x+7x+1x = (4+7+1)x = 12x

Think of it like saying

4 boxes + 7 boxes + 1 box = 12 boxes

Replace each "boxes" with the letter "x".

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

-5x-3(-3) = -7

Apply distributive property:

(-5x)*-3 + (-3)*-3

15x + 9 = -7

      -9    -9

15x = -15

Divide both sides by 15:

15x/15 = x

-15/15 = -1

[tex]x=-1[/tex]

Hope this helped!

Yes, if function f(x) = 5, then f is defined for all x, including x = 1.

Yes, f is defined for every x, including x = 1, if f(x) = 5. And if f is defined at x = 1, then f(1) = 5. The equation f(x) = 5 means that the function f takes on the value 5 for all x, so if the function is defined at x = 1, its value at that point must be 5.

The term "function" refers to a relationship between a set of inputs and outputs. To put it simply, a function is a relationship between inputs where each input is associated to exactly one output.

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The value of constant a is 2.45.

To find the value of the constant a, we need to make sure that the pdf (probability density function) is properly normalized. The pdf must satisfy the following property:

∫[a, ∞] f(x) dx = 1

In this case, we have pdf:

∫[a, ∞] (12/x^3) dx = 12∫[a, ∞] (1/x^3) dx

= 12 [-1/(2x^2)]ₐ∞

= 12 * (1/(2a^2))

= 6/ a²

Therefore, to ensure that the integral is equal to 1, we need:

6/ a² = 1

Solving for a:

a^2 = 6

a = ±√6

Since x is always positive, we have a = √6 ≈ 2.45.

So, the constant a is equal to 2.45.

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Answer:

(t + 3)(7t - 2)

Step-by-step explanation:

7t² - 19t - 6

consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term

product = 7 × - 6 = - 42 and sum = - 19

the factors are 21 and - 2

use these factors to split the t- term

7t² + 21t - 2t - 6 ( factor the first/second and third/fourth terms )

7t(t + 3) - 2(t + 3) ← factor out (t + 3) from each term

(t + 3)(7t - 2) ← in factored form

Answer:

196 grams of zinc

Step-by-step explanation:

[tex]\frac{4}{11}=\frac{z}{539}\\ \\(539)(4)=11z\\\\2156=11z\\\\196=z[/tex]

Thus, the jar of the chemical will contain 196 grams of zinc.

Answer:f

Step-by-step explanation:

its not that hard

The function is concave up for  x < 1 and concave down for x > 1 because the second derivative is positive for x < 1 and negative for x > 1. As a result, the critical point at x  < 1 is a relative maximum.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is common to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The derivative of the function f(x) can be found by taking the derivative of the expression e^(-x) (x^2 + 2x) using the product rule:

f'(x) = -e^(-x) (x^2 + 2x) + e^(-x) (2x + 2) = 2e^(-x) - 2xe^(-x) (x + 1)

Setting f'(x) equal to zero and solving for x gives us the critical points:

0 = 2e^(-x) - 2xe^(-x).(x + 1)

2xe^(-x).(x + 1) = 2e^(-x)

x(x + 1) = e^x

x^2 + x - e^x = 0

Next, we determine the concavity of the function at the critical points by analyzing the second derivative of the function:

f''(x) = 2e^(-x) + 2xe^(-x) + 2xe^(-x).(x + 1) - 2e^(-x).(x + 1)

= 2e^(-x).(1 - x)

Since the second derivative is positive for x < 1 and negative for x > 1, the function is concave up for x < 1 and concave down for x > 1. Thus, the critical point at x < 1 corresponds to a relative maximum.

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Changing a figure's location without spinning, reflecting, or changing its size is known as a translation in geometry.So g(x) = ln[1/8(x - 3)] + 1.

When you group "3" with the "right-left" variable, which is "x," you will have 3 units to the right.

However, "x" is the opposite of what it seems to be, therefore in order to shift right, you must subtract 3 from "x," making ln(x) into ln (x - 3).

Simply add 1 to the function to advance it up one unit, making ln(x-3) become ln(x-3) + 1.

In order to multiply the "horizontal variable" (also known as "x") by a factor of 8, you must divide by 8 (or multiply by 1/8), because "x" is the opposite of what it seems to be.

Ln(x - 3) + 1 so becomes Ln[1/8(x - 3)] + 1.

so that g(x) = ln[1/8(x - 3)]

+ 1.

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Answer:

Step-by-step explanation:

what two numbers can you multiply that will equal to 30 when you multiply but 13 when you add them?

10+3=13     10*3=30  

so we can use 10 and 3

since the first symbol (x^2+13x) is positive than the bigger number you got earlier (10) will be positive

(x+10)

since the second symbol (13x+30) is positive than our next symbol will be positive as well

(x+3)

combine them so now they are (x+10)(x+3)

Answer:

Basket A contains 8 balls, basket B contains 8 + 6 = 14 balls, and basket C contains 17 - (8 + 6) = 3 balls.

Let's call the number of balls in basket A "x".

Since there are 6 more balls in basket B than in basket A, we can write the equation for the number of balls in basket B as x + 6.

And since the total number of balls in baskets B and C is 17, we can write the equation for the number of balls in basket C as 17 - (x + 6) = 17 - x - 6.

So the total number of balls in baskets A, B and C is x + (x + 6) + (17 - x - 6) = x + x + 6 + 17 - x - 6 = 22.

Therefore, we can solve for x:

2x + 6 = 22

2x = 16

x = 8

So basket A contains 8 balls, basket B contains 8 + 6 = 14 balls, and basket C contains 17 - (8 + 6) = 3 balls.

Regarding the carpet, a room measuring 5 m x 7 m is 35 m². If each box of carpet covers 10 m², then 35 m² will need 35/10 = 3.5 boxes of carpet. This means that there will be 3.5 boxes * 10 m²/box = 35 m² of carpet. So there will be no carpet left over.

Answer:

-----------------------------

We have:

Use the difference of the first two equations to find A:

Then find B, using third equation:

Finally find C, using second equation:

Area of the room is:

If each box covers 10 m² we need to buy 4 boxes:

Carpet left over:

The ESE (estimated standard error) in the bottom of the independent-measure t statistic measures the variability in the sample data used to calculate the t statistic and provides information on the precision of the t statistic.

The t statistic is used to compare the difference between two means from independent groups to determine if the difference is significant or not.

The ESE reflects the degree of uncertainty in the difference between the two sample means and is calculated as the standard deviation of the sampling distribution of the difference between the two sample means. The ESE is an estimate of the standard deviation of the population difference and is used to calculate the t statistic.

The ESE is an important measure because it provides information on the precision of the t statistic, which is used to make inferences about the population difference. If the ESE is large, it means that the sample difference is less precise and the t statistic is less significant. If the ESE is small, it means that the sample difference is more precise and the t statistic is more significant.

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Answer:

The answer is C

Step-by-step explanation:

This is because the graph shifts to the right as the value correlated with x is 6, meaning the new zeros of the graph would be at (0,0) and (6,0)

The volume in units of cubic inches is 101.63 cubic inches.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

1 quart is equal to 57.75 cubic inches. So, to convert a volume of 1.75 quarts to cubic inches, we multiply by 57.75:

1.75 quarts × 57.75 cubic inches/quart = 101.63 cubic inches

Therefore, the volume of the box of ice cream in cubic inches is 101.63 cubic inches.

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Domain: (-6, -1]

This is where the graph lines up with the x-axis.

Range: [-6, 4)

This is where the graph lines up with the y-axis.

See the two pictures for a visual reason why.

The integral is evaluated and the value of the integral is found to be 3/2.

Given that,

The integral is ∫∫(5+10y) dy dx

To find : To evaluate the iterated integral,

= ∫(5y + 10y²/2) dx

= ∫ (5y + 5y²) dx

Substituting the limits x and x² in the variable y

= ∫ (5x + 5x² - (5x² + 5x⁴)) dx

= ∫(5x + 5x² - 5x² - 5x⁴) dx

= ∫(5x - 5x⁴) dx

= (5x²/2 - 5x⁵/5)

= (5/2 - 1)

= 3/2

Hence, The integral is evaluated and the value of the integral is found to be 3/2.

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