lf m/1 = 2x + 3, and m/2 = 3x + 7, which is the value of x?

Continuous Exponential Model

It's an equation that models the growth of a certain variable in time. If P(t) is the number of insects in a colony at a time t, and Po is the initial number of insects of the colony, then the model can be written as:

Where k is the growth rate.

We are given the model equation:

Where the time is in weeks.

A. This corresponds to an original number of insects of Po = 1840

B. The rate of increase can also be determined with the equation. k = 0.145. This corresponds to a rate of 14.5% each week.

C. Now we find the number of insects for t = 16:

It's expected to be 18723 insects in the colony after 16 weeks.

D. For the colony to have 12000 insects, we need to solve the equation:

Dividing by 1840:

Applying logs on each side:

Dividing by 0.145:

Calculating:

t ≈ 13 weeks

It will take approximately 13 weeks for the population to reach 12000

To calculate the required sample size for an inventory observation using mean-per-unit estimation, the auditor typically considers the following factors:

1. Tolerable Misstatement: The auditor establishes a tolerable misstatement level, which represents the maximum error or discrepancy they are willing to accept in the inventory balance. This is usually determined based on professional judgment and regulatory requirements.

2. Expected Misstatement: The auditor estimates the expected misstatement in the inventory balance. This estimation can be based on prior audit experience, internal control effectiveness, or other relevant factors.

3. Risk of Incorrect Acceptance: The auditor assesses the risk of incorrect acceptance, which is the risk that the auditor concludes the inventory balance is materially correct when it actually contains significant misstatements. This risk is generally set based on professional judgment and the auditor's understanding of the client's business.

4. Population Size: The auditor determines the total number of items in the inventory population. This can be obtained from the client's records or through physical counts.

5. Variability of the Population: The auditor considers the variability or dispersion of the inventory population. This can be measured using statistical techniques or based on prior audit experience.

By taking these factors into account, the auditor can use statistical formulas or software tools to calculate the required sample size. The formulas often involve considerations such as confidence levels, desired precision, and statistical distributions. The specific formula used may vary depending on the circumstances and the sampling methodology chosen by the auditor.

It's worth noting that auditing standards and methodologies may evolve over time, so auditors should refer to the most current professional guidance and tools available to determine the appropriate sample size for inventory observations.

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(a) The solution to a system of linear equations is represented graphically by the intersection point(s) of the corresponding lines.

(b) False. Matrix multiplication is not commutative.

(c)False. Not every system of equations has a solution.

The solution to a system of linear equations can be represented graphically by plotting the equations on a coordinate plane. Each equation will have a corresponding line, and the solution to the system is the point(s) where these lines intersect. If there is a single point of intersection, it represents a unique solution to the system. If the lines are parallel and do not intersect, it indicates that the system has no solution. In the case of overlapping lines, every point on the overlapping region represents infinitely many solutions.

Matrix multiplication is not commutative, which means that changing the order of multiplication can lead to different results. In general, for matrices A and B, the product AB is not equal to the product BA. The order of multiplication matters because the dimensions of the matrices involved must align properly. For example, if A is a 2x3 matrix and B is a 3x4 matrix, then AB is a valid multiplication, but BA is not. It's important to consider the order of matrices when performing matrix multiplication.

Every system of equations does not necessarily have a solution. There are three possible scenarios for a system of equations: it can have a unique solution, it can have infinitely many solutions, or it can have no solution. The existence of a solution depends on the relationships between the equations. If the equations are consistent and intersect at a point, there is a unique solution. If the equations are consistent and represent the same line, there are infinitely many solutions. However, if the equations are inconsistent and do not intersect, there is no solution to the system. So, not every system of equations has a solution.

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The expression for the word problem can be written as x + 12 = 5 ( x - 32).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that in 12 years I will be five times as old as I was 32 years ago. The expression in the mathematical form will be calculated as:-

x + 12 = 5 ( x - 32 )

Here, x will be the present age.

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The resulting (f+g)(x) for the functions f(x)=14x²+8x+12 and g(x)=9x+4 is D. 14x²+17x+16.

To find (f+g)(x), we need to add the two functions, f(x) and g(x), together. Since f(x) is given as 14x²+8x+12 and g(x) is given as 9x+4, we simply add the like terms.

Adding f(x) and g(x) together gives us (14x²+8x+12) + (9x+4) = 14x²+17x+16.

Therefore, the answer is (f+g)(x) = 14x²+17x+16 (Option D).

This method of adding functions involves adding the coefficients of like terms together. We can use this method to add any two functions with the same variables and exponents, which results in the combined function.

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In the accumulated value of the Investment after 8 years is approximately $8060.16. The correct answer is C. $8060.16

In the given values into the formula A = P(1 + r/n)^(nt). In this case:
P = $5000 (initial investment)
r = 0.05 (5% interest rate as a decimal)
n = 12 (compounded monthly, so 12 times per year)
t = 8 (investment period in years)
Now, we'll input these values into the formula:
A = 5000(1 + 0.05/12)^(12*8)
Calculating the values within the parentheses:
A = 5000(1 + 0.0041667)^(96)
Now, calculating the power:
A = 5000(1.0041667)^96
Finally, finding the accumulated value:
A = 5000 * 1.61279163 ≈ $8060.16
So, the accumulated value of the investment after 8 years is approximately $8060.16. The correct answer is C. $8060.16.

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The formula for calculating the accumulated value of an investment with compound interest is A=P(1+r/n)^(nt), where A is the final amount, P is the principal investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Using this formula and plugging in the given values, we get A=5000(1+0.05/12)^(12*8) which simplifies to A=5000(1.004167)^96. After rounding to two decimal places, the answer is option C, $8060.16. This means that after 8 years of monthly compounding at 5%, the initial investment of $5000 has accumulated to a value of $8060.16. Compound interest is a powerful tool for increasing the value of an investment over time, as it allows the interest to be earned on both the initial investment and the accumulated interest.
Using the compound interest formula A=P(1+r/n)^(nt), we can find the accumulated value of an investment of $5000 at a 5% annual interest rate, compounded monthly for 8 years. In this formula:

- A represents the accumulated value
- P represents the initial investment, which is $5000
- r represents the annual interest rate, which is 0.05 (5% as a decimal)
- n represents the number of times interest is compounded per year, which is 12 (monthly)
- t represents the number of years, which is 8

Plug in the values and calculate A:

A = 5000*(1+0.05/12)^(12*8)
A = 5000*(1+0.0041667)^(96)
A = 5000*(1.0041667)^96
A ≈ $7452.93

So, the accumulated value of the investment is approximately $7452.93 (Option A).

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Answer:

please see the photo above for detailed analysis.

Answer:

43 1/3 minutes to iron 10 shirts

Step-by-step explanation:

Number of shirts : Time taken

3 shirts : 13 minutes

10 shirts : x minutes

3 / 13 = 10 / x

Cross product

3 * x = 13 * 10

3x = 130

Divide both sides by 3

3x / 3 = 130 / 3

x = 43 1/3 minutes

x = 43 minutes 20 seconds

It will take 43 minutes 20 seconds to iron 10 shirts

\(ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065\)

Answer:

Step-by-step explanation:

Answer:

12a^2+13a+3

explanation:

multiply:

(3a+1)(4a+3)=(fxg)

12a^2+13a+3

The final answer is that the probability of getting a cookie with no more than 5 chips is 0.2851.

After reading the question , it seems that it follows the Poisson Distribution of Univariate Probability Distribution. The pdf of this distribution is given by-

P(X=x) = \(e^{-λ}\)\(\frac{λ^{x} }{x!}\) where λ is the mean value and x is the random variable.

Now, here λ = 7 and we have to find P(X<=5).

So, P(0)=     e^{-7}\frac{λ^{0} }{0!}

           = e^(-7)

            = 0.0009

    P(1)= e^{-7}\frac{λ^{1} }{1!}

         = 0.0009 x 7

         = 0.0063.

    P(2)= e^{-7}\frac{λ^{2} }{2!}

          =(0.0009 x 49)/2

            = 0.0220

In a similar manner , P(3), P(4) And P(5) can be calculated.

And , the P(getting a cookie with no more than 5 chips) = P(0) + P(1)+ P(2)+P(3)+P(4)+P(5)

This value comes out to be = 0.0009+0.0063+ 0.0220+ 0.0514+0.0900+0.1260 = 0.2966.

Hence, the probability of  getting a cookie with no more than 5 chips is 0.2966.

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Answer:

Step-by-step explanation:

S = 4πr²

First of all divide both sides by 4π

That's

Find the square root of both sides in order to isolate r

That's

We have the final answer as

Hope this helps you

1) The x-intercept lies at (1, 14), and the y-intercept lies at (3, 42).

2) This means that after 3 cuts, the length of the string is 33 inches.

3) Therefore, the 42-inch string can be cut into 14 pieces of 3 inches each.

The x-intercept is the point on the graph where a line crosses the x-axis.

The y-intercept is the point on the graph where a line crosses the y-axis.

The x- and y-intercepts are the coordinate points for graphing data.

Thus, the x- and y-intercepts are coordinate points where the graph of a function or an equation touches the two axes.

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A perfect square trinomial factors to a binomial squared, option a.

A perfect square trinomial is a trinomial expression that can be factored into the square of a binomial. It has the form:

(ax² + bx + c)²

To factor it, you can take the square root of the first term (ax²) and the square root of the last term (c). The middle term (bx) will be twice the product of these square roots. Therefore, the factored form of the perfect square trinomial is:

(ax² + bx + c)² = (√(ax^2) + √(c))² = (√(ax^2) + √(c))(√(ax^2) + √(c))

This can be simplified to:

(ax² + bx + c)² = (√(ax²) + √(c))² = (√(a)x + √(c))²

So, a perfect square trinomial factors into the square of a binomial, where the first term of the binomial is the square root of the coefficient of the squared term, and the second term is the square root of the constant term.

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Step-by-step explanation:

C=b/a

c=kb/a

where as k is the constant

c=kb/a

we substitute

33=22k/6

crossed multiply

33*6= 22k

198=22k

we divide both sides by 22

198/22=22k/22

K=9

Answer: C, StartFraction c a Over b EndFraction = 9

Step-by-step explanation: edge :)

Answer:

Hey there!

We want to change the equation for each line into slope intercept form, or y=mx+b form.

Luckily, the first one is already in slope intercept form.

The second line can be converted to: y=-3/4x-7/4.

The third line can be converted to: -8y=-6x+4, or y=3/4x-1/2

Line one and line two are neither perpendicular or parallel.

Line one and line three are perpendicular.

Lines two and three are neither perpendicular or parallel.

This is because parallel lines have same slope, and perpendicular lines have opposite reciprocal slopes.

Hope this helps :)

Answer:

Line 1 and Line 2: Neither

Line 1 and Line 3: Perpendicular

Line 2 and Line 3: Neither

Step-by-step explanation:

To make the answering process easier, begin by converting each formula into the format y = mx +b:

Line 1: y = -4/3x + 1 (already in format)

Line 2:

-4y = 3x + 7

Divide all terms by -4:

y = -3/4x - 7/4

Line 3:

6x - 8y = 4

Subtract both sides by 6x:

-8y = -6x + 4

Divide all terms by -8:

y = 3/4x - 1/2

We can determine the relationships of the lines:

Line 1 and Line 2: Neither. They do not have the same slope, and they are not opposite reciprocals of each other.

Line 1 and Line 3: Perpendicular. The slopes of each line are opposite reciprocals: (-4/3 and 3/4)

Line 2 and Line 3: Neither. The slopes are the same but one is negative.

Answer:

I am not quite sure of the answer but probably

125 dollars

Step-by-step explanation:

375÷3

=125

Answer:

what variable do you want to find?

Step-by-step explanation:

Answer:

Hyperbole

Step-by-step explanation:

because i did that test

Answer:

Both r hyperbole

Step-by-step explanation:

Answer:

Step-by-step explanation:

ii) ratio = 60:12 = 5:1

iii) unit rate is 5

iv) 60 = 12M

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer and the probability that the resulting integer will be divisible by 11, then the common fraction = \(\frac{1}{10}\)

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer.

The probability that the resulting integer will be divisible by 11.

The way to tell if a number is divisible by 11 is the following :

If the sum of every other digit, starting with the first is equal to the sum of every other digit, starting with the second, then the number is evenly divisible by 11.

Our given numbers are 2, 3, 4, 7 and 8.

Which 3 numbers summed are equivalent to the sum of other 2.

We can see,

2 + 3 + 7 = 12

8 + 4 = 12

There are 3! = 6 ways to use the 2, 3, 7, and

2! = 2 ways to use the 8 and 4.

\(6*2\) = 12

There are 5! = \(5*4*3*2*1\) = 120 different possibilities

So,

We can write,

= \(\frac{12}{120}\)

= \(\frac{1}{10}\)

Therefore,

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer and the probability that the resulting integer will be divisible by 11, then the common fraction = \(\frac{1}{10}\)

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The digits 2, 3, 4, 7, and 8 will be put in random order to make a positive five-digit integer, and the probability that the resulting integer will be divisible by 11, then the common fraction = 1/10

The digits 2, 3, 4, 7, and 8 will be put in random order to make a positive five-digit integer.

The probability that the resulting integer will be divisible by 11.

The way to tell if a number is divisible by 11 is the following :

If the sum of every other digit, starting with the first is equal to the sum of every other digit, starting with the second, then the number is evenly divisible by 11.

Our given numbers are 2, 3, 4, 7, and 8.

Which 3 numbers summed are equivalent to the sum of the other 2.

We can see,

2 + 3 + 7 = 12

8 + 4 = 12

There are 3! = 6 ways to use the 2, 3, 7, and

2! = 2 ways to use the 8 and 4.

6*2 = 12

There are 5! = 120 different possibilities

So,

We can write,

= 12/120

= 1/10

Therefore,

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer and the probability that the resulting integer will be divisible by 11, then the common fraction = 1/10

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The probability that Susan also bought a candy bar, given that she bought a sheet of bus tickets, is approximately 33.75%.

To calculate the probability that Susan bought a candy bar given that she bought a sheet of bus tickets, we can use the concept of conditional probability.

Let's denote the event of buying a candy bar as A and the event of buying a sheet of bus tickets as B.

The probability of buying a candy bar, P(A), is given as 12% or 0.12.

The probability of buying a sheet of bus tickets, P(B), is given as 8.0% or 0.08.

The probability of buying both a candy bar and a sheet of bus tickets, P(A ∩ B), is given as 2.7% or 0.027.

We want to calculate the probability of buying a candy bar given that a sheet of bus tickets was purchased, which is P(A|B).

By using the formula for conditional probability:

P(A|B) = P(A ∩ B) / P(B)

Substituting the values we have:

P(A|B) = 0.027 / 0.08

Calculating this, we find:

P(A|B) ≈ 0.3375 or 33.75%

Therefore, the probability that Susan also bought a candy bar, given that she bought a sheet of bus tickets, is approximately 33.75%.To calculate the probability that Susan bought a candy bar given that she bought a sheet of bus tickets, we can use the concept of conditional probability.

Let's denote the event of buying a candy bar as A and the event of buying a sheet of bus tickets as B.

The probability of buying a candy bar, P(A), is given as 12% or 0.12.

The probability of buying a sheet of bus tickets, P(B), is given as 8.0% or 0.08.

The probability of buying both a candy bar and a sheet of bus tickets, P(A ∩ B), is given as 2.7% or 0.027.

We want to calculate the probability of buying a candy bar given that a sheet of bus tickets was purchased, which is P(A|B).

By using the formula for conditional probability:

P(A|B) = P(A ∩ B) / P(B)

Substituting the values we have:

P(A|B) = 0.027 / 0.08

Calculating this, we find:

P(A|B) ≈ 0.3375 or 33.75%

Therefore, the probability that Susan also bought a candy bar, given that she bought a sheet of bus tickets, is approximately 33.75%.

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Answer:

Slope is -12.5

x-intercept is 75

y-intercept is 6

Step-by-step explanation:

See attached image

Answer: 3x^2 − 7x − 6

Rοunding up tο the nearest whοle cupcake, yοu shοuld buy 8 cupcakes tο ensure that yοur rοbοt has enοugh cupcakes tο last fοr the next 14 days.

An equatiοn is a mathematical statement that indicates that twο expressiοns are equal. It cοntains an equals sign (=) between twο expressiοns, with οne expressiοn οn each side οf the equals sign. Equatiοns can cοntain variables, cοnstants, cοefficients, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Here,

If yοur rοbοt eats 4 cupcakes every 7 days, it means it eats 4/7 = 0.57 cupcakes per day (rοunded tο twο decimal places).

Tο buy enοugh cupcakes fοr the last 14 days, yοu need tο multiply the number οf days by the daily cοnsumptiοn rate:

0.57 cupcakes per day x 14 days = 7.98 cupcakes

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Complete question:

If your robot eats 4 cupcakes every 7 days. So to buy enough cupcakes for the last 14 days, how much cupcake is consumed daily?

0.0004732

12/ 25358

answer depends if you want to round it