Show that the roots of the equation kx² + 6x - k/4- 5/2=0 are real for all values of k

The probability that the first account containing substantial errors will occur on or after the fifth audited account can be expressed as \((1 - p)^4 \times p,\) where p represents the probability of finding substantial errors in any given audited account.

To determine the probability that the first account containing substantial errors will occur on or after the fifth audited account, we can approach this problem using the concept of a geometric distribution.

In a geometric distribution, we are interested in the number of trials required until the first success occurs.

In this case, a "success" refers to finding an account with substantial errors.

Let's assume that the probability of finding an account with substantial errors in any given audited account is denoted by p.

Therefore, the probability of not finding an account with substantial errors in any given audited account is 1 - p.

The probability that the first account with substantial errors occurs on or after the fifth audited account is the probability of having four consecutive accounts without substantial errors (1 - p) raised to the power of 4, multiplied by the probability of finding substantial errors in the fifth account (p).

Mathematically, this can be expressed as:

P(first error on or after fifth account) \(= (1 - p)^4 \times p\)

The probability p will depend on the specific circumstances and data available.

It could be estimated based on historical data, industry knowledge, or expert opinion.

It's important to note that this calculation assumes that the probability of finding substantial errors is constant for each account and that the accounts are independent of each other.

Real-world scenarios may have additional complexities and considerations that should be taken into account for a more accurate estimation of the probability.

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Answer:

\((x * 0.75) + 15 = $24\)

Step-by-step explanation:

please mark brainliest

Answer:

200

Step-by-step explanation:

Given that :

Slope intercept equation :

y=200x+10000

The number of spots being added per year is the value of slope in the equation ;

The general form of a slope intercept equation is :

y = mx + c

Where m = slope

Comparing the equation given to the general formula ; m corresponds to 200 ; hence number of spots added per year = 200

Answer:

1 1/2 (1 + 1/2)

Step-by-step explanation:

3 2/3 * 3/4 is 2 3/4. 2 3/4 divided by 1 5/6 is 1 1/2.

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer: B the means and medians are not the same.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I made a 100% on quiz, all credit goes to dude above me

Answer:

1 is the number that goes in the blank

Step-by-step explanation:

3(2x+1)

Distribute

3*2x+3*1

6x+3

Answer:

3*2x+3*1

6x+3

hope it help

Step-by-step explanation:

also it is one to one since the inverse is y = x² given that x > or = to zero.

why?

Since the value inside of the square roo should be absolute value as negative numbers make the function complex.

Answer:

Cheer up...٩(●˙—˙●)۶٩(●˙—˙●)۶٩(●˙—˙●)۶

Step-by-step explanation:

Hahahah

Answer:

:

To find the new function all you have to do is apply the operation in the order that is specified. In this case, subtract the two functions:

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Answer link

Answer:

X=8.7 (1dp)

Step-by-step explanation:

X=8.7

Please give Brainliest

Answer:

B.X+2

Step-by-step explanation:

-2^3+12X-2^2+9X-2-22

-8+48-18-22

40-40=0

The following is a factor of the polynomial is x+2.

Factor theorem is a special kind of the polynomial remainder theorem that links the factors of a polynomial and its zeros.

The factor theorem removes all the known zeros from a given polynomial equation and leaves all the unknown zeros. The resultant polynomial has a lower degree in which the zeros can be easily found.

As per the factor theorem, (y – a) can be considered as a factor of the polynomial g(y) of degree n ≥ 1, if and only if g(a) = 0. Here, a is any real number. The formula of the factor theorem is g(y) = (y – a) q(y). It is important to note that all the following statements apply for any polynomial g(y):

Given:

f(x)=x³ + 12x² + 9x - 22

To the above equation (x + 2) is a factor of x³ + 12x² + 9x - 22.

As,

f(-2)= (-2)³ + 12(-2)² + 9(-2) - 22

f(x)= -8 + 48 -18 -22

f(x)= 40 -40

f(x) = 0

Hence, the factor of x+2

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Using the linear function, the monthly cost for 6 HCF is $36.72.

If the monthly water bill is a linear function with a slope of 1.65, it means that for every additional HCF used, the cost increases by $1.65.

Let's denote the monthly cost as C(HCF) and the number of HCF used as HCF. We know that C(12) = $46.62.

Now, to find the monthly cost for 6 HCF (C(6)), we can use the slope information:

C(12) = $46.62

C(12) - C(6) = $46.62 - C(6) = (12 HCF - 6 HCF) * 1.65

C(6) = $46.62 - (6 HCF * 1.65)

Now, let's calculate:

C(6) = $46.62 - (6 * 1.65)

C(6) = $46.62 - 9.90

C(6) = $36.72

So, the monthly cost for 6 HCF is $36.72.

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Answer:

12.5

Step-by-step explanation:

add all  numbers and divide by 6

Answer:

Option 4
y = 2x + 3

Step-by-step explanation:

Equation of a line in slope intercept form is
y = mx + b
where m = slope and b = y-intercept

Slope m = rise/run = Δy/Δx with Δy = change in y values between any two points on the line and Δx = corresponding change in x values

b is the y-intercept, value of y when x = 0 and indicates the point at which the line crosses the y-axis

Let's take two distinguishable integer points on the line

(0, 3) and (1, 5) are two points

rise = Δy = 5 - 3 = 2
run = Δx = 1 - 0 = 1

So slope = 2/1 = 2

Since y = 3 at x = 0, y-intercept b = 3

Equation of line is
y = 2x + 3

Option 4)

Answer:

4)y=2x+3

You can see this clearly as the y-intercept is 3 and going two spaces up and one to the side is the slope.

Step-by-step explanation:

answer is v=5

Step-by-step explanation:

10v-3v=7v

7v=35

v=35/7

v=5

Answer: \(v=5\)

Simplify both sides of the equation

\(10v+-3v=35\)

\((10v+-3v)=35\) (Combine Like Terms)

\(7v=35\)

Divide both sides by 7

\(7v/7=35/7\\v=5\)

We cannot determine which of the two options is the best one to get admitted to Yale.

In 2017, the mean of SAT scores in Ohio was 1149 with a standard deviation of 212. To get admitted to Yale, you need to score 1460 in the SAT or 33 in the ACT. So which of the two options is the best one to get accepted to Yale?

Solution: Given that the mean SAT scores in Ohio in 2017 was 1149, with a standard deviation of 212. Therefore, the normal distribution of SAT scores can be written as N (1149, 212).To get accepted into Yale, you need an SAT score of 1460 or an ACT score of 33.Because SAT scores are normally distributed, we can find the probability of scoring 1460 or higher by converting this score to a z-score. Using the formula below;Z = (X - µ)/σwhere X = 1460, µ = 1149 and σ = 212Z = (1460 - 1149)/212Z = 1.47Using the normal distribution table, we can find that the probability of obtaining a z-score of 1.47 or more is approximately 0.429. Therefore, the probability of obtaining a score of 1460 or higher on the SAT is 0.429.However, if you take the ACT instead, you will need to score at least 33. Unfortunately, we don't have enough information to compare the probability of scoring 33 or higher on the ACT to the probability of scoring 1460 or higher on the SAT. Therefore, we cannot determine which of the two options is the best one to get admitted to Yale.

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The given mean and standard deviation can be used to calculate the z-score of a student's SAT score. The z-score will tell us how many standard deviations a student's score is above or below the mean. To find which test score (SAT or ACT) would give you a better chance of getting into Yale, we will need to convert the ACT score to an equivalent SAT score and then compare that to your SAT score converted to a z-score.

SAT scores are normally distributed in Ohio in 2017 with mean = 1149 and standard deviation = 212.To get accepted into Yale, you need an SAT score of 1460 or an ACT score of 33.Z-score of 1460 can be calculated as below:z = (x - μ) / σwhere x = 1460, μ = 1149 and σ = 212.z = (1460 - 1149) / 212z = 1.4747So, a student needs to score 1.4747 standard deviations above the mean to get into Yale.Using the standard normal distribution table, we can find that the probability of a randomly selected student scoring higher than 1.4747 standard deviations above the mean is approximately 7.6%.This means that if a student scores a 1460 on the SAT, they would be in the top 7.6% of all test-takers in Ohio in 2017.Now, we need to find the equivalent SAT score of an ACT score of 33. According to the College Board, the equivalent SAT score for an ACT score of 33 is 1460. So, if a student scores a 33 on the ACT, they would be in the top 1% of all test-takers, and this score would be equivalent to a 1460 on the SAT.Therefore, if a student can score a 33 on the ACT, they would have a better chance of getting into Yale than if they scored a 1460 on the SAT.

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Answer:

A.) $800

B.) $1,000

Wherever the functions are specified, if f is the inverse of g and/or g is the inverse of f, then f(g(x)) = x and g(f(x)).

Therefore,

Given that f(x) and g(x) are inverse functions in this problem, finding the graph of f(g(x)) is our goal.

As a result of the relationship mentioned above, we can conclude that:

f(g(x)) = x

The below is straightforward, as you can see.

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Based on the empirical rule, the probability that the hedge fund returns over 50% next year is approximately 5%.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline that applies to a normal distribution (also called a bell curve). It states that for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the average.

Approximately 95% of the data falls within two standard deviations of the average.

Approximately 99.7% of the data falls within three standard deviations of the average.

In this case, we know the average return of the hedge fund is 26% per year, and the standard deviation is 12%. We want to approximate the probability that the fund returns over 50% next year.

To do this, we need to determine how many standard deviations away from the average 50% falls. This can be calculated using the formula:

Z = (X - μ) / σ

Where:

Z is the number of standard deviations away from the average.

X is the value we want to find the probability for (50% in this case).

μ is the average return of the hedge fund (26% per year in this case).

σ is the standard deviation (12% in this case).

Let's calculate the Z-value for 50% return:

Z = (50 - 26) / 12

Z ≈ 24 / 12

Z = 2

Now that we have the Z-value, we can refer to the empirical rule to estimate the probability. According to the rule, approximately 95% of the data falls within two standard deviations of the average. This means that there is a 95% chance that the hedge fund's return will fall within the range of (μ - 2σ) to (μ + 2σ).

In our case, the range is (26 - 2 * 12) to (26 + 2 * 12), which simplifies to 2 to 50.

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Answer:

brahmagupta ..........

Answer:

A. Brahmagupta

Step-by-step explanation:

It is the "Correct Answer"

Answer:

15.75 per hour

Step-by-step explanation:

$63/4 Hours = 15.75

Answer:

equation can be used to represent the possible ways that Jeremiah and Samantha can split the 38 apples? y=×+38

Answer:

-3p

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

5p - 4p = 1p - 4p = -3p

\(\log^8 x -4 \log^8 x\\\\=-3 \log^8 x\)

Therefore, the area under the curve of the function \(f(x) = 7x + x^2\) over the interval [0,1] is 7/2.

To find a formula for the Riemann sum for the given function, we'll start by dividing the interval [a, b] = [0, 1] into n equal subintervals. Let Δx be the width of each subinterval, given by Δx = (b - a) / n.

Next, we'll choose the right-hand endpoint of each subinterval as our sample point to evaluate the function. Let's denote the right-hand endpoint of the ith subinterval as xᵢ. Then, xᵢ = a + iΔx.

The Riemann sum for this function using right-hand endpoints is given by:

R = Σ f(xᵢ)Δx,

where the sum is taken from i = 1 to n.

In this case, the function \(f(x) = 7x + x^2\), so the Riemann sum becomes:

R = Σ (7xᵢ + (xᵢ)²)Δx,

where xᵢ = a + iΔx.

Substituting the values, we have:

R = Σ (7(a + iΔx) + (a + iΔx)²)Δx,

where the sum is taken from i = 1 to n.

Now, we can simplify this expression:

R = Σ (7a + 7iΔx + a² + 2aiΔx + (iΔx)²)Δx,

R = Σ (7a + a² + (2a + 7i)Δx + (i²)(Δx²))Δx,

where the sum is taken from i = 1 to n.

Finally, we can take the limit of this Riemann sum as n approaches infinity to calculate the area under the curve over [a, b]:

A = lim(n→∞) Σ (7a + a² + (2a + 7i)Δx + (i²)(Δx²))Δx.

By taking the limit, we get the definite integral

A = ∫[a,b] \((7a + a^2 + 2ax + 7x) dx\)

where the integration is taken from x = a to x = b.

In this specific case, where a = 0 and b = 1, the definite integral becomes:

A = ∫[0,1]\((7(0) + (0)^2 + 2(0)x + 7x) dx\)

= ∫[0,1] 7x dx,

= [7x²/2] from 0 to 1,

= 7/2.

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