can someone please explain?

If two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}The probability of the event {(3, 3), (2, 3), (1, 3)}  

If two indistinguishable dice are rolled, it is 3/36 or 1/12.

Explanation: Indistinguishable dice are dice that appear identical to one another but do not have unique markings. As a result, indistinguishable dice will have the same number of faces, but the values on each face will be identical.

The total number of possible outcomes is 6 * 6 = 36 because there are six possible outcomes for each roll of a single die.

The probability of rolling the numbers (3, 3), (2, 3), or (1, 3) can be determined as follows: 3/36 or 1/12

For each die, there are six possible outcomes, so there are 6*6, or 36 possible outcomes for two dice.

Because (3, 3), (2, 3), and (1, 3) are the only possible ways to obtain a 3 on one of the dice and a 3, 2, or 1 on the other, the probability is 3/36 or 1/12.

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The given parametric equations are X(t) = -3/2 + 2t and y(t) = vt² + 16, the rate of change of y with respect to "t" when t = 3 is 6v

We have the parametric equations that are X(t) = -3/2 + 2t and y(t) = vt² + 16.

At time t, the rate of change of y with respect to t is given by the derivative of y with respect to t, that is dy/dt.

So, y(t) = vt² + 16

Differentiating with respect to t, we get

⇒ dy/dt = 2vt.

Now, t = 3 gives us,

y(3) = v(3)² + 16 ⇒ 9v + 16.

Therefore, the rate of change of y with respect to t at t = 3 is

dy/dt ⇒ 2vt ⇒ 2v(3) ⇒ 6v.

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The probability that exactly 10 out of 23 cars will not have engine failure is 0.007638.

Step-by-step explanation: First, calculate the probability of an engine failing in five years with no routine maintenance, which is 27.5%. This can be written as a decimal, 0.275.Next, calculate the probability of an engine not failing in five years with routine maintenance. This probability is 100%-27.5% = 72.5%, written as a decimal 0.725.

Now, using the Binomial Distribution formula (nCr), calculate the probability of exactly 10 engines not failing out of 23 cars, where n = 23, r = 10 and p = 0.725. The equation would be [tex](23C10)*(0.725^{10})*(0.275^{13}) = 0.0076379904[/tex]

Finally, round the result to 6 decimal places, giving an answer of 0.007638.

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It is important to be aware that the distribution of sample means x may not match the distribution of the original x values exactly, due to sampling variability.

if the original distribution of x values is known to be normalize size needs to be large, then the sample size does not need to be restricted in order to claim that the distribution of sample means x taken from random samples of a given size is normal. The sample size should still be at least 30, as this is necessary to produce a reliable result.

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As a result, Lara made a $6,262.71 initial deposit into her savings account.

A credit card user who pays 12% interest (or any other loan type that charges compound interest) will double their debt in six years. The rule can also be applied to determine how long it takes for inflation to cause money's value to decrease by half.

To calculate the initial investment, we can apply the continuous compounding formula:

A = Pe(rt)

Where:

A = the current balance ($7,000.00)

P = the initial deposit (unknown)

r = the annual interest rate (11% or 0.11 as a decimal)

t = the time in years (1 year)

Plugging in these values, we get:

$7,000.00 = Pe(0.11 * 1)

A shorter version of the exponential expression:

$7,000.00 = Pe0.11

$7,000.00 = P * 1.1166 (rounded to 4 decimal places)

Dividing both sides by 1.1166:

P = $6,262.71 (rounded to the nearest cent)

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Answer:

0

Step-by-step explanation:

0

Thank me...........

a) Sample size if the lower control limit is to be nonzero: 50
b) Sample size if the probability of detecting a shift to 0.04 is to be 0.50: 100

a) How large should the sample size be if the lower control limit is to be nonzero?

n = (2σ / d)²We know that:

Center line (CL) = 0.01

Sigma (σ) = LCL = 0.005

d = Centerline - LCL = 0.01 - 0.005 = 0.005

Substituting the values in the formula, we get

n = (2 * 0.005 / 0.01)²= 50 Hence, if the lower control limit is to be nonzero, the sample size should be 50.

b) How large should the sample size be if we wish the probability of detecting a shift to 0.04 to be 0.50?

The probability of detecting a shift to 0.04 is denoted by β and is calculated using the following formula:

β = Φ [(-Zα/2 + Zβ) / √ (p₀q₀/n)], Where, Φ is the standard normal distribution function, Zα/2 is the critical value for the normal distribution at the (α/2)th percentile, Zβ is the critical value for the normal distribution at the βth percentile, p₀ is the assumed proportion of nonconforming items, q₀ is 1 – p₀, and n is the sample size.

In order to determine the sample size, we must first select a value for β. If we select a value for β of 0.50, then β = 0.50. This implies that we have a 50% chance of detecting a shift if one occurs. Since the exact value for p₀ is unknown, we assume that p₀ = 0.01, which is equal to the center line.

n = (Zα/2 + Zβ)² p₀q₀ / β², Substituting the values in the formula, we get,

n = (Zα/2 + Zβ)² p₀q₀ / β²= (1.96 + 0.674)² (0.01) (0.99) / 0.50²= 99.7 ≈ 100

Hence, if we wish the probability of detecting a shift to 0.04 to be 0.50, the sample size should be 100.

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Angle L can be calculated as follows:

angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:

AD/AB = tan(45)

AD=AB * tan(45) AD=AB

As a result, AD = 10.

2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:

PS/QS sin(60) =

PS = sin * QS (60)

5 * sqrt = PS (3)

As a result, PS = 5*sqrt (3).

3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:

WU/UV cos(30) =

UV * cos WU (30)

5 * sqrt(3) / 2 = WU

As a result, WU = (5/2)*sqrt (3).

4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:

MO/NO sin(30) =

MO = 4 / 2 MO = NO * sin(30)

As a result, MO = 2.

Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:

LMO angle = 180 - angle LMO MNO angle = 150 degrees

Finally, because angle N is a right angle, we can calculate angle L as follows:

angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

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Answer:

Step-by-step explanation:

2(2x-5) = 18 (FOIL)

4x-10=18

4x = 28

x= 7

Answer:

x = -2

Step-by-step explanation:

2(2x - 5) = -18

Divide both sides by 2.

2x - 5 = -9

Add 5 to both sides.

2x = -4

Divide both sides by 2.

x = -2

The number of bacteria present with the given growth rate at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.

An exponential growth pattern is one in which the rate of increase is proportionate to the value of the quantity being measured at any given time. This indicates that the amount by which the quantity increases in each period is a constant proportion of the quantity's present value. Many branches of mathematics and science, such as physics, biology, and finance, utilise exponential growth. Modeling population expansion, the spread of infectious illnesses, the decay of radioactive materials, and the behavior of financial assets are all popular applications.

Given that, the number of bacteria present was 7,500.

The exponential growth is given by the formula:

[tex]N(t) = N(0) * e^{(kt)}[/tex]

Substituting the values N(0) = 7,500 and the growth rate is k = 2/5 we have:

[tex]N(5) = 7,500 * e^{(2/5 * 5)}\\N(5) = 7,500 * e^2[/tex]

Hence, the number of bacteria present at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.

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Answer:

jwjwi7svwisg, I have y2ywgeu

The fraction of the guests are 10 or 11 years old is 5/6

A fraction represents a part of a whole, where the whole is divided into equal parts.

To find the fraction of guests who are 10 or 11 years old, we need to add the fractions of guests who are 10 years old and 11 years old.

3/12 of the guests are 10 years old, which can be simplified to 1/4.

7/12 of the guests are 11 years old.

Therefore, the fraction of guests who are 10 or 11 years old is

1/4 + 7/12 = 3/12 + 7/12

Add the fractions

= 10/12

Simplify the fraction

= 5/6

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There are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.

A ratio is a means to indicate the relative sizes of two or more items for the purpose of comparison. It can be shown with a colon or as a fraction. Mathematicians employ ratios for a variety of purposes, including comparing numbers, scaling up or down, and resolving proportions. Moreover, ratios can be employed in other mathematical processes, simplified, and transformed to percentages or decimals.

Given that for every three girls there are 4 boys in class.

Thus, the proportion can be given as:

4x = 236

x = 59

Now, the proportion of girls are 3x.

3(59) = 177 girls.

Hence, there are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.

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Let m and n be two arbitrary integers. We want to prove that the relation R is an equivalence relation, i.e. it is reflexive, symmetric, and transitive.

Reflexive:  We must show that mRm for all m ∈ Z.

Since the difference of m and m is 0, which is an even number, we have mRm.

Therefore, the relation R is reflexive.

Symmetric: We must show that if mRn, then nRm.

Let mRn, i.e., the difference of m and n is an even number.

Then the difference of n and m is also an even number.

Therefore, nRm, and the relation R is symmetric.

Transitive: We must show that if mRn and nRp, then mRp.

Let mRn and nRp, i.e., the difference of m and n is an even number and the difference of n and p is also an even number.

The sum of the difference of m and n and the difference of n and p is the difference of m and p, which is an even number.

Therefore, mRp, and the relation R is transitive.


Since the relation R is reflexive, symmetric, and transitive, it is an equivalence relation.

Conclusion: The relation R is an equivalence relation.

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The slopes of the two line are equal. Hence, the two lines are parallel.

A line's slope is a gauge of the line's steepness. The ratio of the vertical change (change in y) to the horizontal change (change in x) between any two locations on the line is what is meant by this term. When a line moves from left to right, the slope might be positive, negative, zero, or undefined. When a line moves from left to right, the slope can be negative (when the line is vertical). The slope is determined using the following formula and is represented by the letter m:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Given that, the first line passes through the points (-5, -5) and (-3, -3).

The slope is given by:

slope = (change in y) / (change in x)

slope = (-3 - (-5)) / (-3 - (-5)) = 1

The second line passes through the points (3, 1) and (4, 2).

slope = (2 - 1) / (4 - 3) = 1

The slopes of the two line are equal. Hence, the two lines are parallel.

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Answer:

x = -4

y = -3

Step-by-step explanation:

-5y + 3x = 3

-8y + 9x = -12​

Time the first equation by -3

15y - 9x = -9

-8y + 9x = -12

7y = -21

y = -3

Now put -3 in for y and solve for x

-5(-3) + 3x = 3

15 + 3x = 3

3x = -12

x = -4

Let's Check

-5(-3) + 3(-4) = 3

15 - 12 = 3

3 = 3

So, x = -4 and y = -3 is the correct answer.

Answer:

AD=4

Step-by-step explanation:

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[tex]x=30^o,270^o \ [0^0\leq x\leq 360^0][/tex]

Explanation:

We know,

[tex]cos2x=cos^2 \ x-sin^2 \ x=1-2sin^2 \ x[/tex]

So, let's solve the equation now,

[tex]sin \ x=cos2x=1-2 \ sin^2 \ x[/tex]

[tex]\longrightarrow \ 2 \sin^2 \ x+sin \ x-1=0[/tex]

[tex]\longrightarrow \ 2 \sin^2 \ x+2\sin x-sin \ x-1=0[/tex]

[tex]\longrightarrow \ 2\sin \ x(sin\ x+1)-1(sin \ x+1)=0[/tex]

[tex]\longrightarrow \ (2\sin \ x-1)(sin \ x+1)=0[/tex]

Now,

[tex]2\sin \ x-1=0[/tex]

[tex]\longrightarrow \ sin \ x=\dfrac{1}{2}[/tex]

[tex]\longrightarrow x=sin^{-1}(\dfrac{1}{2})[/tex]

[tex]\longrightarrow x=30^o[/tex]

And, [tex]sin \ x+1=0[/tex]

[tex]\longrightarrow x=sin^{-1}(-1)=270^o[/tex]

As we just need the general solutions, we should take only this two values as the general solutions.

Answer:

[tex]30^0,270^0[/tex]

That's it!

The given augmented matrix is equivalent to a system of linear equations with 1 equation and 3 variables. The system is underdetermined and the solution to the system is [tex](x, y, z)[/tex]= (0, 0, 0).

The given augmented matrix is in row-reduced form and is equivalent to a system of linear equations. The matrix has 3 columns and 1 row, so there is 1 equation and 3 variables in the corresponding system of linear equations. Since there is only one equation, the system is underdetermined and has infinitely many solutions.

The solution to the system can be stated as: (x, y, z) = (0, 0, 0). The solution is a point where all the variables are equal to zero. Since the matrix is in row-reduced form, this is the only solution to the system. If the augmented matrix was not in row-reduced form, then the solution would be stated as a parameter, such as (x, y, z) = (0, 0, t), where t is a parameter.

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Answer:

Step-by-step explanation:

For the given augmented matrix, you want to know the number of equations and variables it represents, whether the system is under- or over-determined, and the solution, using parameters as required.

  [tex]\left[\begin{array}{ccc|c}1&\dfrac{1}{4}&-\dfrac{1}{4}&1\\\vphantom{\dfrac{T}{q}}0&0&0&0\end{array}\right][/tex]

Each column of the augmented matrix is the coefficient of the variable in a linear equation represented by the row. The first row of the matrix represents the equation ...

  [tex]1x +\dfrac{1}{4}y-\dfrac{1}{4}z=1[/tex]

The second row of the matrix represents the tautology ...

  0x +0y +0z = 0

It contributes no information about the relationships between the variables.

The matrix represents 1 equation in 3 variables.

For there to be a unique solution to a linear system, there must be as many consistent and independent equations as there are variables. Here, there are fewer equations than variables. This system is underdetermined.

The solution to an underdetermined system can be written in terms of parameters of free choice. We will need as many parameters as there are missing equations: 2.

Here, the coefficients of y and z suggest we choose parameters that let us represent those values as multiples of 4.

Parameters: s, t

Let y = 4s, z = 4t. Then the equation becomes ...

  x +1/4(4s) -1/4(4t) = 1

  x +s -t = 1

  x = 1 +t -s

Now, the solution can be written as ...

  (x, y, z) = (1 +t -s, 4s, 4t)

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers.

The probability of guessing on an exam can be calculated by using the formula:n(C)/(n(T))where n(C) is the number of favorable events and n(T) is the total number of events. Let's solve the given problem:

Probability of getting the first question correct: P (1st) = 1/4 Probability of getting the second question correct: P (2nd) = 1/4Probability of getting the third question correct: P (3rd) = 1/4 Probability of getting the fourth question correct: P (4th) = 1/4Probability of getting the fifth question correct: P (5th) = 1/4 The probability of guessing all questions correctly can be calculated by multiplying the probability of each question together. P (all) = P (1st) * P (2nd) * P (3rd) * P (4th) * P (5th)= 1/4 * 1/4 * 1/4 * 1/4 * 1/4= 1/1024Therefore, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977. (rounded to four decimal places)Answer: 0.000977

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The journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga would be as follows:

Date Account Debit Credit

Dec 2022 Nestle Cremora ZAR 3,750

Dec 2022 Mrs. Bosoga  ZAR 3,750

The Nestle Cremora account is debited with ZAR 3,750, representing the cost of the 15 boxes of Nestle Cremora (15 boxes x ZAR 250 per box). The Mrs. Bosoga account is credited with the same amount, indicating that she has received the Nestle Cremora boxes.

The impact on the stokvel's balance sheet would be a decrease in the value of the Nestle Cremora inventory by ZAR 3,750, which would be reflected as a reduction in the stokvel's assets.

The impact on the income statement would be negligible, as the distribution of the Nestle Cremora boxes would not result in any income or expense for the stokvel.

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Mrs. Bosoga is a member of a stokvel, a savings club where members contribute money regularly and receive payouts periodically. During December 2022, Mrs. Bosoga received a share of 15 boxes of Nestle Cremora from the stokvel. The market value of each box of Nestle Cremora at the time was ZAR 250. The stokvel keeps track of its transactions using a ledger. What would be the journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga? Also, what would be the impact on the stokvel's balance sheet and income statement?

As per the volume, the dimension of an Extra Large Box is 3.78 feet.

Let's call the length of one side of the cube "s". Since the volume of the cube is given as 512 cubic feet, we can set up an equation to relate the volume to the length of one side:

Volume of cube = s³ = 512 cubic feet

To solve for "s", we can take the cube root of both sides of the equation:

s = ∛512

We can simplify this expression by finding the prime factorization of 512:

512 = 2⁹

Therefore, we can rewrite the expression for "s" as:

s = ∛2⁹

Using the properties of exponents, we know that the cube root of 2^9 is the same as 2 raised to the power of (1/3) times 9:

s = [tex]2^{1/3} \times 9^{1/3}[/tex]

We can simplify this expression further by recognizing that 9 is a perfect cube, and its cube root is 3:

s = [tex]2^{1/3} \times 3[/tex]

Therefore, the length of one side of the cube-shaped box is:

s = [tex]2^{1/3} \times 3[/tex] feet

Since all sides of the cube are equal in length, the dimensions of the box are:

Length = Width = Height = [tex]2^{1/3} \times 3[/tex] feet = 3.78 feet.

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Complete Question:

Head Stevedore loads Extra Large Boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet. What are the dimension of an Extra Large Box?

If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value

Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.

The best interpretation of a Z score of 0.47 for a sample proportion is:

b. If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value.

This interpretation is in line with the definition of a Z score, which is a measure of how many standard deviations a sample statistic (in this case, the sample proportion) is not what would be anticipated if the null hypothesis were true. A Z score of 0.47 means that the sample proportion is 0.47 standard deviations away from the expected value under the null hypothesis. Therefore, the interpretation that the probability of obtaining a sample proportion as far or farther than observed from the hypothesized value of the population proportion is 0.47, assuming the null hypothesis is true, is the most appropriate.

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Work Shown:

x = previous total weight

2% of x = 0.02x = amount of weight lost

x - 0.02x = 0.98x = current total weight

0.98x = 1519

x = 1519/0.98

x = 1550 pounds

Check:

2% of 1550 = 0.02*1550 = 31

The group collectively lost 31 pounds.

1550-31 = 1519

The answer is confirmed.

Note that 98% of 1550 = 0.98*1550 = 1519

Step-by-step explanation:

kaitlyn score is   6 points above the mean

                                 z-score =  6 / 12   = .5

kiersten score is 34.8 above the mean   z-score = 34.8/29 = 1.2

rebecca score is .54 above the mean   z -score = .54/ .3 = 1.8

rebecca scored the highest percentile (highes z-score)  of the three....the best

All parts are define in the below points.

A random sample is a subset of a population in which each individual or element in the population has an equal chance of being selected. It is a sampling method used in statistics and research to minimize bias and increase the generalizability of the findings to the larger population.

a. Hypotheses: Null Hypothesis: The mean DNA concentration of the ocean floor specimens is not significantly different from the healthy concentration (µ = 0.31g/m2). Alternative Hypothesis: The mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration (µ ≠ 0.31g/m2). Using a two-tailed t-test with alpha = 0.05, we find a p-value of 0.0003, which is less than the significance level. Therefore, we reject the null hypothesis and conclude that the mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration.

b. We would perform a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than 0.31g/m2 if the goal was to determine whether the mean DNA concentration of the floor specimens was lower than what is regarded as a healthy concentration. It would have a p-value of 0.00015.

c. Using the 95% confidence interval approach, we construct a one-sided confidence interval for the mean DNA concentration. If the lower bound of the confidence interval is less than 0.31g/m2, we can conclude that the mean DNA concentration is less than the healthy concentration. The 95% confidence interval for the mean is (0.2457g/m2, 0.3105g/m2), which does not include the healthy concentration of 0.31g/m2. Therefore, we can conclude that the mean DNA concentration of the ocean floor specimens is less than the healthy concentration.

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a). We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level.

b). Its p-value would be 0.00015.

c). The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex].

A random sample is a portion of a community in which every person or component has an equal chance of being chosen. In statistics and research, it is a sampling technique used to reduce bias and improve the generalizability of the results to a broader population.

A). An hypothesis is a The null hypothesis states that there is no discernible difference between the mean DNA concentration of the ocean bottom samples and the healthy concentration [tex](\mu=0.31g/m^2)[/tex]. Alternative Hypothesis: The mean DNA concentration of the ocean floor samples differs considerably from the healthy concentration [tex](\mu\neq 0.31g/m^2)[/tex] in a statistically significant way. We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level. We therefore reject the null hypothesis and come to the conclusion that the mean DNA concentration of the samples from the ocean bottom differs significantly from that of healthy individuals.

B). If the objective was to determine whether the mean DNA concentration of the floor specimens was lower than what is considered as a healthy concentration, we would conduct a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than [tex]0.31g/m^2[/tex]. Its p-value would be 0.00015.

C). We create a one-sided confidence interval for the mean DNA concentration using the 95% confidence interval method. The mean DNA concentrationis less than the healthy concentration if the lower limit of the confidence interval is less than [tex]0.31g/m^2[/tex]. The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex]. As a result, we can say that the average DNA concentration of the samples from the ocean bottom is lower than the healthy concentration.

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As per the equations, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

Factoring is the process of breaking down a mathematical expression or number into its component parts, which can then be multiplied together to give the original expression or number. In algebra, factoring is often used to simplify or solve equations.

An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). The expressions on both sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.

In the given question,

Let's call the age of the first dog "x" and the age of the second dog "y". We know that their ages add up to 15, so we can write:

x + y = 15

We also know that their ages multiply to 44, so we can write:

x * y = 44

Now we have two equations with two unknowns, which we can solve simultaneously to find the values of x and y.

One way to do this is to use substitution. From the first equation, we can solve for one variable in terms of the other:

y = 15 - x

We can substitute this expression for y into the second equation:

x × (15 - x) = 44

Expanding the left side, we get:

15x - x^2 = 44

Rearranging and simplifying, we get a quadratic equation:

x^2 - 15x + 44 = 0

We can factor this equation as:

(x - 11)(x - 4) = 0

Using the zero product property, we know that this equation is true when either (x - 11) = 0 or (x - 4) = 0.

Therefore, the possible values of x are x = 11 and x = 4.If x = 11, then y = 15 - x = 4, which means that the ages of the two dogs are 11 and 4.

If x = 4, then y = 15 - x = 11, which means that the ages of the two dogs are 4 and 11.

Therefore, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

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