Let f(x,y) be a joint probability density, that is, f(x,y) dxdy is the probability that X lies between x and x + dx and Y lies between y and y + dy. If X and Y are independent, then

If X and Y are independent, show that the mean and variance of their sum is equal to the sum of the means and variances, respectively, of X and Y; that is, show that if W= X+Y, then

The required answer is the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

Explanation:-

a. Economic order quantity (EOQ) is defined as the optimal quantity of inventory to be ordered each time to reduce the total annual inventory costs.

It is calculated as follows: EOQ = sqrt(2DS/H)

Where, D = Annual demand = 100 x 52 = 5200S = Order cost = $57 per order H = Annual holding cost = 0.30 x 10.75 = $3.23 per bag per year .Therefore, EOQ = sqrt(2 x 5200 x 57 / 3.23) = 234 bags. The average time between orders (TBO) can be calculated using the formula: TBO = EOQ / D = 234 / 100 = 2.34 weeks ≈ 2 weeks (rounded to nearest whole number).

Hence, the EOQ is 234 bags and the average time between orders is 2 weeks (approx).b. R is the reorder point, which is the inventory level at which an order should be placed to avoid a stockout.

It can be calculated using the formula:R = dL + zσL

Where,d = Demand per day = 100 / 5 = 20L = Lead time = 1 week (5 working days) = 5 day

z = z-value for 92% cycle-service level = 1.75 (from standard normal table)σL = Standard deviation of lead time demand = σ / sqrt(L) = 16 / sqrt(5) = 7.14 (approx)

Therefore,R = 20 x 5 + 1.75 x 7.14 = 119.2 ≈ 120 bags

Hence, the reorder point R should be 120 bags.c. An inventory withdraw of 10 bags was just made. Is it time to reorder?The current inventory level is 310 bags, which is greater than the reorder point of 120 bags. Since there are no open orders or backorders, it is not time to reorder.d. The store currently uses a lot size of 500 bags (i.e., Q = 500).What is the annual holding cost of this policy.

Annual ordering cost. Without calculating the EOQ, how can you conclude the lot size is too large?Annual ordering cost = (D / Q) x S = (5200 / 500) x 57 = $592.80 per year.

Annual holding cost = Q / 2 x H = 500 / 2 x 0.30 x 10.75 = $806.25 per year. Total annual inventory cost = Annual ordering cost + Annual holding cost= $592.80 + $806.25 = $1,399.05Without calculating the EOQ, we can conclude that the lot size is too large if the annual holding cost exceeds the annual ordering cost.

In this case, the annual holding cost of $806.25 is greater than the annual ordering cost of $592.80, indicating that the lot size of 500 bags is too large.e.

The annual cost saved by shifting from the 500-bag lot size to the EOQ can be calculated as follows:Total cost at Q = 500 bags = $1,399.05Total cost at Q = EOQ = Annual ordering cost + Annual holding cost= (D / EOQ) x S + EOQ / 2 x H= (5200 / 234) x 57 + 234 / 2 x 0.30 x 10.75= $245.45 + $93.68= $339.13

Annual cost saved = Total cost at Q = 500 bags - Total cost at Q = EOQ= $1,399.05 - $339.13= $1,059.92

Hence, the annual cost saved by shifting from the 500-bag lot size to the EOQ is $1,059.92.

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The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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Answer:

Solving the quadratic equation \(8v^2+37v=0\) we get: \(\mathbf{v=0\:or\:v=\frac{-37}{8}}\)

Step-by-step explanation:

We need to solve the quadratic equation: \(8v^2+37v=0\)

We can solve the quadratic equation of form \(ax^2+bx+c=0\) using quadratic formula: \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

We need to put values of a , b and c in order to find the solutions of quadratic equations.

In the given equation: \(8v^2+37v=0\) we have, a =8, b=37, c=0

Putting values and finding the values for n:

\(v=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\v=\frac{-37\pm\sqrt{(-37)^2-4(8)(0)}}{2(8)}\\v=\frac{-37\pm\sqrt{(-37)^2-0}}{2(8)}\\v=\frac{-37\pm\sqrt{1369}}{2(8)}\\v=\frac{-37\pm37}{2(8)}\\v=\frac{-37+37}{2(8)}\:or\:v=\frac{-37-37}{2(8)}\\v=\frac{0}{2(8)}\:or\:v=\frac{-74}{2(8)}\\v=0\:or\:v=\frac{-37}{8}\)

So, solving the quadratic equation \(8v^2+37v=0\) we get: \(\mathbf{v=0\:or\:v=\frac{-37}{8}}\)

The square of a number is increased by 5 times the number \(6x^{2} +5x-4=0\)

What is quadratic equation?
A quadratic equation is a second order equation written as a\(x^{2}\) + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Product of 6 and the square of a number is increased by 5 times the number, he result is 4.

Consider x as the number,

The question can be written as:

\(6(x^{2} )+5(x)=4\)

\(6(x^{2} )+5(x)-4=0\)

Hence, the answer for the given question is \(6x^{2} +5x-4=0\).

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In an analysis of variance, you reject the null hypothesis when the F ratio is:
b. much larger than 1.

Here's a step-by-step explanation:
1. The null hypothesis states that there are no significant differences among the groups being compared.
2. Variance is the measure of how much the individual data points in a dataset vary from the mean.
3. The F ratio is the ratio of two variances, specifically, the variance between group means and the variance within groups.
4. When the F ratio is much larger than 1, it indicates that the variance between group means is much larger than the variance within groups.
5. This suggests that there is a significant difference among the group means, leading to the rejection of the null hypothesis.

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The five elements to be assessed during sample selection in audit sampling are Sapmlinf Frame, Sample Size, Sampling Method, Sampling Interval, Sampling Risk.

1. Sampling Frame: The sampling frame is the list or source from which the sample will be selected. It is important to ensure that the sampling frame represents the entire population accurately and includes all relevant elements.

2. Sample Size: Determining the appropriate sample size is crucial to ensure the sample is representative of the population and provides sufficient evidence for drawing conclusions. Factors such as desired confidence level, acceptable level of risk, and variability within the population influence the determination of the sample size.

3. Sampling Method: There are various sampling methods available, including random sampling, stratified sampling, and systematic sampling. The chosen sampling method should be appropriate for the objectives of the audit and the characteristics of the population.

4. Sampling Interval: In certain sampling methods, such as systematic sampling, a sampling interval is used to select elements from the population. The sampling interval is determined by dividing the population size by the desired sample size and helps ensure randomization in the selection process.

5. Sampling Risk: Sampling risk refers to the risk that the conclusions drawn from the sample may not be representative of the entire population. It is important to assess and control sampling risk by considering factors such as the desired level of confidence, allowable risk of incorrect conclusions, and the precision required in the audit results.

During the sample selection process, auditors need to carefully consider these elements to ensure that the selected sample accurately represents the population and provides reliable results. By assessing and addressing these elements, auditors can enhance the effectiveness and efficiency of the audit sampling process, allowing for meaningful generalizations about the population.

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J is equal to 24 ____________________________

Answer:

  about 3.08 L

Step-by-step explanation:

You want the number of litres in the volume of a cylindrical can 14 cm in diameter and 20 cm high.

A litre is a cubic decimeter, 1000 cubic centimeters. As such, it is convenient to perform the volume calculation using the dimensions in decimeters:

The volume of the cylinder is given by the formula ...

  V = (π/4)d²h . . . . . . . where d is the diameter and h is the height

  V = (π/4)(1.4 dm)²(2.0 dm) ≈ 3.079 dm³ ≈ 3.08 L

The cylindrical can will hold about 3.08 litres.

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a/a+b is the same as a/(a+b). This is because the division of two numbers is represented by the symbol '/', and when a and b are being divided, it is written as a/b.

In this case, a and b are being divided by a+b, so it is written as a/(a+b). This is known as a fraction, which represents a ratio of two numbers. This fraction represents the proportion of a to the total of a+b. The numerator (a) represents the part of the total that you are interested in, and the denominator (a+b) represents the entire quantity.

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Answer: Option D: $7803

Step-by-step explanation:

just multiply 459 by 17 and you get your answer.

A scientist is going to measure the amount of rain we get today. Look at the table and pick the best answer that describes it. X (hours) 2 6 00 y (rain) 02 6 9 12 a Nonlinear b Ос Nonproportional Proportional Rational Od INTL 2​

Answer:

No.

Step-by-step explanation:

Because it is a decimal. Don't forget to thank me!!!

Answer:

If two figures have the same size and shape, then they are congruent. so if they have the same shape and size even if they are flipped or mirrored they are congruent.

Step-by-step explanation:

The term congruent is often used to describe figures like this, the pictire below. if you look up congruent shapes and look at many examples that will definitely help you understand alot more better what congruent means.

Considering the equation of an ellipse, it is found that the height of the tunnel 10 feet from the edge is of 14 feet.

The following is the equation for a horizontal ellipse of center with coordinates (h,k):

(x - h)²/a² + (y - k)²/b² = 1.

In relation to this issue, we have that:

The origin is where the center is.

Since the major axis is 70, 2a = 70 and a = 35.

The maximum height is 20, therefore b is equal to 20.

As a result, the ellipse's equation is as follows:

x²/35² + y²/20² = 1.

It is determined that x = 25 when the tunnel is 10 feet from the edge since 35 – 10 = 25; therefore, the height y is calculated as follows:

25²/35² + y²/20² = 1

0.51 + y²/20² = 1

y²/20² = 0.49

y² = 20² x 0.49

y =√(20² x 0.49)

y = 14 feet.

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Answer:

i think its c

Step-by-step explanation:

Answer:

the answer is c because the others are false

The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.

Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:

= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3

= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]

= (1/3) × [(9/2 + 6) - 0]

= (1/3) × (21/2)

= 7/2

Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

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Answer:

The expression Barak could use to find the amount he will spend to feed his pet lizards for one day = Number of pets × number of crickets per pet × cost of each crickets

Step-by-step explanation:

Pet lizards = 4

Each lizard eats 5 crickets

4 pet lizards will eat = 4 × 5 crickets

= 20 crickets

A cricket = 12 cents

That is, $0.12

Cost of 20 crickets = 20 × $0.12

= $2

The expression Barak could use to find the amount he will spend to feed his pet lizards for one day

= Number of pets × number of crickets per pet × cost of each crickets

= (4) (5) (0.12)

= $2.4

Answer:

Circumference is equal to pi by diameter

22/7 ×4

the answer is equal to C= π×4

Answer:

B. C=pi x 4

Step-by-step explanation:

Answer:

35h + 85 = 225

Step-by-step explanation:

Since the shop charges $35 per hour, multiply h by 35 like this: 35h

$85 is already added on top of that, so add 85 to it like this: 35h + 85

All of this has to equal 225 since Amelia paid $225

35h + 85 = 225

Answer:

fourth graph in second pic

Step-by-step explanation:

first lets substitute points to see whether the graph increases or decreases

sooo

y = -2(2^0)

y = -2

(0, -2)

y = -2(2^1)

y = -4

(1, -4)

y = -2(2^2)

y = -2(4)

y = -8

(2, -8)

with these points we can tell that the graph is decreasing, since there is two graphs decreasing, we can use the points to see if the parabola lies on the points (i think its called parabola)

its the last graph. fourth graph on page 2

If the parent function \(\sf y=(1.6)^x\) is translated 5 units up and 9 units to the right, then you should subtract 9 from x and add 5 to the whole function. Thus,

1) translation the parent function \(\sf y=(1.6)^x\) 9 units to the right gives you the function \(\sf y=(1.6)^{x-9}\).

2) translation the function \(\sf y=(1.6)^{x-9}\) 5 units up gives you the function \(\sf y=(1.6)^{x-9}+5\)

Therefore, the correct choice is C

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The statement " For any scalar c, uT(cv) = c(uTv)" is True, as it is distributive property of matrix. The statement "u and v are orthogonal" is true as u · v = 0. The statement " vectors in R(A) are orthogonal to vectors in N(A)." is False. Vectors in R(A) are orthogonal to vectors in \(N(A)^{perpendicular}\), not to vectors in N(A) itself. The statement "(\(V^t\))*V = ||v||²" is True. (\(V^t\))*V is a p x p matrix with the diagonal elements. The last statement is True as x is orthogonal to every vector in the subspace W spanned by the \(v_i's\).

The statement is true because of the distributive property of matrix multiplication. Using the fact that (cv)u = c(vu), we have

uT(cv) = (cv)Tu = c(vTu) = c(uTv)

If the distance from vector u to vector v is equal to the distance from u to -v, then we can write it mathematically as

||u - v|| = ||u - (-v)||

Expanding the above equation, we get

||u - v|| = ||u + v||

Now, let's square both sides of the above equation

||u - v||² = ||u + v||²

Expanding the squares, we get

(u - v) · (u - v) = (u + v) · (u + v)

where "·" denotes the dot product.

Simplifying the above equation, we get

u · u - 2u · v + v · v = u · u + 2u · v + v · v

The above equation can be further simplified as

2u · v = -2u · v

Hence, we get

u · v = 0

which means that u and v are orthogonal or perpendicular to each other. Therefore, the given statement is true.

The statement is false. Consider a matrix A with a single column vector v, which is not the zero vector. Then N(A) is the set of all scalar multiples of v, and R(A) is the set of all scalar multiples of Av. Any non-zero scalar multiple of Av is not orthogonal to v, so vectors in R(A) are not necessarily orthogonal to vectors in N(A). However, it is true that vectors in R(A) are orthogonal to vectors in\(N(A)^{perpendicular}\), which is the orthogonal complement of N(A).

The statement is true. Let V be an n x p matrix with columns v₁, v₂, ..., \(v_p\). Then, (\(V^t\))*V is a p x p matrix whose (i,j)-th entry is given by the dot product of the ith and jth columns of V

(\(V^t\))*\(v_{(i,j)}\) = viT vj

If i = j, then this simplifies to ||\(v_i\)||². Otherwise, if i ≠ j, then \(v_i\) and \(v_j\) are different columns of V, so they are orthogonal and their dot product is zero. Therefore, the diagonal entries of (\(V^t\))*V are ||v₁||², ||v₂||², ..., ||\(v_p\)||².

The statement is true. Let W be the subspace spanned by the vectors v₁, v₂, ..., \(v_p\), and let x be a vector that is orthogonal to each \(v_j\). This means that x is orthogonal to every linear combination of the \(v_i's\), since such a combination is a sum of scalar multiples of the \(v_j's\). Therefore, x is orthogonal to every vector in W, which means that x is in \(W^{perpendicular}\).

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--The given question is incomplete, the complete question is given

"  Are the following statements true or false? 1. For any scalar c, uT(cv) = c(uTv). 2. Let u and v be non zero vectors. If the distance from u to v is equal to the distance from u to -v, then u and v are orthogonal 3, For a square matrix A, vectors in R(A) are orthogonal to vectors in N(A). 4. (V^t)*V = ||v||^2,  5. If vectors vi , . . . , y, span a subspace W and if x is orthogonal to each vj for j = 1 , . . . , p, then x is in W^perpendicular?"--

The labor productivity of this manufacturing process in terms of dollars per labor hour is $73.47.

To find the labor productivity of this manufacturing process in terms of dollars per labor hour, we need to calculate the total revenue from the tuxedos and divide it by the total number of labor hours.

Total revenue from tuxedos = 96 tuxedos * $225 per tuxedo

                                               = $21,600

Total number of labor hours = 7 employees * 42 hours per employee

                                               = 294 labor hours

Labor productivity = Total revenue / Total number of labor hours

                               = $21,600 / 294 labor hours

                               = $73.47 per labor hour

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Answer: About 175 homeruns

Step-by-step explanation:

For every 135 games played, he hit 22 home runs, which makes an average of 1 home run every 6.136 games. Take that number and divide 1075 by it.

1075 / 6.136 = about 175.

Carlos Gonzales hits 175 runs in his total of 1075 games in his career.

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,

Number of games played by Carlos Gonzales = 135.

And runs hit by Carlos Gonzales = 22 runs.

To find the runs hit by Carlos Gonzales in 1075 games,

Use ratio property,

In 135 games = 22 runs hit,

in 1 game = 22 / 135 runs hit,

In 1075 games = (22/135)x1075 = 175.18 = 175 (approx)

The runs hit by Carlos Gonzales in 1075 games is 175.

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The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

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the answer

155

324

5/9 (87/3(1/12)= 155/324

The probability that exactly 3 books and 1 magazine are sold in an hour is approximately 0.0001228.

Define probability ?

Probability is a fundamental concept in mathematics and statistics that quantifies the likelihood or chance of an event occurring.

To solve these problems, we can use the Poisson distribution and the concept of conditional probability.

1. Probability of selling exactly 3 books and 1 magazine in an hour

The probability mass function (PMF) of the Poisson distribution is given by:

P(X = k) = \((e^{(-\lambda)} * \lambda^k) / k!\)

P(Y = k) =  \((e^{(-\lambda)} * \lambda^k) / k!\)

We want to find the probability that exactly 3 books and 1 magazine are sold, so we calculate:

P(X = 3) * P(Y = 1)

P(X = 3) = \((e^{(-6)} * 6^3) / 3!\)

P(Y = 1) = \((e^{(-6)} * 6^1) / 1!\)

P(X = 3) = (0.00247875)

P(Y = 1) = (0.049575)

Probability of selling exactly 3 books and 1 magazine = P(X = 3) * P(Y = 1)

= (0.00247875) * (0.049575)

= 0.0001228

Therefore, the probability that exactly 3 books and 1 magazine are sold in an hour is approximately 0.0001228.

2. Expected total number of purchases conditioned on selling 12 books:

Given that 12 books were sold in the past hour, we need to find the expected total number of purchases during that time. Let's denote the random variable for the total number of purchases as Z.

To calculate the expected value, we use the concept of conditional probability. We can condition on the event that 12 books were sold and consider the remaining purchases as independent of this event.

The expected value of Z conditioned on the event that 12 books were sold is given by:

E(Z | X = 12) = E(X + Y | X = 12)

             = E(X | X = 12) + E(Y | X = 12)

             = 12 + E(Y | X = 12)

E(X | X = 12) is simply 12 since the number of books sold is fixed at 12.

E(Y | X = 12) is the expected number of magazines sold given that 12 books were sold. Since each customer independently buys a magazine with a probability of 1/3, the expected number of magazines sold is:

E(Y | X = 12) = E(Y) = λ * p

Here, λ is the rate of the Poisson process, which is 6 customers per hour, and p is the probability of selling a magazine, which is 1/3.

E(Y | X = 12) = (6 * 1/3) = 2

Therefore, the expected total number of purchases conditioned on selling 12 books is:

E(Z | X = 12) = 12 + E(Y | X = 12)

             = 12 + 2

             = 14

Hence, the expected total number of purchases during the hour, conditioned on selling 12 books, is 14.

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The probability that all the resulting pieces have a length of at least 8.5cm is 0.6058.

The length of the stick is 43cm.

Two points are selected at random along the length of the stick, and the stick is broken at those two points.

Then we need to find the probability that all the resulting pieces have a length of at least 8.5cm.

Let the length of the first piece be x.

The length of the second piece is (43 - x), since the total length is 43cm.

For the resulting pieces to have a length of at least 8.5cm, we need to have: x ≥ 8.5 and (43 - x) ≥ 8.5x ≥ 8.5 and x ≤ 34.5

So the length of the first piece must be between 8.5cm and 34.5cm.

The second piece will then have a length of (43 - x), which will also be between 8.5cm and 34.5cm.

Therefore, the probability of getting two points such that all the resulting pieces have a length of at least 8.5cm is:

P = probability that the first piece has a length between 8.5cm and 34.5cm.

The probability can be represented as: P = (34.5 - 8.5)/43P = 26/43

P = 0.6058.

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It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.

To prove the claim by induction, first establish the base case. I assume \(n\in\Bbb N\), so for \(n=1\) we have

\(21^1 + 9 = 21 + 9 = 30\)

and of course 30 = 5×6 is divisible by 5.

Assume the claim is true for \(n=k\), that \(5 \mid 21^k + 9\). This means that for some integer \(\ell\), we can write

\(21^k + 9 = 5\ell\)

Now the induction step: when \(n=k+1\), we have

\(21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)\)

which is divisible by 5. QED