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Assume a normal distribution and find the following probabilities.
(Round the values of z to 2 decimal places, eg. 1.25. Round your answers to 4 decimal places, e.g. 0.2531)
(a) P(x<21-25 and 0-3)
(b) Pix 2481-30 and a-8)
(c) P(x-25-30 and 0-5)
(d) P(17 (e) Pix 2 7614-60 and 0-2.86)
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Answer:

Ive attached a picture

Step-by-step explanation:

a. There are 10 kg salt in the tank after t minutes

b.  After 30 minutes, the amount of salt in the tank is still 10 kg.

a) After t minutes, the amount of salt in the tank can be found by the formula:

Amount of salt = initial amount of salt + (rate of salt in - rate of salt out) x time

The initial amount of salt is 10 kg, and the rate of salt in is 0.01 kg/L x 15 L/min = 0.15 kg/min. The rate of salt out is also 0.01 kg/L x 15 L/min = 0.15 kg/min, because the solution is kept thoroughly mixed. Therefore, the amount of salt in the tank after t minutes is:

Amount of salt = 10 + (0.15 - 0.15) x t = 10 kg

b) After 30 minutes, the amount of salt in the tank is still 10 kg. This is because the rate of salt in and the rate of salt out are equal, and so the amount of salt in the tank remains constant. Therefore, the answer is the same as part (a), which is 10 kg

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The confidence interval:

Lower Endpoint: 6.418

Upper Endpoint: 6.782

To construct the confidence interval, we can use the formula:

CI = x ± z(σ/√n)

Where:

x = sample mean = 6.6

σ = population standard deviation = 2.3

n = sample size = 432

z = z-score for 90% confidence level = 1.645 (from the standard normal distribution table)

Plugging in the values, we get:

CI = 6.6 ± 1.645(2.3/√432)

CI = 6.6 ± 0.182

Therefore, the 90% confidence interval for the true mean number of reproductions per hour for the bacteria is:

Lower Endpoint: 6.418

Upper Endpoint: 6.782

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The given polynomial can be factored as 20 p³ - 1.

The given polynomial is,

20 p³ - 1

We have to factor the polynomial.

There are two terms, 20 p³ and 1.

Here we have to find the greatest of all the common factors.

Here it is 1.

So 20 p³ - 1 = 1 (20 p³ - 1)

Hence the polynomial can be factored as 20 p³ - 1.

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The measure of the selected angles from the attached figure of coordinate plane equals to 44° are ∠2 and ∠4.

In the figure of the coordinate plane,

Measure of angle ABD = 90 degrees

measure of angle ABD = 44° + measure of angle 1

⇒  measure of angle 1 =  measure of angle ABD - 44°

⇒  measure of angle 1 =  90° - 44°

⇒  measure of angle 1 =  46°

Angles formed in the second quadrant.

measure of angle 1 + measure of angle 2 = 90°

⇒measure of angle 2 = 90° - 46°

⇒measure of angle 2 = 44°

From the figure,

Measure of ∠ABC = 44°

Using the result of vertically opposite angle we have,

Measure of angle 4 =Measure of ∠ABC

⇒Measure of angle 4 =  44°

Therefore, the measure of the angles in the figure equals to 44° are ∠2 and ∠4.

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The parametric equations for the line of intersection are:
x = 61 - 5t
y = 2t - 30
z = t

To find the parametric equations for the line of intersection of the given planes, we first need to solve the system of equations:

1. x + 2y + z = 1
2. 2x + 5y + 32 = 4

Step 1: Solve for x from equation 1:
x = 1 - 2y - z

Step 2: Substitute x in equation 2 with the expression found in step 1:
2(1 - 2y - z) + 5y + 32 = 4

Now we can use elimination to solve for one variable. Let's eliminate y by multiplying the first equation by 5 and subtracting it from the second equation:

Step 3: Simplify and solve for y:
2 - 4y - 2z + 5y + 32 = 4
y - 2z = -30

Step 4: Designate z as the parameter t:
z = t

Step 5: Substitute z with t in the expression for y:
y = 2t - 30

Step 6: Substitute z with t in the expression for x:
x = 1 - 2(2t - 30) - t
x = 1 - 4t + 60 - t
x = 61 - 5t

Now we have the parametric equations for the line of intersection:
x = 61 - 5t
y = 2t - 30
z = t

Note that we can choose any value of z for the parameter t, since z is unconstrained.

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Answer:

Step-by-step explanation:

You want the common ratio and first 3 terms of a decreasing geometric progression with the sum of the first three terms being 7, and their product being 8.

Let the first term be represented by x, and let r represent the common ratio. Then the first three terms are ...

  x, xr, xr²

Their sum is ...

  7 = x +xr +xr²

Their product is ...

  8 = (x)(xr)(xr²) = (xr)³

Taking the cube root of the product equation, we have ...

  2 = xr

Substituting this into the first equation, we have ...

  7 = x +2 + 2r

  5 = x +2r   ⇒   x = 5 -2r

And substituting back into the above, we get ...

  2 = (5 -2r)(r)

  2r² -5r +2 = 0

  (2r -1)(r -2) = 0

  r = 2 or 1/2

We want r < 1, so r = 1/2.

  x = 5 -2(1/2) = 4

For x = 4, r = 1/2, the first three terms are ...

  x, xr, xr² = 4, 2, 1

__

Additional comment

The equations are nicely solved by a graphing calculator. In the attached, we used y instead of r. We want the solution with y<1.

The two solutions give rise to terms 4, 2, 1 (decreasing) or 1, 2, 4 (increasing).

The probability that it is a hardcover or a reference book  will be 0.37. in other words, the probability is the number that shows the happening of the event.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes,

Event H; Selected base is hardcover

Reselected book is a reference book

P(H) = 0.28

P(R) = 0.22

P(H∩R)=0.13

The probability that it is a hardcover or a reference book;

P(H∪R)=P(H)+P(R)-P(H∩R)

P(H∪R)=0.28+0.22-0.13

P(H∪R)=0.37

Hence, the probability that it is a hardcover or a reference book will be 0.37.

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Answer:

D

Step-by-step explanation:

The volume of a single coin is indeed:

Volume of a single coin = π × (radius)² × height

= 3.14 × (1.4 in)² × 0.0625 in

= 0.38465 in³ (rounded to the nearest hundredth)

Therefore, the total volume of 230 coins can be found by multiplying the volume of a single coin by the number of coins:

Total volume of 230 coins = 0.38465 in³/coin × 230 coins

= 88.47 in³ (rounded to the nearest hundredth, unrounded its 88.4695)

Hence, the answer is (D) 88.47 in³.

The appropriate answer would be option B: two-tailed dependent samples t-test.

Since we are comparing scores from the same group of participants at two different points in time (first separation vs second separation), we would use a dependent samples t-test.

Therefore, the options are A and B. We cannot determine whether the test would be one-tailed or two-tailed based on the information given.

A one-tailed test would be appropriate if we had a specific directional hypothesis (e.g., we expect the scores to be higher on the first separation compared to the second separation). A two-tailed test would be appropriate if we had a non-directional hypothesis (e.g., we expect there to be a difference between the scores, but we do not have a specific expectation about the direction of the difference).

Since we do not have information about the directional hypothesis, the appropriate answer would be option B: two-tailed dependent samples t-test.

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Note that this prompt examines the given data using scatter plot whose details is analyzed below.

1) The scatter plot showing the relationship between the numbers of points scored and the numbers of rebounds is attached.

2) The association between the numbers of points scored and the numbers of rebounds is a positive one. This means that generally, there is a tendency to get more points when the number of rebounds is high.

3) No, we cannot conclude that greater numbers of points scored cause

greater or lesser numbers of rebounds. This would be an inverse relationship which contradicts our findings above.

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The height of the original sculpture in centimeters is 195 cm

From the question, we have the following parameters that can be used in our computation:

Scale = 1 : 15

Scale height = 13 cm

Using the above as a guide, we have the following:

13 cm : height = 1 : 15

Express the ratio as fraction

So, we have

height/13 cm = 15/1

Cross multiply

So, we have

height = 13 cm * 15/1

Evaluate

height = 195 cm/1

So, we have

height = 195 cm

Hence, the value of the actial height = 195 cm

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The limit of the ratio of the probabilities is[tex]$\frac{3}{4}$[/tex].

Given: [tex]$\$ P(Z=0)=p \$[/tex], [tex]\$ P(Z=1)=q \$[/tex], [tex]\$ P(Z=3)=r \$$[/tex], where[tex]$\$ p+q+r=1 \$$[/tex] and [tex]$\$ E[Z] < 1 \$$[/tex].

(a) To find the recursion formula for [tex]$\$ W_{-} a(u) \$$[/tex], we use the following formula:

[tex]$$W_a(u)=P(Z=a)+\sum_{k=0}^{u-1} P(Z=a+3 k) W_a(u-1-k)$$[/tex]

where [tex]$\$ \mathrm{a} \$$[/tex] is a non-negative integer and [tex]$\$ \mathrm{u} \$$[/tex] is a positive integer.

Using the given probabilities, we have:

[tex]$$\begin{aligned}& W_0(u)=p+\sum_{k=0}^{u-1} r W_0(u-1-k) \\& W_1(u)=q+\sum_{k=0}^{u-1} p W_1(u-1-k)+\sum_{k=0}^{u-1} r W_1(u-1-k-1) \\& W_3(u)=r+\sum_{k=0}^{u-1} q W_3(u-1-k)\end{aligned}$$[/tex]

(b) To find [tex]$\$ 19$[/tex], we use the fact that [tex]$\$ W_{-} O(u)+W_{-} 1(u)+W_{-} 3(u)=1 \$$[/tex] for all positive integers [tex]$\$[/tex] u [tex]\$$[/tex].

We take the limit as [tex]$\$$[/tex] u [tex]$\$$[/tex] approaches infinity:

[tex]$$\lim _{u \rightarrow \infty} W_0(u)+\lim _{u \rightarrow \infty} W_1(u)+\lim _{u \rightarrow \infty} W_3(u)=1$$[/tex]

Since [tex]$\$ E[Z] < 1 \$$[/tex], we have. Also, from part (a), we have:

[tex]$$\begin{aligned}& \lim _{u \rightarrow \infty} W_0(u)=\lim _{u \rightarrow \infty} W_0(u-1) \\& \lim _{u \rightarrow \infty} W_1(u)=p \lim _{u \rightarrow \infty} W_1(u-1)+\lim _{u \rightarrow \infty} W_1(u-2)\end{aligned}$$[/tex]

solve for the limits as:

[tex]$$\begin{aligned}& \lim _{u \rightarrow \infty} W_0(u)=\frac{p}{1-r} \\& \lim _{u \rightarrow \infty} W_1(u)=\frac{q p}{1-p-r}\end{aligned}$$[/tex]

Therefore, we have:

[tex]$$\lim _{u \rightarrow \infty} f(u)=\lim _{u \rightarrow \infty} \frac{W_1(u)}{W_0(u)+W_1(u)}=\frac{q p}{p+(1-r)}=\frac{3}{4}$$[/tex]

Thus, the limit of the ratio of the probabilities is[tex]$\frac{3}{4}$[/tex].

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Yes, Cyrus can cover 6 miles by running 40 times.

Given that, Cyrus plans to run at least 6 miles each week, Cyrus has a circular route in the neighborhood to run, having a circumference of 340 yards,

We need to find if Cyrus runs that route 40 times during the week, will he cover at least 6 miles or not,

So,

1 mile = 1760 yards

Therefore,

6 miles = 1760 × 6 = 10560 yards

The circumference of the route = 340 yards

He took 40 rounds, so the total distance covered = 340 × 40 = 13600 yards.

Since, 6 miles = 10560 yards and he covered 13600 yards

Hence, yes, he can cover 6 miles by running 40 times.

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Outliers can affect the performance of the classifier and make it difficult to find a linear decision boundary.

True. The level of significance in statistics refers to the probability of making a Type I error, which is rejecting a true null hypothesis. It is typically denoted as alpha and set by the analyst or researcher prior to conducting a hypothesis test. It is considered the amount of risk that an analyst is willing to take in rejecting a true null hypothesis.

True. Linear separability is the ability to classify data points in a dataset using a linear decision boundary. If a dataset is not linearly separable, it means that a linear boundary cannot accurately classify all the data points. One of the reasons why this may happen is due to experimental errors that lead to errant data points. These outliers can affect the performance of the classifier and make it difficult to find a linear decision boundary.

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The statements that are supported by the graph are:

Given that the equation of the function is

f(x) = (x - 2)(x - 6)

From the equation of the graph, we can see that

Minimum = (4, -4)

This means that the vertex is at (4, -4)

The x coordinate of the vertex is the axis of symmetry

So, we have

x = 4

Next, we set the function to 0 to determine the zeros

So, we have

(x - 2)(x - 6) = 0

Solve for x

x = 2 and x = 6

This means that the zeros are at (2, 0) and (6, 0).

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Nine cans must be chosen to guarantee that we have three cans of the same type of soft drink.

To guarantee that we have three cans chosen from the same type of soft drink, we need to consider the worst-case scenario, which is that we choose two cans from each type of soft drink (a total of eight cans) and none of them is the same type. In this case, we would need to choose at least nine cans to guarantee that we have three cans chosen from the same type of soft drink.

To see why this is the case, imagine choosing eight cans from the four different types of soft drinks. There are two possibilities:

1. We choose two cans from each type of soft drink, and none of them is the same type. In this case, we would need to choose at least one more can from any of the types of soft drinks to guarantee that we have three cans chosen from the same type.

2. We choose three cans from at least one type of soft drink. In this case, we already have three cans chosen from the same type.

Therefore, we need to choose at least nine cans to guarantee that we have three cans chosen from the same type of soft drink, regardless of which cans we choose.

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Answer: x = 4.

Step-by-step explanation:

Taking the logarithm of both sides with base 3, we get:

x = log3(81)

x = log3(3^4)  [Since 81 is equal to 3 raised to 4th power]

x = 4

Therefore, the solution is x = 4.

Answer:

Step-by-step explanatiON

X=81/3

X=4

Matching the algebraic expressions with their correct solutions gives:

8y - 6 - 4y + 3 → 4y - 3

y - 1 - 2 + 3y → 4y - 3

1 + y - 1 + 4y + 2 → 2 + 5y

4 + 5y - 3y - 4 + 3y + 2 → 2 + 5y

6 - 3y + 6y - 6 + 6y → 9y

Let us solve each of the algebraic expressions given:

1) 8y - 6 - 4y + 3

= 4y - 3

2) 6 - 3y + 6y - 6 + 6y

= 9y

3) y - 1 - 2 + 3y

= 4y - 3

4) 1 + 18y - 1 - 9y

= 9y

5) 1 + y - 1 + 4y + 2

= 5y + 2

6) 4 + 5y - 3y - 4 + 3y + 2

= 5y + 2

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The value of x is 11.6 ( option C).

Similar triangles are triangles that have the same shape, but their sizes may vary. The angles of similar triangles are congruent.

Also the ratio corresponding sides of similar triangles are equal. This means for two triangles to be similar , the corresponding angles must be equal and the ratio of corresponding sides are equal.

Therefore,

29/50 = x/20

29×20 = 50x

580 = 50x

divide both sides by 50

580/50 = x

x = 580/50

x = 58/5

x = 11.6

therefore the value of x 11.6

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In other words, the system has infinitely many solutions, parameterized by the values of the free variables a and b.

The final step of the Gauss-Jordan elimination can be interpreted as the following system of equations:

x1 - 2x2 + 21x3 = 0

x4 + x5 = 1

x6 - 2x7 = 0

x8 + x9 = 1

From the second and fourth equations, we can conclude that x4 and x8 are free variables, which means they can take on any value. Let's set them to be a and b, respectively.

Then, using the first and third equations, we can solve for x2, x3, x5, and x7 in terms of a and b:

x2 = (21/2)a - (1/2)b

x3 = a/2 - (21/4)b

x5 = 1 - a

x7 = b/2

Finally, substituting these values into the remaining equations, we can solve for x1 and x6:

x1 = 2x2 - 21x3 = -19a + (209/4)b

x6 = 2x7 = b

Therefore, the solution to the system of equations is:

x1 = -19a + (209/4)b

x2 = (21/2)a - (1/2)b

x3 = a/2 - (21/4)b

x4 = a

x5 = 1 - a

x6 = b

x7 = b/2

x8 = a

x9 = 1 - a

In other words, the system has infinitely many solutions, parameterized by the values of the free variables a and b.

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The value of the missing ratio = 25. That is 5/25.

Ratio is an expression that shows the quantity of a variable that is found in another variable. It can be represented as a:b or can be written as a numerator all over a denominator. That is a/b.

To determine the missing part of the ratio, the following is carried out.

if 1 = 5, 2 = 10 then 5 = 25 = 1/5

Therefore the value of the missing part of the ratio is 5 and the complete ratio is written as 5/25.

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$1,560

To calculate simple interest, we use the formula:

Simple interest = Principal * Rate * Time

Given that Bianca invested $6,500 at a rate of 3%, the principal is $6,500 and the rate is 0.03 (since 3% is equivalent to 0.03 as a decimal).

We are asked to find the simple interest after 8 years, so the time is 8 years.

Using the formula, we get:

Simple interest = $6,500 * 0.03 * 8

Simple interest = $1,560

Therefore, the simple interest on Bianca's investment will be $1,560 after 8 years.

The prime factorization for 168 is 2 x 2 x 2 x 3 x 7.

(a) The prime factorization for 294 is 2 x 3 x 7 x 7.
(b) The prime factorization for 1,584 is 2 x 2 x 2 x 2 x 3 x 3 x 7.
(c) The prime factorization for 187 is 11 x 17.
(d) The prime factorization for 51 is 3 x 17.

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If A is an m x n matrix, and let B be an n xp matrix such that AB = 0, then rank A + rank B ≤ n

To start, we can use the fact that for any matrix A, rank A + dim Nul A = n, where n is the number of columns in A. This is a result of the rank-nullity theorem.

Now, let's consider the subspaces associated with A and B. The column space of A, Col A, is a subspace of R^m, and the null space of A, Nul A, is a subspace of R^n. Similarly, the column space of B, Col B, is a subspace of R^n, and the null space of B, Nul B, is a subspace of R^p.

We want to show that rank A + rank B ≤ n, so let's consider the dimensions of the subspaces. We know that dim Col A = rank A and dim Col B = rank B. We also know that AB = 0, which means that every column of B is in the null space of A, Nul A. In other words, Col B is a subset of Nul A.

Using the fact that dim Col B + dim Nul B = n, we can write:

rank B + dim Nul B = n - dim Col B

Since Col B is a subset of Nul A, we know that dim Nul A ≥ dim Col B. Therefore:

dim Nul B ≥ dim Nul A

Substituting this inequality into the previous equation, we get:

rank B + dim Nul B ≥ rank B + dim Nul A = n - dim Col A

Finally, we can use the fact that rank A + dim Nul A = n to substitute for dim Nul A:

rank B + dim Nul B ≥ n - rank A

Adding rank A to both sides, we get:

rank A + rank B + dim Nul B ≥ n

But we know that dim Nul B ≥ 0, so:

rank A + rank B ≤ n

Therefore, we have shown that rank A + rank B ≤ n, as desired.

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The probability that more than one flat screen television will be produced in 2 hours is 0.2642.

(a) To find the probability that no flat screen television was produced on a particular day, we can use the Poisson distribution formula:

P(X = 0) = (e^(-λ) * λ^0) / 0!

where λ is the average number of flat screen televisions produced per day, which is 3 in this case.

P(X = 0) = (e^(-3) * 3^0) / 0! = 0.0498 (rounded to four decimal places)

Therefore, the probability that no flat screen television was produced on a particular day is 0.0498.

(b) To find the probability that there are at most nine flat screen televisions produced in 3 days, we can use the cumulative Poisson distribution formula:

P(X ≤ 9) = ∑(k=0 to 9) [(e^(-λ) * λ^k) / k!]

where λ is the average number of flat screen televisions produced per day, which is 3 in this case. To find the probability for 3 days, we need to multiply λ by 3.

P(X ≤ 9) = ∑(k=0 to 9) [(e^(-9) * 9^k) / k!] = 0.5874 (rounded to four decimal places)

Therefore, the probability that there are at most nine flat screen televisions produced in 3 days is 0.5874.

(c) If the production line only functions 8 hours a day, we can adjust λ accordingly. Since there are 24 hours in a day and the production line is functioning for 8 hours, the average number of flat screen televisions produced in 2 hours would be λ/3.

So, the new λ would be 3/3 = 1.

To find the probability that more than one flat screen television will be produced in 2 hours, we can use the Poisson distribution formula:

P(X > 1) = 1 - P(X ≤ 1)

P(X ≤ 1) = (e^(-1) * 1^0) / 0! + (e^(-1) * 1^1) / 1! = 0.7358 (rounded to four decimal places)

P(X > 1) = 1 - 0.7358 = 0.2642 (rounded to four decimal places)

Therefore, the probability that more than one flat screen television will be produced in 2 hours is 0.2642.

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The graph of a Square ABCD with vertices A(-7,5) B(-4,7) C(-2,4) and D(-5,2) is represent upper square and after 90° counterclockwise rotation the lower square represents ABCD in above figure.

A quadrilateral is a polygon that has number of four sides. This also implies that a quadrilateral has exactly four vertices, and exactly four angles. We have to graph a square with vertices A(-7,5), B(-4,7) ,C(-2,4) and D(-5,2) 90 counterclockwise. Now, steps to draw the square :

In case of rotating a figure of 90 degrees counterclockwise, each point of the figure has to be changed from (x, y) to (-y, x) and graph the rotated figure. So, now the vertices of square be A(-7,5), B(-4,7) ,C(-2,4) and D(-5,2). Now, draw the square for these point, lower square in above figure. Both graphs of square ABCD present in above figure.

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Complete question:

The above figure complete the question.

graph and label 9 and 10 and their given rotation about the origin. Give the coordinates of the images.

Square ABCD with vertices A(-7,5) B(-4,7) C(-2,4) and D(-5,2) 90 counterclockwise.

The probability that the airline will lose at least 10 suitcases in a week is 0.1723 or about 17.23%.

Given information:

µ = 6.7 (mean)

σ = 3.5 (standard deviation)

We need to find the probability of losing at least 10 suitcases in a week. We can use the normal distribution formula to solve this problem:

P(X ≥ 10) = 1 - P(X < 10)

To use this formula, we need to standardize the variable X to the standard normal distribution with mean 0 and standard deviation 1. We can do this using the following formula:

Z = (X - µ) / σ

Substituting the given values, we get:

Z = (10 - 6.7) / 3.5

Z = 0.943

Now, we can use a standard normal distribution table or calculator to find the probability of Z being greater than or equal to 0.943. The table or calculator will give us the probability of Z being less than 0.943, which we can then subtract from 1 to get the desired probability.

Using a standard normal distribution table, we find that P(Z < 0.943) = 0.8277.

Therefore, P(X ≥ 10) = 1 - P(X < 10) = 1 - P(Z < 0.943) = 1 - 0.8277 = 0.1723.

So, the probability that the airline will lose at least 10 suitcases in a week is 0.1723 or about 17.23%.

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