Please help me find the arc!

Answer:

Step-by-step explanation:

Approach: If four numbers a, b, c and d are in proportion then a:b = c:d. The solution is to sort the four numbers and pair up the first 2 together and the last 2 together and check their ratios this is because, in order for them to be in proportion, the product of means has to be equal to the product of extremes.

Volume of sphere with radius r = 7 m is [tex]v_1=1,436.026 \ \text{m}^3[/tex].

Step-by-step explanation:

We know that volume of sphere  [tex]=\dfrac{4}{3}\pi r^3[/tex] given that [tex]\pi =3.14,\ r=7 \ \text{ft}[/tex].

volume of sphere  [tex]=\dfrac{4}{3}\pi r^3=v_1[/tex]

[tex]\implies v_1=\dfrac{4}{3}\pi r^3[/tex]

[tex]\implies v_1=\dfrac{4}{3}\pi(7)^3[/tex]

[tex]\implies v_1=\dfrac{4}{3}\pi (343)[/tex]

[tex]\implies v_1=\dfrac{4}{3}(3.14)(343)[/tex]

[tex]\implies v_1=1,436.026 \ \text{m}^3[/tex]

∴ Volume of sphere with radius r = 7 m is [tex]v_1=1,436.026 \ \text{m}^3[/tex].

It would be important to have more information about the driving conditions, types of vehicles, and other factors that could influence gas mileage in order to draw more conclusive insights from this data.

Based on the graph provided, it appears that both Amy and Laura's average gas mileage fluctuated over the course of the four weeks. Amy's average gas mileage started at around 30 miles per gallon (mpg), decreased in week 2, and then increased again in weeks 3 and 4. Laura's average gas mileage started at around 25 mpg, increased in week 2, decreased in week 3, and then increased again in week 4.

However, one could make some tentative observations. For example, Amy's average gas mileage appears to be consistently higher than Laura's over the four-week period, and both of their average gas mileage values appear to be somewhat volatile, with significant changes occurring from week to week.

Overall, it would be important to have more information about the driving conditions, types of vehicles, and other factors that could influence gas mileage in order to draw more conclusive insights from this data.

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Answer:

The lower limit and upper limits of the athlete's height can be calculated by subtracting and adding the absolute error, respectively.

Lower Limit = 165.5 cm - 0.1 cm = 165.4 cm

Upper Limit = 165.5 cm + 0.1 cm = 165.6 cm

Therefore, the athlete's height lies between 165.4 cm and 165.6 cm, inclusive.

The number of male students that went on the school trip given that there are 30 female students is 24

Given that we have the following statement:

Every teacher is assigned 4 male students and 5 female students

The above statement means that we have the following ratio

Ratio = Male : Female

So, we have the following equation

Male : Female = 4 : 5

When the number of female students is 30, we have the following

Male : 30 = 4 : 5

Express as fraction

Male/30 = 4/5

So, we have

Male = 4/5 * 30

Evaluate

Male = 24

Hence, the number of male students is 24

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Answer:0.65

Step-by-step explanation:

The standard error of the sample mean is approximately 0.682, rounded to the hundredths place.

To calculate the standard error of the sample mean, we need to find the sample mean and the standard deviation of the data. Then we can divide the standard deviation by the square root of the sample size.

First, let's calculate the sample mean:

Mean = (64.5 + 64 + 66.5 + 64 + 62.5 + 61 + 63) / 7 = 64.14

Next, let's calculate the standard deviation. We will use the sample formula for standard deviation (Bessel's correction):

Calculate the squared differences from the mean for each temperature:

(64.5 - 64.14)² = 0.1904

(64 - 64.14)² = 0.0204

(66.5 - 64.14)² = 5.5376

(64 - 64.14)² = 0.0204

(62.5 - 64.14)² = 2.6836

(61 - 64.14)² = 9.8324

(63 - 64.14)² = 1.2696

Calculate the sum of the squared differences:

Sum = 0.1904 + 0.0204 + 5.5376 + 0.0204 + 2.6836 + 9.8324 + 1.2696 = 19.5544

Calculate the variance:

Variance = Sum / (n - 1) = 19.5544 / (7 - 1) = 3.25907

Calculate the standard deviation:

Standard Deviation = sqrt(Variance) = sqrt(3.25907) = 1.80597

Finally, let's calculate the standard error of the sample mean:

Standard Error = Standard Deviation / sqrt(n) = 1.80597 / sqrt(7) ≈ 0.682

Therefore, the standard error of the sample mean is approximately 0.682, rounded to the hundredths place.

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Answer:

1. E, 2. C, 3. A, 4. D

Step-by-step explanation:

The negative sign means a that the image is on the opposite side.

The positive sign means a that the image is on the same side.

The magnitude of any factor between [0,1[ means that the image is contracted.

The magnitude of any factor equal to 1 means that the image is not dilated.

The magnitude of any factor between ]1,infinity[ means that the image is expanded.

Circle A can be made similar to circle B by dilating circle A by scale factor 4.

Circles can be made similar by performing transformations such as dilations, translation, etc.

The given parameters are:

Circle A

[tex](x,y)=(6,7)[/tex] --- center

[tex]r=4[/tex] --- radius

Circle B

[tex](x,y)=(2,4)[/tex] --- center

[tex]r=16[/tex] --- radius

To do this, we simply make both circles have the same radius.

Given that:

[tex]r_A=4[/tex] --- radius of A

[tex]r_B=16[/tex] --- radius of B

Dilating the radius of A by 4 will make both circles have the same radius.

i.e.

[tex]R=r_A\times4[/tex]

[tex]R=4\times4[/tex]

[tex]R=16[/tex]

Now, the new radius of A is 16; same as B

Both circles now have the same radius, means that the circles are similar.

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Answer: 7/20

Step-by-step explanation:

35+17=52

80-52=28

28/80=7/20

Answer:

28

Step-by-step explanation:

35+17=52

80-52=28

so your answer is 28

We want to copy the original triangle using only two of its sides and the included angle. To do this, we'll create a new triangle with the same side lengths and angle measures as the original triangle.

To copy a triangle using two of its sides and the included angle, follow these steps:

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Answer:

28

Step-by-step explanation:

a = b * h

a = 4 * 7 = 28

Answer: See below

Step-by-step explanation:

To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:

Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.

Then, the addition problem becomes:

A B C

D E F

We know that the sum of each column must be the same, so:

C + F = 10 + B

B + E = 10 + A

We can rewrite these equations as:

C - B + F = 10

B - A + E = 10

Since we are given that the sum of the two numbers is the same, we know that:

C + F + D + E = 1112

We can substitute C and F in terms of A and B using the equations above:

C = 10 + B - F

F = 10 + C - B

Substituting these expressions into the equation for the sum, we get:

10 + B - F + C + D + E = 1112

Simplifying this equation, we get:

B - F + C + D + E = 1102

Now we can substitute in the expressions for C and F in terms of A and B:

B - (10 + B - F) + (10 + C - B) + D + E = 1102

Simplifying and canceling out terms, we get:

F - C - D - E = -92

We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.

Trying different values for A and D, we find that A = 2 and D = 3 works:

A B C

D E F

2 7 9

1 7 3

The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:

2 7 9

1 7 3

4 5 2

The smallest sail, A, has a base length of 6 m and a height range of 5 to 8 m. The largest sail, sail C, has a smaller area than double that of sail A.

The table of possible dimensions and areas of the sails is:

Base Height Area

Sail A 6 m 5 m 15 m²

Sail B 6.14 m 7 m 21.5 m²

Sail C 14 m 4 m 28 m²

Let's assume that sail A has a height of 5 meters, then its area would be:

Area of Sail A = 1/2 x Base x Height = 1/2 x 6 x 5 = 15 square meters

If sail C has an area less than twice the area of sail A, then its area must be less than 2 x 15 = 30 square meters. Let's assume that sail C has an area of 28 square meters.

To find the dimensions of sail A and sail C, we can use the formula for the area of a triangle:

Area = 1/2 x Base x Height

For sail A, we already know the base and the area, so we can solve for the height:

15 = 1/2 x 6 x Height

Height = 5 meters

So sail A has a base of 6 meters and a height of 5 meters.

For sail C, we know the area and we have assumed a base length of 14 meters (to keep the height reasonable). Solving for the height:

28 = 1/2 x 14 x Height

Height = 4 meters

So sail C has a base of 14 meters and a height of 4 meters.

To find the dimensions of sail B, we can assume a height between 5 and 8 meters (since sail A has a height between 5 and 8 meters), and then solve for the base and the area using the formula for the area of a triangle:

Area = 1/2 x Base x Height

Let's assume sail B has a height of 7 meters:

Area of Sail B = 1/2 x Base x 7

Area of Sail B = 1/2 x (Area of Sail A + Area of Sail C)

Area of Sail B = 1/2 x (15 + 28)

Area of Sail B = 21.5 square meters

Solving for the base:

21.5 = 1/2 x Base x 7

Base = 6.14 meters (rounded to two decimal places)

So sail B has a base of 6.14 meters and a height of 7 meters.

Therefore, the table of possible dimensions and areas of the sails is:

Base Height Area

Sail A 6 m 5 m 15 m²

Sail B 6.14 m 7 m 21.5 m²

Sail C 14 m 4 m 28 m²

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Answer:

Step-by-step explanation:

a) 2x-6 is equivalent to 1) -6+2x

b) 5/3-x+1/3 is equivalent to 4) x-3+x

c) 2x-3 is equivalent to 3) -6.9++4.9

d) 3x+0 is equivalent to 2) 3x

e) 3/5-13/5 is equivalent to 5) 3/2x+2+1/2x

So, if the minuend increases by 128 units, then the subtrahend does not need to increase in order to decrease the difference by 67 units.

An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign (=) between two expressions, with one expression on each side of the equals sign. Equations can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to determine the value of the variable that makes both sides of the equation equal. Equations are an important tool in mathematics and are used in various fields such as physics, engineering, finance, and economics to model and solve problems.

Here,

Let's denote the minuend by M, the subtrahend by S, and the difference by D.

In a subtraction, we have: D = M - S

If the minuend increases by 128 units, then the new minuend M' is given by: M' = M + 128

We want to find how much the subtrahend must increase, let's call it x, so that the difference decreases by 67 units. This means that the new difference D' is given by: D' = D - 67

Substituting the expressions for D, M, and M' in terms of S, we get:

D' = (M + 128) - (S + x) - 67

Simplifying this expression, we get:

D' = (M - S) + 61 - x

But we know that D = M - S, so we can substitute it in the above expression:

D' = D + 61 - x

Now, we can substitute the values we know:

D' = D - 67 (since we want the difference to decrease by 67 units)

Therefore, we get:

D - 67 = D + 61 - x

Simplifying this expression, we get:

x = 128 - 67 - 61

x = 0

In other words, the difference will automatically decrease by 67 units when the minuend increases by 128 units.

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Complete question:

In a subtraction, if the minuend increases by 128 units, find by how much the subtrahend must increase so that the difference decreases by 67 units.

The vertices of net that represents a container is 8 vertices.

A cuboid is a three-dimensional geometric shape that is formed by six rectangular faces or sides. It is also known as a rectangular prism. A cuboid has six faces, twelve edges, and eight vertices. The opposite faces of a cuboid are congruent and parallel to each other.

A cuboid can be defined by its length, width, and height, which are the three dimensions of the cuboid. The length is the longest side, the width is the shorter side, and the height is the distance between the two parallel faces.

Cuboids are common in many everyday objects, such as boxes, buildings, and books. They are also important in geometry and engineering as they have a simple shape that is easy to work with and can be used to represent more complex shapes.

The figure which is shown below is a cuboid. Net has 12 edges, 6 faces and 8 vertices.

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The complete question is:

The net below represent a container. What solid figure does it show?

How many vertices does the container have?

The surface area of the given triangular prism having an isosceles triangle   base with sides 40,41 and 43 cm, is 2274 cm².

Area is a measure of the size of a two-dimensional shape or surface, such as a rectangle, triangle, circle, or any other shape that has length and width. It is usually expressed in square units, such as square meters, square centimeters, square feet, or square inches.

To find the surface area of a triangular prism, we need to find the area of each face of the prism and add them up.

The triangular base of the prism is an isosceles triangle with sides of 40 cm, 41 cm, and 43 cm.We may use Heron's formula to determine the area of this triangle:

s = (40 + 41 + 43) / 2 = 62

A = √(s(s-40)(s-41)(s-43)) = √(622221*19) = 798

Therefore, the area of the triangular base is 798 cm².

The height of the prism is given as 18 cm, which is also the length of the rectangular side of the prism.

The two other faces of the prism are rectangles with lengths equal to the base of the triangle (41 cm), and widths equal to the height of the prism (18 cm). The area of each rectangle is:

A = lw = 4118 = 738

Therefore, the area of both rectangles is 2*738 = 1476 cm².

The total surface area of the prism is the sum of the area of the base and the area of both rectangular sides:

Total surface area = Area of base + 2*(Area of rectangle)

Total surface area = 798 + 2*738

Total surface area = 2274 cm².

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Therefore, the values of angles B and C in pentagon ABCDE are 163 degrees and 205 degrees, respectively.

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The two rays are usually represented by lines or line segments, and they can be positioned in various ways relative to each other, creating different types of angles. Angles are typically measured in degrees or radians and can range from 0 degrees (a zero angle, where the two rays coincide) to 360 degrees (a full rotation of one ray around the vertex). Angles are used in many areas of mathematics, physics, and engineering, and they are important for understanding geometric concepts such as shape, symmetry, and proportion.

Here,

In a regular pentagon, all angles have the same measure of 108 degrees. However, in this problem, the angle measures of pentagon ABCDE are not given to be regular, and only the measures of angles A, E, and D are specified to be 90 degrees. To find the value of x, we can use the fact that the sum of the interior angles of a pentagon is equal to 540 degrees. Therefore, we can set up an equation based on this fact:

A + B + C + D + E = 540

Substituting the given values, we have:

90 + (6x + 1) + (8x - 11) + 90 + 90 = 540

Simplifying and solving for x, we get:

14x + 160 = 540

14x = 380

x = 27

Now that we have the value of x, we can use it to find the measures of angles B and C:

B = 6x + 1

= 6(27) + 1

= 163 degrees

C = 8x - 11

= 8(27) - 11

= 205 degrees

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To solve the problem, we need to multiply the distance each runner will run by the number of runners and get the total distance of the race. So we have:

distance per runner = 3/8 mile

number of runners = 4

total distance = distance per runner x number of runners

total distance = 3/8 x 4

total distance = 12/8 miles

To simplify the answer, we can divide both the numerator and denominator by 4, which gives us:

total distance = 3/2 miles

Therefore, the race is 3/2 miles long.

Answer:

[tex]\frac{12}{8}[/tex] or 1 [tex]\frac{4}{8}[/tex] or 1 [tex]\frac{1}{2}[/tex]  These are all the same answer.

Step-by-step explanation:

Helping in the name of Jesus.

We must determine the voltage's rate of change with regard to time. The voltage changes sinusoidally with time in an AC circuit. the current flow in the circuit is [tex]3.817[/tex] Amperes.

To calculate the current flow in the circuit, we need to use the formula:

[tex]I = C x dV/dt[/tex]

Where:

I is the current flow in the circuit (in Amperes)

C is the capacitance of the capacitor (in Farads)

dV/dt is the rate of change of voltage with respect to time (in Volts per second)

First, we need to calculate the rate of change of voltage with respect to time. In an AC circuit, the voltage varies sinusoidally with time. The formula for voltage in an AC circuit is:

[tex]V = Vm sin(ωt)[/tex]

Where:

Vm is the maximum voltage (in Volts)

ω is the angular frequency (in radians per second)

t is the time (in seconds)

We know that the voltage is 240 V and the frequency is 60 Hz. We can use these values to calculate Vm and ω:

[tex]Vm = √2 x Vrms = √2 x 240 = 339.4 V[/tex]

[tex]ω = 2πf = 2π x 60 = 377 rad/s[/tex]

Now, we can calculate [tex]dV/dt:[/tex]

[tex]dV/dt = ω Vm cos(ωt)[/tex]

At  [tex]t = 0[/tex] (i.e. when the voltage is at its maximum), [tex]cos(ωt) = 1. Therefore, dV/dt = ω Vm = 127,234 V/s.[/tex]

Finally, we can calculate the current flow:

[tex]I = C x dV/dt = 30 x 10^-6 F x 127,234 V/s = 3.817 A[/tex]

Therefore, the current flow in the circuit is 3.817 Amperes.

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Answer: We can simplify the given equation as follows:

sin(x/2) = sqrt(2) - sin(x/2)

2sin(x/2) = sqrt(2)

sin(x/2) = sqrt(2)/2

x/2 = pi/4 or x/2 = 3pi/4 (using the standard angles for sin)

x = pi/2 or x = 3pi/2

However, we need to check if these solutions satisfy the original equation since we simplified it along the way.

For x = pi/2, we have:

sin(pi/4) = sqrt(2) - sin(pi/4)

sqrt(2)/2 = sqrt(2) - sqrt(2)/2

sqrt(2)/2 = sqrt(2)/2

This is true, so x = pi/2 is a solution.

For x = 3pi/2, we have:

sin(3pi/4) = sqrt(2) - sin(3pi/4)

-sqrt(2)/2 = sqrt(2) - (-sqrt(2)/2)

-sqrt(2)/2 = sqrt(2)/2

This is not true, so x = 3pi/2 is not a solution.

Therefore, the only solution in the interval [0, 2pi) is x = pi/2.

Step-by-step explanation:

Answer:

To divide two mixed numbers, we first need to convert them into improper fractions.

Converting 3 1/5 to an improper fraction:

3 1/5 = (3 × 5 + 1) / 5 = 16/5

Converting 1 7/9 to an improper fraction:

1 7/9 = (1 × 9 + 7) / 9 = 16/9

Now we can rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction:

16/5 ÷ 16/9 = 16/5 × 9/16

We can simplify the expression by canceling out the common factor of 16 in the numerator and denominator:

(16 ÷ 16) / (5 ÷ 1) × (9 ÷ 16) / (1 ÷ 1) = 1 / 1 × 9 / 16 = 9/16

Therefore, 3 1/5 ÷ 1 7/9 = 9/16 in simplest form.

Step-by-step explanation:

Solution of expression  3 1/5 divided by 1 7/9 are, 9/5

We have,

To find 3 1/5 divided by 1 7/9 in simplest form.

Now, We can divide,

3 1/5 divided by 1 7/9

3 1/5 ÷ 1 7/9

16/5 ÷ 16/9

16 / 5 × 9/16

9 / 5

Therefore, Solution of expression are, 9/5

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The value of the expression [tex]5x + 1 / 4 y^2\\[/tex] when x = 3 and y = 2 is 16.

When someone is experiencing "joy," for instance, the user wants them to feel shocked or very happy. The user will be positively impression if you convey surprise or extreme joy. When someone is experiencing "fright," they want them to feel extremely saddened or disgusted.

A phraseme is a multi-word , multi-morphemic statement whose components contain at least a single word that is selectionally limited. It is also known as a set phrase, persist longer, idiom phrase, multiword expression, or idiom.

To evaluate the expression [tex]5x + 1 / 4 y^2[/tex] when x = 3 and y = 2, we substitute x = 3 and y = 2 into the expression and simplify as follows:

[tex]5x + 1/4 y^2 = 5(3) + 1/4 (2)^2[/tex](substitute x = 3 and y = 2)

= 15 + 1/4(4)

= 15 + 1

= 16

Therefore, the value of the expression [tex]5x + 1 / 4 y^2[/tex]when x = 3 and y = 2 is 16.

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question

What is the value of the expression[tex]5x + 1 /4 y^2[/tex] when x = 3 and y = 2?

The x-intercept is 26. This means that if Stanley were to buy only pizzas (and no sub sandwiches), he would need to buy 26 pizzas to spend exactly $130 on food.

What do you mean by Algebraic expression ?

An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and operations such as addition, subtraction, multiplication, division, and exponentiation.

The given equation is 5x + 6.50y = 130. To find the x-intercept, we set y = 0 and solve for x.

5x + 6.50(0) = 130

5x = 130

x = 26

Therefore, the x-intercept is 26. This means that if Stanley were to buy only pizzas (and no sub sandwiches), he would need to buy 26 pizzas to spend exactly $130 on food.

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Answer:

Cannot be determined

Step-by-step explanation:

Without any additional information, we cannot accurately determine the probability that the code number for a new customer will begin with the number 7.

To calculate the probability, we would need to know the total number of possible code numbers that can be assigned to new customers and how many of those code numbers start with the number 7. If we have that information, we can calculate the probability as follows:

Probability = Number of code numbers starting with 7 / Total number of possible code numbers

For example, if there are 1000 possible code numbers and 50 of them start with the number 7, the probability of a new customer's code number starting with 7 would be:

Probability = 50 / 1000

Probability = 0.05 or 5%

Answer:

4500

Step-by-step explanation:

250 x 18 = 4500

To determine the number of milliliters (mLs) of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection, we can use the following formula:

To calculate the adecuated dose of Erythromycin we have to follow the following procedure:

Where:

First, we need to convert the ordered dose from grams to milligrams (mg), as the concentration of Erythromycin sup is given in milligrams. 0.4g is equal to 400mg.

Next, we can substitute the values into the formula:

Therefore, the number of mLs of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection is 8 mLs. It is important to note that the medication should be administered as prescribed by a healthcare provider, and the patient should complete the entire course of treatment, even if symptoms improve.

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1. The probability that an infected patient’s length of stay will be greater than 7 days is 0.3085.

2. The 70th percentile in stay length for a patient given that they have a

post-operative infection is 7.04.

3. The probability that the average stay length of the next 2 infected patients is less than 5.5 days is 0.3632.

4. The probability that a patient is infected and then stays for 3 to 4 days is  0.1587.

1. Probability of an infected patient staying more than 7 days:

We can standardize the normal distribution using the formula: Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.

So, Z = (7 - 6) / 2 = 0.5.

Using a standard normal distribution table or calculator, we can find the probability that a patient will stay longer than 7 days as:

P(Z > 0.5) = 0.3085.

2. The 70th percentile in stay length for an infected patient:

We can use the inverse standard normal distribution function to find the Z-score corresponding to the 70th percentile.

Using a standard normal distribution table or calculator, we find that the Z-score corresponding to the 70th percentile is approximately 0.52.

So, Z = 0.52 = (X - 6) / 2.

Solving for X, we get:

X = 6 + 0.52 * 2 = 7.04.

3. Probability that the average stay length of the next 2 infected patients is less than 5.5 days:

The average length of stay of 2 infected patients can be modeled by a normal distribution with a mean of 6 days (the mean of a single infected patient's length of stay) and a standard deviation of σ/√2, where σ is the standard deviation of the length of stay of a single infected patient.

So, the standard deviation of the average length of stay of 2 infected patients is:

σ/√2 = 2/√2 = 1.414 days.

Using the standardized normal distribution formula, we get:

Z = (5.5 - 6) / 1.414 = -0.3536.

Using a standard normal distribution table or calculator, we can find the probability that the average stay length of the next 2 infected patients will be less than 5.5 days as:

P(Z < -0.3536) = 0.3632.

4. Probability that a patient is infected and then stays for 3 to 4 days:

We can standardize the normal distribution as before using the formula:

Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.

For X = 3 days, Z = (3 - 6) / 2 = -1.5.

For X = 4 days, Z = (4 - 6) / 2 = -1.

Using a standard normal distribution table or calculator, we can find the probability that a patient is infected and then stays for 3 to 4 days as:

P(-1.5 < Z < -1) = P(Z < -1) - P(Z < -1.5) = 0.1587

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