The scatter plot to the right shows the cost (y), in dollars, of orange trees based on their ages (x), in years. Based on the scatter plot, which equation represents the line of best fit for the cost of the orange trees?
A y=15.7x
B y=11.8x+29.2
C y=15.7+40.0
D y=11.8x​

Therefore , the solution of the given problem of volume comes out to be  roughly 1,814.4 cubic feet.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, you must be aware of an object's volume in order to calculate its dimensions. It is standard practice to translate an object's weight to mass units like grams and kilograms.

Here,

V = r2h, where r is the radius and h is the height, is the expression for a cylinder's volume.

We are informed that the cylindrical has a 9-foot height and an 8-foot radius. (since the diameter is 16 ft).

When the formula's numbers are substituted, we obtain:

=> V = π(8 ft)²(9 ft)

=> V = π(64 ft²)(9 ft)

=> V = 1,814.37 ft³

We can calculate this result as V = 1,814.4 ft³ by rounding to the nearest tenth.

The cylinder's capacity is therefore roughly 1,814.4 cubic feet.

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The probability that a person selected at random at this conference is a doctor or a woman is 63%.

The theory of probability is a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes.

We will solve the problem using the union rule of probability. Using the given information, we can calculate the probabilities as follows:

P(doctor) = 53%

P(woman) = 41%

P(female doctor) = 31%

To find the probability that a person selected at random at this conference is a doctor or a woman, we can use the formula:

P(doctor or woman) = P(doctor) + P(woman) - P(doctor and woman)

We can calculate P(doctor and woman) by multiplying the probabilities of being a female doctor:

P(doctor and woman) = P(female doctor) = 31%

Substituting in the values, we get:

P(doctor or woman) = 53% + 41% - 31%

P(doctor or woman) = 63%.

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The graph for y = 4(1/4)ˣ is B)

Explain graphs.

A graph is a visual representation of a set of data, typically in the form of a diagram or a chart. A graph is made up of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs can be used to display various types of information, including mathematical functions, relationships between variables, and patterns in data. They are commonly used in fields such as science, engineering, economics, and social sciences to convey complex information in a simple and easy-to-understand manner.

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The correct centre measure, with a mean value of approximately 5 gallons, will be C. Coffee Ground, with a mean value of about 5 gallons, which will show which shop usually sells the most coffee per hour.

By summing up all the data points and dividing by the total number of data points, the mean is determined.

To determine which coffee shop typically sells the most amount of coffee per hour, we can compare the measures of center, specifically the mean and median, of the two datasets.

Calculating the mean for each dataset, we get:

Coffee Ground: (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5)/12 = 6.125 gallons

Wide Awake: (2.5+10+4+18+4+3+6+5+2.5)/9 = 6.0556 gallons

Therefore, Coffee Ground has a higher mean than Wide Awake, suggesting that Coffee Ground typically sells more coffee per hour.

Calculating the median for each dataset, we get:

Coffee Ground: 5 gallons

Wide Awake: 4.5 gallons

Therefore, the median for Wide Awake is lower than that of Coffee Ground, suggesting that Wide Awake typically sells less coffee per hour.

Based on these measures of center, we can conclude that the answer is: C. Coffee Ground, with a mean value of about 5 gallons.

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Answer:

a. The scale factor of the smaller cylinder to the larger cylinder is the ratio of their radii, which is 4/6 or 2/3.

b. The circumference of the base of a cylinder is given by 2πr, where r is the radius of the base. Thus, the ratio of the circumferences of the bases of the two cylinders is:

(2π)(4)/(2π)(6) = 4/6 = 2/3

c. The lateral area of a cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height. The ratio of the lateral areas of the two cylinders is:

(2π)(4)(9)/(2π)(6)(9) = 4/6 = 2/3

d. The volume of a cylinder is given by the formula πr²h. Thus, the ratio of the volumes of the two cylinders is:

(π)(4²)(9)/ (π)(6²)(9) = 16/36 = 4/9

e. If the volume of the smaller cylinder is 144π cm³, then we can use the formula for the volume of a cylinder to solve for the height of the smaller cylinder:

144π = π(4²)h

h = 9 cm

Since the two cylinders are similar, we know that the ratio of their heights is the same as the ratio of their radii, which is 2/3. Thus, the height of the larger cylinder is:

(2/3)(9) = 6 cm

Using the formula for the volume of a cylinder, we can now calculate the volume of the larger cylinder:

V = π(6²)(6) = 216π cm³

Step-by-step explanation:

pa brainliest po.

Answer:

look below its the answer i promise

Step-by-step explanation:

The answer to the given question about IQR is option b Bus 14, with an IQR of 6.

To determine which bus is the most consistent, we need to look at the measure of variability for each data set. In this case, we are given the interquartile range (IQR) and the range for each bus. The IQR is a better measure of variability than the range because it is less affected by outliers.

Bus 47 has an IQR of 8, which means that the middle 50% of the data falls within a range of 8 minutes. Bus 14 has an IQR of 6, which means that the middle 50% of the data falls within a range of 6 minutes.

Since Bus 14 has a smaller IQR, it is more consistent than Bus 47. This means that the travel times for Bus 14 are more similar to each other than the travel times for Bus 47. Therefore, we can conclude that Bus 14 is the most consistent of the two buses.

Therefore, the correct answer is:

Bus 14, with an IQR of 6.

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This is challenging to visualize but similar to your other problem. You want to maximize x and y to maximize c.

The problem just boils down to solving the linear system.

2x + 2y = 10

3x + y = 9

I changed the less than or equal signs to equal signs because we want the largest values not the ones less than the max. I think you know how to solve this system based on the difficulty of the problem but I can give a solution. Let's use elimination. Multiplying the second equation by two and adding it to the first we have...

   -2(3x + y = 9)

+ (2x + 2y = 10)

----------------------

-4x = -8

x = 2

Then y = 9 - 3x (from eq 2) = 9 - 3(2) = 3

Then the max value of c = 4(2) + 2(3) = 14

Answer:x+y=c

Step-by-step explanation:

Answer:

800$

Step-by-step explanation: not sure

The school begin with 25 cookies based on remaining 24 cookies and first selling of 4% cookies.

Let us assume the initial number of cookies be x. So, the remaining cookies percentage = 96%

Now, we are given the remaining cookies number. So, the equation will be -

96% × x = 24

Solving the equation by firstly converting the percentage into decimal

0.96x = 24

Rewriting the equation to further calculate the value of x

x = 24/0.96

Performing division on Right Hand Side of the equation

x = 25

Thus, there were total 25 cookies.

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Answer: 122 cm²

Step-by-step explanation:

Answer:

d.

Step-by-step explanation:

To determine the rows where the expression (p ∧ q) ∨ (p ∧ r) is true, we can construct a truth table with columns for p, q, r, p ∧ q, p ∧ r, (p ∧ q) ∨ (p ∧ r), as shown below:

```

p | q | r | p ∧ q | p ∧ r | (p ∧ q) ∨ (p ∧ r)

----------------------------------------------

T | T | T | T | T | T

T | T | F | T | T | T

T | F | T | F | T | T

T | F | F | F | F | F

F | T | T | F | F | F

F | T | F | F | F | F

F | F | T | F | F | F

F | F | F | F | F | F

```

The rows where the expression (p ∧ q) ∨ (p ∧ r) is true are the first, second, and third rows, where the last column is true. Therefore, the rows where the expression is true are:

```

p | q | r

--------

T | T | T

T | T | F

T | F | T

```

Answer:

Step-by-step explanation:

To find:-

Answer:-

The given coordinates of the triangle are , A(3,-4) ; B(-2,1) and C(5,0) .

To find out the coordinate of the centroid we can use the below formula ,

[tex]\longrightarrow \boxed{\rm{Centroid\ (G)}= \bigg(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\bigg)} \\[/tex]

where ,

On substituting the respective values, we have;

[tex]\longrightarrow G =\bigg(\dfrac{3-2+5}{3},\dfrac{-4+1+0}{3}\bigg) \\[/tex]

[tex]\longrightarrow G =\bigg(\dfrac{ 6}{3},\dfrac{-3}{3}\bigg) \\[/tex]

[tex]\longrightarrow \boldsymbol{ G = (2,-1) }\\[/tex]

Hence the centroid of the given triangle is (2,-1) .

Now the given equation of the line is,

[tex]\longrightarrow x - 3y = 4 \\[/tex]

Convert this into slope intercept form of the line, which is,

Slope intercept form:-

[tex]\longrightarrow y = mx + c\\[/tex]

where, m is the slope of the line and c is the y-intercept .

So , we have;

[tex]\longrightarrow -3y = 4-x\\[/tex]

[tex]\longrightarrow 3y = x - 4 \\[/tex]

[tex]\longrightarrow y =\dfrac{x-4}{3} \\[/tex]

[tex]\longrightarrow y =\dfrac{1}{3}x-\dfrac{4}{3} \\[/tex]

On comparing it with the slope intercept form, we have;

[tex]\longrightarrow m =\dfrac{1}{3}\\[/tex]

Secondly we know that the slopes of parallel lines are equal . So the slope of the line parallel to the given line would also be ⅓ .

Now we may use point slope form of the line to find out the equation of the required line. The point slope form of the line is,

Point slope form:-

[tex]\longrightarrow y - y_1 = m(x-x_1) \\[/tex]

where the symbols have their usual meaning.

Here the line will pass through the centroid of the triangle which is (2,-1) .

On substituting the respective values, we have;

[tex]\longrightarrow y - (-1) =\dfrac{1}{3}(x-2) \\[/tex]

[tex]\longrightarrow 3( y +1) = x - 2 \\[/tex]

[tex]\longrightarrow 3y + 3 = x -2\\[/tex]

[tex]\longrightarrow x - 2 - 3 - 3y = 0 \\[/tex]

[tex]\longrightarrow\boxed{\boldsymbol{ x - 3y - 5 =0}} \\[/tex]

This is the required equation of the line.

Answer:

[tex]728 \: {m}^{2} [/tex]

Step-by-step explanation:

Given:

l = 15 m (length)

w = 16 m (width)

h = 4 m (height)

Find: a (surface) - ?

First, let's find the area of the base:

a (base) = l × w

a (base) = 15 × 16 = 240 m^2

Since the rectangular prism has 2 bases, we multiply this number by 2:

240 × 2 = 480 m^2 (area of both bases)

Now, let's find the lateral surface area:

a (lateral) = 2(4 × 15) + 2(4×16) = 2 × 60 + 2 × 64 = 120 + 128 = 248 m^2

Finally, in order to find the whole surface area, we have to add the lateral surface area and both bases area together:

a (surface) = a (lateral) + a (base)

a (surface) = 248 + 480 = 728 m^2

(a)  Total urine volume is excreted during this time period is 442.34 mL.

(b) Equations for the velocity of urine is v = (-3 x [tex]V_t[/tex] + 7.35) / 2.46 x [tex]10^{-5}[/tex]

(a) To determine the total urine volume excreted during this time period, we need to integrate the flow rate function over the given time period. However, we are given two different equations for the flow rate for different ranges of time:

For t < 12 seconds, V = -0.306 x  [tex](t-7)^2[/tex]  + 15

For 12 ≤ t < 26.7 seconds, V = -3 x [tex]V_t[/tex]  + 7.35

To find the total urine volume, we need to first determine the time at which the flow rate changes from the first equation to the second.

We can do this by setting the two equations equal to each other and solving for t:

-0.306 x  [tex](t-7)^2[/tex]  + 15 = -3 x [tex]V_t[/tex] + 7.35

0.306 x  [tex](t-7)^2[/tex] + 3 x [tex]V_t[/tex]  = 7.65

0.306 x [tex](t-7)^2[/tex] = 7.65 - 3 x [tex]V_t[/tex]

[tex](t-7)^2[/tex] = (7.65 - 3 x [tex]V_t[/tex] ) / 0.306

t = 7 +/- [tex]\sqrt{((7.65 - 3 \times Vt) / 0.306)}[/tex]

Since t < 12 for the first equation, we can ignore the negative root and use the positive root to find the time at which the flow rate changes:

t = 7 + [tex]\sqrt{((7.65 - 3 \times 12) / 0.306)}[/tex]= 10.76 seconds

Now we can integrate each equation separately over their respective time ranges:

For 0 ≤ t < 10.76 seconds:

∫ V dt = ∫ (-0.306 x [tex](t-7)^2[/tex] + 15) dt

= [-0.102 x [tex](t-7)^3[/tex] + 15t] from t=0 to t=10.76

= 121.86 mL

For 10.76 ≤ t < 26.7 seconds:

∫ V dt = ∫ (-3 x [tex]V_t[/tex] + 7.35) dt

= [-1.5 x [tex]V_t^2[/tex] + 7.35t] from t=10.76 to t=26.7

= 320.48 mL

Therefore, the total urine volume excreted during this time period is:

121.86 mL + 320.48 mL = 442.34 mL

(b) To develop equations for the velocity of urine as it exits the body, we need to use the continuity equation, which states that the flow rate (V) is equal to the cross-sectional area (A) multiplied by the velocity (v):

V = A x v

We are given that the urethra has a diameter of 5.6 mm, which means the radius is 2.8 mm (or 0.0028 m).

The cross-sectional area can be calculated using the formula for the area of a circle:

A = π x [tex]r^2[/tex]

A = 3.14 x [tex](0.0028)^2[/tex]

A = 2.46 x   [tex]10^{-5}[/tex] [tex]m^2[/tex]

Now we can rearrange the continuity equation to solve for the velocity:

v = V / A

Substituting the given equations for V, we get:

For t < 12 seconds:

v = (-0.306 x [tex](t-7)^2[/tex] + 15) / 2.46 x  [tex]10^{-5}[/tex]

For 12 ≤ t < 26.7 seconds:

v = (-3 x  [tex]V_t[/tex] + 7.35) / 2.46 x [tex]10^{-5}[/tex]

Note that the velocity will be in units

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Question:-

The flow of urine from the bladder, through the urethra, and out of the body, is induced by increased pressure in the bladder resulting from muscle contractions around the bladder with simultaneous relaxation of the muscles in the urethra. The mean pressure in the bladder can be estimated using the velocity of urine as it exits the body. Assume that the bladder is about 5 cm above the external urethral orifice. (This height is different for males and females.) The flow rate of urine from the bladder can be approximately described with the following equations, where t is time in seconds, and V is flow rate in mL/s:

V = -0.306 X (t – 7)2 + 15 Osts 12

V = -3 X Vt 12 + 7.35 12 st < 26.7

(a) How much total urine volume is excreted during this time period?

(b) Develop equations for the velocity of as it exits the body. Assume that the urethra is 5.6 mm in diameter.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the concept of similar triangles.

Let's draw a diagram to visualize the situation:

     * Statue top

      |

      |

      |  9 m

      |

      |

      |

     / \

    /   \    4 m

Kimberly

We can see that we have two right triangles, one formed by Kimberly, the ground, and the point where the statue touches the ground, and the other formed by the statue, the ground, and the point where Kimberly's head touches the ground.

These two triangles are similar because they have the same angles. In particular, the angle at Kimberly's eye is the same as the angle at the top of the statue. This means that the corresponding sides are proportional.

Let's call the height of the statue "h". Then, we have:

h/9 = (h+4)/4

We can solve for "h" by cross-multiplying:

4h = 9(h+4)

4h = 9h + 36

5h = 36

h = 7.2

Therefore, the height of the statue is 7.2 meters. To find out how much taller the statue is than Kimberly, we subtract their heights:

7.2 m - 1.5 m = 5.7 m

So the statue is 5.7 meters taller than Kimberly.

The solutions to the equation log4(x² - 2x) = log4(3x + 8) are x = 8 and x = -1.

To solve the equation log4(x² - 2x) = log4(3x + 8), we can use the property of logarithms that says if logb(a) = logb(c), then a = c.

Using this property, we can set the expressions inside the logarithms equal to each other:

x² - 2x = 3x + 8

Now we have a quadratic equation that we can solve:

x² - 2x - 3x - 8 = 0 x² - 5x - 8 = 0

We can factor this equation using the product-sum method:

x² - 5x - 8 = (x - 8)(x + 1)

Setting each factor equal to zero gives us the possible solutions:

x - 8 = 0 or x + 1 = 0

Solving for x in each case gives us:

x = 8 or x = -1

However, we need to check if either of these solutions make the argument of the logarithm negative or zero. If the argument is negative or zero, then the logarithm is undefined.

For the first solution, x = 8, we have:

log4(8² - 2(8)) = log4(3(8) + 8) log4(48) = log4(32)

Both arguments are positive, so x = 8 is a valid solution.

For the second solution, x = -1, we have:

log4((-1)² - 2(-1)) = log4(3(-1) + 8) log4(3) = log4(5)

Again, both arguments are positive, so x = -1 is also a valid solution.

Therefore, the solutions to the equation log4(x² - 2x) = log4(3x + 8) are x = 8 and x = -1.

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the simplified form of the given expression is 2cd³(12c + 5d²).just by using simple mathematics we are able to solve to get answer.

what is simplified form ?

Simplified form refers to the expression of a mathematical expression or equation in a way that is easier to read, understand, and manipulate. Simplification involves combining like terms, factoring out common factors, reducing fractions, or using identities to transform the original expression to an equivalent but simpler form. The simplified form of an expression should have no unnecessary or redundant terms or factors and should be as concise and clear as possible.

In the given question,

Simplified form refers to the expression of a mathematical expression or equation in a way that is easier to read, understand, and manipulate.

Simplification involves combining like terms, factoring out common factors, reducing fractions, or using identities to transform the original expression to an equivalent but simpler form.

The simplified form of an expression should have no unnecessary or redundant terms or factors and should be as concise and clear as possible.

The given expression is a polynomial in two variables c and d. We can simplify it by factoring out the common factors from each term:

24c² d³ + 10cd⁵ =2cd³(12c + 5d²)

Therefore, the simplified form of the given expression is 2cd³(12c + 5d²)

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what is simplified form of 24c² d³+10cd⁵ ?

Answer: C and D

Step-by-step explanation:

Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.

In mathematics, a function is a rule or relationship that maps each input value (also known as the "argument" or "independent variable") to a corresponding output value (also known as the "value" or "dependent variable").

In other words, a function is a way to describe how one set of values (the inputs) are transformed into another set of values (the outputs). Functions are often represented using algebraic equations or graphical representations, such as graphs or charts.

For example, the function f(x) = 2x + 1 maps each input value x to the output value 2x + 1. So, if we input x=2, the output value would be f(2) = 2(2) + 1 = 5. Similarly, if we input x=3, the output value would be f (3) = 2(3) + 1 = 7.

(a) Based on the scatter plot, we can see a positive linear relationship between the hours spent on homework and the test scores. As the number of hours spent on homework increases, the test scores also tend to increase.

(b) To use Paul's function to predict the test score for 3 hours of homework, we can substitute x = 3 into the equation:

[tex]y = 8x + 40[/tex]

[tex]y = 8(3) + 40[/tex]

[tex]y = 24 + 40[/tex]

[tex]y = 64[/tex]

Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.

(c) In the context of the situation, the number 40 in Paul's model represents the baseline or minimum test score that a student would get if they didn't study at all. This is the y-intercept of the line and indicates that a student who does not spend any time on homework is predicted to get a score of 40.

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The amount of money in an account at the end of 5 years will be $14,014.40.

To calculate this, we can use the continuous compounding formula: [tex]A = Pe^(rt)[/tex] where P = 10,000, r = 6.75% (0.0675), t = 5.

Now, the amount of money in an account at the end of 5 years will be:

A = 10,000*e^(0.0675*5)

A = 10,000*e^0.3375

A = 10,000*1.40143960839

A = 14014.3960839

A = $14,014.40

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The following formula is used: P(n,r) = n! / (n - r)! to the calculate  the number of permutations.

The formula used to calculate the number of permutations when a permutation is any arrangement of r objects

selected from n possible objects is P(n,r).

P(n,r) is the formula used to calculate the number of permutations.

Let us try to understand the concept of permutations first.

Permutations refer to the different ways of arranging elements.

It is represented as nPr called as n-permute-r.

Here, n represents the total number of elements present, and r represents the number of elements taken for each

permutation.

To calculate the number of permutations, the following formula is used:

P(n,r) = n! / (n - r)!

Where n! is equal to n-factorial that refers to the product of all numbers starting from 1 up to n.

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There are infinitely many solutions to this system.

We can solve the system of equations by elimination method:

10x = 5y - 8 (multiply both sides by 3)

15x = -5y - 2

30x = 15y - 24

15x = -5y - 2

Adding these two equations, we get:

45x = 13y - 26

Dividing both sides by 13, we get:

y = (45/13)x + 2

So any ordered pair (x, y) that satisfies this equation will also satisfy the system of equations given. There are infinitely many solutions to this system.

For example, if we let x = 13, then:

y = (45/13)(13) + 2 = 47

So one possible solution is (13, 47). Another possible solution is (26, 92/3).

Answer:

The answer to your problem is, 23.6 or 49.8

Step-by-step explanation:

Surface area of cube=4 x a²----> 4 x 2²-----> 16  ft²

Surface area of triangular prism=2*[a*c]+2*[a*b/2]---> 2*[2*1.4]+[2*1]

Surface area of triangular prism=5.6+2----> 7.6 ft²

Surface area of the figure=16 ft²+7.6 ft²----> 23.6 ft²

Thus the answer to your problem is, 23.6 or 49.8

It could be either one did the same quiz but I had different answers every time so choose which one you have :).

Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.

Long-distance travel refers to a journey between two locations that are far apart. The best option for long-distance travel is the train because it is dependable and affordable. Communication that takes place over a long distance is referred to as long-distance. His lover in Colorado gave him a long-distance call.

We may construct a proportion to calculate how long it will take Scott to complete 52 kilometers at the same speed:

52 km/m at 20 km/85 min.

We can cross-multiply to find the value of m:

20 km * m equals 85 min * 52 km.

Simplifying:

20m = 4420

20 divided by both sides:

m = 221

Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.

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The probability that a randomly selected user is online less than 15 hours a week is 0.1056 (approx).

As per the given statement, u.s. internet users spend an average of 18.3 hours a week online. If 95% of users spend between 13.1 and 23.5 hours a week, we need to determine the probability that a randomly selected user is online less than 15 hours a week.

To find the probability that a randomly selected user is online less than 15 hours a week, we need to use the Z-score formula, which is defined as:

Z = (X - μ) / σ

Where Z is the z-score, X is the value of the element, μ is the mean of the population, and σ is the standard deviation. Therefore, the probability of a randomly selected user being online less than 15 hours per week can be calculated as follows:Z = (15 - 18.3) / σ

We know that 95% of users spend between 13.1 and 23.5 hours per week, which means that the standard deviation is given by:

13.1 - 18.3 = 5.4 hours (lower bound)

23.5 - 18.3 = 5.2 hours (upper bound)

Therefore, σ = (5.4 + 5.2) / 4 = 2.65 hours

Hence, the z-score can be calculated as follows:Z = (15 - 18.3) / 2.65 = -1.25

Thus, the probability that a randomly selected user is online less than 15 hours a week is P(Z < -1.25). Using a standard normal distribution table, we can find that P(Z < -1.25) = 0.1056 (approx).

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Port C is approximately 148.96 kilometers to the east of Port A, at a bearing of 013.93 degrees from the positive x-axis.

How to find distance and direction?

To find the distance and direction of Port C from Port A, we can use basic trigonometry and vector analysis.

First, we need to draw a diagram of the situation. We can assume that Port A is located at the origin (0,0) of a two-dimensional coordinate system, and that the ship sails in a straight line from A to B on a bearing of 050 degrees, which means that its direction is 40 degrees clockwise from the positive x-axis. Since Port B is 80 kilometers to the east of A, we can represent it as the point (80,0) in the coordinate system.

Next, the ship sails from B to C on a bearing of 062 degrees, which is 22 degrees clockwise from its previous direction. To calculate the distance and direction of C from A, we need to find the vector that represents the displacement of the ship from B to C, and add it to the vector that represents the displacement from A to B.

To find the vector that represents the displacement from B to C, we can use basic trigonometry. Let d be the distance from B to C, and let θ be the angle between the displacement vector and the positive x-axis. Then, we have:

cos(θ) = adjacent/hypotenuse = 80/d

sin(θ) = opposite/hypotenuse = (d*sin(22))/d = sin(22)

Solving for d, we get:

d = 80/cos(θ) = 80/cos(arctan(sin(22)/cos(22))) ≈ 92.56 km

Therefore, the vector that represents the displacement from B to C is (dcos(θ), dsin(θ)) ≈ (64.39 km, 35.77 km) in the coordinate system.

To find the vector that represents the displacement from A to C, we can add the two vectors:

(80,0) + (64.39,35.77) ≈ (144.39,35.77)

Therefore, the distance from A to C is the magnitude of this vector:

|AC| = sqrt((144.39)² + (35.77)²) ≈ 148.96 km

To find the direction of C from A, we can use the inverse tangent function:

tan⁻¹(35.77/144.39) ≈ 13.93 degrees

Therefore, Port C is approximately 148.96 kilometers to the east of Port A, at a bearing of 013.93 degrees from the positive x-axis.

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