Suppose that the duration of a particular type of criminal trial is known to have a mean of 15 days and a standard deviation of 5 days. We randomly sample 9 trials. Find the probability that the total length of the 9 trials is at least 171 days. (Round your answer to four decimal places.)

Answer: A.

Step-by-step explanation:

1/4 is not in fact a natural number, it's a rational number, a ratio.

Answer:

108 pens

Step-by-step explanation:

48/4=x/9

4x=432

x=108

Answer:

Since there are 12 pens packed in each box, because there are 48 packed in 4 boxes, there will be ( 12 times 9 ) 108 pens in 9 boxes.

Answer: 60 miles

Step-by-step explanation:

Given

It takes ferry 2 hours to travel to town A and only \(1.5\ hr\) to travel back to town B.

Speed of current is \(u=5\ mph\)

Suppose the speed of the ferry is \(v\) mph

Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.

\(\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph\)

Distance between the towns is \(2\times (35-5)=60\ \text{miles}\)

Answer:

The distance between the two towns is 60 miles.

Step-by-step explanation:

Let the distance between A and B is d.

A to B , t = 2 hour

B to A , t' = 1.5 hour

Speed of current, u = 5 mph

Let the speed of ferry is v.

distance = speed x time

d = (v - 5) x 2 = (v + 5) x 1.5

2 v - 10 = 1.5 v + 7.5

0.5 v = 17.5

v = 35 mph

So, the distance is

d = (35 - 5) x 2 = 60 miles.

Answer:

D no because 18 is paired with itself

Answer:

Answers are below

Step-by-step explanation:

The domain of the function is all real numbers.

The range of the function is also all real numbers.

I graphed the function on the graph below.

Answer:

148x+76y=3640

The orchestra tickets costed $21, the balcony tickets costed $7

Step-by-step explanation:

You do 148x because we know that they sold 148 tickets we just need to know the cost and 76 because we know that have sold 76 balcony tickets.

I’m don’t really know how to say the rest

The price of each ticket will be;

The price of balcony ticket = $910

So, The price of orchestra ticket = $2730

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A theater earns $3640 from a concert.

And, An orchestra ticket costs three times as much as a balcony ticket.

Now,

Since, An orchestra ticket costs three times as much as a balcony ticket.

Let price of balcony ticket = x

So, The price of orchestra ticket = 3x

Hence, We can formulate;

⇒ x + 3x = $3640

⇒ 4x = $3640

⇒ x = $3640/4

⇒ x = $910

Thus, The price of balcony ticket = x

                                                   = $910

So, The price of orchestra ticket = 3x

                                                  = 3 × $910

                                                  = $2730

Thus, The price of each ticket will be;

The price of balcony ticket = $910

So, The price of orchestra ticket = $2730

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

The probability that a player will be asked a math question and then a music question is 0.03125

The size of the sections are given as:

Music = 0.5

Sport = 0.5

Others = 1

So, the total size is:

Total = 0.5 + 0.5 + 1 + 1 + 1

Evaluate

Total = 4

The probability of asking a math question is:

P(Math) = 1/4 = 0.25

The probability of asking a music question is:

P(Music) = 0.5/4 = 0.125

The required probability is:

P(Math and Music) = P(Math) * P(Music)

This gives

P(Math and Music) = 0.25 * 0.125

Evaluate

P(Math and Music) = 0.03125

Hence, the probability that a player will be asked a math question and then a music question is 0.03125

Read more about probability at:

https://brainly.com/question/25870256

#SPJ1

Answer:

different between the two are that they are am and pm

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

To learn more about solution, click here:

https://brainly.com/question/25785824

#SPJ4

The number of ways Aaron can arrange the 5 songs on the playlist is equal to 120 ways.

Number of songs = 5

Consider that there are 5 options for the first song.

4 options for the second song since one song has already been used.

3 options for the third song.

2 options for the fourth song.

And only 1 option for the last song.

So the total number of arrangements is equal to,

= 5 × 4 × 3 × 2 × 1

= 120

Alternatively, use the formula for permutations of n objects taken x at a time,

ⁿPₓ= n! / (n - x)!

Here,

The number of songs  n = 5

The number of slots on the playlist x = 5

⁵P₅ = 5! / (5 - 5)!

     = 5!

     = 120 ways

Therefore, the total number of ways Aaron can arrange his 5 songs on playlist is 120.

Learn more about ways here

brainly.com/question/14972885

#SPJ4

Answer:

Number = 12

Step-by-step explanation:

2n-7=n+5 (+7 to both sides)

2n=n+12 (-n to both sides)

n=12

Answer:

the mode remains the same

Step-by-step explanation:

42 is outlier.

mod is the most repetitive number of a number string, and outlier does not change it.

the mode remains the same.

The probability is approximately 0.9167 or 91.67%.

To find the probability that the sum of two dice numbers does not exceed 10, we need to determine the favorable outcomes (sums less than or equal to 10) and the total possible outcomes when rolling two dice.

There are 36 possible outcomes when rolling two dice because each die has six faces (1, 2, 3, 4, 5, and 6), and the total number of outcomes is obtained by multiplying the number of outcomes for each die (6 * 6 = 36).

Now let's determine the favorable outcomes (sums less than or equal to 10):

When the sum is 2: There is only one combination (1 + 1).

When the sum is 3: There are two combinations (1 + 2 and 2 + 1).

When the sum is 4: There are three combinations (1 + 3, 2 + 2, and 3 + 1).

When the sum is 5: There are four combinations (1 + 4, 2 + 3, 3 + 2, and 4 + 1).

When the sum is 6: There are five combinations (1 + 5, 2 + 4, 3 + 3, 4 + 2, and 5 + 1).

When the sum is 7: There are six combinations (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1).

When the sum is 8: There are five combinations (2 + 6, 3 + 5, 4 + 4, 5 + 3, and 6 + 2).

When the sum is 9: There are four combinations (3 + 6, 4 + 5, 5 + 4, and 6 + 3).

When the sum is 10: There are three combinations (4 + 6, 5 + 5, and 6 + 4).

Adding up the favorable outcomes, we get: 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.

Therefore, the probability that the sum of the two dice numbers does not exceed 10 is given by:

Probability = Favorable outcomes / Total outcomes = 33 / 36 = 11/12 ≈ 0.9167.

So, the probability is approximately 0.9167 or 91.67%.

Learn more about  probability   from

https://brainly.com/question/30390037

#SPJ11

Answer:

x = -2

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 5 and 6x from both sides of the equation:

8x (-6x) + 5 (-5) = 6x (-6x) + 1 (-5)

8x - 6x = 1 - 5

2x = -4

Isolate the variable, x. Divide 2 from both sides of the equation:

(2x)/2 = (-4)/2

x = -4/2

x = -2

x = -2 is your answer.

~

Answer:

He will pay 60 feet of wire for $13.80

E(X)\(= 1(1/36) + 2(2/36) + 3(4/36) + 4(6/36) + 5(8/36) + 6(10/36)\)

= 4.47 approximately, to two decimal places. Hence, the required values are pmf of X and E(X).

Given that two fair six-sided dice are tossed independently. Let X denotes the maximum of the six-sided two tosses a. We need to find the pmf of X and E(X).a. What is the pmf of X? Probability mass function (pmf) gives the probability of each value of a random variable.

Here X represents the maximum value when two fair six-sided dice are tossed independently. The possible values of X are {1, 2, 3, 4, 5, 6}.Since X denotes the maximum value, the pmf of X isP(X = 1) = P(1, 1) = 1/36P(X = 2) = P(1, 2) + P(2, 1) = 2/36P(X = 3) = P(1, 3) + P(2, 3) + P(3, 1) + P(3, 2) = 4/36P(X = 4) = P(1, 4) + P(2, 4) + P(3, 4) + P(4, 1) + P(4, 2) + P(4, 3) = 6/36P(X = 5) = P(1, 5) + P(2, 5) + P(3, 5) + P(4, 5) + P(5, 1) + P(5, 2) + P(5, 3) + P(5, 4) = 8/36P(X = 6) = P(1, 6) + P(2, 6) + P(3, 6) + P(4, 6) + P(5, 6) + P(6, 1) + P(6, 2) + P(6, 3) + P(6, 4) + P(6, 5) = 10/36

To know more about decimal places visit:-

https://brainly.com/question/30650781

#SPJ11

25% off means the new price of the item is 75% of the originl price ( 100% - 25% = 75%)

Multiply the original price by 75%:

20 x 0.75 = 15

The sale price is £15

S.P:25x/100

0.25x=20

x=20/0.25

x=80

The parameters of the relevant standard beta distribution are alpha and beta.

These are two parameters that determine the shape of the beta distribution

.The standard beta distribution is a continuous probability distribution that is defined on the interval [0, 1]. It is often used to model the probability of success or failure in a binary experiment.

The two parameters of the standard beta distribution determine the shape of the distribution. Alpha is the shape parameter that determines the slope of the distribution, while beta is the shape parameter that determines the height of the distribution.

The standard beta distribution is often used in Bayesian statistics to model the prior probability of a parameter. It is also used in applications such as modeling the proportion of a population that has a particular characteristic or modeling the probability of default on a loan.

Learn more about alpha and beta at

https://brainly.com/question/2264128

#SPJ11

The solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

To solve the system of equations:

2X + 4Y + 2Z = 144 (Equation 1)

0.5X + 0.25Y = 60 (Equation 2)

1.5X + 0.5Y + Z = 36 (Equation 3)

We can use row operations to simplify and solve the system.

Let's start with Equation 2. Multiply both sides of Equation 2 by 4 to eliminate decimals:

2X + Y = 240 (Equation 4)

Now, let's solve Equations 1 and 4 using row operations. Multiply Equation 4 by -2 and add it to Equation 1:

-4X - 2Y = -480 (Equation 5)

2X + 4Y + 2Z = 144 (Equation 1)

   2Y + 2Z = -336  (Equation 6)

Next, let's solve Equations 3 and 6 using row operations. Multiply Equation 6 by -3 and add it to Equation 3:

-3Y - 3Z = 1008 (Equation 7)

1.5X + 0.5Y + Z = 36 (Equation 3)

1.5X - 2.5Z = -972 (Equation 8)

We now have a simplified system of equations:

2Y + 2Z = -336 (Equation 6)

1.5X - 2.5Z = -972 (Equation 8)

-3Y - 3Z = 1008 (Equation 7)

Now, we can solve this system by using additional row operations.

Multiply Equation 6 by 1.5 and add it to Equation 8:

-4Z = -1452

Solving for Z, we get Z = 363.

Substituting the value of Z back into Equation 6, we can solve for Y:

2Y + 2(363) = -336

2Y = -1062

Y = -531.

Finally, substituting the values of Y and Z into Equation 7, we can solve for X:

-3(-531) - 3(363) = 1008

X = -171.

Therefore, the solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

for such more question on system of equations

https://brainly.com/question/4262258

#SPJ8

The dimensions that maximize the area are, 96cm and 84cm.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let the height of poster be h and breadth be b,

bh = 15630cm square........(1)

Height of the printed area=h-10-10 = h - 20

(decrement of 10 from top and bottom)

the breadth of the printed area b-6-6 = b-12

(decrement of 9 from both sides)

for maximum printed area:

A=(h-20)(b-12) should be maximum

\(A = (h - 20)(\frac{15360 }{h}-12)\)

From equation (1)  

\(A = 15360-12h-\frac{307200}{h} +240\)

A = 15600 - 12h - (307200/h)

differentiate with respect to h (it should be=0)

\(\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}\)

\(12 = \frac{307200}{h} \\h = 160 cm\)

from equation (1),

\(bh = 15630cm^2\\b = 96cm\)

dimension of printed area,

= h - 20

= 160 - 20

= 140 cm

= b - 12

= 96 - 12

= 84 cm

Therefore, the dimensions that maximize the area are, 96cm and 84cm.

To know more about the area, click on the link

https://brainly.com/question/25292087

#SPJ4

Answer:

The correct answer is

b) Below 0

The correct option is (d) To the left of 0.

If the graph for a linear regression crosses the y-axis in negative values, the y-intercept of the regression line would be located to the left of 0 on the y-axis.

Therefore, the correct option is (d) To the left of 0. How to find the y-intercept of the regression line?

The y-intercept of a regression line is the value where the regression line intersects with the y-axis. It is the point where x = 0. In order to find the y-intercept of the regression line, we can use the equation of the regression line, which is y = mx + b. Here, m is the slope of the line and b is the y-intercept.

Therefore, if the regression line crosses the y-axis in negative values, it means that the y-intercept (b) is negative, and the line intersects the y-axis to the left of 0.

To know more about linear regression visit :

https://brainly.in/question/15157554

#SPJ11

use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

a. The volume of a rectangular package is given by V = LWH, where L is the length, W is the width, and H is the height. From the problem statement, we have:

L = W + 10

H = W - 12

Substituting these expressions into the formula for volume, we get:

V = (W + 10)(W)(W - 12)

V = W^3 - 2W^2 - 120W

So the polynomial function that calculates the volume of a package with width, w, is:

V(w) = w^3 - 2w^2 - 120w

b. To find the dimensions that will give us the maximum allowable volume, we need to find the maximum value of the volume function V(w), subject to the constraint that the volume cannot exceed 4800 cubic inches. We can use the method of calculus to find the maximum value.

First, we need to find the derivative of V(w):

V'(w) = 3w^2 - 4w - 120

Setting V'(w) equal to zero and solving for w, we get:

3w^2 - 4w - 120 = 0

(w - 6)(3w + 20) = 0

The only positive solution is w = 6 inches (since the width cannot be negative). To verify that this is a maximum, we need to check the sign of the second derivative of V(w):

V''(w) = 6w - 4

When w = 6, V''(w) = 32, which is positive. Therefore, the function V(w) has a local minimum at w = 6, which is also the global maximum (since V(w) approaches infinity as w goes to infinity).

So the dimensions that will give us the maximum allowable volume of 4800 cubic inches are:

Width = 6 inches

Length = 16 inches (since L = W + 10 = 16)

Height = -6 inches (since H = W - 12 = -6, we interpret this as a package with the top and bottom sides flipped, so that the height is positive)

Therefore, the maximum volume of the package that meets the size requirement is:

V = LWH = (16)(6)(6) = 576 cubic inches.

Hope this helped!

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

For similar question on standard deviation.

https://brainly.com/question/12402189  

#SPJ8

After answering the provided question, we can conclude that As a result, the probability of drawing a non-red letter is 11/13, or approximately 0.846, or 84.6%.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

The alphabet has a total of 26 letters, four of which are red. As a result, the likelihood of drawing a red letter is:

P(red) = 4/26 = 2/13

Drawing a non-red letter is the complementary event to drawing a red letter. The number of letters that are not red is:

26 - 4 = 22

As a result, the likelihood of drawing a non-red letter is:

Non-red P(non-red) = 22/26 = 11/13

As a result, the likelihood of the complementary event of drawing a red letter is:

P(non-red) = P(complementary event) = 11/13

As a result, the likelihood of drawing a non-red letter is 11/13, or approximately 0.846, or 84.6%.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

The values that are solutions to inequality are -6 and 5.

Options A and D are the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

x² + 3x - 4 > 0

Now,

Substituting x = -6, -2, 0, 5

(-6)² + 3(-6) - 4 > 0

36 - 18 - 4 > 0

36 - 22 > 0

14 > 0

True.

x² + 3x - 4 > 0

(-2)² + 3 x (-2) - 4 > 0

4 - 6 - 4 > 0

-6 > 0

This is not true.

x² + 3x - 4 > 0

0 + 3 x 0 - 4 > 0

0 + 0 - 4 > 0

-4 > 0

This is not true.

x² + 3x - 4 > 0

5² + 3 x 5 - 4 > 0

25 + 15 - 4 > 0

40 - 4 > 0

36 > 0

This is true.

Thus,

-6 and 5 are the solutions to inequality.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Answer:

y = -1/30x + 14

Step-by-step explanation:

Height (changing by -1) is the dependent variable, therefore is represented by y

Time (changing by +30) is the independent variable, therefore is represented by x

14 = where we started from

Slope = Change in y / Change in x

Slope = -1/30x

Equation = -1/30x + 14

Hope this helps!