Which decimals round to 2.5 when rounding to the nearest tenth​

The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

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Answer:

he needs to mix 18 pineapple cups

Step-by-step explanation:

48÷8=6

3×6=18

8-3

48-18

The big-O notation for the growth rate of fines in East Overshoe is O(n), where n represents the number of days the fine goes unpaid.

In the given scenario, the fine increases by $1 for each day the fine goes unpaid. This means that the growth rate of the fine is directly proportional to the number of days. As the number of days increases, the fine increases linearly by $1 for each day.

The big-O notation is a notation used to describe the upper bound or worst-case scenario of the growth rate of a function or algorithm. In this case, the growth rate of the fine is linear because it increases by a constant amount ($1) for each day. Therefore, we can represent the growth rate as O(n), where n represents the number of days.

It's important to note that the big-O notation describes the upper bound of the growth rate and doesn't necessarily represent the exact growth rate in all cases. In this scenario, it assumes that the fine increases by $1 for each day, but there could be other factors or constraints that affect the actual growth rate. However, in terms of the fine amount alone, the growth rate can be described as O(n).

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The probability that they are both left-handed is 0.01

Probability is the number of ways of achieving success.

the total number of possible outcomes.

Probability takes values between 0 (no chance) and 1 (certain) inclusive.

Complement Rule (probability that an event doesn't occur): P(A') = 1 - P(A) .

Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .

Multiplication rule: P(A ∩ B) = P(A) × P(B) for independent events. P(A ∩ B)

For both, the persons selected at random are left-handed

10 % out of 100 % are left-handed.

Hence the probability that the person is left-handed

P(L) = 10 /100 = 1 / 10 = 0.1

where P(L) is the probability that the person is left-handed.

Therefore both the persons selected are left-handed

= 0.1 * 0.1

= (0.1)^2

= 0.01

Hence the probability that they are both left-handed is 0.01.

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a)Hesse diagram is a diagrammatical representation of a finite partially ordered set in the form of a drawing or graph. A Hesse diagram of a partial order with 4 elements that has exactly one least and two maximal elements is shown below:

b) Let A = {a, b, c, d}. Then the set of all pairs belonging to the above relation is {(a,a), (b,b), (c,c), (d,d),(a,b), (a,c), (a,d), (b,d), (c,d)}

Explanation: In general, a partially ordered set is a set with a partial order relation, which is a binary relation that is reflexive, antisymmetric, and transitive.

Partially ordered sets are often represented using Hesse diagrams. A Hasse diagram is a visual representation of the partial order relation.

The elements of the set are represented as points or nodes in the diagram, and the relation between the elements is represented by lines or edges between the nodes.

The direction of the edges is usually from the smaller elements to the larger elements.

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I attached a picture showing a graph of y<6 and y>=x-6. As you can see, the point (10,5) is in y<6 and y>=x-6.

You can also tell this because y<6 highlights everything with the y value of less than 6. 5 is less than 6, so instantly you can realize that (10,5) is a solution to the system.

It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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Hello !

Answer:

\(\boxed{\sf x=1}\)

Step-by-step explanation:

We want to find the value of x that satisfies the following equation :

\(\sf 9x+6=2x+13\)

To begin, let's substract 2x from both sides of the equation :

\(\sf 9x+6-2x=2x+13-2x\\\sf 7x+6=13\)

Now, let's substract 6 from both sides :

\(\sf 7x+6-6=13-6\\\sf 7x=7\)

Finally, let's divide both sides by 7 :

\(\sf\frac{7x}{7} =\frac{7}{7}\\\boxed{\sf x=1}\)

Have a nice day ;)

The right choice is: A whole number constant could have been subtracted from the exponential expression.

Let be an exponential function of the form \(y = A\cdot e^{B\cdot x}\), where \(A\) and \(B\) are real numbers. A horizontal asymptote exists when \(e^{B\cdot x} \to 0\), which occurs for \(B\cdot x \to - \infty\).

For this function, the horizontal asymptote is represented by \(y = 0\) and to change the value of the asymptote we must add the parent function by another real number (\(C\)), that is to say:

\(y = A\cdot e^{B\cdot x} + C\) (1)

In this case, we must use \(C = -3\) to obtain an horizontal asymptote of -3. Thus, the right choice is: A whole number constant could have been subtracted from the exponential expression.

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Answer: C. A whole number constant could have been added to the exponent.

Step-by-step explanation: On Edge!

The correct answer is:

Becca should have multiplied the dividend and the divisor by 10 and moved the decimal point in the quotient to the right.

In order to divide decimals, both the dividend and the divisor should be adjusted so that there are no decimal places in the divisor. Becca's mistake was not considering this adjustment.

To correctly divide 1.8 by 0.3, Becca should have multiplied both the dividend (1.8) and the divisor (0.3) by 10 to eliminate the decimal places. This would result in the problem becoming 18 ÷ 3.

Performing the division correctly, we find that 18 ÷ 3 equals 6, with no remainder.

Therefore, Becca's mistake was not adjusting the dividend and the divisor by multiplying both by 10.

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To write linear density in Wileyplus, first identify the mass of the linear object, as well as the length of the linear object. Then, divide the mass by the length to calculate the linear density.

To write linear density in WileyPlus, you can use the following steps:

1. First, open the WileyPlus platform and navigate to the assignment or problem you are working on.

2. Next, identify the linear density equation you need to use. The most common equation for linear density is p = m/L, where p is the linear density, m is the mass, and L is the length.

3. Once you have identified the equation, input the values for the mass and length into the equation. For example, if the mass is 10 grams and the length is 2 meters, the equation would be p = 10/2.

4. Solve the equation to find the linear density. In this example, the linear density would be 5 grams per meter.

5. Finally, input the linear density into the appropriate field in WileyPlus. This may be a text box, a drop-down menu, or another type of input field.

By following these steps, you can easily write linear density in WileyPlus. Remember to always double-check your work and make sure that your answer is accurate and complete before submitting it.

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a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

I think 13 cm. You add the numbers 5,5,3 together to get 13

Step-by-step explanation:

Answer:

25 cm

Step-by-step explanation:

The constant of proportionality between the pages read and the time is 1.25

It is a constant relationship between different measurable quantities.

Data of the problem:

We calculate the rate, dividing the number of page by the time passed and we get:

Rate = pages/time

Rate = 10/8

Rate = 1.25

Rate = 15/12

Rate = 1.25

Rate = 25/20

Rate = 1.25

We also can calculate with the formula:

y = mx

Where:

10 = m*8

m = 10/8

m = 1.25

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Answer:

Step-by-step explanation:

4(23ft)($1.12/ft)=$103.04

Answer:

Step-by-step explanation:

∠Q = 180-∠T = 89°

∠S = 360-∠T-∠Q-∠R = 360-91-89-27 = 153°

The table shows the total cost to be a member of the gym for different numbers of months.



Number of months. total costs

3. $53.97

6. $77.94

12. $125.88



Create a function that gives the total cost C, in dollars to be a member of the gym given the number of months M of membership.

_____________________________________

Total cost = M* (factor per month ) + b

_____________________________________

The expression for a linear equation is

*The slope-intercept form.

y = mx + b

m= (y2-y1)/ (x2-x1) (I)

y-intercept is (0, b)

*and the point-slope form

y- y1 = m(x-x1) (II)

________________________

Point 1 (3, 53.97)

Point 2 (12, 125.88)

Replacing in (II)

The slope m = (y2- y1)/ (x2-x1) = (125.88- 53.97)/(12-3) = 7.99

y - 53.97 = 7.99* (x- 3)

y = 7.99 x - 7.99* 3 + 53.97

y = 7.99x + 30

____________________

Verifying

y = 7.99x + 30

x= 3

y = 7.99*3 + 30

y= 53.97

x= 6

y = 7.99*6 + 30

y= 77.94

x= 12

y = 7.99*12 + 30

y= 125.88

_________________________

Answer

The linear function is y = 7.99x + 30

You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.

A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.

The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.

The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.

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Answer:

the answer is 6

Step-by-step explanation:

there are 6 side you times the 6 with the area of an equilateral triangle so the area of hexagon = 6

Answer:

17

Step-by-step explanation:

Input x=4 into the equation

y= 3(4)+5

y= 12+5

y=17

Answer:

y=17

Step-by-step explanation:

if x=4,

y=3(4)+5

y=12+5

y=17

Answer:

dum bot answerd

Step-by-step explanation:

Answer:

12m

Step-by-step explanation:

The interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

\(P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%\)

Here we had  where mean of distribution of X is \(\mu\)  and standard deviation from mean of distribution of X is \(\sigma\).

When Ryan runs the 400 meter dash, his finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 0.5 seconds.

The interval of times that represents the middle 68% of his finishing times in the 400 meter race is,

\(P(75 - 0.5 < X < 75 + 0.5) = 68\%\\P(74.5 < X < 75.5) = 68\%\)

Thus. the interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.

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The cost of each desk is $42.

The initial cost to make these new school desks is $635.

What is a solution of linear function?

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

Assume that the cost of each desk be m.

The initial cost to make these new school desks be c.

Then the total cost will represent by the equation:

y = mx + c .....(i)

Putting x =21 and y = 1517 in the equation (i)

1517 = 21m + c ...(ii)

Putting x = 47 and y = 2609 in the equation (i)

2609 = 47m + c ...(iii)

Subtract equation (ii) from (iii)

47m + c =2609

21m + c = 1517

(-)     (-)     (-)

___________

26m = 1092

Divide both sides by 26

m = 42

Putting m = 42 in equation (ii)

1517 = 21 × 42 + c

1517 = 882 + c

c = 1517 - 882

c = 635

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Note that the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D' is given as attached. Note that when a shape is reflected, it must be reflected over a line. In this case, the line of reflection is y = -3.

A line of reflection is a line that acts as a mirror, reflecting a figure across the line so that the image is a mirror image of the original.

When a shape is reflected, it must be reflected over a line. The line of reflection of quadrilateral ABCD onto quadrilateral A'B'C'D is

From the given graph, we have the following observations

ABCD was flipped over to form A'B'C'D'

The line of reflection is between both shapes.

Using points C and C' as references;

We have:

C = (-3, -1)

C" = (-3, -5)

Notice that both points have the same x-coordinate

This means that the line of reflection is parallel to the x-axis and passes through the y-axis.

The point at which it passes through the y-axis is calculated using the mid-point formula.

Therefore, we have:

y = (y1+y2)/2

y = (-1-5)/2

y = -6/2

y = -3

Hence, the line of reflection is y = -3
See the attachment for the line of reflection.

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Answer:

Step-by-step explanation:

The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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