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2 months ago

3. Give the domain of y= √6-X using set builder notation.

Mathematics

1 answer:

Inessa [12.5K]2 months ago

8 0

Answer:

{x | x ≤ 6}

Step-by-step explanation:

Given:

y = √(6 - x)

Objective:

Identify the domain.

We begin by setting the expression 6 - x to be greater than or equal to 0.

Therefore:

6 - x ≥ 0

Adding x to each side yields:

6 - x + x ≥ 0 + x

Resulting in:

6 ≥ x

This can be rephrased as:

x ≤ 6

In set-builder notation, this can be expressed as: {x | x ≤ 6}

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P varies inversely with x. If P = 14 when x= 16, find the value of P when x = 21.

tester [12383]

Answer:

Option C. 32/3

Step-by-step explanation:

It is understood that

A relationship between two variables, x and y, signifies inverse variation if it can be represented as either $p*x=k$ or $p=k/x$

It is also known that

For p=14, x=16

Determine the value of k

$k=p*x$

By substituting these values

$k=(14)*(16)=224$

This shows that

The equation equals

$p=\frac{224}{x}$

Calculate the value of p when x=21

Substitute the given value of x into the equation

$p=\frac{224}{21}$

Simplify

Divide both the numerator and denominator by 7

$p=\frac{32}{3}$

7 0

11 days ago

a resorvoir can be filled by an inlet pipe in 24 hours and emptied by an outlet pipe 28 hours. the foreman starts to fill the re

zzz [12365]

To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour

Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.

Please ask me any questions you may have!

4 0

1 month ago

Read 2 more answers

The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and w

lawyer [12517]

Answer:

in steps

Step-by-step explanation:

In a fair roulette game, the likelihood of the ball landing on RED remains constant, regardless of prior spins.

a) 18/38

b) 18/38

c) Yes, I have confidence in my responses. Since it's fair, the number of RED slots does not change.

8 0

11 days ago

Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 40 emp

Zina [12379]

Answer:

a) The likelihood that none of the sampled employees are from the Hawaii plant is 1.74%.

b) The chance that exactly 1 employee from the sample is found working in the Hawaii plant is 8.70%.

c) There is an 89.56% chance that 2 or more employees in the sample are from the Hawaii plant.

d) The probability that 9 employees from the sample are working at the Texas plant is 8.70%.

Step-by-step explanation:

Each employee has two potential employment locations: either Texas or Hawaii. Thus, the binomial probability distribution can be utilized to solve this scenario.

Binomial probability distribution

This distribution defines the probability of achieving exactly x successes in n trials where there are only two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

Here, $C_{n,x}$ denotes the number of ways to choose x objects from a set of n, represented by the subsequent formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of success occurring.

In this context, we know:

The sample comprises 10 employees, therefore $n = 10$ .

a. Calculate the probability that none of the sampled employees are from the Hawaii plant (to 4 decimals)?

Given that 20 out of 60 employees are based in Hawaii:

$p = \frac{20}{60} = 0.333$

We aim to find P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.333)^{0}.(0.667)^{10} = 0.0174$

Thus, the likelihood that none in the sample are from Hawaii stands at 1.74%.

b. Calculate the probability that 1 employee from the sample is from the Hawaii plant?

This is represented as P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{10,1}.(0.333)^{1}.(0.667)^{9} = 0.0870$

Therefore, there is an 8.70% possibility that 1 employee in the sample comes from Hawaii.

c. Calculate the probability that 2 or more employees in the sample are from the Hawaii plant?

We can observe two scenarios: either fewer than 2 employees are from Hawaii or 2 and beyond. The combined probabilities equal decimal 1. So:

$P(X < 2) + P(X \geq 2) = 1$

We seek to find $P(X \geq 2)$ .

$P(X \geq 2) = 1 - P(X < 2)$

From problems a and b, we possess values for both probabilities.

$P(X < 2) = P(X = 0) + P(X = 1) = 0.0174 + 0.0870 = 0.1044$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1044 = 0.8956$

Accordingly, the chance that 2 or more employees in this sample operate at the Hawaii plant is 89.56%.

d. Calculate the likelihood that 9 employees in the sample are working at the Texas plant?

This corresponds to the probability found in part b for 1 employee working in Hawaii.

Consequently, there is an 8.70% chance that 9 employees belong to the Texas plant.

6 0

1 month ago

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers.

babunello [11817]

Answer:

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.

Step-by-step explanation:

Prior concepts

A normal distribution is characterized as a "probability distribution that is symmetric around the mean, indicating that data close to the mean are more frequent than those further away".

The Z-score refers to "a statistical measurement that reflects the relationship of a value to the mean of a group, measured in standard deviations".

Let X denote the random variable of interest, and we identify its distribution:

$X \sim N(\mu=15,\sigma=4)$