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2 months ago

Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min. interpret the key features for this situation

Mathematics

1 answer:

Leona [12.6K]2 months ago

7 0

Answer:

The main aspects are

50ft³ = volume

0.5ft³/min = filling rate

Time= 100 minutes

Step-by-step breakdown:

Chiang is in the process of filling a 50ft container with water at a speed of 0.5 ft/min.

50ft³ = volume

0.5ft³/min = flow rate

It’s important to note that we still need to determine how long it will take to fill the 50 ft³ container.

Time = volume / rate

Time = 50 ft³ / 0.5 ft³/min

Time = 50 / 0.5 min

Time = 100 min

The main aspects are

50ft³ = volume

0.5ft³/min = filling rate

Time= 100 minutes

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On her birthday, Sonia distributed chocolates in an orphanage. She gave 5 chocolates to each child and 20 chocolates to adults.

Svet_ta [12734]

Answer with explanation:

Total number of children = x

Total chocolates shared = y

In total, the chocolates distributed to the children equals 5 times the number of children, or 5 x.

Chocolates received by adults equal 20.

Let the number of adults be z.

Expressing this situation as an equation:

y = 5 x + 20 z

$z=\frac{y-5 x}{20}$

⇒Number of adults = z

$=\frac{y-5 x}{20}$

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1 month 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.

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1 month ago

The width of a rectangle is 61 centimeters more than the length. The perimeter is 406 centimeters. Find the length and the width

lawyer [12517]

$Step \; 1: \; Assign \; Variables \; for \; the \; unknown \; that \; we \; need \; to \; find$

$Let \; x \; be \; length \; of \; the \; rectangle$

$Step \; 2: \; Set \; up \; equation \; based \; on \; information \;\\ given \; about \; the \; rectangle$

$Statement \; 1: Width \; of \; a \; rectangle \; \\is \; 61cm \; more \; than \; the \; length\\\\Width \; = \; 61+x\\\\Statement \; 2: \; The \; perimeter \; is \; 406cm\\\\Perimeter=2(Length+Width)\\Perimeter =2(x+61+x)\\\\So \; the \; mathematical \; equation \; would \; be \\ 2(x+61+x)=406$

$Step \; 3: \; Solve \; the \; equation \; by \\ undoing \; whatever \; is \; done \; x.\\\\2(x+61+x)=406\\Group \; and \; Combine \; like \; terms \; inside \; the \; parenthesis\\\\2(2x+61)=406\\Distribute \; 2 \; in \; the \; left \; side \; of \; the \; equation\\\\4x+122=406\\Subtract \; 122 \; on \; both \; sides\\\\4x+122-122=406-122\\Simplify \; on \; both \; sides\\\\4x=284\\Divide \; on \; both \; sides\\\\\frac{4x}{4}=\frac{284}{4}\\Simplify \; fractions \; on \; both \; sides\\\\x=71$

$Conclusion:\\Length=x=71cm\\Substituting \; 71 \; for \; x \; and \; find \; Width \; value.\\Width=61+x=71+61=132cm\\\\Length \; is \; 71 cm \; and \; Width \; is 132cm$

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16 days ago

At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two

PIT_PIT [12445]

There are 290 calories in a cheeseburger and 230 calories in an order of fries. Explanation: When considering 4 cheeseburgers and 5 fries totaling 2,310 calories, and 3 cheeseburgers with 2 fries equating to 1,330 calories, these representations set up equations that yield results regarding calorie counts for each item.

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20 days ago

A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2.50 and the snacks cost $0.75. After the game, they

lawyer [12517]

Let x represent the hot dogs

and y represent the snacks

The equation x + y = 175

Rewrite x as 175 - y

And the second equation: 2.50x + 0.75y = 262.50

Substitute to get 2.50(175 - y) + 0.75y = 262.50

Which simplifies to 437.50 - 2.50y + 0.75y = 262.50

Rearranging gives -1.75y = -175

Hence, solving for y results in y = -175 / -1.75 = 100

Thus, 100 snacks and 75 hot dogs were sold

7 0

17 days ago

Read 2 more answers