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2 years ago

Amir wants to create a 4-digit password for his phone.

Mathematics

1 answer:

AnnZ [28]2 years ago

7 0

Answer:

360

Step-by-step explanation:

Given that Amir wants to create a 4-digit password for his phone.

He wants to choose 4 different numbers between 1 and 5 inclusive.

The total number of 4-digit passwords that Amir can create will be achieved by using permutation

6P4 = 6!/ ( 6 - 4)!

6P4 = (6 × 5 × 4 × 3 × 2!)/2!

6P4 = 6×5×4×3 = 360

Therefore, the total number of 4-digit passwords that Amir can create is 360 different passwords.

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Anna set up a lemonade stand on her block over the summer. She recorded each day’s high temperature and the number of cups of le

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Answer:

Residual = -2

The negative residual value indicates that the data point lies below the regression line.

Step-by-step explanation:

We are given a linear regression model that relates daily high temperature, in degrees Fahrenheit and number of lemonade cups sold.

$y = -34+ \frac{3}{5} x$

Where y is the number of cups sold and x is the daily temperature in Fahrenheit.

Residual value:

A residual value basically shows the position of a data point with respect to the regression line.

A residual value of 0 is desired which means that the regression line best fits the data.

The Residual value is calculated by

Residual = Observed value - Predicted value

The predicted value of number of lemonade cups is obtained as

$y = -34+ \frac{3}{5} (95)\\\\y = -34+ 3 (19)\\\\y = -34+ 57\\\\y = 23$

So the predicted value of number of lemonade cups is 23 and the observed value is 21 so the residual value is

Residual = Observed value - Predicted value

Residual = 21 - 23

Residual = -2

The negative residual value indicates that the data point lies below the regression line.

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Mr. Brent uses 1/4 cup of blue paint and 1/4 cup of yellow paint to make each patch of green paint. How many batches of green pa

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let x = the amoun of raw sugar in tons a procesing plant is a sugar refinery process in one day . suppose x can be model as expo

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Answer:

The answer is below

Step-by-step explanation:

A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?

Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:

$f(x)=\lambda e^{-\lambda x}\\But\ \lambda= 1/\mu=1/4 = 0.25\\Therefore:\\f(x)=0.25e^{-0.25x}\\$

a) P(x > 5) = $\int\limits^\infty_5 {f(x)} \, dx =\int\limits^\infty_5 {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_5=e^{-1.25}=0.2865$

b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.

That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757

c) Let b be the amount of raw sugar should be stocked for the plant each day.

P(x > a) = $\int\limits^\infty_a {f(x)} \, dx =\int\limits^\infty_a {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_a=e^{-0.25a}$

But P(x > a) = 0.05

Therefore:

$e^{-0.25a}=0.05\\ln[e^{-0.25a}]=ln(0.05)\\-0.25a=-2.9957\\a=11.98$

a ≅ 12

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