Which describes this pattern 10, 15, 20, 25, 30

X y

Allushta [10]

Answer:

$D)\ \{3,-1\}$

Step-by-step explanation:

Image of $x=0$ is $y=3$

Image of $x=2$ is $y=-1$

Hence $\{0,2\}$ corresponds to $\{3,-1\}$

3 0

2 years ago

Find the length of 1 side of square if the area is 49 sq.cm<br> method needed

ladessa [460]

Answer:

It would be 7cm

Step-by-step explanation:

please find step by step explanation on the picture

7 0

1 year ago

The computers of nine engineers at a certain company are to be replaced. Four of the engineers have selected laptops and the oth

Gala2k [10]

Answer:

(a) There are 70 different ways set up 4 computers out of 8.

(b) The probability that exactly three of the selected computers are desktops is 0.305.

(c) The probability that at least three of the selected computers are desktops is 0.401.

Step-by-step explanation:

Of the 9 new computers 4 are laptops and 5 are desktop.

Let X = a laptop is selected and Y = a desktop is selected.

The probability of selecting a laptop is = $P(Laptop) = p_{X} = \frac{4}{9}$

The probability of selecting a desktop is = $P(Desktop) = p_{Y} = \frac{5}{9}$

Then both X and Y follows Binomial distribution.

$X\sim Bin(9, \frac{4}{9})\\ Y\sim Bin(9, \frac{5}{9})$

The probability function of a binomial distribution is:

$P(U=k)={n\choose k}\times(p)^{k}\times (1-p)^{n-k}$

(a)

Combination is used to determine the number of ways to select <em>k</em> objects from <em>n</em> distinct objects without replacement.

It is denotes as: ${n\choose k}=\frac{n!}{k!(n-k)!}$

In this case 4 computers are to selected of 8 to be set up. Since there cannot be replacement, i.e. we cannot set up one computer twice or thrice, use combinations to determine the number of ways to set up 4 computers of 8.

The number of ways to set up 4 computers of 8 is:

${8\choose 4}=\frac{8!}{4!(8-4)!}\\=\frac{8!}{4!\times 4!} \\=70$

Thus, there are 70 different ways set up 4 computers out of 8.

(b)

It is provided that 4 computers are randomly selected.

Compute the probability that exactly 3 of the 4 computers selected are desktops as follows:

$P(Y=3)={4\choose 3}\times(\frac{5}{9})^{3}\times (1-\frac{5}{9})^{4-3}\\=4\times\frac{125}{729}\times\frac{4}{9}\\ =0.304832\\\approx0.305$

Thus, the probability that exactly three of the selected computers are desktops is 0.305.

(c)

Compute the probability that of the 4 computers selected at least 3 are desktops as follows:

$P(Y\geq 3)=1-P(Y$

Thus, the probability that at least three of the selected computers are desktops is 0.401.

6 0

2 years ago

28. Barrett's mom has a flower vase that is shaped like a perfect cylinder.

zimovet [89]

Answer:

Vase volume is 452.16 in³

Step-by-step explanation:

The question asks for the volume of a cylinder of radius r and height h. The relevant formula is V = (pi)(r)^2*h

With h = 9 in and r = 4 in, that max volume (of water) is

V = (3.14)(4 in)^2*(9 in) = 452.`16 in³

5 0

2 years ago

An urn contains balls numbered 1 through 20. A ball is chosen, returned to the urn, and a second ball is chosen. What is the pro

stira [4]

<h2>Answer:</h2>

The probability is:

$\dfrac{1}{400}$

<h2>Step-by-step explanation:</h2>

It is given that:

An urn contains balls numbered 1 through 20.

A ball is chosen, returned to the urn, and a second ball is chosen.

This means that this is a case of a replacement.

Hence, one of the event is independent of the other.

Now we know that the probability to get a particular number of ball is:

$\dfrac{1}{20}$

( Since, there are total 20 balls and a ball of one particular number is just unique )

i.e. $\text{Probability of getting a 8}=\dfrac{1}{20}$

Hence, the probability that the first and second balls will be a 8 is:

$=\dfrac{1}{20}\times \dfrac{1}{20}\\\\\\=\dfrac{1}{400}$

7 0

2 years ago

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