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IrinaK [193]
3 years ago
8

A line has a slope of 2 and contains the points (1, 3) and (2, y). The value of y is

Mathematics
1 answer:
Phantasy [73]3 years ago
8 0
Y=mx+b

y=2x+b

point (1,3)

substitute to find b

3=2*1+b

3=2+b

b=1

equation is y=2x+1

point (2,y)

substitute to get y

y=2*2+1

y=4+1

y=5

point (2,5)

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Complete the equation of the line through (-9 -9) and (-6 0)
Katena32 [7]

Answer:

y = 3x + 18

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 9, - 9) and (x₂, y₂ ) = (- 6, 0)

m = \frac{0+9}{-6+9} = \frac{9}{3} = 3, thus

y = 3x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (- 6, 0), then

0 = - 18 + c ⇒ c = 0 + 18 = 18

y = 3x + 18 ← equation of line

7 0
3 years ago
Oranges sell for $5.00 per bag. If the bag weighs 2 pounds, how much is the price per pound?
svetoff [14.1K]

Answer:

$2.50

Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
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.

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