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3 years ago

What is the slope of the points (4, -2) and (-4, -4)?

Mathematics

2 answers:

timofeeve [1]3 years ago

7 0

Answer:

= 1/4

Step-by-step explanation:

We can find the slope given two points by using the following formula

m = (y2-y1)/(x2-x1)

= (-4 - -2)/(-4 -4)

= (-4+2)/(-4-4)

= -2/-8

= 1/4

Nostrana [21]3 years ago

7 0

Answer:

I think the slope is 1/4

Step-by-step explanation:

if you use the slope equation y1-y2/x1-x2, then you get (-2 - -4)/(4 - -4), which is 2/8, which is 1/4

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Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and on

Nookie1986 [14]

Answer:

The probability that he ends up with a full house is 0.0083.

Step-by-step explanation:

We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.

We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).

We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);

If he is given with two kings.
If he is given one king and one ace.

Only in these two situations, he will end up with a full house.

Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.

So, the ways in which we can draw two kings from available three kings is given by = $\frac{^{3}C_2 }{^{47}C_2}$ {∵ one king is already there}

= $\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}$ {∵ $^{n}C_r = \frac{n!}{r! \times (n-r)!}$ }

= $\frac{3}{1081}$ = 0.0028

Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = $\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}$

= $\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}$

= $\frac{6}{1081}$ = 0.0055

Now, probability that he ends up with a full house = $\frac{3}{1081} + \frac{6}{1081}$

= $\frac{9}{1081}$ = 0.0083.

3 0

4 years ago

Read 2 more answers

Hanna is recovering hundreds of treasure chests from an ancient shipwreck she is able to recover 8 chests every 4 hours

gizmo_the_mogwai [7]

Answer:

idk what you are asking. But she is able to recover 2 chest per hour and would take however many chests divided by 2 for the time. EX: 300 chests. 300/2=150 hours.

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

Is this a right triangle? 16 inches, 30 inches, and 34 inches O NO O YES

lesantik [10]

Answer:

Yes

Step-by-step explanation:

To be able to make a right triangle, it needs to follow the Pythagorean theorem

Thus, 16^2+30^2=34^2 needs to be true

256+900=1156

and sqrt1156=34

so yes

3 0

3 years ago

I NEED THIS NOW..

amm1812

24 bought 75, which, when multiplied out, equals 1800. 30 bought 60, which, when multiplied out, equals 1800.

1800+1800=3600.

3600*1/3=1200.

1200 cookies were returned.

5 0

4 years ago

Minimizing Packaging Costs If an open box has a square base and a volume of 107 in.3 and is constructed from a tin sheet, find t

uysha [10]

Answer:

The dimensions of the box that minimizes the amount of material of construction is

Square base = (5.98 × 5.98) in²

Height of the box = 2.99 in.

Step-by-step explanation:

Let the length, breadth and height of the box be x, z and y respectively.

Volume of the box = xyz = 107 in³

The box has a square base and an open top.

x = z

V = x²y = 107 in³

The task is to minimize the amount of material used in its construction, that is, minimize the surface area of the box.

Surface area of the box (open at the top) = xz + 2xy + 2yz

But x = z

S = x² + 2xy + 2xy = x² + 4xy

We're to minimize this function subject to the constraint that

x²y = 107

The constraint can be rewritten as

x²y - 107 = constraint

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x and y

L(x,y,z) = x² + 4xy - λ(x²y - 107)

We then take the partial derivatives of the Lagrange function with respect to x, y and λ. Because these are turning points, at the turning points each of the partial derivatives is equal to 0.

(∂L/∂x) = 2x + 4y - 2λxy = 0

λ = (2x + 4y)/2xy = (1/y) + (2/x)

(∂L/∂y) = 4x - λx² = 0

λ = (4x)/x² = (4/x)

(∂L/∂λ) = x²y - 107 = 0

We can then equate the values of λ from the first 2 partial derivatives and solve for the values of x and y

(1/y) + (2/x) = (4/x)

(1/y) = (2/x)

x = 2y

Hence, at the point where the box has minimal area,

x = 2y

Putting these into the constraint equation or the solution of the third partial derivative,

x²y - 107 = 0

(2y)²y = 107

4y³ = 107

y³ = (107/4) = 26.75

y = ∛(26.75) = 2.99 in.

x = 2y = 2 × 2.99 = 5.98 in.

Hence, the dimensions of the box that minimizes the amount of material of construction is

Square base = (5.98 × 5.98) in²

Height of the box = 2.99 in.

Hope this Helps!!!

5 0

3 years ago