1.) Enter the missing numbers in the boxes to complete the table of equivalent ratios.

X^2- 6x - 7 = 0 can someone help me solve this by completing the square

Crazy boy [7]

I think it’s X=-3+(the square root of 2)

3 0

3 years ago

Suppose box A contains 4 red and 5 blue poker chips and box B contains 6 red and 3 blue poker chips. Then a poker chip is chosen

sergejj [24]

Answer:

0.5172 = 51.72% probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Coin chosen from box B is red.

Event B: Blue poker chip transferred.

Probability of choosing a red coin:

7/10 of 4/9(red coin from box A)

6/10 of 5/9(blue coin from box A). So

$P(A) = \frac{7}{10}*\frac{4}{9} + \frac{6}{10}*\frac{5}{9} = \frac{28 + 30}{90} = 0.6444$

Blue chip transferred, red coin chosen:

6/10 of 5/9. So

$P(A \cap B) = \frac{6}{10}*\frac{5}{9} = \frac{30}{90} = 0.3333$

What is the probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3333}{0.6444} = 0.5172$

0.5172 = 51.72% probability a blue poker chip was transferred from box A to box B, given that the coin just chosen from box B is red

5 0

3 years ago

Someone help please:

frozen [14]

Answer:

The sharing cone holds about 9 times more popcorn than the skinny cone.

Step-by-step explanation:

Cone volume:

$V = \frac{\pi r^{2}h}{3}$

r is the radius and h is the inches.

Skinny-size cone:

Radius is r, height h. So

$V_{sk} = \frac{\pi r^{2}h}{3}$

Sharing size:

Radius is now 3r. So

$V_{sh} = \frac{\pi (3r)^{2}h}{3} = \frac{9\pi r^{2}h}{3} = 3\pi r^{2}h$

How many times more popcorn?

$r = \frac{V_{sh}}{V_{sk}} = \frac{3\pi r^{2}h}{\frac{\pi r^{2}h}{3}} = \frac{3*3\pi r^{2}h}{\pi r^{2}h} = 9$

The sharing cone holds about 9 times more popcorn than the skinny cone.

6 0

3 years ago

Find an equation of the plane orthogonal to the line

jolli1 [7]

The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.

The tangent vector for the line is

d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩

Then the plane that passes through the origin with this as its normal vector has equation

⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0

We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,

(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0

Simplifying this expression and writing it standard form gives

⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0

7 (x - 9) - 7 (y - 6) - 6z = 0

7x - 63 - 7y + 42 - 6z = 0

7x - 7y - 6z = 21

so that

a = 7, b = -7, c = -6, and d = 21

4 0

3 years ago

Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs

Serjik [45]

Answer:

3.25 + 5.50S is less than or equal to 30

7 0

2 years ago