A bag contains 5 red marbles, 10 white marbles, and 9 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red?

Answer:

[tex]y = 5[/tex].

Or, equivalently:

[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].

Step-by-step explanation:

Every plane in [tex]\mathbb{R}^{3}[/tex] could be represented with a vector equation of the form [tex]\vec{n}\, (\vec{r} - \vec{r}_{0}) = 0[/tex], where:

Notice that in this question, the coordinates (and hence the position vectors) of the points in this plane are already given. For example, the position vector of the point [tex](1,\, 5,\, -3)[/tex] is the vector:

[tex]\begin{aligned}\vec{r}_{0} = \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\end{aligned}[/tex].

Specifically in [tex]\mathbb{R}^{3}[/tex], normal vectors of a plane could be found by:

Subtracting position vectors of points in this plane from each other would give directions that are parallel to this plane:

[tex]\begin{aligned}\begin{bmatrix}2 \\ 5 \\ -3\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix}\end{aligned}[/tex].

[tex]\begin{aligned}\begin{bmatrix}3 \\ 5 \\ 2\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix}\end{aligned}[/tex].

The cross product between these two vectors in [tex]\mathbb{R}^{3}[/tex] would be:

[tex]\begin{aligned} \vec{n} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \times \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix} = & \begin{bmatrix}0 \times 5 - 0 \times 0 \\ 0 \times 2 - 1 \times 5\\ 1 \times 0 - 0 \times 2\end{bmatrix} = \begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix}\end{aligned}[/tex].

(Note that the cross product between other directions parallel to the plane might give other normal vectors that are parallel to the one in this example.)

Using the position vector of the point [tex](1,\, 5,\, -3)[/tex] as [tex]\vec{r}_{0}[/tex], one possible vector equation for this plane would be:

[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].

Expand the dot product and simplify to obtain a scalar equation for this plane:

[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \begin{bmatrix}x - 1 \\ y - 5 \\ z - (-3)\end{bmatrix} = 0\end{aligned}[/tex].

[tex]0\, (x - 1) + (-3)\, (y - 5) + 0\, (z - (-3)) = 0[/tex].

[tex](-3)\, (y - 5) = 0[/tex].

[tex]y = 5[/tex].

Answer:

30° and 60°

Step-by-step explanation:

Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.

Making the statements into equations :

Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]

Greater of the opposite interior angles exceeds smaller by 30° :

⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]

By exterior angle property :

⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]

Substituting Equation 3 in Equation 1 :

⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°

⇒ 2 (∠x₁ + ∠x₂) = 180°

⇒ ∠x₁ + ∠x₂ = 90°

⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]

Substituting Equation 4 in Equation 2 :

⇒ 90° - ∠x₁ = ∠x₁ + 30°

⇒ 2∠x₁ = 60°

⇒ ∠x₁ = 30°

Substituting the value of ∠x₁ in Equation 2 :

⇒ ∠x₂ = 30° + 30°

⇒ ∠x₂ = 60°

The measures of the interior angles are 30° and 60°

Answer:

A function means that we get one input and one output.  In this example that means for every x-value that we have, we only have one y-value.

Looking at the first option, we can see that there is no x-value that has more than one y-value which means that it is a function.

The rest of the options are seen with at least two values for one x-value in one of the points.  Therefore, they wouldn't be considered a function leaving us with only option A as the solution.

Answer:

I believe, 6.

Step-by-step explanation:

Not sure if the rest of the question is the answer choices but the absolute of any number, is it's exact opposite. The reason for this is that an absolute number, or |?| is equal to whatever distance it is from 0. Since adding 1, and subtracting 1, both do such but in opposite directions, the absolute value of both would be 1.

Replacing the first card illustrates an independent event, while not replacing the card illustrates a dependent event

In probability, when a selected card or item is replaced before another item is selected, then the event is an independent event.

This is so because, the selected card do not have effect on the probability of selecting the next card

However, if the card is not replaced, then the event is dependent

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Answer: i think is b

Step-by-step explanation: because I do read lesson so I guess I think is b that why.

Answer:

about 31%

Step-by-step explanation:

[tex]1 - {.91}^{4} = 1 - .6857 = .3143 = 31\%[/tex]

Answer:

8.227 then rounded to tenth is 8.2

Step-by-step explanation:

just smart.

please rate good. have a good day.

Answer:

See below ~

Step-by-step explanation:

Section (xiii) :

Section (xiv) :

It is indicated in the diagram that CE = EB :

Answer: xiii: x=4        xiv:  x=5 y=11

Step-by-step explanation:

Ok, for xiii, there is a ratio.

BD:DC   aka 3:x   You're trying to solve for x (DC)

On the other side of the equation, it's AB:AC aka 6:8  This ratio can be simplified to 3:4 (when you divide both sides by 2)

To set things up:

3:x = 3:4

Notice the similarity? Since they are equal to one another, x must be 4.

Now for xiv, you're trying to find the values of x and y.

DE=3 and AB=x+1

DE=1/2 of AB

so,  

3=(x+1)/2 Solving for x, multiply both sides by 2

6=x+1        subtract both sides by 1

-1     -1

x=5    

If you plug x to AB, AB = 6

Plug x to BE = 4

To find y, notice how there is a dash that marks them as congruent, so the lengths BE and EC must be equal.

so y-7=4     (adding 7 to both sides)

     +7    +7

y=11

Applying the angle of intersecting secants and tangents theorem, m(KNL) is: A. 264°.

The angle of intersecting secants and tangents theorem states that the angle formed outside a circle has a measure that equals 1/2 the positive difference of the measures of the intercepted arcs.

60 = 1/2(18x - 6 - 5x - 17) [angle of intersecting secants and tangents theorem]

Solve for x

2(60) = 13x - 23

120 = 13x - 23

120 + 23 = 13x

143 = 13x

x = 143/13

x = 11

m(KNL) = (18x - 6 + 5x + 17)

m(KNL) = 23x + 11

Plug in the value of x

m(KNL) = 23(11) + 11

m(KNL) = 264° (option A)

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Answer:the mean is 90

Step-by-step

you find the sum of the values then divide them by the amount of numbers in the set

Answer:

y out put x input and 3 is input and as 5 . tell me if you get it right

Answer:

True, (-∞, ∞)      5 ≤ 11

Step-by-step explanation:

−11 ≤ −5                       Add 16 to both sides

−11 + 16 ≤ −5 + 16

5 ≤ 11

Answer:18 feet

Step-by-step explanation:

It would be 18 feet because if you add 8 feet from how far him and Sidney are then 10 feet from how far Sidney and Ling are.

The approximate angle that the ladder makes with the ground is 37 degrees

The given question will be solved using the SOH CAH TOA identity.

The given statement will form a right triangle with the following parameters

Hypotenuse = 5m

Height(opposite) .= 3m

Determine the approximate measure of ∠θ

sin ∠θ = opp/hyp
sin ∠θ = 3/5
sin ∠θ = 0.6
∠θ = arcsin(0.6)
∠θ = 37degrees

Hence the approximate angle that the ladder makes with the ground is 37 degrees

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height= 8 in

length= 14 in

width= 3 in

the volume of the given rectangular prism.

[tex]v = whl[/tex]

[tex]v = 8 \times 14 \times 3[/tex]

[tex]v = 336 \: {in}^{3} [/tex]

hence, the volume of the given rectangular prism is 336 cubic inches.

answer= option D

[tex]\large\boxed{Formula: V= lbh}[/tex]

All the values are given so we'll simply have to solve.

Let's solve!

Substitute the values according to the formula.

We'll have to multiply the length, breadth and the height.

[tex]V= 14 \times 3 \times 8[/tex]

[tex]\large\boxed{V= 336 \: {in}^{3}}[/tex]

We get a whole number to the final answer so we won't have to round off.

Therefore, the volume of the given rectangular prism is 336 cubic inches.

Correct option: Option D

Vertex is same x coordinate

Means y is changed

f(x) has vertex (4,3)

g(x) has vertex (4,-3)

Total change

So the transmission is f(x)-6

Answer:

[tex]\textsf{D)} \quad f(x)-6[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

From inspection of the graph, g(x) is a translation of f(x) by 6 units down.

[tex]\implies g(x)=f(x)-6[/tex]

Answer:

Step-by-step explanation:

Guess My Mystery Fraction

1. My fraction has a denominator of 4*12

2. My fraction can be simplified to 5/8

3. My fraction has a numerator of 10*3

Answer:

45, 75

Step-by-step explanation:

3+5 = 8

120 / 8 = 15

15 x 3 = 45

15 x 5 = 75

Answer:

45,75

3+5 = 8

120 / 8 = 15

15 x 3 = 45

15 x 5 = 75

Step-by-step explanation:

have a great day!

[tex]\text{Given that,} ~ x-y = 5~ \text{amd}~ xy = 4\\\\\text{Now,}\\\\x^3 -y^3\\\\=(x-y)(x^2 +xy+y^2)\\\\=(x-y)[(x-y)^2 +2xy +xy]\\\\=(x-y)[(x-y)^2 +3xy]\\\\=5(5^2+3\cdot 4)\\\\=5(25+12)\\\\=5(37)\\\\=185[/tex]

Solving a system of equations we will see that two large trucks and one small truck can hold 2.625 tons

Let's define the variables:

x = volume that a small truck holds.

y = volume that a large truck holds.

Then we can write the system of equations:

4x + 4y = 10.5 tons

y = 2x

Replacing the second equation into the first one we get.

4x + 4*(2x) = 10.5 tons

12x = 10.5 tons

x = 10.5 tons/12 = 0.875 tons

and:

y = 2x = 2*0.875 tons = 1.75 tons

Then the cargo that two large trucks and one small truck can hold is:

2* 1.75 tons + 0.875 tons = 2.625 tons

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Answer:

g(x) = a(x − h)2 + k, where a ≠ 0.

Step-by-step explanation:

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.

Answer:

A =64.03

Step-by-step explanation:

tan A = 2.053

A = Arctan( 2.053)

A =64.03

The partial differential expression is equal to the expression 30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²) and the total differential formula is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).

In the first part of this question we must apply the concept of partial derivatives to find the form of the entire expression, whose variables are two. Partial differentiation is a generalization of the ordinary differentiation:

[tex]\frac{\partial f}{\partial x} = 6\cdot x^{5}+12\cdot x^{3}\cdot y^{4}+y^{6}[/tex]     (1)

[tex]\frac{\partial^{2} f}{\partial x^{2}} = 30\cdot x^{4}+36\cdot x^{2}\cdot y^{4}[/tex]     (2)

[tex]\frac{\partial^{2} f}{\partial x \,\partial y} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex]     (3)

[tex]\frac{\partial f}{\partial y} = 12\cdot x^{4}\cdot y^{3} +6\cdot x \cdot y^{5}[/tex]     (4)

[tex]\frac{\partial^{2} f}{\partial y^{2}} = 36\cdot x^{4}\cdot y^{2} + 30\cdot x\cdot y^{4}[/tex]     (5)

[tex]\frac{\partial f}{\partial y \,\partial x} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex]     (6)

Then, the entire expression is:

30 · x⁴ + 36 · x² · y⁴ + 36 · x⁴ · y² + 30 · x · y⁴

30 · (x⁴ + x · y⁴) + 36 · (x² · y⁴ + x⁴ · y²)

30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²)

In the second part we must determine the total differential of z with respect to two variables:

[tex]\Delta z = \frac{\partial f}{\partial x}\cdot \Delta x + \frac{\partial f}{\partial y}\cdot \Delta y[/tex]     (7)

If we know that z = sin (x³ + y³), Δx = 0.3 and Δy = 0.2, then the total differential of the function is:

Δz = 3 · cos (x³ + y³) · x² · (0.3) + 3 · cos (x³ + y³) · y² · (0.2)

Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³)

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Using z-scores, it is found that a female who weighs ​1700g has the more extreme value relative to the group from which they came.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For the newborn male, we have that [tex]X = 1700, \mu = 3217.9, \sigma = 780.1[/tex], hence the z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1700 - 3217.9}{780.1}[/tex]

Z = -1.946.

For the newborn female, we have that [tex]X = 1700, \mu = 3086.5, \sigma = 523.8[/tex], hence the z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1700 - 3086.5}{523.8}[/tex]

Z = -2.645.

Due to the higher absolute value of the z-score, a female who weighs ​1700g has the more extreme value relative to the group from which they ca,e.

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Answer:

650

Step-by-step explanation:

let the unknown feet of room = X

5 paints = 250 square feet of room

13 paints = X

cross multiply

5*X = 250*13

X =3250÷5

X = 650 square feet of room