there are 7 green marbles in a bag and 9 yellow marble. you randomly select three marbles. what is the probability that all three marbles are green when a)

Simone buy 5 books and 17 vinyl records.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Simone bought a total of 22 used books and vinyl records during a yard sale for a total of $78.50.

And, Books cost $3.00 each and the vinyl records cost $5.50 each.

Let number of books = x

And, Number of vinyl records = y

Hence, We cam formulate;

⇒ x + y = 22  .. (i)

⇒ 3x + 5.50y = 78.50  .. (ii)

Substitute the value of x from (i) in (ii), we get;

⇒ 3x + 5.50y = 78.50

⇒ 3(y - 22) + 5.50y = 78.50

⇒ 3y - 66 + 5.50y = 78.50

⇒ 8.50y = 78.50 + 66

⇒ 8.50y = 144.5

⇒ y = 17

From (i);

⇒ x + y = 22  

⇒ x + 17 = 22  

⇒ x = 5

Thus, Simone buy 5 books and 17 vinyl records.

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Answer:

Domain is all real numbers, x ≠ -5

Range is all real numbers, y ≠ 0

Step-by-step explanation:

Answer:

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

Step-by-step explanation:

Answer:

Step-by-step explanation: so a straight line always equals to 180 where 41 is its a straight line so we know the total should be 180 degrees so to find x you need to subtract 180 minus 41 which equals 139 which is your answer im not super sure but trust your gut im trusting mines with this one so i hope this helps

Answer:

To solve for x in the equation −12(x + 5) = -10, we will use the following steps:

Distribute the -12 to the terms inside the parentheses:

-12x - 60 = -10

Add 60 to both sides of the equation to isolate the variable term:

-12x = 50

Finally, divide both sides of the equation by -12 to solve for x:

x = -50/12

Simplifying the answer, we get:

x = -25/6 or -4.1667 (rounded to four decimal places)

Step-by-step explanation:

TRUE. An independent premise is a premise that can stand alone and support the conclusion of an argument without relying on other premises.

It provides separate evidence for the conclusion, distinguishing it from dependent premises, which require other premises to support the conclusion effectively.

On the other hand, a dependent premise is a premise that cannot support the conclusion on its own and requires other premises to be persuasive. Dependent premises often serve as links between independent premises, helping to establish a chain of reasoning that leads to the conclusion.

It's essential to distinguish between independent and dependent premises because they play different roles in constructing a persuasive argument.

Independent premises provide stronger support for the conclusion because they offer separate evidence. Dependent premises, while still valuable, are weaker because they rely on other premises to be persuasive.

Therefore, constructing a sound argument requires a mix of independent and dependent premises. Independent premises provide the foundation for the argument, while dependent premises help to strengthen the connections between the independent premises and the conclusion.

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answer

22.5pages

example: 30÷4*3

By using Pythagoras theorem and distance formula the length of CP is obtained as 3.43 units.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

To find the length of CP, first find the coordinates of point P, and then use the distance formula to calculate the length of CP.

Let A be at the origin (0, 0), and let B be on the positive x-axis at (6, 0). Then we can find the coordinates of C using the Pythagorean theorem -

AC² + BC² = AB²

AC² + (3√3)² = 6²

AC² = 9

AC = 3

So C is located at (3, 3√3). We can find the coordinates of M by taking the average of the coordinates of A and B, which gives -

M = ((0+6)/2, (0+0)/2) = (3, 0)

Similarly, find the coordinates of N by taking the average of the coordinates of B and C, which gives -

N = ((6+3)/2, (0+3√3)/2) = (4.5, 1.5√3)

Now find the equation of the line passing through M and C, which is the line containing median AM -

slope = (3√3 - 0)/(3 - 0) = √3

y - 0 = √3(x - 3)

y = √3x - 3√3

And find the equation of the line passing through N and A, which is the line containing median CN -

slope = (0 - 3√3)/(0 - 6) = √3/2

y - 0 = (√3/2)(x - 6)

y = (√3/2)x - 3√3

Now, find the intersection point of these two lines, which is point P -

√3x - 3√3 = (√3/2)x - 3√3

x = 6/3.5

x = 12/7

y = √3(12/7) - 3√3

y = 3√3/7

So P is located at (12/7, 3√3/7).

Now use the distance formula to find the length of CP:

CP² = (12/7 - 3)^2 + (3√3/7 - 3√3)²

CP² = (33/7)^2 + (6√3/7)^2

CP² = 1089/49 + 72/49

CP² = 1161/49

CP = √1161/7

Therefore, the length of CP is (approximately) 3.43.

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When receiving ammunition, unit personnel perform three tasks: ensuring items requested match item numbers on DA Form 3151-R, loading and securing the ammunition, and placarding the vehicle.

The first task performed by unit personnel when receiving ammunition is to ensure that the items requested match the item numbers on DA Form 3151-R. This form serves as a record of the types and quantities of ammunition being received. By comparing the requested items with the item numbers on the form, personnel ensure accuracy and prevent any discrepancies or errors in the delivery.

The second task involves the loading and securing of the ammunition. Unit personnel are responsible for safely and efficiently loading the ammunition onto the designated vehicle or storage area. This includes following proper handling procedures, using appropriate equipment, and adhering to safety protocols. The ammunition must be securely stored and arranged to prevent shifting or damage during transportation.

The final task is to placard the vehicle. Placarding involves visibly displaying the necessary warning signs or labels on the vehicle that indicate the presence of ammunition. This step is crucial for safety and compliance purposes, as it alerts other personnel and drivers to exercise caution when approaching or handling the vehicle. Clear and prominent placarding helps prevent accidents and ensures that everyone involved is aware of the potential hazards associated with transporting ammunition.

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Answer:  a)  y - 4 = 2/3(x) - 2

b)  y - 4 = -3/2(x) -2

Step-by-step explanation:

equation of original line:  y = 2/3x -5

point on a line parallel to original line:  (3,4)

The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:

(y - y1) = 2/3(x - x1)

point (x1, y1) is (3, 4)

plug (3,4) into the equation:

y - 4 = 2/3(x - 3)

y - 4 = 2/3(x) - 2

rewrite in slope-intercept form:  y = 2/3(x) + 2

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line:  - 1/m

Therefore, the slope of the perpendicular line = -3/2

Equation for the perpendicular line is:

y - 4 = -3/2(x) -2

Answer:

D is the correct answer.

The fraction of red apples in the bag is 3/ (4+x).

Let there be "x" number of green apples and "y" number of red apples in the bag.

According to the given information,

3/4 * x = y

Therefore, y = 3/4 * x

Since the fraction of red apples is y/ (x+y)

Therefore, fraction of red apples = 3/4 * x / (x+3/4 * x)

Simplifying,

Fraction of red apples = 3/ (4+x)

Therefore, the fraction of red apples in the bag is 3/ (4+x).

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Answer:

$368,640

Step-by-step explanation:

288,000 * .28 = 80640

288,000 + 80640 = 368640

111 years that is last option , it took for the U.S. government to seize the land from America's Indigenous population

The difference between two numbers is calculated using the subtraction technique. If you have a group of objects and take off a few of them, the group of objects gets smaller.

For instance, out of the nine cupcakes you bought for your birthday party, seven were gobbled by your friends. There are currently only two cupcakes left. This can be written as the following subtraction formula: Nine less seven equals two, or "nine less seven equals two." When 7 is subtracted from 9, the outcome is 2, or (9 - 7) Here, we divided the difference between the two numbers, 9, and 7, by one another.

1887 - 1776 = 111 years it took for the U.S. government to seize the land from America's Indigenous population

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Answer:

y= -1, x= -1

5x+6y=-11

-(5x-2y=-3)

     8y=-8

      y=-8/8

      y= -1

5x+6(-1)=-11

5x-6     = -11

        5x=-11+6

        5x=-5

          x=-5/5

          x=-1

The required solution of the simultaneous equation is x = -1 and y = -1.

Given that,
To solve the given simultaneous equation,
5x+6y= −11
5x = 2y −3

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
5x = 2y −3 - - - - - (1)
5x+6y= −11
By substitution, from equation 1
2y - 3 + 6y = -11
8y = -8
y = -1
Now,
5x = -2 - 3
x = -1

Thus, The required solution of the simultaneous equation is x = -1 and y = -1.

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As a linear combination of the orthonormal basis vectors discovered in part (a), write v = (3, 1, 2) in this format. Therefore,

(a) Using the Gram-Schmidt process, the orthonormal basis for ℝ³ is \(\left{ \left( -1, 0.1 \right) \div \sqrt{1.01}, \left( 0.282, -0.028 \right) \div \sqrt{5.3664} \right}\)}.

(b) The vector v = (3, 1.2) can be approximated as \(v \approx -2.9175 \cdot \frac{(-1, 0.1)}{\sqrt{1.01}} + 0.2698 \cdot \frac{(0.282, -0.028)}{\sqrt{5.3664}}\).

(a) To find an orthonormal basis for ℝ³ using the Gram-Schmidt process, we start with the given basis vectors and follow these steps:

Step 1: Normalize the first vector

Let's normalize the first vector (-1, 0.1):

\(v_1 = \frac{(-1, 0.1)}{\left\| (-1, 0.1) \right\|}\)

The magnitude of \(\[(-1, 0.1) = \|(-1, 0.1)\| = \sqrt{(-1)^2 + (0.1)^2} = \sqrt{1 + 0.01} = \sqrt{1.01}\]\)

So, \(v_1 = \frac{(-1, 0.1)}{\sqrt{1.01}}\)

Step 2: Project and subtract from the second vector

Now, we project the second vector (1, 2, -1) onto v₁ and subtract that projection from the second vector:

\(\text{proj}_{v_1} v_2 &= \left((1, 2, -1) \cdot v_1\right) v_1 \\\\v_2' &= (1, 2, -1) - \text{proj}_{v_1} v_2\)

The dot product of (1, 2, -1) and v₁ is ((1)(-1) + (2)(0.1) + (-1)(0)) = -1 + 0.2 + 0 = -0.8

\(\text{proj}_{v_1}^{v_2} &= (-0.8) v_1 \\&= (-0.8)(-1, 0.1) / \sqrt{1.01} \\&= \left( \frac{0.8}{\sqrt{1.01}}, -\frac{0.08}{\sqrt{1.01}} \right)\)

\(v_2' = (1, 2, -1) - \frac{(0.8, -0.08)}{\sqrt{1.01}}\)

Step 3: Normalize the resulting vector

Now, we normalize the resulting vector v₂' obtained in the previous step:

\(v_2 = \frac{v_2'}{\left\| v_2' \right\|}\)

The magnitude of \(\[v_2' = \|v_2'\| = \sqrt{0.2^2 + 2.08^2 + (-1)^2} = \sqrt{0.04 + 4.3264 + 1} = \sqrt{5.3664}\]\)

So, \(\[v_2 = \frac{v_2'}{\sqrt{5.3664}}\]\)

Now we have an orthonormal basis {v₁, v₂}.

(b) To express v = (3, 1.2) as a linear combination of the orthonormal basis vectors {v₁, v₂} obtained in part (a), we can use the following equation:

v = c₁ * v₁ + c₂ * v₂

Let's solve for c₂ and c₂:

v = c₁ * v₁ + c₂ * v₂

(3, 1.2) = c₁ * v₁ + c₂ * v₂

To find c₁ and c₂, we can take the dot product of both sides with v₁ and v₂:

(3, 1.2) · v1 = (c₁ * v₁ + c₂ * v₂) · v₁

(3, 1.2) · v₂ = (c₁ * v₁ + c₂ * v₂) · v₂

The dot products simplify to:

3 = c₁ * (v₁ · v₁)

1.2 = c₂ * (v₂· v₂)

Since v₁ and v₂ are orthonormal, their dot products with themselves are 1:3 = c₁

1.2 = c₂

Therefore, the linear combination is:

v = 3 * v₁ + 1.

2 * v₂

Substituting the values of v₁ and v₂:

\([3 \cdot \left( \frac{(-1, 0.1)}{\sqrt{1.01}} \right) + 1.2 \cdot \left( \frac{v_2'}{\sqrt{5.3664}} \right)]\)

Simplifying the expression, we have:

v ≈ \(\[(-2.97, 0.297) + \frac{(0.282, -0.028)}{\sqrt{5.3664}}\]\)

Adding the components together:

v ≈ \(\[\left( -2.97 + \frac{0.282}{\sqrt{5.3664}}, 0.297 - \frac{0.028}{\sqrt{5.3664}} \right)\]\)

So, v ≈ (-2.97 + 0.0525, 0.297 - 0.0272) ≈ (-2.9175, 0.2698)

Therefore, v ≈ (-2.9175, 0.2698) can be expressed as a linear combination of the orthonormal basis vectors found in part (a).

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Answer:

cost of a taco: $1.25

cost of a burrito: $2.50

Step-by-step explanation:

Let the cost of a taco be $t and the cost of a burrito be $b.

t +3b= 8.75 -----(1)

4t +2b= 10

Divide both sides by 2:

2t +b= 5

Making b the subject of formula:

b= 5 -2t -----(2)

Substitute (2) into (1):

t +3(5 -2t)= 8.75

Expand:

t +3(5) +3(-2t)= 8.75

t +15 -6t= 8.75

t -6t= 8.75 -15

-5t= -6.25

t= -6.25 ÷(-5)

t= 1.25

Substitute t= 1.25 into (2):

b= 5 -2(1.25)

b= 5 -2.5

b= 2.50

Thus, the cost of a taco is $1.25 and the cost of a burrito is $2.50.

Let's calculate E(Z^3), which is the third moment of Z, given that Z follows a standard normal distribution N(0, 1) and X follows a normal distribution N(μ, σ^2).

First, recall that the third moment of a random variable, E(Z^3), represents the expected value of the cube of Z. In this case, Z is a standard normal random variable, which has a symmetric probability density function (PDF) about the mean 0.

To calculate E(Z^3), we can use the formula:

E(Z^3) = ∫ z^3 * f(z) dz

where f(z) is the PDF of the standard normal distribution, and the integral is taken from negative infinity to positive infinity.

Since the PDF of Z is symmetric about the mean 0, the values of z^3 * f(z) will be positive for positive z values and negative for negative z values. These positive and negative values will cancel each other out when integrating over the entire range of Z, resulting in E(Z^3) = 0.

In summary, the third moment of Z, E(Z^3), for a standard normal random variable Z is 0 due to the symmetry of the PDF about the mean 0.

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Answer:

x = 5/3

y = -8/3

Step-by-step explanation:

To solve y = 2x - 6​ substitute the y for -x - 1 and solve for x.

-x - 1 = 2x - 6 Now you can solve this like a regular inequality. Start by subtracting 2x on both sides.

-3x - 1 = -6 Now add 1 to both sides

-3x = -5 Divide by -3 on both sides

x = 5/3 (the negatives cancel and become positive)

Because you have x, you can go back and properly solve for y. Substitute x for 5/3

y = 2(5/3) - 6 Simplify the right side to get your answer.

y = 10/3 - 6 In order to subtract 6, you first have to convert it to a fraction with a denominator of 3. To do this, put 6 over 1 (6/1) then find the least common denominator of 3 and 1, which is 3. Now multiply 1 by 3 and 6 by 3 to get 18/3

y = 10/3 - 18/3

y = -8/3

I hope this helped :)

all answers can be written multiple ways

7. 65/140, 13/28, or 46.43%

8. 18/140, 9/70, or 12.86%

9. 110/140, 11/14, or 78.57%

10. 95/140, 19/28, or 67.86%

Answer: 36

Step-by-step explanation:

13 plus 9 plus 14 equals 36

Answer:

Step-by-step explanation:

Similarity property,

" If the two triangles are similar then their corresponding sides will be proportional."

14). If ΔPQR ~ ΔUVW,

     \(\frac{PQ}{UV}=\frac{QR}{VW}=\frac{PR}{UW}\) [Statement}

     \(\frac{15}{10}=\frac{9}{6}=\frac{6}{4}\)

     \(\frac{3}{2}=\frac{3}{2}=\frac{3}{2}\)  [True}

Therefore, ΔPQR ~ ΔUVW [Theorem - SSS]

15). If ΔFHE ~ ΔDHG,

     \(\frac{EH}{HG}=\frac{HF}{DH}\) [Statement]  

     \(\frac{24}{6}=\frac{36}{9}\)

     4 = 4

Therefore, ΔFHE ~ ΔDHG [Theorem - AA]

Since the rate of bacteria growth is proportional to the number present, we can express this relationship using a differential equation:

dN/dt = kN,

where N is the number of bacteria, t is the time, and k is the constant of proportionality.

Given that the number of bacteria doubles in three hours, we can write:

dN/dt = kN,

dN/N = k dt.

To solve this equation, we integrate both sides:

∫ dN/N = ∫ k dt,

ln(N) = kt + C,

where C is the constant of integration.

Now, let's consider the specific conditions. When the number of bacteria doubles, N/N0 = 2, where N0 is the initial number of bacteria.

ln(2) = k(3) + C,

C = ln(2) - 3k.

Now, let's find the time it takes for the number of bacteria to triple, which means N/N0 = 3:

ln(3) = k(t) + ln(2) - 3k,

ln(3) - ln(2) = k(t) - 3k,

ln(3/2) = k(t - 3),

t - 3 = (ln(3/2))/k,

t = (ln(3/2))/k + 3.

Therefore, in how many hours will the number of bacteria triple is given by (ln(3/2))/k + 3. The value of k depends on the specific growth rate of the bacteria in the culture.

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Answer:

16524534887

Step-by-step explanation:

Answer:

16524534887

Step-by-step explanation:

just multiply, takes a while but you can do it

or you can just use a calculator

Answer:

median= 1/3

Step-by-step explanation:

Answer:

y=x+k

Step-by-step explanation:

her rate never changes because"pay her $200 no matter how long the work takes"

Th statement "All of the generators of Z60 are prime" is false.The statement "Q is cyclic" is true. The statement "If every subgroup of a group G is cyclic, then G is cyclic" is false.

To disprove the statement, we need to find a generator of Z60 that is not prime. Z60 represents the integers modulo 60. One example of a generator of Z60 is 1, but it is not a prime number.

The prime factors of 1 are 1 and itself, which violates the definition of a prime number. Therefore, not all generators of Z60 are prime, and the statement is false.

The set of rational numbers, Q, is cyclic. A cyclic group is a group that can be generated by a single element. In the case of Q, it can be generated by the element 1. Every element in Q can be expressed as an integer multiple of 1, and thus, Q is cyclic.

To disprove the statement, we need to find a counterexample. Consider the group G = Z4, the integers modulo 4 under addition. Every subgroup of G is cyclic since the subgroups are {0}, {0, 2}, {0, 1, 2, 3}, which can all be generated by a single element.

However, G itself is not cyclic since it cannot be generated by a single element. Therefore, the statement is false.

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The standard deviation of the data is 24.8

The standard deviation is a measure of the spread or variability of a set of data from the mean. It is calculated as the square root of the variance, which is the average of the squared differences between each data point and the mean.

The formula for the sample standard deviation is:

s = √([∑(xi - x)^2]/(n-1))

where s is the standard deviation, xi is each individual data point, x is the sample mean, n is the sample size, and  is the sum of all the squared differences.

The standard deviation is s=24.8

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