what are the solutions to 6x^2 - 5x - 4 = 0

The probability of selecting a black sock is 5/6 and there are 24 socks in total. By setting up and solving a simple equation, we find that there are 20 black socks in the drawer.

This question is about the concept of probability in mathematics. The probability of an event occurring is calculated by the number of desired outcomes divided by the total number of possible outcomes. In this case, we are given that the probability of reaching into a drawer without looking and magically pulling out a black sock is 5/6. With a total of 24 socks in the drawer, to figure out how many socks are black, we can set up a simple equation where x represents the number of black socks. Thus, x/24 = 5/6. Solving this equation, we get x = (5/6) * 24, which simplifies to x = 20. So, there are 20 black socks in the drawer. That's indeed a lot of black socks!

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Answer:

The correct answer is: A

Step-by-step explanation:

x+5

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Final answer:

The length of the square's diagonal with side lengths of 7 inches is found using the Pythagorean theorem, leading to a diagonal of approximately 9.899 inches.

Explanation:

To find the length of the square's diagonal when the side lengths are 7 inches, we can use the Pythagorean theorem. The diagonal of a square creates two right triangles, with the diagonal being the hypotenuse. You can think of this as half of the square divided along the diagonal. Each of these triangles has two legs that are each equal to the side of the square and a hypotenuse which is the diagonal we want to find.

The formula for the Pythagorean theorem is a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse. Since the legs are both 7 inches (the side length of the square), we have:

7² + 7² = c²
49 + 49 = c²
98 = c²

This simplifies to:

c = √98
c ≈ 9.899 inches (rounded to three decimal places)

Therefore, the diagonal of the square is approximately 9.899 inches long.

Answer:  They are not mutually exclusive events.

Step-by-step explanation:

Let A be the event of getting a sum of 6 on dice.

Let B be the events of getting doubles .

A={ (1,5), (2,4), (3,3), (4,2), (5,1) }

B = { (1,1) , (2,2), (3,3),  (4,4), (5,5), (6,6) }

Since we know that Mutaullty exclusive events are those when there is no common event between two events.

i.e. there is empty set of intersection.

But we can see that there is one element which is common i.e. (3,3).

So, n(A∩B) = 1 ≠ ∅

Hence, they are not mutually exclusive events.

Answer:

They are not mutually exclusive events.

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

684

Step-by-step explanation:

see photo for step by step explanation.

The area of the pool is the amount of space on it.

The area of the pool is 684 square feet

The dimensions of the pool are:

10ft by 20ft, 8ft by 20ft and 27ft by 12ft

The area of the pool is then calculated as:

A = 10 * 20 + 8 * 20 + 27 * 12

Evaluate the products

A = 200 + 160 + 324

Evaluate the sums

A = 684

Hence, the area of the pool is 684 square feet

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Answer:

Options B, C and D are correct choices.

Step-by-step explanation:

Please consider the complete question.

Mr. Shen likes for his homework assignments to have 2  addition problems for every 3 subtraction problems.

Which of the following homework assignments could

Mr. Shen create?

Choose 3 answers:

A. 3 addition problems and 4 subtraction problems .

B. 6 addition problems and 9 subtraction problems .

C. 16 addition problems and 24 subtraction problems.

D. 8 addition problems and 12 subtraction problems.

E. 15 addition problems and 10 subtraction problems.

To solve our given problem, we need to find the number that have same ratio.

Let us compare each ratio.

A. [tex]\frac{3}{2}\neq \frac{4}{3}[/tex]

Since the ratio of corresponding numbers is not same, therefore, option A is incorrect.

B. [tex]\frac{6}{2}=\frac{9}{3}[/tex]

[tex]3=3[/tex]

Since the ratio of corresponding numbers is same, therefore, option B is the correct choice.

C. [tex]\frac{16}{2}=\frac{24}{3}[/tex]

[tex]8=8[/tex]

Since the ratio of corresponding numbers is same, therefore, option C is the correct choice.

D. [tex]\frac{8}{2}=\frac{12}{3}[/tex]

[tex]4=4[/tex]

Since the ratio of corresponding numbers is same, therefore, option D is the correct choice.

E. [tex]\frac{15}{2}\neq \frac{10}{3}[/tex]

Since the ratio of corresponding numbers is not same, therefore, option E is incorrect.

Final answer:

Aubrey requires 2 cans of white paint to cover the triangular sail with an area of 12 square feet, given that one can covers 10 square feet.

Explanation:

Aubrey is painting a triangular sail as part of a mural with a base of 4 feet and a height of 6 feet. To calculate the area of the triangle, the formula is 1/2 × base × height. Thus, the area is 1/2 × 4 × 6, which equals 12 square feet. One can of special white paint covers 10 square feet. Therefore, Aubrey will need to use 2 cans of paint to cover the entire sail, since you can't purchase a fraction of a can.

23rd term of the given geometrical sequence is [tex]a_{23} = 25(1.8)^{22}[/tex].

Function to represent sequence is [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]

" Geometric sequence is defined as the sequence whose ratio of the consecutive terms is always constant."

Formula used

nth term of the geometric sequence

[tex]a_{n} = a r^{n-1}[/tex]

a = first term

r = common ratio

[tex]a_{n}[/tex] = nth term

According to the question,

First term of the geometric sequence 'a' = 25

Common ratio of the geometric sequence 'r'  = 1.8

Substitute the value in the formula to get 23rd term,

[tex]a_{23} = 25(1.8)^{23-1}[/tex]

⇒[tex]a_{23} = 25(1.8)^{22}[/tex]

Function to represent this sequence

[tex]a, a(r),a(r)^{2} , a (r)^{3} , ....... ,a(r)^{n}[/tex]

= [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]

Hence, 23rd term of the given geometrical sequence is [tex]a_{23} = 25(1.8)^{22}[/tex].

Function to represent sequence is [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]

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Answer:

Step-by-step explanation:

Answer: 28.26

Step-by-step explanation: I think it's 28.26, I tried

Answer:

Step-by-step explanation:

hi

To determine which fraction is equivalent to 1/3, we can compare each fraction to 1/3 and simplify if necessary. The fraction that is equivalent to 1/3 is 4/12.

To determine which fraction is equivalent to 1/3, we can compare each fraction to 1/3 and simplify if necessary. Let's go through each option:

Therefore, the fraction that is equivalent to 1/3 is 4/12.

Answer:

A

Step-by-step explanation:

All rectangles are parallelograms and all their sides are parallel.

The question seems to require using ordered pairs to locate Sam and the theater, but lacks the specific coordinates or context needed for a precise answer. Ordered pairs are essential in geometry for representing positions.

The question seems to pertain to locating positions or objects using ordered pairs, which falls under the domain of algebra and geometry in mathematics. An ordered pair (x, y) is used to define the positions on a plane, with 'x' representing the horizontal component and 'y' representing the vertical component.

Unfortunately, the question lacks specific information about the coordinates of Sam and the theater, making it impossible to provide exact ordered pairs without additional context. In scenarios involving maps or spatial planning such as finding locations in a city or arranging objects with a spatial relation to each other, ordered pairs serve as a crucial means of representation.

Exercises involving ordered pairs deepen understanding of coordinate systems, which are fundamental in geometry and crucial for various applications in science and engineering.