A fair die is rolled six times. Calculate the probability of obtaining exactly two 3s. (Round your answer to four decimal places.)
Show work in steps so I can understand how to set up the problem and solve it better. Been stuck on this for awhile! Thanks

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

1/5x

Step-by-step explanation:

1/5x

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

$54.87

Step-by-step explanation:

The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.

The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.

The total area to be covered with mulch is 108 - 15 = 93 square feet.

The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.

Therefore, the total cost of the mulch will be $54.87.

Triangle OMG is a right angled triangle

Triangle is a shape with 3 sides and 3 angles

To determine whether the triangle is acute, right, or  obtuse, from the coordinate point, we can see that the x and y coordinate of one of the vertices are the same, this is an indication that the triangle is right triangle.

In conclusion, triangle OMG is a right angled triangle

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Answer:

D

Step-by-step explanation:

use the sine or cosine ratio in the right triangle.

using the sine ratio and the exact value

sin45° = \(\frac{\sqrt{2} }{2}\) , then

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{4}\) = \(\frac{\sqrt{2} }{2}\) ( cross- multiply )

2x = 4\(\sqrt{2}\) ( divide both sides by 2 )

x = 2\(\sqrt{2}\)

The value of x is 2√2.

Hence the correct option is D.

Given that a right triangle with acute angles 45° each, and hypotenuse is 4 units,

we need to find the length of the perpendicular,

In a right triangle, the length of the perpendicular (also known as the altitude) can be found using trigonometric ratios.

In this case, since we have an angle of 45°, we can use the sine or cosine function.

Let's use the sine function to find the length of the perpendicular:

sin(45°) = opposite / hypotenuse

sin(45°) = perpendicular / 4

1/√2 = perpendicular / 4

perpendicular = 4/√2

perpendicular = 2√2

Hence the value of x is 2√2.

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Answer:

No

Step-by-step explanation:

No. I am not helping because you spam random "answers" to gain points for your account. If you want to be taken seriously, take everyone else seriously.

9514 1404 393

Answer:

  10.  x = 4

  11.  x = -5

Step-by-step explanation:

10. Use the perimeter formula. Collect terms, subtract* the constant, divide by the coefficient of the variable.

  P = 2(L+W)

  42 = 2(5x +(x-3))

  21 = 6x -3 . . . . . . divide by 2, collect terms

  24 = 6x . . . . . . . . add 3

  4 = x . . . . . . . . . .  divide by 6

__

11. Collect terms, subtract the constant, divide by the coefficient of the variable.

  -8x -3(2x +1) = 67

  -8x -6x -3 = 67 . . eliminate parentheses

  -14x -3 = 67 . . . . . collect terms

  -14x = 70 . . . . . . . add 3

  x = -5 . . . . . . . . . . divide by -14

_____

* "Subtract" and "add the opposite" are the same mathematical operation. In both these problems, the constant we want to get rid of is -3, so we add 3 (the opposite of -3). Of course, that operation is done to both sides of the equation.

Step-by-step explanation:

this is the answer

hope it helped!!!

Answer:

60°

Step-by-step explanation:

Angles in a triangle sum to 180°.            70° + 50° = 120°.               180°-120°=60°

Mathematics provides a framework for developing critical thinking, problem-solving, and analytical skills that are valuable in many aspects of life.

What is mathematics?

Mathematics is a fundamental discipline that plays a crucial role in our daily lives and in shaping our understanding of the world.

Mathematics is a field of study that deals with the properties and relationships of numbers, quantities, shapes, and patterns. It involves using logical reasoning, abstraction, and symbolic manipulation to understand and solve problems related to these concepts.

Mathematics is important for many reasons. First and foremost, it is a fundamental tool for understanding and describing the world around us. It plays a crucial role in science, technology, engineering, economics, finance, and many other fields by providing tools for modeling and analyzing complex phenomena.

Mathematics is also essential for making accurate predictions and decisions based on data and evidence, as well as for designing and optimizing systems and processes.

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Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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Answer:

D stays for 1 and as B is -6

the length of BD should be 7

good luck <3!

Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

The length of each side of the wood is 5 centimetres.

Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².

Hence, using quadratic equation let's find the length of each side of the wood.

Therefore,

8s² = 200

Hence,

8s² = 200

divide both sides of the equation by 8

s² = 200 / 8

s² = 25

s = √25

s = 5 centimetres

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Answer:

The standard form of an equation of a circle with center at (h, k) and radius r is

(x - h)² + (y - k)² = r²

The composite mapping (f o g)(x) ≥ 3 for the functions f(x) = 2x + 1 and g(x) = x² + 1. And (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

A mapping is composite when the co- domain of the first mapping is the domain of the second mapping.

For the functions f(x) = 2x + 1 and g(x) = x² + 1

If x > 0, say x = 1 then;

g(x) = 1² + 1

g(x) = 2

(f o g)(x) = 2(2) + 1

(f o g)(x) = 4 + 1

(f o g)(x) = 5

If x = 0, then;

g(x) = 0² + 1

g(x) = 1

(f o g)(x) = 2(1) + 1

(f o g)(x) = 2 + 1

(f o g)(x) = 3

For the functions f(x) = x² and g(x) = x

If x < 0, say x = -0.5, then;

g(x) = -0.5

(f o g)(x) = (-0.5)²

(f o g)(x) = 0.25

In conclusion, the composite mapping (f o g)(x) ≥ 3 for functions f(x) = 2x + 1 and g(x) = x² + 1 and (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

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The requried, there are 240 possible ways the race can finish with a mouse placing first, second, and third.

To find the number of ways the race can finish with a mouse placing first, second, and third, we can use the concept of permutations.

Since the mouse is guaranteed to finish first, there are 5 mice to choose from for the first position.

Once the first place is determined, there are 4 mice left for the second position.

After the first two positions are filled, there are 3 mice left for the third position.

Now, we need to determine the order of the cats. There are 4 cats to choose from for the fourth position.

The total number of ways the race can finish with a mouse placing first, second, and third is given by the product of these choices:

Number of ways = 5 (for first place) * 4 (for second place) * 3 (for third place) * 4 (for fourth place)

Number of ways = 5 * 4 * 3 * 4

Number of ways = 240

There are 240 possible ways the race can finish with a mouse placing first, second, and third.

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The probability of observing at least one head in 10 tosses of a fair coin is approximately 0.999 or 99.9%.

When you flip a fair coin, there are two possible outcomes: heads or tails. Since the coin is fair, the probability of observing heads is the same as the probability of observing tails, and each individual coin toss is independent of all the others.

To find the probability of observing at least one head in 10 coin tosses, we can use the complement rule. The complement of the event "observing at least one head" is the event "observing no heads" or "observing all tails."

The probability of observing all tails in 10 coin tosses is (1/2)^10, since the probability of observing tails on any given toss is 1/2, and the tosses are independent.

Therefore, the probability of observing at least one head in 10 coin tosses is:

1 - (1/2)^10

This is the probability of the complement of the event "observing all tails," which is the event "observing at least one head."

We can calculate this probability using a calculator or by simplifying the expression:

1 - (1/2)^10 = 1 - 1/1024

= 1023/1024

≈ 0.999

So the probability of observing at least one head in 10 coin tosses is approximately 0.999, or 99.9%. This means that it is very likely (but not guaranteed) that you will observe at least one head if you flip a fair coin 10 times.

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Answer:

Total people = 240

Step-by-step explanation:

Let the total number of people by 'x'.

\(\sf \text{Number of men =$ \dfrac{1}{4}*x$} \\\)

\(\sf \text{Number of women =$\dfrac{1}{3}x$}\)

Number of children = 100

When we subtract the total number of men and women from the total people 'x', we get the number of children.

\(\sf x - \left(\dfrac{1}{4}x+\dfrac{1}{3}x\right)= 100\\\\x - \left(\dfrac{1*3}{4*3}x+\dfrac{1*4}{3*4}x\right)=100\\\\\)

      \(x- \dfrac{4+3}{12}x=100\\\\x - \dfrac{7}{12}x = 100\\\\ \dfrac{12}{12}x-\dfrac{7}{12}x = 100\\\\ \dfrac{5}{12}x=100\\\)

          \(\sf x = 100*\dfrac{12}{5}\\\)

          x = 20 * 12

          x = 240

The tree grew about 3.83 inches between the first and third week.

An equation is an expression that shows the relationship between two or more numbers and variables.

On the first week, the tree was 27 1/2 inches (27.5) tall. On the second week, it was 29 1/4 inches (29.25) tall. On the third week, it was 31 1/3 inches (31.33) tall.

The length grown = 31.33 - 17.5 = 3.83 inches

The tree grew about 3.83 inches between the first and third week.

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Answer: (Answer in explanation)

Step-by-step explanation:

(12)B > 180

Her goal is to make more than 180 so if she wants to sell each book for $12 then so if she sells 14 books or above she would get more than $180.

So B could equal anything 16 and above but in my case I chose 24

(12)24 = 288 > 180

So write a equation like mine that equals a number that's greater than 180. Keep in mind each book sells for $12 each. Then solve for B which is how many books she has to sell to get the number greater than 180.

Answer:

35

Step-by-step explanation:

The area of the parallelogram will be equal to 28 units squared. Hence, option B is correct.

The phrase "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bound by the contract by parallel lines." As a consequence, a quadrilateral that is bordered by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides.

As per the data obtained from the given values,

Length of base (b) of parallelogram = 7

Length of height (h) of parallelogram = 4

Use the formula of area (A) of a parallelogram,

\(Area = Base*Height\)

A = 7 × 4

A = 28 units squared.

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Answer:

Answers are below in bold

Step-by-step explanation:

1) A = 1/2bh          Use this equation to find the area of each triangular base

A = 1/2(8)(6)         Multiply

A = 1/2(48)           Multiply

A = 12cm²           Area of each triangular base

2) A = L x W        Use this equation to find the area of the bottom rectangular face

A = 20 x 8          Multiply

A = 160 cm²       Area of the bottom rectangular face

3) A = L x W        Use this equation to find the area of the back rectangular face

A = 20 x 6          Multiply

A = 120 cm²       Area of the back rectangular face

4) A = L x W        Use this equation to find the area of the sloped rectangular face

A = 20 x 10         Multiply

A = 200 cm²      Area of the sloped rectangular face

5) To find the total surface area of the triangular prism, add together all of the numbers.

A = 12 + 12 + 160 + 120 + 200       Add

A = 504 cm²       Total area of the triangular prism

Answer:

14.1

Step-by-step explanation:

Answer: buy all the crop tops

Step-by-step explanation:

Answer:

Well with that amount of money u should most definitely buy them, if you liked the of course

Step-by-step explanation:

I'm just saying

Answer:

2/8

Step-by-step explanation:

I think this is subtraction (if not just tell me i'll edit)

6/8 - 2/4 = 6/8 - 4/8 = 2/8

Answer:

4/8

Step-by-step explanation:

2/4 is equivalent to 4/8

She was 2/8 left over btw