Topic: Probability


Only complete question 13.

Answer:

8a^3.

Step-by-step explanation:

(a+b)^3=a^3+b^3+3a^2b+3ab^2

(a-b)^3=a^3-b^3-3a^2b+3ab^2

(a+b)^3+(a-b)^3=2a^3+6ab^2

According to the question

(a+b)^3+(a-b)^3+6a(a^2-b^2)

Put in the value

=2a^3+6ab^2 +6a^3–6ab^2

=8a^3

In the simplest form expression (a + b)³ + (a - b)³ + 6a(a² - b²) can be written as,  8a³

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Given that,

A algebraic identity,

(a + b)³ + (a - b)³ + 6a(a² - b²)

It is known that,

(a + b)³  = a³ + b³ + 3ab(a + b)

(a - b)³  =  a³ - b³ - 3ab(a - b)

So, now we can substitute expressions

(a + b)³ + (a - b)³ + 6a(a² - b²)

a³ + b³ + 3ab(a + b) + a³ - b³ - 3ab(a - b) +  6a(a² - b²)

a³ + b³ +  3a²b + 3ab² + a³ - b³ -3a²b + 3ab² + 6a³ - 6ab²

8a³

Hence, the simplest form is 8a³

To know more about algebraic expressions check:

https://brainly.com/question/24875240

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Answer: If the function is: f(x) = (x^2−3x−10)/(x−5) The function has no holes.

If the function is f(x) = x^2−3x−10/x−5 then the hole is at x = 0 (the left side goes up, and the right side goes down, as the numerator is a negative number)

Step-by-step explanation:

I am not shure of what is the function, as you used no parentheses in it, so i will solve it for two different functions:

We have the function:

f(x) = (x^2−3x−10)/(x−5)

We want to find the "hole", this means that we want to find the value of x where the denominator is equal to zero.

If you look at the function, is easy to think that in x = 5 the denominator will be equal to zero, but we need to prove it.

First, we need to see if the numerator part is also zero when x = 5.

so

5^2 - 3*x - 10 = 25 -15 - 10 = 0

Ok, let's find the other root of the quadratic function:

x^2 - 3*x - 10 = (x - 5)*(x - b) = x^2 - (b + 5)*x + (b*5)

then we have: (b + 5) = 3 and b*5 = -10

then b = -2, this means that we can write the numerator part as:

x^2 - 3*x - 10 = (x - 5)*(x + 2)

then our function is:

f(x) =   (x - 5)*(x + 2)/(x - 5) = x + 2

This function has no holes.

Now, if the function actually is:

f(x) = x^2−3x−10/x−5

Then we have an x on the denominator of the third term of the equation, this denominator is 0 only when x = 0

Answer:

The correct option is;

105 band members

Step-by-step explanation:

The 5 values are

Minimum value = 80

Q₁ = 90

Q₂ = 105

Q₃ = 115

Maximum value = 130

Whereby the horizontal axis indicates the number of band members is a school, while the 5 values of the box plot are the percentiles of the schools in Orange County and also that the lines are graduated in increments of 5, we have that the median = 105 which is the 50% mark, therefore;

50% of high schools in Orange County have more than 105 band members.

Answer:

The answer would be 105

Step-by-step explanation:

I got this right on Khan Academy <33

Answer:

0.62

Complete question:

What is the probability that at Aya will be offered a coupon on at least one of the days she visits the website?

Step-by-step explanation:

assuming,

A: Aya gets a coupon one day. P(A) = 0.15

B: Aya doesn't get a coupon one day. P(B) = 1 - 0.15 = 0.85

Aya doesn't get a coupon in any of 6 days  = P(B)^6 = 0.85^6 = 0.38

The probability of Aya getting at least 1 coupon after 6 days is the complement of don't getting any coupon after 6 days, that is:

1 - P(B)^6=  1 - 0.38 = 0.62

Answer: Attached graph in the explanation.

Step-by-step explanation:

Hi, to answer this question we have to graph points in a Cartesian coordinate graph.

The horizontal axis is called the x-axis, and the vertical axis is the y-axis.

To graph a point, first we have to locate its position on the x-axis, and then find its location on the y-axis, and finally plot where these meet.

For example, to plot the point (2, 3), we have to find the positive 2 on the x-axis and the positive 3 on the y-axis.

Finally when we have plotted all the points, we simply link all the points to form a line.

Answer:

75.96 Degrees

Step-by-step explanation:

Use the trigonometric functions of Sine Cosine and Tangent

(SOH CAH TOA)

The unknown angle is near the adjacent side of 2 and the opposite side of 8

Therefore you use the Tangent function

However, since it's the angle that needs to be found, you need to use Arc Tangent (The inverse operation)

Unknown Angle = ArcTan (8 / 2)

Unknown Angle = 75.96 Degrees

Note: ArcTan is just Tan to the power of -1

On my calculator I have to click shift then click the tan function to access this it may be different on yours

Answer: 5.25 miles

Step-by-step explanation:

The complete question is:

A certain element has a half life of 4.5 billion years.

You find a rock containing a mixture of the element and lead. You determine that 30% of the original element remains; the other 70% decayed into lead. How old is the rock?

Answer:

Age of rock = 7.82 billion years

Step-by-step explanation:

For a first order decay, fraction remaining is given by the formula 0.5n where n = number of half lives elapsed.

We are given that;

fraction remaining = 30% = 0.3

Thus;

0.3 = 0.5n

To find n, we have to use the log function;

log 0.3 = n log 0.5

-0.5229 = -0.301 n

n = -0.5229/-0.301

n = 1.737

We are given that;

Half life = 4.5 billion years

So, 1.737 half lives would give;

1.737 × 4.5 = 7.82 billion years

So, age of rock = 7.82 billion years

Step-by-step explanation:

Surface area of a cylinder:

A = (2 x pi x r x h) + (2 x pi x r^2)

(2 x pi x 5 x 25) + (2 x pi x 5^2)

785.3981 + 157.0796 = 942.4777cm^2

Volume of cylinder:

V = pi x r^2 x h

pi x 5^2 x 25 = 1963.4954cm^3

Answer & Step-by-step explanation:

We use decimals every day while dealing with money, weight, length etc. Decimal numbers are used in situations where more precision is required than the whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale.

Answer:

b.) 104

Step-by-step explanation:

Percent formula:

x/y = p/100

where x is the fraction, y is the total, and p is the percent

This means:

x = number of games the team won

y = total number of games

p = percent the number of teams won

Let's plug these values into the equation:

x/y = p/100

x/160 = 65/100

Solve by cross-multiplying:

x/160 = 65/100

100(x) = 100x

160(65) = 10,400‬

100x = 10,400

/100     /100

x = 104

Therefore, the team won 104 games.

*diagram of floor plan is attached below

Answer:

30m²

Step-by-step Explanation:

From the floor plan shown in the attached diagram, the hall way and the living room both takes the shape of a rectangle.

To find the total area of floor to be covered, we can use the formula of the area of a rectangle to find the area of the hall way + the area of the living room.

Area of rectangle = L*B

For the hall way, L = 3.2m, B = 1.5m

Area of hall way = 3.2*1.5 = 4.8m²

For the living room, L = 6m, B = 4.2m

Area of Living room = 6*4.2 = 25.2m²

Therefore, area of floor to be covered = 4.8m² + 25.2m² = 30m²

Answer:

30m²

Step-by-step explanation:

Answer:

1)4

2)5

3)6

Step-by-step explanation:

1)2x+5=3x+1

2x-3x=1-5

-1x=-4

x=4

2)3x+2=4x-3

3x-4x=-3-2

-1x=-5

x=5

3)4x-3=3x+3

4x-3x=3+3

1x=6

x=6

Hope it helps

Answer:

4

lolz sorry for a late answer bud

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Since there are a total of 14 t shirts and 7 of them were green, the experimental probability that the next one is also green is 7/14=1/2. Hope this  helps!

Answer: 76 m^2

Step-by-step explanation:

[tex]A=\frac{4+15}{2}*8 = 76\;m^2[/tex]

Answer:

Step-by-step explanation:

Answer:

47/73

Step-by-step explanation:

There are 73 people who like tea. 47 are women, 26 are men. This means that the probabili that the person chosen is a women is 47 out of the 73.

Answer:

x=2

Step-by-step explanation:

6x−5=13−3x

Step 1: Simplify both sides of the equation.

6x−5=13−3x

6x+−5=13+−3x

6x−5=−3x+13

Step 2: Add 3x to both sides.

6x−5+3x=−3x+13+3x

9x−5=13

Step 3: Add 5 to both sides.

9x−5+5=13+5

9x=18

Step 4: Divide both sides by 9.

[tex]\frac{9x}{9}[/tex]= [tex]\frac{18}{9}[/tex]

x = 2

Answer: x=2

Step-by-step explanation:

Start by adding 3x to 6x, this eliminates the variables on the right side of the equation and leave you with 9x-5=13. From here, add five to both sides of the equation, which cancels out on the left side and leads you to have 18 on the right side. Remember that you want to have a lone variable, so you take the current equation of 9x=18 and divide both sides by 9, which cancels out on the left side and leaves the right side as 2. Therefore, x=2.

Answer:

245/999

Step-by-step explanation:

0.245bar = n

1000 n - n = 245

999n = 245

n = 245/999

Answer:

The third side is sqrt(77)

Step-by-step explanation:

Since this is a right triangle we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

2^2 + b^2 = 9^2

4+ b^2 = 81

Subtract 4 from each side

b^2 = 81-4

b^2=77

Take the square root of each side

sqrt(b^2) = sqrt(77)

b = sqrt(77)

The third side is sqrt(77)

Answer:

110 - 2x

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

x + 50 + 5x - 40 + 110 - 2x = 180, that is

4x + 120 = 180 ( subtract 120 from both sides )

4x = 60 ( divide both sides by 4 )

x = 15

Thus

x + 50 = 15 + 50 = 65°

5x - 40 = 5(15) - 40 = 75 - 40 = 35°

110 - 2x = 110 - 2(15) = 110 - 30 = 80°

The largest angle is (110 - 2x)° = 80°

Answer:

21.66666667

Step-by-step explanation:

3x-4(0)=65

3x=65

x=21.66666667

You replace y wil 0 when you are sovling for x

Answer:

x=< -1

Step-by-step explanation:

move the constant to the right-hand side and change its sign. 2x<-5+3

Calculate the sum

2x<-2

Divide both sides of the inequality by 2

x <-1

Answer:

44 cm

Please see the attached picture for full solution

Hope it helps....

Good luck on your assignment

Answer:

x = 2

Step-by-step explanation:

5x = 10

x = 2

Answer:

C. x < 10

Step-by-step explanation:

2x - 8 < 12

Add 8 to both sides

2x < 20

Divide both sides by 2

x < 10

Answer:

Option C

Step-by-step explanation:

We are given the inequality 2x - 8 < 12,

[tex]2x - 8 < 12,\\2x < 20,\\x < 10\\\\Conclusion - Option C[/tex]

As you can tell, for the first step we added 8 on either side of the inequality sign, resulting with the cancelation of 8, and the addition of 8 and 20. Dividing 2 on either side of this simplified inequality, we resulted in x < 10. Note that if we were to divide by a negative value, this less than sign would be taken as a greater than sign ( same rule applies for the multiplication of a negative number ).

Solution ⇒ Option C