Vanessa has 16 songs on a Classic Rock CD. Six of the songs are by the Beatles, 4 are by the Rolling Stones, 4 are by the Who, and 2 are by the Doors. Vanessa plays the CD. She selects a setting that randomly chooses songs to play.
Find the probability of each event:
a) The first 3 songs played are by the Beatles.
b) The first 2 songs played are by the Rolling Stones and the next 2 songs are by the Beatles.
c) The first 2 songs played are by the Doors, and the next song played is either by the Beatles or the Rolling Stones.

Answer:

The answer is 10/143

Step-by-step explanation:

Answer:

Step-by-step explanation:

784-263=521

784+521=1305

answer=1305

The solutions to the trigonometric equation in the desired interval are given as follows:

[tex]\theta = \frac{\pi}{3}, \theta = \frac{5\pi}{3}[/tex]

The trigonometric equation is given by:

[tex]\sqrt{3}\cot{\theta} - 1 = 0[/tex]

Solving it similarly to an equation, we have that:

[tex]\sqrt{3}\cot{\theta} = 1[/tex]

[tex]\cot{\theta} = \frac{1}{\sqrt{3}}[/tex]

Since [tex]\cot{\theta} = \frac{1}{\tan{\theta}}[/tex], we have that the equation is equivalent to:

[tex]\tan{\theta} = \sqrt{3}[/tex]

The tangent is positive in the first and in the fourth quadrant. In the first quadrant, the angle [tex]\theta[/tex] with [tex]\tan{\theta} = \sqrt{3}[/tex] is:

[tex]\theta = \frac{\pi}{3}[/tex]

In the fourth quadrant, the equivalent angle is:

[tex]\theta = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}[/tex]

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Answer:

[tex]\log_8{(3)} + \log_8{(7)}[/tex]

Step-by-step explanation:

Product Rule for Logarithms

[tex]\log_b{(mn)} = \log_b{(m)} + \log_b{(n)}[/tex]

Instead of 21 you can write 3 · 7, because 21 = 3 · 7.

[tex]\log_8{(21)} = \\= \log_8{(3 \cdot 7)} =\\= \log_8{(3)} + \log_8{(7)}[/tex]

If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.

Given There is a triangle abc.

Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

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Answer:D-E is parallel to FG which is parallel to B-C meaning all three are parallel

Step-by-step explanation:

1. 5:15 = 1/3
scale factor is 1/3going from bigger to smaller

2. 2/8 = 1/4

14 x 1/4 = 3.5

X = 3.5

Answer:

the angles of a triangle always equal 180 so

34+x-5+4y=180

simplify

29+x+4y=180

-29

x+4y=151

-4y

x=-4y+151

then put this into the original equation

29-4y+151+4y=180

simplify

29+151=180

so this proves that this works

-1/4x-151=y

Hope This Helps!!!

∠ROQ and ∠TOS are vertically opposite angles, so must be equal, which means they are 122°

Answer: A=9x^4

Step-by-step explanation:

Hii, do you need to find the area of a square with a side length of 3x^2? Let me help you out! (:

To find the area of a square, you need to square its side length.

Sounds strange, right?

The formula is shown below.

[tex]\LARGE\boldsymbol{A=a^2}[/tex]

Here "A' (capital A) denotes the area

"a" (lower-case a) denotes the side length

The 2 above the a tells us that we need to multiply the side length times itself.

Alright, now it's just a matter of sticking in the known values...

[tex]\sf A=(3x^2)^2[/tex]

Simplify

[tex]\sf A=9x^4[/tex]

Voila! There's our answer, cheers! (;

Hope I helped! Best wishes! (:

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Answer:

B. (4,2)

Step-by-step explanation:

The answer is where the lines intersect.

Hope this helps!

If not, I am sorry.

Answer:

(4,2)

Step-by-step explanation:

the solution is where both lines intersect. We would write the point as (x,y). That’s why the answer is (4,2) not (2,4)

Answer

The answer is A. y = x²

Answer:

c2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the range of y=|x| is not all real numbers its [0,inf)

sign - ...

Zekrom

The inequality is 100*[tex]3^{t}[/tex]≤ 656100.

The correct option is (B).

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

From the table attached below:

a=300, r= 900/300 = 3

As, it is GP

Now,

f(t) = [tex]ar^{t-1}[/tex]

f(t) = [tex]300*3^{t-1}[/tex]

f(t) = 300/3 *[tex]3^{t}[/tex]

f(t) = 100*[tex]3^{t}[/tex]

Inequality is used to determine greater than or equal to 656100

100*[tex]3^{t}[/tex]≤ 656100

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If Bruce can deduct 40% from other interest then the total interest deducted is $2927.

Given Adjusted gross income=$36500, mortgage interest =$2787 and other interest $350.

It is said that 40% of other interest can be deducted by Bruce but it is not said that nothing will be deducted by Bruce from Mortgage interest so we will deduct full of mortgage interest and 40% of other interest. So,

Mortgage interest =$2787

Other interest=$350

Other interest deductable=40%*350

=$140

So the total will be 2787+140 =$2927.

Hence the interest deducted by Bruce is $2927if only 40% of  other interest is deductable.

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Answer:

Should have ended with "at most -15, not "at least -15."

Step-by-step explanation:

[tex]\leq[/tex] -15 means less than or equal to -15

So it can be -15, but also anything less than -15.  The phrase "at most -15, not "at least -15" says exactly that.

Answer:

79°

Step-by-step explanation:

An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.

If the angle is 281° it can go 79° more degrees before getting back to the start.

360° - 281° = 79°

Answer:

c is the answer.

Answer:

x = 3

TU = 35

UV = 35

TV = 70

Step-by-step explanation:

As U is the midpoint of TV:

⇒ TU = UV

⇒ 8x + 11 = 12x - 1

⇒ 8x + 11 - 11 = 12x - 1 - 11

⇒ 8x = 12x - 12

⇒ 8x - 12x = 12x - 12 - 12x

⇒ -4x = -12

⇒ -4x ÷ -4 = -12 ÷ -4

⇒ x = 3

Substitute the found value of x into the expression for TU:

⇒ TU = 8x + 11

⇒ TU = 8(3) + 11

⇒ TU = 24 + 11

⇒ TU = 35

Using the transitive property of equality:

As UV = TU and TU = 15 then UV = 35

Using the segment addition postulate:

⇒ TV = TU + UV

⇒ TV = 35 + 35

⇒ TV = 70

Hence

Step-by-step explanation:

well you can distribute the sqrt(15x) to the (√3x + √5) and then combine the radicals using the product property of radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex].

[tex](\sqrt{3x} + \sqrt{5})\sqrt{15x} + 2\sqrt{30}\\(\sqrt{3x} * \sqrt{15x}) + (\sqrt{5} * \sqrt{15x}) + 2\sqrt{30}\\\sqrt{45x^2} + \sqrt{75x} + 2\sqrt{30}\\[/tex]

Now we can simplify the radicals using the same property we used to combine them but instead of combining into one radical we'll separate them into two radicals where one of the radicals simplifies into a number without a radical

[tex](\sqrt{9} * \sqrt{x^2} * \sqrt{5}) + (\sqrt{25} * \sqrt{3x}) + 2\sqrt{30}\\3x\sqrt{5} + 5\sqrt{3x} + 2\sqrt{30}[/tex]

Answer: Coordinates: (1,3) length RS: 3 length RT: 2 ST: 3.6

Step-by-step explanation:

a^2+b^2=c^2

3^2+2^2=c^2

9+4=c^2

13=c^2

3.6=c

Answer:

24 gallons

Step-by-step explanation:

Since the 2 gallons of gas increased the fill ratio from 1/6 to 1/4, we can find how much of the tank the 2 gallons filled by solving the equation 1/4 - 1/6 = 1/12. This means that each gallon of gas is 1/24th of the tank.

Thus, the tank has a fuel capacity of 24 gallons.

Answer:

24

Step-by-step explanation:

Let x be the total fuel capacity of the tank, in gallons.

Then from the given information

x/6 + 2 = x/4,

Multiplying both sides by 12 to remove the fractions, we get

2x + 24 = 3x so x = 24. 

Therefore, the total fuel capacity of the tank is 24 gallons.

Delete the commas if necessary.

============================================================

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

[tex]n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\[/tex]

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

-----------------------------

To recap, we have...

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.

The expression is 17.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Given:

10+(6-3) 22-4-1

Using the BODMAS rule,

First solve the bracket term

10+ 3 * 22 -4-1

Now, perform multiplication

10+66-4-1

Now, subtraction

10+66-5

=10+61

And lastly addition

=71.

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Answer:

17

Step-by-step explanation:

the answer is 17 :)

Given the polynomial f(x)=x³+5x²+2x-8 and f(1)=0.

Factorization is the process of determining the components of a given value or mathematical statement. The integers that are multiplied to create the original number are known as factors. The components of 18 include, for instance, 2, 3, 6, 9, and 18, as well as;

18 = 2 x 9

18 = 2 x 3 x 3

18 = 3 x 6

In a similar way, the factors in the case of polynomials are the polynomials that are multiplied to create the original polynomial. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3. We can also locate the polynomials' zeros after factorization. Zeroes in this situation are x = -2 and x = -3.

2. Now, to write f(x) as the product of (x-1) and another factor.

x³+5x²+2x-8 = (x-1)(x²-6x+8).

3. Now, to write f(x) as the product of three linear factors.

x³+5x²+2x-8 = (x-1)(x²-6x+8)= (x-1)(x-4)(x-2)

4. Look at the sketch below.

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as the following pic you can see the answer.

#diameter is 8 so radius is 4