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zvonat [6]
3 years ago
14

Suppose you have 60 red marbles and 40 blue marbles in a

Mathematics
1 answer:
andrew-mc [135]3 years ago
6 0

Answer:  The required probability is 0.26.

Step-by-step explanation: Given that there are 60 red marbles and 40 blue marbles in a  box 10 marbles are picked without replacement.

We are to find the probability of selecting 6 red marbles.

Since the marbles are picked up without replacement, so it is a situation of combination.

Let S denote the sample space of the experiment of drawing 10 marbles and E denote the event that 6 marbles are red.

So,

n(S)=^{100}C_{10}=\dfrac{100!}{10!(100-10)!}=\dfrac{100!}{10!90!}=17310309456440,\\\\\\n(E)=^{60}C_6\times^{40}C_4=\dfrac{60!}{6!54!}\times\dfrac{40!}{4!36!}=50063860\times91390.

Therefore, the probability of event E is given by

P(E)=\dfrac{n(E)}{n(S)}=\dfrac{50063860\times91390}{17310309456440}=0.26.

Thus, the required probability is 0.26.

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A cone with volume 246 ft cubic if the height is 15 find the radius
Liula [17]

Answer:

r = 3.95 ft

Step-by-step explanation:

Volume of cone = \frac{1}{3} \pi r^{2} h = 246 ft³

246 = \frac{1}{3} * \frac{22}{7} * r^2 * 15

r² = \frac{246*3*7}{22*15*5}

r = \sqrt{15.65}

r = 3.95 ft

8 0
2 years ago
The functions f(x) and g(x) are described below: f(x) = 7x + 9 g(x) = 7x −4 The graph of g(x) is obtained by shifting down the g
Slav-nsk [51]
Correct Answer:
Option A

Solution:

f(x) = 7x + 9
g(x) = 7x - 4

We can re-write g(x) as:

g(x) = 7x + 9 - 13

Since 7x+9 is equal to f(x), we can write:

g(x) = f(x) - 13

This relation shows that g(x) is obtained by shifting f(x) 13 units vertically down. So the correct answer is option A.
6 0
3 years ago
The slopes of perpendicular lines are
romanna [79]

Answer:

A. Negative reciprocals

7 0
2 years ago
Simplify -3x³y²(-4x²y•y•y•y•y)²
AnnZ [28]

-3x^3y^2(-4x^2 \underbrace{y\cdot y\cdot y\cdot y}_{y^4})^2\\\\=(-3)(-4)(x^3x^2)(y^2y^4)\\\\=12x^{3+2}y^{2+4}\\\\=\boxed{12x^5y^6}\\\\Used:\\\\a^n\cdot a^m=a^{n+m}

3 0
3 years ago
Read 2 more answers
Solve the exponential equation for x<br> 3^7x+4=(1/27)^x-3
velikii [3]

Answer:

The solution is x = \frac{1}{2}

Step-by-step explanation:

To solve this exponential equation, we must write both sides as powers of 3.

The equation given is:

3^{7x + 4} = (\frac{1}{27})^{x-3}

Since 3^3 = 27, we have that 3^{-3} = \frac{1}{3^3} = \frac{1}{27}, so\frac{1}{27} = 3^{-3}

Then

3^{7x + 4} = (\frac{1}{27})^{x-3}

3^{7x + 4} = (3^{-3})^{x-3}

3^{7x + 4} = 3^{-3(x-3)}

3^{7x + 4} = 3^{-3x + 9}

Since both sides are now powers of 3, we can equal them:

7x + 4 = -3x + 9

10x = 5

x = \frac{5}{10}

x = \frac{1}{2}

The solution is x = \frac{1}{2}

6 0
3 years ago
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