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SCORPION-xisa [38]
3 years ago
5

Thuy rolls a number cube 7 times. which expression represents the probability of rolling a 4 exactly 2 times?

Mathematics
2 answers:
Nady [450]3 years ago
6 0
The result of rolling a number cube 7 times is a 7-digit number composed of digits 1,2,3,4,5 and 6 so that digits can repeat. The total number of possibilities is 6^7.

The number of possibilities where 4 appears exactly two times is 5^5*(7!-6!/2).
 5^5 is the number of 5-digits numbers composed of digits 1,2,3,5 and 6 so that digits can repeat.
7! is the number of permutations of digits 1,2,3,4,4,5 and 6.
6! is the number of permutations of digits 1,2,3,{4,4},5 and 6.
We don't want to subtract all numbers where digits 4 appear side by side. That's why we must divide 6! by 2.

Finally, the probability is P=5^5(7!-6!/2)/7^7
mel-nik [20]3 years ago
5 0

Answer:

The answer is C I just took the test!!!!!!!

Step-by-step explanation:


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The equation y−5=−2(x−3) is in point-slope form. Which shows this equation in slope-intercept form?
MAXImum [283]

y - 5 = -2(x - 3)

Distribute -2.


y - 5 = -2x + 6

Add 5 to both sides.


y = -2x + 11

B) y = -2x + 11

4 0
3 years ago
Find the approximate area of a triangle that has vertices at A(-4,2),B(6,4)C(3,-1)
MrMuchimi

area \: of \: triangle \:  =  \frac{1}{2}  |( - 16) - (22)|
=  \frac{1}{2}  | - 44|
= | - 22|
area \: of \: triangle \:  = 22
6 0
3 years ago
Mr eliot is extremely careful with his money. He recently invested part of his $150,000 life savings in gold bullion and the res
DIA [1.3K]

Answer:

The amount invested in gold bullion by Mr. Eliot  =   $50,000

Step-by-step explanation:

Total amount of savings Me. Eliot ha s = $150,000

Let us assume the amount invested in gold bullion = $m

So, the amount invested in bank = $150,000 - m

Now, 5% on m = \frac{5}{100}  \times m = 0.05 m

So, the profit in gold bullion  =  0.05 m

and 3% on (150,000 -m)   = \frac{3}{100}  \times  (150,000 -m) = 0.03  (150,000 -m)

= 4,500 - 0.03 m

So, the profit in bank =  4,500 - 0.03 m

Now,  the total profit  = $5,500

⇒Profit from gold bullion + ban = $5,500

⇒0.05 m +  4,500 - 0.03 m = $5,500

or, 0.02 m = 1000

⇒ m = 1000/0.02 = 50,000

Hence, the amount invested in gold bullion  =  m = $50,000

3 0
3 years ago
In a triangle ABC, measure of angle B is 90 degrees. AB is 3x-2 units and BC is x+3. If the area of the triangle is 17 sq cm, fo
Scorpion4ik [409]

Answer:

x=\frac{8}{3}\ cm

Step-by-step explanation:

we know that

The area of the right triangle ABC is equal to

A=\frac{1}{2}(AB)(BC)

we have

A=17\ cm^2

AB=(3x-2)\ cm

BC=(x+3)\ cm

substitute the values

17=\frac{1}{2}(3x-2)(x+3)

34=(3x-2)(x+3)

34=3x^2+9x-2x-6

3x^2+7x-6-34=0

3x^2+7x-40=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

3x^2+7x-40=0

so

a=3\\b=7\\c=-40

substitute in the formula

x=\frac{-7(+/-)\sqrt{7^{2}-4(3)(-40)}} {2(3)}

x=\frac{-7(+/-)\sqrt{529}} {6}

x=\frac{-7(+/-)23} {6}

x=\frac{-7(+)23} {6}=\frac{16}{6}=\frac{8}{3}

x=\frac{-7(-)23} {6}=-5

therefore

The solution is

x=\frac{8}{3}\ cm

6 0
3 years ago
What transformation was not done to the linear parent function, f(x) = x, to
Butoxors [25]

Answer:

C.

Step-by-step explanation:

The function shifted <em>left</em> five units instead of <em>right</em> five units.

There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.

7 0
2 years ago
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