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qaws [65]
3 years ago
10

The histogram shows the scores of each participant in a game for a total of 100 participants. What is the ratio of participants

who score 80 to 99 to the total number of participants? 17 participants scored 80-99
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0
10/002728182.2777272829 error
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Find the 2th term of the expansion of (a-b)^4.​
vladimir1956 [14]

The second term of the expansion is -4a^3b.

Solution:

Given expression:

(a-b)^4

To find the second term of the expansion.

(a-b)^4

Using Binomial theorem,

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here, a = a and b = –b

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

Substitute i = 0, we get

$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4

Substitute i = 1, we get

$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b

Substitute i = 2, we get

$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}

Substitute i = 3, we get

$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}

Substitute i = 4, we get

$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}

Therefore,

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}

Hence the second term of the expansion is -4a^3b.

3 0
3 years ago
7. Virus growth is an example of which type of function?
Karolina [17]

Answer:

Since many viruses can infect a large number of different cell types, ... An example is potato yellow dwarf virus, which can grow in leafhoppers

5 0
3 years ago
Solve(100 points to right answer)If you get it wrong or type random stuff you will be reported
anygoal [31]

Answer:

24 ft

Step-by-step explanation:

Hypotenuse = √9²+16²=√81+256=√400=20ft

the upper side of the stuff = 4 ft

total = 20+4=24

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3 years ago
What is the rate of change when the input is 9 and the output is also 9
Damm [24]
0 right? It's not changing at all.
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What is completely factored form of x^4+8x^2-9
olganol [36]
X^4 + 8x^2 - 9 
= (x^2 + 9)(x^2 - 1)
= (x^2 + 9)(x + 1)(x - 1)  Answer
4 0
3 years ago
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