Answer:
a) 8*88*10⁻⁶ ( 0.00088 %)
b) 0.2137 (21.37%)
Step-by-step explanation:
if the test contains 25 questions and each questions is independent of the others, then the random variable X= answer "x" questions correctly , has a binomial probability distribution. Then
P(X=x)= n!/((n-x)!*x!)*p^x*(1-p)^(n-x)
where
n= total number of questions= 25
p= probability of getting a question right = 1/4
then
a) P(x=n) = p^n = (1/4)²⁵ = 8*88*10⁻⁶ ( 0.00088 %)
b) P(x<5)= F(5)
where F(x) is the cumulative binomial probability distribution- Then from tables
P(x<5)= F(5)= 0.2137 (21.37%)
The equation for which square method is possible is x²-8=1
Step-by-step explanation:
For checking which of the equation satisfies the complete square condition, we proceed by checking each of the available options
1). x²+20x=52
Rewriting it as x²+20x-52
This binomial expression is not a perfect square since the product of the coefficient of x²(i.e. 1) and independent constant (i.e. 52) is not a perfect square.
2). 5x² + 3x = 9
This equation can be rearranged as 5x²+3x-9=0
This binomial expression is not a perfect square since the product of the coefficient of x²(i.e. 5) and independent constant(i.e. 9) is not a perfect square.
3.) x² −8=1
This equation can be rearranged as x²=9
Hence x= ±3
This binomial expression is a perfect square and can be done by the square method.
4). 3x² −x+17=0
This binomial expression is not a perfect square since the product of the coefficient of x²(i.e. 3) and independent constant(i.e. 17) is not a perfect square.
Answer:
Step-by-step explanation:
The Caucasus Mountains
Answer:
The first term is 3. The common difference is 2.
Step-by-step explanation:
The first term is x.
The common difference is d.
The second term is x + d.
3rd term: x + 2d
4th term: x + 3d
7th term: x + 6d
"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"
x + 3d = 3 * x Eq. 1
"the seventh term exceeds twice the third term by 1"
x + 6d = 2(x + 2d) + 1 Eq. 2
Simplify Eq. 1:
2x = 3d
Simplify Eq. 2:
x + 6d = 2x + 4d + 1
x = 2d - 1
Multiply both sides of the last equation by 2.
2x = 4d - 2
2x = 3d (simplified Eq. 1)
Since 2x = 2x, then the right sides are equal.
3d = 4d - 2
d = 2
2x = 3d
2x = 3(2)
2x = 6
x = 3
Answer: The first term is 3. The common difference is 2.
