Answer:
1/6 of the vegetables space will be used for the tomatoes
Answer:
1/12 of the Garden
Step-by-step explanation:
When adding fractions, the denominators need to be the exact same number. Therefore, you need to find the LCM. The LCM of 3 and 4 is 12, so all the denominators will be 12.
2/3 * 4/4 = 8/12
1/4 * 3/3 = 3/12
8/12 + 3/12 = 11/12
Now you need to subtract it from 1 (the garden).
12/12 - 11/12 = 1/12
Answer:
Step-by-step explanation:
Given that the total number of sample pills is 200
ie., n=200
Let us assume it success if a pill is ineffective.
The probability of success in each trial is
∴ p=0.05
We know that the total probability is p+q=1
The probability of failure is q
q=1-p
q=1-0.05
∴ q=0.95
Let X be the random variable of the number of ineffective pills in a sample of 200 pills.
Hence X has Binomial distribution with parameter n=200 and p=0.05
The formula for Mean in Binomial distribution is
Substitute the values in the above formula we get
∴
The formula for Standard deviation in Binomial distribution is
Substitute the values in the above formula we get
∴
Now we have to find the probability that fewer than 10 in a sample of 200 pills will be ineffective.
That is to find the area to the left of x=9.5
The formula is
Substitute the values in the formula we get
∴
Now P(X<10)=P(Z<-0.16)
=0.4364
The probability that fewer than 10 out of 200 birth-control pills will be ineffective is approximately 0.817, or 81.7%.
Probability is a mathematical concept used to quantify the likelihood of an event occurring. It ranges from 0 (impossible) to 1 (certain). It plays a crucial role in statistics and decision-making, helping to predict outcomes, assess risk, and make informed choices. To find the probability that fewer than 10 in a sample of 200 birth-control pills will be ineffective, we can use the binomial probability formula:
P(X < 10) = Σ (n choose k) * p^k * (1-p)^(n-k), where:
n = sample size = 200,
k = number of ineffective pills,
p = probability of a pill being ineffective = 0.05.
Calculating this probability using the formula, we get:
P(X < 10) ≈ 0.817, or 81.7%.
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3x+2y=14
2x-4y=4
6x+4y=28
2x-4y=4
8x = 32
x = 4
2y = 14 - 12 = 2
y = 1
(x , y) = (4 , 1)
Question:How can check your solution by writing the system as a matrix equation and using the inverse matrix?.
To check the solution, represent the system of equations as a matrix equation, find the inverse of the coefficient matrix, and multiply both sides of the equation by the inverse.
To check the solution by writing the system as a matrix equation and using the inverse matrix, we need to represent the system of equations as a matrix equation. Let's consider the given system of equations:
3x + 2y = 14
2x - 4y = 4
To do this, we can write the coefficients and constants of the system of equations as matrices:
[3 2] [x] = [14]
[2 -4] [y] = [4]
Now, we can write the system of equations as a matrix equation: AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
Next, we need to find the inverse of matrix A. If the inverse exists, we can multiply both sides of the matrix equation by the inverse of A to find the solution for X.
If we find the inverse of A and multiply both sides of the equation by the inverse, we get:
X = A-1B
Substituting the values of A-1 and B, we can find X, which represents the solution to the system of equations. Therefore, we can check our solution by writing the system as a matrix equation and using the inverse matrix.
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