Answer:
The correct answer is :
statistical inference
Step-by-step explanation:
statistical inference is the process of making scientific conclusions and stating truths about parameter on a larger population from existing data gotten from a sample of the population. In this example, only 250 women were sampled, out of the larger total population of the women in the zip code, and due to the data from the findings from these 250 women, a conclusion was drawn that held true for all the women in the zip code. Inference is made based on the laws of probability that allows conclusion to be made on a population from random sampling.
There are different approaches of statistical inference, and these include:
1. Bayesian estimation: here, conclusions are made based on a combination of prior judgments (based on previous studies) and new observations from experimental results.
2. Likelihood approach: here, prior probability results are disregarded and not used, instead, well-understood and advantageous properties of the parameter are used to draw conclusion.
The instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
<h3>What is the instantaneous rate of change of the function at the given point?</h3>
The instantaneous rate of change is simply the change in the derivative value at a specific point.
Given the data in the question;
- f(x) = −4x² − 3x + 1
- Point x = -3
To determine the instantaneous rate of change of the function, first find the derivative of the function.
f(x) = −4x² − 3x + 1
Applying sum rule, with respect to x
d/dx[ -4x² ] + d/dx[ -3x ] + d/dx[ 1 ]
[ 2 × -4x¹ ] + [ 1 × -3x⁰ ] + d/dx[ 1 ]
[ -8x ] + [ -3 ] + d/dx[ 1 ]
-8x - 3 + d/dx[ 1 ]
Differentiate using constant rule
-8x - 3 + [ 0 ]
-8x - 3
f'(x) = -8x - 3
Next, plug x = -3 into the derivative and simplify.
f'(x) = -8x - 3
f'(-3) = -8(-3) - 3
f'(-3) = 24 - 3
f'(-3) = 21
Therefore, the instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
Learn more about instantaneous rate of change here: brainly.com/question/28122560
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The product of the matrices is an identity matrix. Therefore, X and A are inverse of each other.
The matrices are given as:
![X = \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right]](https://tex.z-dn.net/?f=X%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26-3%5C%5C4%262%5Cend%7Barray%7D%5Cright%5D)
![A = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%2015%26%5Cfrac%203%7B10%7D%5C%5C-%5Cfrac%2025%20%26-%5Cfrac%201%7B10%7D%5Cend%7Barray%7D%5Cright%5D)
To check the matrices are inverse, we calculate their products.
![A \times X = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right] \times \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right]](https://tex.z-dn.net/?f=A%20%5Ctimes%20X%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%2015%26%5Cfrac%203%7B10%7D%5C%5C-%5Cfrac%2025%20%26-%5Cfrac%201%7B10%7D%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26-3%5C%5C4%262%5Cend%7Barray%7D%5Cright%5D)
Multiply the rows of A by the column of X.
This gives
![A \times X = \left[\begin{array}{cc}\frac 15 \times -1 + \frac{3}{10} \times 4&\frac 15 \times -3 + \frac{3}{10} \times 2\\ -\frac 25 \times -1 - \frac{1}{10} \times 4&-\frac 25 \times -3 + -\frac{1}{10} \times 2\end{array}\right]](https://tex.z-dn.net/?f=A%20%5Ctimes%20X%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%2015%20%5Ctimes%20-1%20%2B%20%5Cfrac%7B3%7D%7B10%7D%20%5Ctimes%204%26%5Cfrac%2015%20%5Ctimes%20-3%20%2B%20%5Cfrac%7B3%7D%7B10%7D%20%5Ctimes%202%5C%5C%20-%5Cfrac%2025%20%5Ctimes%20-1%20-%20%5Cfrac%7B1%7D%7B10%7D%20%5Ctimes%204%26-%5Cfrac%2025%20%5Ctimes%20-3%20%2B%20-%5Cfrac%7B1%7D%7B10%7D%20%5Ctimes%202%5Cend%7Barray%7D%5Cright%5D)
![A \times X = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=A%20%5Ctimes%20X%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The product of A and X is an identity matrix.
This means that; both matrix are inverse of each other
Read more about matrix at:
brainly.com/question/4017205
Answer:
There are 48 cups in 3 gallons!
Hope this helped! :)
3:1 =300%
2:3:5 =50%
1:4 =25%
1:2:5 =62.5%
