The system of equations can be solved using linear combination to eliminate one of the variables.2x − y = −4→10x − 5y = −203x +

The sum of 15% of corn and 12% of beans totals 27%

To find 27% of 360, calculate 360 * 0.27
The result is 97.2
Rounded, this is 97.

Answer:

0.24

Explanatory steps:

These events can occur simultaneously, indicating they are not mutually exclusive.

For events A and B where mutual exclusivity does not apply,

P(A and B) = P(A) * P(B|A)

Let A represent the event of being "over 21 years old" and B represent the event of "consuming alcohol."

The likelihood of a student being over 21 years is 0.3, reflecting that 30% of the students are in that age range.

The probability that a student consumes alcohol given they are over 21 stands at 0.8.

This results in

P(A and B) = 0.3(0.8) = 0.24

Answer:

a) In this case, we have a z-score of 1.57, characterized as:

This signifies that our score is 1.57 standard deviations above the average of all test scores.

b)

Using the normal standard distribution or Excel, we computed:

This represents 2.275% of the dataset.

Step-by-step explanation:

Previous concepts

Normal distribution denotes a "probability distribution that is symmetric around the mean, indicating that data close to the mean occurs more frequently than data further from it".

The Z-score serves as "a statistical measurement representing a value's relation to the average (mean) of a set, calculated in terms of standard deviations away from the mean".

Solution to the problem

Part a

For this instance, we hold a z-score of 1.57, which is defined as:

This shows that our score is 1.57 deviations above the overall test score average.

Part b

A z-score of z=-2 indicates that your friend's score is 2 deviations below the other test scores.

Assuming a normal distribution, we can derive the percentage:

Using the normal standard distribution or Excel, we discovered:

This represents 2.275% of the data.

Step-by-step explanation:

The difference quotient represents the slope of the line connecting two points on a curve. To achieve the most accurate estimate, we need to use points that are nearest to x = 0. For this problem, the relevant points are (-0.001, 1.999) and (0.001, 2.001).

m = (2.001 − 1.999) / (0.001 − (-0.001))

m = 1

To determine the values of b that fulfill 3(2b+3)^2 = 36

we start with
3(2b+3)^2 = 36
Divide both sides by 3
(2b+3)^2 = 12
Next, take the square root of both sides
(2b+3)} = (+ /-) \sqrt{12} \\ 2b=(+ /-) \sqrt{12}-3

b1=\frac{\sqrt{12}}{2} -\frac{3}{2}
b1=\sqrt{3} -\frac{3}{2}

b2=\frac{-\sqrt{12}}{2} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}
Thus,

the solutions for b are
b1=\sqrt{3} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}