What is the equation for this graph? Use y=mx+b

Answer:

Increasing: (2, ∞) Decreasing: (-∞,2)

Step-by-step explanation:

Think of the parabola (just for visualization purposes) as the direction of a rubber ball being thrown from above. The ball starts to decrease in position, eventually hitting the ground, and then starts to increase back to the orginal height and beyond.

So, because parabolas extend infinitely in both the positive and negative direction, we can use intervals to express the parts of the graph where it increases and decreased.

The minimum value point, or vertex is the point where the parabola changes direction. The vertex is visibly at (2,-4). So, the interval for decreasing would be (-∞,2) and increasing would be (2,∞)

Note: We use the symbol "[" to indicate that a value is included in the interval.

Because infinity is a concept and not a number, we have to use the non-inclusive version of it: "(" (simple parentheses) to indicate that infinity is NOT included in the interval, but it simply keeps extending in both directions.

I hope this helps you out.

Answer:

95.02% of squirrels have a weight between 3 and 5 pounds.

Step-by-step explanation:

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.1 pounds

Standard Deviation, σ = 0.5 pounds

We are given that the distribution of weight is a bell shaped distribution that is a normal distribution.

Formula:

P(weight between 3 and 5 pounds)

95.02% of squirrels have a weight between 3 and 5 pounds.

Final answer:

Using the concepts of normal distribution and Z-scores, it is found that approximately 95% of the squirrels have weights between 3 and 5 pounds.

Explanation:

The problem involves the use of the concept of normal distribution in statistics. In this case, we have a mean of 4.1 pounds and a standard deviation of 0.5 pounds. We have two weight points, namely 3 pounds and 5 pounds. To find out the percentage in this interval, we need to convert the weights into z-scores, which standardizes them. The formula for this is Z = (X - μ) / σ, where X is the weight point, μ is the mean, and σ is the standard deviation.

The Z-score for 3 pounds is Z1 = (3 - 4.1) / 0.5 = -2.2, and the Z-score for 5 pounds is Z2 = (5 - 4.1) / 0.5 = 1.8. Looking these Z-scores up in the standard normal table (or using a calculator with a normal distribution function), we get 0.9857 for Z1 and 0.9641 for Z2. The difference between these values gives the percentage of squirrels within the interval, which is 0.9641 - (1 - 0.9857) = 0.950 or 95%. Hence, approximately 95% of the squirrels have a weight between 3 and 5 pounds.

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The correct option is polygon E.

What are polygons?

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given that, Which polygons have at least one pair of parallel sides but are not parallelograms,

Such polygons are called trapezoid.

A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.

Hence, the correct polygon is E.

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Final answer:

The numbers 8 and 400 have different orders of magnitude. They also possess a ratio relationship, with 400 being 50 times bigger than 8. While not directly related through square and square root, both numbers share these relationships with other numbers.

Explanation:

The relationship between the values 8 and 400 can be understood through the concept of order of magnitude in mathematics. The order of magnitude is a rough measure of the size of a number, typically based on powers of 10.

An important factor in analyzing this relationship is understanding the concept of ratio and interval level data. Unlike interval level data, the ratio between the numbers, in this case 8 and 400, carries meaningful information in a ratio scale data. In this case, 400 is 50 times bigger than 8.

Another mathematical relationship between 8 and 400 is square and square root, since 400 is the square of 20, and 8 is the square root of 64. So, although there is no direct square or square root relationship between 8 and 400, they share these relationships with other numbers.

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Answer:

They both come in the 8 times table.

Answer: True

Step-by-step explanation:

Let p= Students who do well in course do not skip class

q= Student who study hard do well in course

So p^q= Student who study hard and who do well in course do not skip class.

If p= true and q=true then p^q= true by discrete maths.

The argument is valid because the conclusion is logically derived from the provided premises. However, it is important to note that the validity of an argument does not guarantee the truth of its premises. The argument may be valid, but its premises could still be false.

The argument provided is valid.

The reasoning follows a valid logicalstructure, specifically a form of argument called a syllogism, where conclusions are drawn from two or more premises. Let's break it down:

"For students to do well in a discrete mathematics course, it is necessary that they study hard." This is a premise, stating that studying hard is a necessary condition for success in a discrete mathematics course.

"Students who do well in courses do not skip classes." This is another premise, suggesting that students who perform well in their courses do not miss classes.

"Students who study hard do well in courses." This is also a premise, indicating that diligent study leads to success in courses.

The conclusion drawn is: "Therefore students who do well in a discrete mathematics course do not skip class." This conclusion logically follows from the given premises. If we accept the truth of the premises, we must also accept the truth of the conclusion.

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Answer:

x-intercept = 10

y-intercept = -8

Step-by-step explanation:

To identify the y-intercept, we will need to format the equation in the form . We can start by subtracting from both sides of the equation:

Divide both sides of the equation by the coefficient of , which is :

The is representative of the y-intercept in .

Identify in the equation :

Therefore, our y-intercept is -8.

To solve for the x-intercept, replace the in the equation with a zero:

Add to both sides of the equation:

You can go ahead and divide by to get rid of the fraction:

Divide both sides of the equation by the coefficient of , which is :

Therefore, our x-intercept is 10.