you deposit $3000 into a bank account that pays 1.25% annual interest, compounded semi-annually. how much interest does the account earn after 4 years?

Final answer:

The limit of a function as x approaches negative infinity is the value that the function f(x) approaches as x becomes very large in the negative direction. For example, the limit of 1/x is 0 as x approaches negative infinity, while the limit of 1/x² approaches positive infinity. Functions that oscillate, like sin(\u03C0/x), do not have a limit at infinity.

Explanation:

When discussing the limit of a function f(x) as x approaches negative infinity, we are essentially asking what value f(x) gets closer to as x becomes very large and negative. For instance, consider the function 1/x. As x approaches negative infinity, 1/x gets closer to 0, and we say that the limit of 1/x as x approaches negative infinity is 0. Similarly, for a function like 1/x² which "blows up" or increases rapidly as x approaches 0 from either side, we notice that as x approaches negative infinity, the function approaches positive infinity since the squared term always results in a positive number.

However, not all functions have limits at infinity. For functions that oscillate, such as sin(\u03C0/x), as x approaches 0, it oscillates indefinitely between -1 and +1 and does not approach a specific value.

The formal definition of a limit at infinity states: If there is a number L such that f(x) gets arbitrarily close to L when x is sufficiently large (positively or negatively), we write lim f(x) = L as x → -∞.

The introduction paragraph should start with an opening statement introducing your chosen topic and providing some context, followed by your thesis statement that clearly states your argument. The given example shows how to create an introduction paragraph for an argument on 'Climate Change'.

In order to write the introduction paragraph for your argument, first remember your chosen topic from lesson 6.02. Your opening statement must introduce the topic and provide some general context about it. For instance, if your topic is 'Climate Change', then your introductory paragraph might start like this:

'In today's rapidly changing world, one issue that stands in prominence is climate change. During the last century, human activities have accelerated this process unnaturally, leading to unpredictable weather and extreme disasters.'

Then present your thesis statement that clearly expresses your stance on the issue. It could be something like:

'This essay aims to argue that proactive international cooperation is crucial in mitigating the detrimental effects of climate change.'

Make sure this paragraph is captivating and clear as it sets the tone for the rest of your essay.

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The probability that a household does not have a cat, given that it doesn't have a dog is 70%. This is a question about conditional probability, and can be solved by applying Bayes theorem and the concept of complements in probability.

Given the question, we need to calculate the probability that a household does not have a cat if it is known that the same household does not have a dog. This question applies to the concept of conditional probability in mathematics.

Let's consider the event of a household having at least one cat as C and the event of a household having at least one dog as D. The question tells us that the probability of a household having a dog given it has a cat P(D|C) = 0.30 and the probability of a household having a cat P(C) = 0.30, and the probability of having a dog P(D) = 0.33. We are asked to find the probability of a house not having a cat given it does not have a dog, P(C'|D').

Using Bayes theorem, the conditional probability P(C'|D') can be calculated using the formula: P(C' | D') = P(D' | C') * P(C') / P(D'), where P(C') is the probability of not having a cat and P(D'| C') is the probability of not having a dog given that there is no cat.

First, find the complement percentages. P(C') = 1 - P(C) = 0.70 and P(D') = 1 - P(D) = 0.67. Then, because P(D'| C') = P(D') (as having a dog does not depend on whether or not you have a cat), the formula simplifies to: P(C' | D') = P(C'). So the probability that a household does not have a cat, given that it doesn't have a dog is 0.70 or 70%.

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Answer:

16 = z - 9

Step-by-step explanation:

I did the same problem and answered this, 16 = z - 9. It was correct.

Answer:

4) 0.37

Step-by-step explanation:

If the principal randomly selects a student in grade 10 from this survey, the probability that the student is opposed to extending the school day is a division of the number of students that opposed from 10 Grade by the total number of students of the 10 Grade.

The table of the question is as:

Grade   In favor  Opposed  Undecided

9             6               4               8

10             10              11               9

11            12              15              11

12             15               6              14

So, there are 10 students in 10 grade that are in favor of the extended school day, 11 students that are Opposed and 9 students that are undecided about the extended school day. then, there are 30 student in 10 Grade

Then, the probability is:

[tex]\frac{11}{10+11+9} =\frac{11}{30}=0.37[/tex]

The correct answer for this completion exercise shown above is the second option (Option B), which is: B. Parent

 Therefore, you have:"In each family of function, the parent function is the most basic function in the family"

 By definition, the most basic fucntion in each family of functions is called “parent fucntion”. A family of function is a set of function that when you graph them, you can notice that they have common charateristics.

Answer: 0.6

Step-by-step explanation:

The fractions have the form shown below:

[tex]\frac{a}{b}[/tex]

Where: a is the numerator and b is the denominator.

To convert a fraction to a decimal number, you must divide the numerator by the denominator.

You know that the fraction is three-fifths, which is written as following:

[tex]\frac{3}{5}[/tex]

Therefore, when you divide the numerator 3 by the denominator 5, you obtain the following decimal number which is equivalent to that fraction:

 [tex]\frac{3}{5}=0.6[/tex]

Answer:

0.6

Step-by-step explanation:

the answer to your question

is the letter  C

Let's explore the equation to see why the graph of the formula that is given sounds like:

((x−5)²/(4)²) + (y²/(7)²) = 1

This equation represents the standard form of an ellipse:

((x−h)²/a²) + ((y-k)²/(b)²) = 1

Where:

*The ellipse's center is (h,k).

*The semi-major axis's length, or horizontal radius, is denoted by a.

*The semi-minor axis's length, or vertical radius, is b.

Comparing the given equation to the standard form, we see that:

*h=5 (center is at x=5)

*a=4 (semi-major axis length)

*b=7 (semi-minor axis length)

Since both a and b are positive and the denominators of both terms are squared, the graph represents an ellipse. Therefore, the correct answer is F. An ellipse.

The given equation is in the form of an ellipse:

((x−5)²/(4)²) + (y²/(7)²) = 1

It matches the standard form of an ellipse equation:

((x−h)²/a²) + ((y-k)²/(b)²) = 1

where (h,k) is the center of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes, respectively.

In this equation, h=5, a=4, and b=7, indicating the ellipse is centered at (5,0) with a horizontal radius of 4 and a vertical radius of 7.

Therefore, the correct answer is F. An ellipse.

Complete Question:

What shape is the graph of the equation below?

A. A line

B. A circle

C. A parabola opening to the right

D. A hyperbola opening to the right and left

E. A hyperbola opening up and down

F. An ellipse

A mathematical expression that compares one number to another is called a ratio or proportion, which includes concepts such as inequalities and proportional relationships.

A mathematical expression that compares one number to another is called a ratio or proportion. Ratios express the relationship between two quantities, while a proportion indicates that two ratios are equivalent. For example, the expression 1/2 = 3/6 signifies a proportion because the two ratios 1/2 and 3/6 are equivalent. A unit rate is a specific kind of ratio where one of the measurements is 1, such as 55 miles per hour (55/1 miles/hour). Additionally, there are other mathematical expressions used for comparison, such as inequalities, which show how two values differ, or the concept that one value 'x' is proportional to another, often used in scientific and engineering contexts.

Answer:

Susan is 13 years old.

Step-by-step explanation:

Susan=x

After 7 years she will be 7+x  then she will be 2x as old as she was 3 year ago.

age 3 yrs ago=x-3

2x-6=7+x

if you simplify....

now she is 13

hope it helps!!!!

Answer:

The recursive rule is an = (-4) · an-1

Step-by-step explanation:

* Lets explain recursive formula for a geometric sequence:

1. Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)

2. Find the common ratio. (The number you multiply or divide.)

3. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.

# a1 = first term;

# an= r • an-1

- Where:

 a1 = the first term in the sequence

 an = the nth term in the sequence

 an-1 = the term before the nth term  

 n = the term number

 r = the common ratio

Ex: {3, 6, 12, 24, 48, 96, ...}

first term = 3, common ratio = 2

The recursive formula  an = 2 · an-1

* In our problem:

- a1 = 4

- r = -16/4 = -4

- The recursive rule is

# an = (-4) · an-1

Answer:

here is the correct answer.

Step-by-step explanation: