What is the gcf of 108 and 132

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:

Answer:

0.835 mg of a 2.000-mg sample remains after 6.55 years.

Step-by-step explanation:

We are given that The half-life of cobalt-60 is 5.20 yr.

Formula of half life : [tex]N(t) = N(0)e^{\frac{-0.693t}{t\frac{1}{2}}}[/tex]

Where N(0) = Initial amount

N(t) = Quantity remaining after time

t = time

[tex]\frac{t}{2} =\text{half life}[/tex]

So, N(0) = Initial amount = 2 mg

t = time = 6.55 years

[tex]\frac{t}{2} =\text{half life} = 5.20 yr [/tex]

Substitute the values in the formula

Therefore,

[tex]N(t) = 2 e^{\frac{-0.693 \times 6.55}{5.20}}[/tex]

[tex]N(t) =0.835[/tex]

Hence 0.835 mg of a 2.000-mg sample remains after 6.55 years.

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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To find out how much sand is in each dump truck when they are the same weight, we can set up an equation based on the given information. Let's assume that the amount of sand in the first truck is x tons. We can then find the value of t that makes the weight of both trucks the same and substitute it into the equation to find x.

To find out how much sand is in each dump truck when they are the same weight, we can set up an equation based on the given information.

Let's assume that the amount of sand in the first truck is x tons. Since the conveyor belt pours sand into the truck at a constant rate of 1/4 ton per minute, the weight of the sand will increase by (1/4) * t tons, where t is the time in minutes.

Similarly, the second truck is being emptied at a rate of 1/8 ton per minute. So, the weight of sand in the second truck will decrease by (1/8) * t tons.

We know that the dump truck weighs 11.25 tons initially and 18 tons when filled. Therefore, we can set up the equation:

11.25 + (1/4) * t - (1/8) * t = 18 - x

Simplifying the equation:

(1/4) * t - (1/8) * t = 18 - 11.25 - x

(1/8) * t = 6.75 - x

t = 6.75 * 8 - 8x

Now, we need to find the value of t that makes the weight of both trucks the same. Let's substitute that value into the equation to find x.

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: The answer is: 6

Step-by-step explanation: I have my ways ;>

Have a nice day!

-Sunny

Hello There!

To multiply fractions, you first want to line up the numerator and the denominator together so they line up with each other.

Next, you want to multiply across. This includes multiplying the numerators together and then multiplying the denominators together.

Finally, you want to find the greatest common factor but only if the fraction can be simplified.

That Is How To Multiply Fractions

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 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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Answer: $103.67

Step-by-step explanation:

Based on the given conditions, formulate: 147 x (8.5% + 1) x (1 - 35%)

Calculate the sum or difference: 147 x 1.085 x (1 - 0.35)

Calculate the sum or difference: 147 x 1.085 x 0.65

Calculate the product or quotient: 159.495 x 0.65

Calculate the product or quotient: 103.67175

Round: 103.67

Answer: $103.67