After modelling the mathematical statement and solving its equivalent mathematical relation, we get x = -36.
<h3>What is Equation Modelling?</h3>
Equation modelling is the process of writing a given mathematical statement in the form of a numeric mathematical expression taking into considerations the operations, constants and other variables.
Given in the question is a number such that twice the difference of a number and 9 is equal to three times the sum of the number and 6.
Assume that the number is x. Now, we will model the equation and solve for x. According to the question, the following mathematical relation represents the statement-
2(x - 9) = 3(x + 6)
2x - 18 = 3x + 18
x = - 36
Therefore, the number is -36.
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Answer:
Volume = 200.96 cubic feet
Step-by-step explanation:
Volume of a cone is given by the formula 
Where r is the radius and h is the height
Given r = 4 and height is 3 times that. So height is 4*3 = 12
Plugging these into the formula we get:
Volume of Cone = 
Thus, Volume = 200.96 cubic feet
Answer:
So we use the t-distribution to compute a confidence interval for the average age of people using online dating services
Step-by-step explanation:
Confidence interval for a mean.
We have to decide between the t-distribution and the z-distribution.
T-distribution: We use the sample standard deviation.
Z-distribution: We use the population standard deviation.
In this problem:
The average age of those that were using online dating services was 35 years old with a sample standard deviation of 12 years.
So we use the t-distribution to compute a confidence interval for the average age of people using online dating services
Answer:
a < -30/31
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
7a + 42 + 8 < -10 + 9a - 64a
<u>Step 2: Solve for </u><em><u>a</u></em>
- Combine like terms (a): 7a + 42 + 8 < -10 - 55a
- Combine like terms: 7a + 50 < -10 - 55a
- [Addition Property of Equality] Add 55a on both sides: 62a + 50 < -10
- [Subtraction Property of Equality] Subtract 50 on both sides: 62a < -60
- [Division Property of Equality] Divide 62 on both sides: a < -30/31
Here we see any number <em>a</em> less than -30/31 would work as a solution to the inequality.
