Answer:
-2x³ - 14x² + 7x - 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
(3x³ - 2x² + 4x - 8) - (5x³ + 12x² - 3x - 4)
<u>Step 2: Simplify</u>
- [Distributive Property] Distribute negative: 3x³ - 2x² + 4x - 8 - 5x³ - 12x² + 3x + 4
- Combine like terms (x³): -2x³ - 2x² + 4x - 8 - 12x² + 3x + 4
- Combine like terms (x²): -2x³ - 14x² + 4x - 8 + 3x + 4
- Combine like terms (x): -2x³ - 14x² + 7x - 8 + 4
- Combine like terms: -2x³ - 14x² + 7x - 4
Answer:
n = 18
Step-by-step explanation:
18/27 = 12/n
18 * n = 12 * 27
18n = 324
n = 324/18
n = 18
The correct answer is: [B]: " 25 a²⁵ b²⁵ " .
_________________________________________________________
<span>Explanation:
_________________________________________________________
Given the expression:
_________________________________________________________
</span>→ " (−5a⁵b⁵)² (a³b³)⁵ " ; Simplify.
_________________________________________________________
Let us being by examining:
______________________________________
→ "(−5a⁵b⁵)² " .
→ "(−5a⁵b⁵)² = (-5)² * (a⁵)² * (b⁵)² = (-5)(-5) * a⁽⁵ˣ²⁾ * b⁽⁵ˣ²⁾ = 25a⁽¹⁰⁾b⁽¹⁰⁾ ;
{Note the following properties of exponents:
(xy)ⁿ = xⁿ * yⁿ ;
(xᵃ)ᵇ = x⁽ᵃ * ᵇ) ;
(xᵃ) * (xᵇ) = x⁽ᵃ ⁺ ᵇ⁾ .}.
______________________________________
Then, we examine:
______________________________________
→ "(a³b³)⁵ " .
→ "(a³b³)⁵ = a⁽³ˣ⁵⁾b⁽³ˣ⁵⁾ = a⁽¹⁵⁾b⁽¹⁵⁾ .
______________________________________
So: " (−5a⁵b⁵)² (a³b³)⁵ = (-5)a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;
________________________________________
Now, we simplify:
→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;
→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ ;
= 25a⁽¹⁰⁾ a⁽¹⁵⁾b⁽¹⁰⁾ b⁽¹⁵⁾ ;
= 25a⁽¹⁰ ⁺¹⁵⁾ b⁽¹⁰⁺¹⁵⁾ ;
= 25a⁽²⁵⁾ b⁽²⁵⁾ ;
_______________________________________________
→ which is: Answer choice: [B]: " 25 a²⁵ b²⁵ " .
______________________________________________
Answer:
The p value for this case would be given by:
Since the p value is higher than the significance level provided we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 20 ounces.
Step-by-step explanation:
Information provided
represent the sample mean
represent the population deviation
sample size
represent the value that we want to test
represent the significance level
z would represent the statistic
represent the p value
Hypothesis to test
We want to test if the true mean is at least 20 ounces, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing the info given we got:
The p value for this case would be given by:
Since the p value is higher than the significance level provided we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 20 ounces.
