Response:
x ≥ 4
Step-by-step breakdown:
Given
- 4(8 - 3x) ≥ 6x - 8 ← distribute the term in parentheses on the left side
- 32 + 12x ≥ 6x - 8 (subtract 6x from both sides)
- 32 + 6x ≥ - 8 (add 32 to both sides)
6x ≥ 24 (divide both sides by 6)
Thus, x ≥ 4
18
He can combine one hat with a scarf, resulting in 18 different combinations for Sam when multiplying 6 by 3.
The test statistic (Z) is 2.5767, and the p-value of the test is 0.009975. The null hypothesis suggests that the smoking rate among students has not changed, while the alternative indicates otherwise. The z-statistic for the sampled proportion is computed, yielding z ≈ 2.5767. As we investigate whether the smoking percentage has shifted over the preceding five years, the two-tailed p-value is found to be 0.009975. This result is significant at a 99% confidence level, demonstrating substantial evidence that the percentage of smoking students has changed.
The question is missing some information. It should be phrased as follows:
<span><span>A container has 50 electronic components, with 10 identified as defective. If 6 components are randomly selected from the container, what is the probability that at least 4 of them are not defective? Additionally, if 8 components are drawn at random from the container, what is the probability that exactly 3 are defective?
</span>Answers
<span>Part 1. 0.02
Part 2. </span></span>0.0375<span><span>
</span>Explanation
Probability denotes the likelihood of an event occurring. It is computed as:
probability = (Number of favorable outcomes)/(Number of total outcomes)
Part 1
When 6 components are chosen, if 4 are confirmed functioning, then 2 must be defective.
P(at least 4 functional) = 4/40</span>× 2/10
= 1/10 × 1/5
= 1/50
= 0.02
Part 2
Choosing 8 components, if 3 are defective, then 5 are functioning.
P(3 defective) = 3/40 × 5/10
= 15/400
= 3/80
= 0.0375
Answer:
- 8
Step-by-step explanation:
Given the expression
(3x² - 5)(4 + 4x²)
Each term from the second factor is multiplied by every term in the first factor, meaning
3x²(4 + 4x²) - 5(4 + 4x²) ← distribute both parentheses
= 12x² + 12
- 20 - 20x² ← combine like terms
= 12 - 8x² - 20
The coefficient for the x² term is - 8
