Response:
I think the answer is 8.48 seconds
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Answer:
y = negative four-thirds x + StartFraction 31 Over 3 EndFraction
y = 2 x + 7
Step-by-step explanation:
Let x denote the smaller number and y denote the larger number.
Part 1
The equation presented indicates that four times some number added to three times a larger number equals 31.
This translates to:
From here, solving for y yields:
- 4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3
⇒ y= - 4/3x + 31/3
This indicates the correct response for this scenario:
y = negative four-thirds x + StartFraction 31 Over 3 EndFraction
Part 2
The statement that seven subtracted from the larger number equals twice the smaller number translates to:
y-7= 2x
Further, solving for y yields:y-7= 2x ⇒
y= 2x+ 7
The correct answer for this equation is:
y = 2 x + 7
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Answer:
The earnings gap, over a career spanning 30 years, between men and women totals $1,200,150
Step-by-step explanation:
Calculated annually.
The typical male earns $90,761 each year.
The typical female earns $50,756 per annum.
Therefore, the annual difference is:
90,761 - 50,756 = 40,005
Across 30 years:
30*40,005 = 1,200,150
The earnings gap over a 30-year career, when comparing men and women, is $1,200,150
Answer:
The anticipated number of tests required to identify 680 acceptable circuits is 907.
Step-by-step explanation:
For any circuit, there are two potential results: it either passes the test or it fails. The likelihood of passing is independent between circuits. Therefore, we apply the binomial probability distribution to address this scenario.
Binomial probability distribution
This distribution calculates the chance of obtaining exactly x successes across n trials, where x has only two possible outcomes.
To find the expected number of trials to achieve r successes with a probability p, the formula is given by:
Circuits from a specific factory pass a certain quality evaluation with a probability of 0.75.
Thus, to determine the expected number of tests needed for 680 acceptable circuits, let’s denote this as E where r = 680.
The expected number of tests necessary to find 680 acceptable circuits is 907.
