Part A
To identify the values of x that make 2x−1 positive
⇒ 2x - 1 > 0
⇒ 2x > 1
⇒ x > 
As a result, for any x greater than
, the expression 2x-1 is positive
Part B
To find values of y making 21−37 negative
⇒ 21-3y < 0
⇒ 21 < 3y
⇒ 7 < y
Thus, for all y values exceeding 7, the expression 21-3y is negative
Part C
To identify values of c that digit 5−3c greater than 80
⇒ 5-3c > 80
⇒ -3c > 75
⇒ -c > 25
⇒ c < -25
Therefore, for values of c less than -25, the expression 5-3c surpasses 80
In this scenario, we have a function of the following form: A: initial amount, b: rate of decrease, x: time in years. Plugging in the values results in an exponential decay function suitable for this situation: y = 1300 * (0.97) ^ x. The estimated fish population in 2010 is then calculated to be approximately 1083.
Answer:
At a confidence level of 90%, the margin of error is calculated to be 0.5133 grams.
Step-by-step explanation:
The formula for margin of error (E) is: (critical value × sample standard deviation) ÷ sqrt(n)
The sample standard deviation is 1.5 grams.
A 90% confidence level translates to 0.9.
Significance level is determined as 1 - C, which equals 1 - 0.9 resulting in 0.1 or 10%.
The sample size (n) is 25.
Degrees of freedom are calculated as n - 1, which is 25 - 1 equaling 24.
The critical value (t) for 24 degrees of freedom at a significance level of 10% is found to be 1.711.
Using these values, we calculate: E = (1.711 × 1.5) ÷ sqrt(25) = 2.5665 ÷ 5 = 0.5133 grams.
This scenario relates to binomial probability, where the results can either be a success or a failure. A success indicates that a selected adult possesses a bachelor's degree. Consequently, the success probability, denoted as p, is 20/100 = 0.2. The number of adults in the sample, represented as n, equals 100, and x, the count of successes, is 60. The probability of having more than 60 adults with a bachelor's degree, represented as P(x >60), can be noted internally as P(x < 60) = binomcdf (100, 0.20, 60). The function binompdf would indicate P(x = 60).
<span>The set of the sequence includes all natural numbers
</span><span>The 4th term in the sequence equals 9
</span><span> The point (4, 9) appears on the sequence's graph.</span>
