To tackle this sinusoidal question, we begin with the following: Using the formula; g(t)=offset+A*sin[(2πt)/T+Delay] According to sinusoidal theory, the duration from trough to crest is typically half of the wave's period. Here, T=2.5 The peak magnitude is calculated as: Trough-Crest=2.1-1.5=0.6 m amplitude=1/2(Trough-Crest)=1/2*0.6=0.3 The offset from the center of the circle becomes 0.3+1.5=1.8 As the delay is at -π/2, the wave will commence at the trough at [time,t=0]. Plugging these values into the formula gives: g(t)=1.8+(0.3)sin[(2*π*t)/2.5]-π/2] g(t)=1.8+0.3sin[(0.8πt)/T-π/2]
Answer:
You need to purchase 3 shirts to be able to use your coupon.
Step-by-step explanation:
Each shirt originally costs $17.99.
There is a 20% discount on this specific brand of shirts.
$17.99 × 0.2 = $3.60 (discount per shirt)
Subtracting the discount from the original price:
$17.99 - $3.60 = $14.39 (price per shirt after discount)
To qualify for the $10 off coupon which requires a $40 minimum purchase:
$40 ÷ $14.39 ≈ 2.779, rounded up to 3 shirts
Therefore, you must buy 3 shirts.
3 shirts × $14.39 = $43.17, surpassing the $40 minimum needed to apply the $10 discount.
Define x as the distance in miles. This scenario can be expressed with the inequality 0.5x + 3 < 10, where x corresponds to the miles traveled. To solve this, begin by subtracting 3 from each side, followed by dividing everything by 0.5. The outcome indicates x < 14, meaning Carl can cover less than 14 miles, though he is 15 miles away from his destination; therefore, he will opt for a bus instead.
Every confidence interval correlates with a specific z value. As the confidence interval expands, so does the corresponding z value.
You can compute the confidence interval using the formula:
Here
represents the mean, z is the respective z value, s denotes the standard deviation, and n indicates the sample size.
Standard deviation is simply the square root of variance:
For a confidence interval of 95%, the z value is <span>1.960.
</span>Now, we can compute the confidence interval for our income:
We are required to tally the number of games scoring 15, 16, 17, and 18. There are 3 games with a score of 15, 2 games scoring 16, 5 games with a score of 17, and 3 games scoring 18. The total comes to 13 games.
