Suppose F⃗ (x,y)=⟨ex,ey⟩F→(x,y)=⟨ex,ey⟩ and CC is the portion of the ellipse centered at the origin from the point (0,1)(0,1) to

Answer:

B ≤ 11 bags

Step-by-step explanation:

Alonso starts with $21. After purchasing eggs for $2.50, he has $21 - $2.50 left = $18.50

Thus, the remaining money for avocados is $18.50.

Each 3 bags of avocados cost $5, making the price for 1 bag $(5/3)

Consequently, if B represents the quantity of avocado bags purchased by Alonso, it could be expressed as:

B ≤ $18.50 ÷ $(5/3)

B ≤ 11.1

B ≤ 11

B ≤ 11 bags

To determine if there is evidence suggesting a change in average height, we can conduct a right-tailed test and formulate both null and alternative hypotheses.

H₀ (null hypothesis): μ = 162.5
H₁ (alternative hypothesis): μ > 162.5

With two samples to analyze, we can calculate the z-score using the formula provided below.



In this formula, Z symbolizes the z-score, Χ denotes the new sample mean, μ indicates the theoretical average, δ represents the standard deviation, and n signifies the sample size. Based on the gathered values, 




Assuming a significance level of α = 0.05. With a z-score of 2.77, we can reference the z-table to ascertain the p-value. This yields P(Z > 2.77) =.0028. Since our p-value is below α, we reject the null hypothesis, indicating that the average height of female freshman students has indeed shifted.
 

Response:

Part A

The best choice is;

b. y = 128(0.989)x + 72

Part B

Ella can consume the tea post 7:22

Detailed clarification:

Here, we observe the temperature variation with time represented in an exponential equation as follows;

Let the temperature at time x (measured in minutes) be y

Thus, y = a × mˣ + b

Where:

b = Curve shift or the limiting value of the decreasing exponential function as x → ∞

When y = 200, x = 0

This leads to 200 = a × m⁰ + c = a + c

Here, c represents the graph's shift, which is the temperature increase = final temperature = 72°F

Thus, a = 200 - 72 = 128°F

When y = 197, at x = 2 minutes

Thus, 197 = 128·m² + 72 =

m² = (197 - 72)/128 = 125/128

m = √(125/128) = 0.98821

Therefore, the exponential cooling equation is given by;

y = 128 × (0.98821)ˣ + 72

Hence the best choice is b. y = 128(0.989)x + 72

Part B

When the tea's temperature reaches 172°F, we have;

172 = 128 × (0.989)ˣ + 72

Thus, (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32

log(0.989)ˣ = log(25/32)

x·log(0.989) = log(25/32)

x = log(25/32)/log(0.989) = 22.32 minutes

Thus, Ella can consume the tea post 7:22.

Answer:

The exponential equation can be expressed as A = 600(1.04)^15

After 15 years, the value of the mutual fund will be $1,081

Step-by-step explanation:

The worth of the mutual fund after a specific number of years can be represented by the compound interest formula shown below;

A = P(1 + r/n)^nt

In this formula, A stands for the mutual fund's value after 15 years, P represents the principal amount invested, which is $600, r denotes the interest rate at 4% or 0.04 (thus, 4% = 4/100 = 0.04), n indicates the number of times compounding occurs per year (in this case, it is done once a year), and t represents the number of years, which is 15.

Now, substituting in these values gives us;

A = 600(1 + 0.04/1)^15

A = 600(1.04)^15

A = $1,081 approximately

To this problem, the solution is 5 seconds.

In this scenario, you have the initial distance of 300 feet, a car speed of 48 feet per second, and a final distance of 60 feet. You also have the equation for calculating the distance, which should simplify the problem. You're asked to find out when the distance equals 60 feet. Thus, the calculation would be:

distance= 300-48t
60 = 300ft - 48t
48t = 300 - 60 = 240
t = 5