Levi invested $8,500 in an account paying an interest rate of 3.4% compounded continuously. Assuming no deposits or withdrawals

Answer: Circle C has a radius of 7 cm.

Explanation:

Referring to the illustration below:

Let's denote the radius of circle C as x.

Circle A's radius can be represented as 2x.

Circle B's radius can be expressed as 4x.

The length of side AC in triangle ΔABC becomes x + 2x = 3x.

For side BC of triangle ΔABC, we get 4x + x = 5x.

Similarly, for side AB of triangle ΔABC, it is 4x + 2x = 6x.

Given that the perimeter of triangle ΔABC totals 98 cm.

Remember, the perimeter refers to the total length around the triangle.

Hence, Perimeter = 6x + 5x + 3x = 98 cm.

Thus, 14x = 98.

From this, we find x = .

Therefore, x = 7.

This concludes that the radius of circle C is 7 cm.

Answer:

The charge for the first three hours is $4 per hour.

Subsequently, the rate decreases to $2 per hour until the sixth hour.

Between the sixth and tenth hours, the cost is reduced further to $1 per hour.

The maximum charge for renting the bike is $30.

Step-by-step explanation:

The incline on the graph indicates the hourly rate for the bike rental.

During the initial three hours, the rental fee rises by $4 for each hour.

From the third to the sixth hour, the graph’s slope indicates a rate of $2 per hour for the rental.

The charge drops to $1 per hour from the sixth to the tenth hour.

After the tenth hour, the price, P, remains constant. The highest fee for the bike rental is $30.

Answer:

The value calculated is Z = 2.53, which exceeds 1.96 at a significance level of 0.05

This leads to the rejection of the null hypothesis H₀

Thus, we accept the alternative hypothesis

This implies that individuals participating in Weight Reducers will lose more than 10 pounds

Step-by-step explanation:

Step(i):-

The size of the random sample 'n' = 50

The new weight-loss program, Weight Reducers International, claims that members will shed an average of 10 pounds within the initial two weeks, with a standard deviation of 2.8 pounds.

Population mean 'μ' = 10 pounds

Population standard deviation 'σ' = 2.8 pounds

Sample mean 'x⁻' = 9

Significance level ∝ = 0.05

Step(ii):-

Null hypothesis: H₀: μ < 10

Alternative hypothesis: H₁: μ > 10

Test statistic calculation

The determined Z value is 2.53

In this case, the critical value Z is 1.96 at the 0.05 significance level

Step(iii):-

Calculated Z value of 2.53 is greater than 1.96 at a significance level of 0.05

Consequently, we reject the null hypothesis H₀

We accept the alternative hypothesis

Conclusion:-

We determine that individuals who sign up for Weight Reducers will experience a weight loss exceeding 10 pounds

Question 1: (2.2, -1.4). Question 2: (1.33, 1). Providing a detailed analysis, the equations for the given lines are specified as (1) passing through points (0, 2.5) and (2.2, 1.4), and (2) through (0, -3) and (2.2, -1.4). We are tasked with locating a common solution or intersection of these equations. This leads to finding x = 2.2, and consequently y = -1.4. Therefore, the solution set is (2.2, -1.4). For question 2, the equations yield a solution of (1.33, 1).