You are really excited to have found a Puch Maxi Moped from the mid Eighties, and the spring weather is making you want to get o

Answer:

The cabin is located 567 yards away.

Step-by-step solution:

The bearing angle of 21.2° corresponds to the interior angle near the cabin in the triangle.

Apply the tangent function:

Opposite side length: 220 yards

Adjacent side length: x (distance to cabin)

tan(21.2°) = opposite / adjacent

tan(21.2°) = 220 yards / x

Multiply both sides by x:

x × tan(21.2°) = 220 yards

Isolate x:

x = 220 yards / tan(21.2°)

x = 220 / 0.388

x = 567 yards

Hence, the cabin is 567 yards away.

Answer:- 1. True. A compass serves the purpose of drawing circles and arcs in geometric constructions.

2. False. A standard geometric construction necessitates the use of a straightedge, compass, and pencil, among other tools, to accurately draw a geometric figure.

3. True. Geometric constructions are crafted using a compass and straightedge.

4. True. Protractors assist in geometric constructions for measuring angles, while rulers are employed to gauge segment lengths.

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

Answer: 10 holly bushes and 12 bayberry shrubs

Step-by-step explanation: use your brain or a calculator to figure out the cost of each type of plant and then total them up

Response:

The fence's length is expressed as 6.28x - 150 cm.

Detailed Breakdown:

Assuming the circular pool has a radius (r) of x cm.

As the pool is circular, its circumference represents the length of the fence. Additionally, subtracting the 150 cm for the gate gives us the actual length of the fence.

Length of fence = Circumference of pool – gate's width.

Length of fence = 2 π r – 150

Length of fence = 2 × 3.14 × x – 150

Therefore, the fence length is 6.28x – 150 cm.