Max wants to start a farm to grow mussels. He needs to determine the best environment for growing them. He is going to try two d

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

The average speed for his entire journey from York to Blackpool is about 61.41 km/h.

Here’s a breakdown of how we arrive at this:

The distance he travelled from York to Leeds is 45 km,

and the speed during that section was 54 km/h.

Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).

Next, the distance from Leeds to Blackpool is 42 km,

and the time for that leg of the journey is 35 minutes, which is 35/60 hours.

This leads to the total duration for his trip as

hours.

The cumulative distance covered equals 45 + 42 = 87 km.

Thus, his average speed is calculated as:

Answer:

a) Which rental company charges a lower daily rate?

Payless rental company.

b) How many days must you rent a car for the total costs to equal?​

3 days.

Step-by-step breakdown:

We are comparing two rental services:

Discount Car Rentals and Payless Car Rentals.

x = rental duration in days

y = total cost.

a) Assuming the rental period starts at 2 days:

We need to formulate the equation for Discount Rentals.

For Discount Car Rentals:

2 days = $185

4 days = $265

6 days = $345

8 days = $425

The cost differential for 2 days = $265 - $185 = $80

Therefore, for 1 day the cost difference is = $80/2

= $40

For a one-day rental,

185 - 40 = $145

Thus, the equation for the payment of Discount Rentals is:

y = 40x + 105

b) For Payless Car Rentals:

The provided equation is: y = 55x + 60.

y = total cost, x = rental days

a) For 1 day:

y = 55(1) + 60

y = $115

b) For 2 days:

y = 55(2) + 60

y = 110 + 60

y = $170

c) For 3 days:

y = 55(3) + 60

= 165 + 60

= $225

d) For 4 days:

y = 55x + 60.

y = 55 × 4 + 60

y = 220 + 60

y = $280

e) For 5 days:

y = 55x + 60.

y = 55 × 5 + 60

y = 275 + 60

y = $335

f) For 6 days:

y = 55x + 60.

y = 55 × 6 + 60

y = 330 + 60

y = $380

g) For 7 days:

y = 55x + 60.

y = 55 × 7 + 60

y = 385 + 60

y = $445

h) For 8 days:

y = 55x + 60.

y = 55 × 8 + 60

y = 440 + 60

y = $500

a) Which rental company charges a lower daily rate?

The total expense of renting a vehicle as calculated above:

For 1 day from Discount Car Rentals = $145

For 1 day from Payless Car Rentals = $115

Based on these calculations, Payless rental company offers the lower rate.

b) For how many days is the rental required to have costs equal?

We set both equations equal to each other:

y = 40x + 105 = y = 55x + 60.

40x + 105 = 55x + 60

105 - 60 = 55x - 40x

45 = 15x

x = 45/15

x = 3 days.

Hence, after 3 days, the total cost of renting a vehicle from either Discount or Payless Car Rentals will be equal.