A dog groomer is offering 20% off a full groom for one dog, and 15% off for each additional dog. You decide to take your two fur

Answer:

First, we must calculate the slope

m=Y2-Y1/X2-X1

= 9 - (-6) / 12 - (-8)

= 15/20

= 3/4

Therefore, the equation with the slope of 3/4 is Y=3/4x

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

Response:

1. Closure

2. Distributive

3. Closure

Detailed explanation:

In this scenario, we are examining the properties that each equation demonstrates.

The first equation shows the closure property.

This indicates that whether we add in one direction or the other, the result remains unchanged. Therefore, we conclude that addition conforms to the closure property in this case.

The third equation also shows the closure property. Regardless of how we approach the addition for this equation, the outcome remains consistent.

The second equation displays the distributive property.

Each element within the parentheses is multiplied by the negative sign before we proceed with further calculations.

The equation that demonstrates a proportional relationship, maintaining a constant of proportionality equal to 14, is: Here,  and are proportional with a constant of proportionality of 14.

The dimensions are 58 ft × 58 ft. Step-by-step explanation: Let the length of the region be represented as x feet, and the width as y feet. Given a perimeter of 234 feet, the area A can be represented as xy. By differentiating the equation with regards to x, we can determine the point of maximum area, revealing that for x = 58.5 feet, the area's maximum occurs when both dimensions are 58.5 ft.