Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit. (Hint: Assume that

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:

The width of the arch measures 105 meters

Detailed explanation:

The function that describes the width of the arch is

f(x) = -0.016(x - 52.5)² + 45

where x denotes the horizontal distance from the left end of the arch or the width at its base

f(x) indicates the vertical height of the arch

According to the given quadratic equation, the vertex coordinates of the parabola are (52.5, 45).

The vertex coordinates indicate that

the arch's height is 45 meters

and half the horizontal span from the left end is 52.5 meters

Therefore, the bridge's total width is calculated as 2 times the half span from the left side, which is 2 × 52.5

resulting in 105 meters

Consequently, the bridge's width is 105 meters.

Answer:

Wouldn't it be 10 out of 26, which is 2.6?

Step-by-step explanation:

There are 10 letters in "County Fair" and a total of 26 letters available, so you divide 26 by 10.

<span>Starting with the equation f = v + at

Subtract v on both sides:

f - v = at

Divide both sides by a:

(f - v) / a = t

Swap the sides:

t = (f - v) / a

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