In a survey of 500 U. S. adults, 45% of them said that lounging at the beach was their "dream vacation.’ Assuming this to be a simple random sample of U. S. adults, the lower confidence limit of the 95% confidence intervals for the proportion of U. S. adults who consider lounging at the beach to be their dream vacation would equal to:

0.4064

Step-by-step explanation:

Number of adults sampled (n) = 500 strikes

Z-score for a 95% confidence interval (Z) = 1.960

Proportion that said that lounging at the beach was their "dream vacation.’ (p) = 0.45

The lower confidence bound (L) for a confidence interval of a proportion is determined by the following expression

 Applying the given data:

The lower confidence bound for the proportion of U.S. adults who consider lounging at the beach to be their dream vacation would equal to 0.4064.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

47 - 90 = 43

43 - 180 = x

x = 137