Last weekend, Lena worked 7.5 hours on Friday, 9.75 hours on Saturday, and 6.25 hours on Sunday.

We start with the following information:

p = probability = 0.12<span>
n = total number of students = 39 </span>

x = number of left-handers = 5<span>
u = mean = p * n = 4.68
σ = standard deviation = √(n*p*(1-p)) = √(39 * 0.12 * 0.88) = 2.03</span>

Finding the z score:

z = (x – u) / σ

<span> z = (5 – 4.68) / 2.03
</span>

z = 0.1576 = 0.16

<span>

</span>Applying standard tables for z gives the p value as:

p value = 0.5636 = 56.36%

 

Consequently, there is a 56.36% probability.

 

Answer:

0.40 feet

Step-by-step explanation:

For the first scenario, a 50-foot building casts a shadow of 1 foot. Let the angle of elevation of the sun from the shadow be denoted as θ.

Then:

Tan θ =

Tan θ =

Tan θ = 50

⇒ θ = 50

      = 88.8542

      =

The elevation angle is roughly .

For a 20-foot pole,

Tan θ =

Tan =

x =

 = 0.4015

 = 0.40 feet

The length of the pole's shadow is 0.40 feet.

Answer:

For a clearer understanding, refer to the attached figure:

Step-by-step breakdown:

1. According to the unique line postulate, only one line segment can be created: BC

This is because a single line can only connect two distinct points.

2. Utilizing the definition of reflection, reflect BC across l.

To identify the line segment reflected over l, we will apply the reflection definition.

3. Based on the reflection definition, C remains as its own image and A represents the image of B.

The reflection definition states that a figure is transformed into a mirror image around a line. Thus, CD serves as the perpendicular bisector of AB, which makes A and B equidistant from D, producing their mirror images.

4. Because reflections maintain length, we find that AC = BC

In a reflection, the figure transforms to create a mirror image, ensuring the lengths remain unchanged.

To determine if there is evidence suggesting a change in average height, we can conduct a right-tailed test and formulate both null and alternative hypotheses.

H₀ (null hypothesis): μ = 162.5
H₁ (alternative hypothesis): μ > 162.5

With two samples to analyze, we can calculate the z-score using the formula provided below.



In this formula, Z symbolizes the z-score, Χ denotes the new sample mean, μ indicates the theoretical average, δ represents the standard deviation, and n signifies the sample size. Based on the gathered values, 




Assuming a significance level of α = 0.05. With a z-score of 2.77, we can reference the z-table to ascertain the p-value. This yields P(Z > 2.77) =.0028. Since our p-value is below α, we reject the null hypothesis, indicating that the average height of female freshman students has indeed shifted.