Question

#2 percentages
there are 55 students in spanish club. a sample of the spanish club students was selected at random and asked whether they intend to enroll in a new study program. of those surveyed, 20% responded that they intend to enroll in the study program. based on this survey, which of the following is the best estimate of the total number of spanish club students who intend to enroll in the study program?
#3 percentages:
jennifer bought a box of crunchy grain cereal. the nutrition facts on the box state that a serving size of the cereal is $\frac{3}{4}$ cup and provides 210 calories, 50 of which are calories from fat. in addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. if p percent of an adults daily allowance of potassium is provided by x servings of crunchy grain cereal per day, which of the following expresses p in terms of x?
#4 ratios, rates, proportionals
the population density of iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to 3.3 in 2014. during this time period, the land area of iceland was 100,250 square kilometers. by how many people did icelands population increase from 1990 to 2014?
#5 analyzing graphs
group 1
group 2
the box plots summarize the masses, in kilograms, of two groups of gazelles. based on the box plots, which of the following statements must be true?
a. the mean mass of group 1 is greater than the mean mass of group 2.
b. the mean mass of group 1 is less than the mean mass of group 2.
c. the median mass of group 1 is greater than the median mass of group 2.
d. the median mass of group 1 is less than the median mass of group 2.
#6 analyzing graphs
two data sets of 23 integers each are summarized in the histograms shown. for each of the histograms, the first interval represents the frequency of integers greater than or equal to 10, but less than 20. the second interval represents the frequency of integers greater than or equal to 20, but less than 30, and so on. what is the smallest possible difference between the mean of data set a and the mean of data set b?

Explanation:

#2

Step1: Identify the total number and percentage

We know the total number of students in the Spanish - club is 55, and the percentage of students who intend to enroll is 20%.

Step2: Calculate the estimated number

We use the formula: Estimated number = Total number×Percentage. So, the number of students who intend to enroll is \(55\times0.20 = 11\).

Step1: Determine the amount of potassium per serving

One serving of cereal provides 180 milligrams of potassium, which is 5% of the daily allowance. So the daily - allowance of potassium is \(\frac{180}{0.05}=3600\) milligrams.

Step2: Find the amount of potassium in \(x\) servings

The amount of potassium in \(x\) servings is \(180x\) milligrams.

Step3: Calculate \(p\)

\(p=\frac{180x}{3600}\times100 = 5x\).

Step1: Calculate the population in 1990

Population = Population density×Land area. In 1990, the population \(P_1=2.5\times100250 = 250625\).

Step2: Calculate the population in 2014

In 2014, the population \(P_2 = 3.3\times100250=330825\).

Step3: Calculate the increase in population

The increase in population \(\Delta P=P_2 - P_1=330825 - 250625 = 80200\).

Answer:

A. 11

#3