Question

#12
questions 22 and 23 refer to the following information.
annual budgets for different programs in kansas, 2007 to 2010
program|year

	2007	2008	2009	2010
agriculture/natural resources	373,904	358,708	485,807	488,106
education	2,164,607	2,413,984	2,274,514	3,008,036
general government	14,347,325	12,554,845	10,392,107	14,716,155
highways and transportation	1,468,442	1,665,636	1,539,480	1,773,893
human resources	4,051,050	4,099,067	4,618,444	5,921,379
public safety	263,461	398,326	355,935	464,231

the table above lists the annual budget, in thousands of dollars, for each of six different state programs in kansas from 2007 to 2010.
which of the following best approximates the average rate of change in the annual budget for agriculture/natural resources in kansas from 2008 to 2010?
a) $50,000,000 per year
b) $65,000,000 per year
c) $75,000,000 per year
d) $130,000,000 per year
#13 use the table in #12
of the following, which programs ratio of its 2007 budget to its 2010 budget is closest to the human resources programs ratio of its 2007 budget to its 2010 budget?
a) agriculture/natural resources
b) education
c) highways and transportation
d) public safety
#14
a square field measures 10 meters by 10 meters. ten students each mark off a randomly - selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. the students count the earthworms contained in the soil to a depth of 5 centimeters beneath the grounds surface in each region. the results are shown in the table below.
region|number of earthworms|region|number of earthworms

a	107	f	141
b	147	g	150
c	146	h	154
d	135	i	176
e	149	j	166

which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters beneath the grounds surface in the entire field?
a) 150
b) 1,500
c) 15,000
d) 150,000
#15
a school district is forming a committee to discuss plans for the construction of a new high school. of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. how many more teachers were invited to join the committee than school and district administrators?

Explanation:

#12

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, the function represents the budget, $a = 2008$, $b = 2010$, and the budget values for agriculture/natural resources in 2008 ($f(2008)$) is $358708$ (in thousands of dollars) and in 2010 ($f(2010)$) is $488106$ (in thousands of dollars).

Step2: Calculate the difference in budget

The difference in budget $\Delta B=f(2010)-f(2008)=488106 - 358708=129398$ (in thousands of dollars).

Step3: Calculate the time - interval

The time - interval $\Delta t=2010 - 2008 = 2$ years.

Step4: Calculate the average rate of change

The average rate of change $\frac{\Delta B}{\Delta t}=\frac{129398}{2}=64699$ (in thousands of dollars per year), which is approximately $\$65000000$ per year.

Step1: Calculate the ratio for human resources

For the human resources program, the 2007 budget $B_{2007}=4051050$ (in thousands of dollars) and the 2010 budget $B_{2010}=5921379$ (in thousands of dollars). The ratio $r_{hr}=\frac{B_{2007}}{B_{2010}}=\frac{4051050}{5921379}\approx0.684$.

Step2: Calculate ratios for other programs

• For agriculture/natural resources: $B_{2007}=373904$, $B_{2010}=488106$, $r_{ag}=\frac{373904}{488106}\approx0.766$.
• For education: $B_{2007}=2164607$, $B_{2010}=3008036$, $r_{ed}=\frac{2164607}{3008036}\approx0.719$.
• For highways and transportation: $B_{2007}=1468442$, $B_{2010}=1773893$, $r_{ht}=\frac{1468442}{1773893}\approx0.828$.
• For public safety: $B_{2007}=263461$, $B_{2010}=464231$, $r_{ps}=\frac{263461}{464231}\approx0.568$.

Step3: Compare the ratios

The ratio closest to that of human resources is for education.

Step1: Calculate the area of the whole field and sub - regions

The area of the whole field $A_{total}=10\times10 = 100$ square meters. The area of each sub - region $A_{sub}=1\times1 = 1$ square meter. There are 10 sub - regions.

Step2: Calculate the average number of earthworms per sub - region

The sum of earthworms in the 10 sub - regions is $107 + 147+146+135+149+141+150+154+176+166 = 1471$. The average number of earthworms per sub - region $\bar{x}=\frac{1471}{10}=147.1$.

Step3: Estimate the number of earthworms in the whole field

Since the area of the whole field is 100 times the area of a sub - region, the estimated number of earthworms in the whole field is $147.1\times100 = 14710\approx15000$.

Answer:

B. $65000000$ per year

#13