#21 in an italian class, 65 percent of the students were women. at the end of the class, 52 percent of the men and 44 percent of the women received a certificate. what percentage of the class received a certificate? (ignore the percent symbol when entering your answer. for example, if the answer is 42.1%, enter 42.1)
#22 what percentage of those who received a certificate were men? (ignore the percent symbol when entering your answer. for example, if the answer is 42.1%, enter 42.1)
#23 the equation p = 215(1.005)^(t/3) can be used to model the population, in thousands, of a certain city t years after 2000. according to the model, the population is predicted to increase by 0.5% every n months. what is the value of n? a) 3 b) 4 c) 12 d) 36
#24 the graph of the exponential function h in the xy - plane, where y = h(x), has a y - intercept of d, where d is a positive constant. which of the following could define the function h? a) h(x)=-3(d)^x b) h(x)=3(x)d c) h(x)=d(-x)^3 d) h(x)=d(3)^x
#25: the scores on the biology test are displayed on a box and whisker plot. 38 72 88 96 102 a) what was the high score on the test? b) what percent of the class scored above a 72? c) what was the median score on the test? d) what percent of the class scored between 88 & 96? e) do you think this is a hard test? explain.
#26: the average minutes per night spent on homework are displayed on the graph. average minutes per night spent on homework 0 20 48 60 190 a) what percent of sophomores spend more than 60 minutes on homework per night? b) what is the range of times that the middle 50% of sophomores spend on homework per night? c) what percent of the sophomores spend less than 20 minutes per night on homework?

Question

Accepted Answer

### #21
# Explanation:
## Step1: Assume total students as 100
Let the total number of students be 100. Then the number of women is $0.65	imes100 = 65$ and the number of men is $100 - 65=35$.
## Step2: Calculate number of men and women with certificates
Number of men with certificates is $0.52	imes35 = 18.2$. Number of women with certificates is $0.44	imes65 = 28.6$.
## Step3: Calculate total number of students with certificates
Total number of students with certificates is $18.2 + 28.6=46.8$.
# Answer:
46.8

### #22
# Explanation:
## Step1: Use results from #21
From #21, number of men with certificates is 18.2 and total with certificates is 46.8.
## Step2: Calculate percentage of men among certificate - receivers
Percentage is $\frac{18.2}{46.8}	imes100\approx38.9$.
# Answer:
38.9

### #23
# Explanation:
## Step1: Recall compound - interest formula
The general compound - interest formula is $A = P(1 + r)^n$, where $r$ is the rate of interest per period and $n$ is the number of periods. Here, the population formula is $P = 215(1.005)^{\frac{t}{n}}$. The annual growth rate is $r = 0.005$ (or 0.5%).
## Step2: Determine the number of periods in a year
If the population increases by 0.5% every $n$ months, in 12 months, the number of $n$ - month periods is $\frac{12}{n}$. And the growth factor in 1 year is $(1 + 0.005)^{\frac{12}{n}}$. For an annual growth rate of 0.5%, we know that if we consider the growth in 1 year, when $t = 1$, the formula $P = 215(1.005)^{\frac{t}{n}}$ should represent the annual growth. Since the growth rate is 0.5% per $n$ months, and in 12 months the growth is also based on this $n$ - month increment. If we assume the number of $n$ - month periods in 12 months, and the growth factor per $n$ - month period is 1.005, we want $(1.005)^{\frac{12}{n}}$ to represent the annual growth. Since the growth rate is 0.5% per $n$ - month period and we know that for an annual growth of 0.5%, the number of $n$ - month periods in a year should be 1. So $\frac{12}{n}=1$, which gives $n = 12$.
# Answer:
C. 12

### #24
# Explanation:
## Step1: Recall the concept of y - intercept
The y - intercept of a function $y = h(x)$ is found by setting $x = 0$. For a function $y=h(x)$, when $x = 0$, $h(0)$ gives the y - intercept.
## Step2: Evaluate each option at $x = 0$
For option A, $h(0)=-3(d)^0=-3$. For option B, $h(0)=3(0)d = 0$. For option C, $h(0)=d(-0)^3 = 0$. For option D, $h(0)=d(3)^0=d$.
# Answer:
D. $h(x)=d(3)^x$

### #25
# Explanation:
## a)
The high score on a box - and - whisker plot is represented by the end of the right - most whisker. So the high score is 102.
## b)
The value 72 is the lower quartile ($Q_1$) of the box - and - whisker plot. 75% of the data lies above the lower quartile. So 75% of the class scored above 72.
## c)
The median is represented by the line inside the box. So the median score is 88.
## d)
The values 88 and 96 are the median ($Q_2$) and the upper quartile ($Q_3$) respectively. 25% of the data lies between the median and the upper quartile. So 25% of the class scored between 88 and 96.
## e)
It could be considered a hard test. The median is 88 and the high score is 102, and a significant portion (25%) of the scores are below 72. Also, the inter - quartile range (IQR) is $96 - 88 = 8$, and the lower 25% of scores are quite spread out from 38 to 72.
# Answer:
a) 102
b) 75
c) 88
d) 25
e) It could be considered a hard test. The median is 88 and the high score is 102, and a significant portion (25%) of the scores are below 72. Also, the inter - quartile range (IQR) is $96 - 88 = 8$, and the lower 25% of scores are quite spread out from 38 to 72.

### #26
# Explanation:
## a)
The value 60 is the upper quartile ($Q_3$) of the box - and - whisker plot. 25% of the data lies above the upper quartile. So 25% of sophomores spend more than 60 minutes on homework per night.
## b)
The inter - quartile range (IQR) represents the range of the middle 50% of the data. The lower quartile ($Q_1$) is 20 and the upper quartile ($Q_3$) is 60. So the range of times that the middle 50% of sophomores spend on homework per night is $60 - 20=40$.
## c)
The value 20 is the lower quartile ($Q_1$) of the box - and - whisker plot. 25% of the data lies below the lower quartile. So 25% of sophomores spend less than 20 minutes per night on homework.
# Answer:
a) 25
b) 40
c) 25

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

#21

Step1: Assume total students as 100

Step2: Calculate number of men and women with certificates

Step3: Calculate total number of students with certificates

Step1: Use results from #21

Step2: Calculate percentage of men among certificate - receivers

Step1: Recall compound - interest formula

Step2: Determine the number of periods in a year

Answer:

#22