Question

7-25. alan is making a bouquet to take home to his grandmother. he needs to choo greenery and one kind of flower for his bouquet. he has a choice of ferns or leaves flower choices are daisies, carnations, and sunflowers.
a. draw a tree diagram to show the different bouquets he could make. how r
b. what is the probability that he will use ferns?
c. what is the probability that he will not use sunflowers?
d. what is the probability that he will use leaves and carnations?
7-26. read the math notes box in this lesson (or use your toolkit) and use the the following problems. the daily high temperatures in degrees fahrenheit for grand forks, north dakota were 7, 1, -3, 0, 4, -1, 2, 5, 7, 7, 3, -2, -4, and -
a. calculate the median temperature.
b. find the first and third quartiles (q1 and q3).
c. what is the interquartile range (iqr)?

Explanation:

For 7-25:

First, identify total possible bouquets: 2 greenery options (ferns, leaves) × 3 flower options (daisies, carnations, sunflowers) = 6 total combinations: (ferns+daisies, ferns+carnations, ferns+sunflowers, leaves+daisies, leaves+carnations, leaves+sunflowers)

Step1: Total possible bouquets

$2 \times 3 = 6$

Step2: Probability for part b

Ferns have 3 bouquets. Probability: $\frac{\text{Number of fern bouquets}}{\text{Total bouquets}} = \frac{3}{6}$

Step3: Probability for part c

Non-sunflower bouquets: 4. Probability: $\frac{4}{6}$

Step4: Probability for part d

Leaves+carnations is 1 bouquet. Probability: $\frac{1}{6}$

First, sort the temperature data: $-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 7, 7, 7$ (13 data points)

Step1: Sort temperature data

Sorted list: $-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 7, 7, 7$

Step2: Find median (part a)

Median = middle value (7th term): $2$

Step3: Find Q1 and Q3 (part b)

Q1 = median of lower half (first 6 terms: $-4, -3, -2, -1, 0, 1$): $\frac{-2 + (-1)}{2} = -1.5$
Q3 = median of upper half (last 6 terms: $3, 4, 5, 7, 7, 7$): $\frac{5 + 7}{2} = 6$

Step4: Calculate IQR (part c)

IQR = Q3 - Q1 = $6 - (-1.5)$

Answer:

a. Tree diagram:
First level: 2 branches (Ferns, Leaves)
Each greenery branch splits into 3 branches (Daisies, Carnations, Sunflowers). Total 6 unique bouquets.
b. $\frac{1}{2}$ or 50%
c. $\frac{2}{3}$ or ~66.7%
d. $\frac{1}{6}$ or ~16.7%

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For 7-26: