Question

1. a spinner, numbered 1-8 is spun once. find each probability.p(a multiple of 2) = __p(3) = __10. josephina is seven years older than cameron and the sum or their ages is 35. what are their ages? you must complete at least 3 trials.trial 1:trial 2:trial 3:trial 4:trial 5:definedodecide

Explanation:

Step1: Identify total outcomes

Total sections on spinner: $n=8$

Step2: Calculate P(multiple of 2)

Multiples of 2: 2,4,6,8 (4 values)
$P(\text{multiple of 2})=\frac{4}{8}=\frac{1}{2}$

Step3: Calculate P(3)

Number of 3s: 1
$P(3)=\frac{1}{8}$

Step4: Define variables for ages

Let Cameron's age = $x$, Josephina's age = $x+7$

Step5: Set up age sum equation

$x+(x+7)=35$
Simplify: $2x+7=35$

Step6: Solve for Cameron's age

$2x=35-7=28$
$x=\frac{28}{2}=14$

Step7: Find Josephina's age

Josephina's age: $14+7=21$
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Trial 1 (Define): Let $x$ = Cameron's age, $x+7$ = Josephina's age

Trial 1 (Do): $x+(x+7)=35 \implies 2x=28 \implies x=14$

Trial 1 (Decide): Cameron=14, Josephina=21 (sum=35, 21-14=7, correct)

Trial 2 (Define): Let $y$ = Josephina's age, $y-7$ = Cameron's age

Trial 2 (Do): $y+(y-7)=35 \implies 2y=42 \implies y=21$

Trial 2 (Decide): Josephina=21, Cameron=14 (matches Trial 1, correct)

Trial 3 (Define): Verify age difference: $J - C =7$, sum $J+C=35$

Trial 3 (Do): Add equations: $2J=42 \implies J=21$, $C=35-21=14$

Trial 3 (Decide): Consistent results, correct ages

Answer:

1. $P(\text{a multiple of 2}) = \boldsymbol{\frac{1}{2}}$

$P(3) = \boldsymbol{\frac{1}{8}}$

1. Cameron's age: $\boldsymbol{14}$, Josephina's age: $\boldsymbol{21}$

(Completed trials:
Trial 1:
Define: Let $x$ = Cameron's age, $x+7$ = Josephina's age
Do: $x+(x+7)=35 \implies x=14$
Decide: Cameron=14, Josephina=21
Trial 2:
Define: Let $y$ = Josephina's age, $y-7$ = Cameron's age
Do: $y+(y-7)=35 \implies y=21$
Decide: Josephina=21, Cameron=14
Trial 3:
Define: Use sum and difference of ages
Do: $J-C=7$, $J+C=35 \implies J=21, C=14$
Decide: Ages are confirmed as 14 and 21)