Proportionality>Generalizing Attributes of Similarity in Shapes(TEKS.Math.7.5.A)
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Texas 7th Grade Math › Proportionality>Generalizing Attributes of Similarity in Shapes(TEKS.Math.7.5.A)
A random sample of 80 teenagers shows 32 prefer streaming music. The city has 50,000 teenagers. How many in the whole population likely prefer streaming?
20000
16000
32000
50000
Explanation
Use the sample proportion: $32/80 = 0.40$. Scale to the population: $0.40 \times 50{,}000 = 20{,}000$. Because this is based on a random sample, it is an estimate and the actual number may differ slightly.
A fair coin was flipped 200 times and landed on heads 116 times. What is the experimental probability of heads?
0.42
0.58
0.5
1.16
Explanation
Use heads/total: $116/200 = 0.58 = 58%$. Experimental results can vary from trial to trial, but with more flips the result tends to get closer to 50%.
A basketball player makes a free throw about 70% of the time. You want to simulate one free throw. Which simulation best models this?
Flip a fair coin; heads = made, tails = missed.
Roll a fair number cube; 1–4 = made, 5–6 = missed.
Spin an 8-section spinner; 6 shaded = made, 2 unshaded = missed.
Use random digits 0–9; 0–6 = made, 7–9 = missed.
Explanation
Using digits 0–9 gives 10 equally likely outcomes, and marking 7 of them as made matches $7/10 = 70%$. The others model $1/2$, $4/6$, or $6/8$, which are $50%$, about $66.7%$, and $75%$, not $70%$.
Event A: It rains tomorrow. The probability of rain tomorrow is 0.35. What is $P(\text{not }A)$?
0.35
0.75
0.65
1.35
Explanation
Use complements: $P(\text{not }A)=1-P(A)=1-0.35=0.65$. Check: $0.35+0.65=1$.
A bag has 4 blue, 3 red, and 5 green marbles. What is $P(\text{blue})$ on one draw? Structure: single draw from a bag; without replacement (single draw).
$4/7$
$1/3$
$3/12$
$5/12$
Explanation
Favorable outcomes: 4 blue. Total outcomes: $4+3+5=12$. So $P(\text{blue})=\frac{4}{12}=\frac{1}{3}$.
Triangle ABC has sides 6, 8, 10 cm. Triangle DEF has sides 9, 12, 15 cm. Are these triangles similar?
Yes, because 6:9 = 8:12 = 10:15
No, because they are not congruent
No, because their perimeters are different
Yes, because both are triangles
Explanation
Similar figures have the same shape with corresponding sides in equal ratios. Order the sides from least to greatest to match: 6↔9, 8↔12, 10↔15. Compute ratios: 6/9=2/3, 8/12=2/3, 10/15=2/3. All corresponding ratios are equal, so the triangles are similar.
What is $P(\text{sum}=8)$ when rolling two fair six-sided dice? Structure: roll two dice; independent (no replacement concept).
$1/6$
$6/36$
$4/36$
$5/36$
Explanation
There are $36$ equally likely ordered outcomes. Sums of $8$: $(2,6),(3,5),(4,4),(5,3),(6,2)$, so 5 favorable. $P=\frac{5}{36}$. Distractors use wrong totals or miscount favorable outcomes.
Rectangle A is 4×6 inches. Rectangle B is 10×15 inches. What is the ratio of corresponding side lengths from Rectangle A to Rectangle B?
5:2
2:5
3:5
1:1
Explanation
For similar rectangles, the ratio of corresponding sides is constant. Pair shorter to shorter and longer to longer: 4:10 = 2:5 and 6:15 = 2:5. The common ratio (scale factor from A to B) is 2:5.
The forecast says there is a 30% chance of rain each day, and days are independent. You want to simulate the weather for a 5-day week. Which simulation best models this?
Roll a fair number cube once per day; rain if 1 or 2, no rain otherwise. Do this for 5 days.
Use random digits 0–9 once per day; rain if the digit is 0, 1, or 2, no rain otherwise. Do this for 5 days.
Spin a spinner with 8 equal sections once per day; rain if it lands on one of 3 shaded sections. Do this for 5 days.
Use a 00–99 table once per day; rain if the number is 00 through 30 (inclusive). Do this for 5 days.
Explanation
Digits 0–9 are 10 equally likely outcomes per day; choosing 0,1,2 as rain gives $3/10=30%$ and repeating 5 times models 5 independent days. The others give $2/6\approx33.3%$, $3/8=37.5%$, or $31/100=31%$.
A coin was flipped 100 times and landed on heads 47 times. Predict heads in 1,000 flips.
500
47
530
470
Explanation
Use the experimental rate from the sample: $47/100 = 0.47$. Scale to 1,000 flips: $0.47 \times 1000 = 470$. Actual results may differ, but larger samples usually stay closer to this proportion.