Proportionality
Texas 7th Grade Math · Learn by Concept
Help Questions
Texas 7th Grade Math › Proportionality
A circle has diameter 8 inches and circumference 25.12 inches
How does the ratio $C/d$ compare to $\pi$?
Less than $\pi$
About half of $\pi$
About twice $\pi$
Approximately equal to $\pi$
Explanation
$\pi$ is the constant ratio $C/d$ for any circle. Compute $C/d = 25.12/8 = 3.14 \approx 3.14159 = \pi$. Thus the ratio is approximately equal to $\pi$, showing why $\pi$ underlies circle measurements.
A coin was flipped 20 times and landed on heads 13 times and tails 7 times. Predict results for 100 trials.
About 65 heads and 35 tails
About 50 heads and 50 tails
About 70 heads and 30 tails
About 13 heads and 7 tails
Explanation
Use the experimental proportion. Heads were $13/20=0.65$, so in 100 flips expect about $0.65\times 100=65$ heads and $35$ tails. The theoretical probability is $1/2$ each, but experimental results can vary due to randomness.
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: $0.35+0.65=1$.
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.
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 $70%$.
On a blueprint with scale 1:50, a room measures 6 cm by 8 cm. What are the actual room dimensions?
0.12 m × 0.16 m
3 m × 4 m
30 m × 40 m
3.6 m × 4.8 m
Explanation
The linear scale factor is $k=50$. Actual lengths: 6×50=300 cm=3 m and 8×50=400 cm=4 m. So 3 m × 4 m. Distractors divide by 50, confuse cm-to-m conversion, or use the wrong factor.
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 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 $P(\text{blue})=\frac{4}{12}=\frac{1}{3}$.
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 number cube labeled 1–6 is rolled, then a coin is flipped. Write outcomes as (number, coin). Which list shows all outcomes?
(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (5,H), (5,T), (6,H)
(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T)
(H,1), (T,1), (H,2), (T,2), (H,3), (T,3), (H,4), (T,4), (H,5), (T,5), (H,6), (T,6)
(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,H)
Explanation
There are 6 numbers and 2 coin results, so $6 \times 2 = 12$ outcomes. List systematically by number: for each 1–6, pair with H and T to get all 12: (1,H), (1,T), …, (6,H), (6,T).