Yesterday, Jack drove 45 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for miles per
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Answer:
1) By SAS theorem, ΔADE≅ΔCDF
2) By SSS theorem, ΔBDE≅ΔBDF
Step-by-step explanation:
Consider isosceles triangle ABC (see diagram).
1. In triangles ADE and CDF:
- AD≅DC (since BD is median, then it divides side AC in two congruent parts);
- AE≅CF (given);
- ∠A≅∠C (triangle ABC is isosceles, then angles adjacent to the base are congruent).
By SAS theorem, ΔADE≅ΔCDF.
2. In triangles BDE and BDF:
- side BD is common;
- DE≅DF (ΔADE≅ΔCDF, then congruent triangles have congruent corresponding sides);
- BE≅FB (triangle ABC is isosceles, AB≅BC, AE≅CF, then BE=AB-AE, FB=BC-CF).
Be SSS theorem, ΔBDE≅ΔBDF.
Answer:
The probability that an 18-year-old man selected at random is greater than 65 inches tall is 0.8413.
Step-by-step explanation:
We are given that the heights of 18-year-old men are approximately normally distributed with mean 68 inches and a standard deviation of 3 inches.
Let X = <u><em>heights of 18-year-old men.</em></u>
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean height = 68 inches
= standard deviation = 3 inches
Now, the probability that an 18-year-old man selected at random is greater than 65 inches tall is given by = P(X > 65 inches)
P(X > 65 inches) = P( >
) = P(Z > -1) = P(Z < 1)
= <u>0.8413</u>
The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.