Answer:
According to my cupcake recipe, it yields $12$ cupcakes and calls for $1\frac{1}{2}$ sticks of butter. I can only purchase whole sticks of butter.
Consequently, a single whole stick of butter will suffice to prepare $100$ cupcakes.
Answer:
a) 0.00019923%
b) 47.28%
Step-by-step explanation:
a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:
The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.
The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.
Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.
b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.
The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.
Important details about isosceles triangle ABC:
- The median CD, which is drawn to the base AB, also acts as an altitude to that base in the isosceles triangle (CD⊥AB). This indicates that triangles ACD and BCD are congruent right triangles, each with hypotenuses AC and BC.
- In isosceles triangle ABC, the sides AB and BC are equal, meaning AC=BC.
- The base angles at AB are equal, m∠A=m∠B=30°.
1. Consider the right triangle ACD. The angle adjacent to side AD is 30°, which dictates that the hypotenuse AC is double the length of the opposite side CD relating to angle A.
AC=2CD.
2. Now, for right triangle BCD, the angle next to side BD is also 30°, so hypotenuse BC is twice the opposite leg CD linked to angle B.
BC=2CD.
3. To calculate the perimeters of triangles ACD, BCD, and ABC:
4. If the total of the perimeters of triangles ACD and BCD is 20 cm greater than the perimeter of triangle ABC, then
5. Given that AC=BC=2CD, the lengths of legs AC and BC of the isosceles triangles are 20 cm.
Answer: 20 cm.
Given a time of 3:59.37 for a mile run, this translates to 3 hours and 59.37 minutes. To convert this entirely into hours: 3 hours + 59.37 minutes (1 hour / 60 minutes) = 3.9895 hours. Thus, the average speed can be calculated as: average speed = 1 mile * (1.61 km / mile) / 3.9895 hours. Consequently, the average speed equals 0.4 km / hour.
