50 students live in a dormitory. the parking lot has the capacity for 30 cars. if each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars?
To find the probability that there won't be enough parking spaces for all the cars, we can use the binomial distribution formula and calculate the probability of having more than 30 cars in a sample of 50. The probability is approximately 0.9999999999.
Explanation:To find the probability that there won't be enough parking spaces for all the cars, we need to find the probability that the number of cars exceeds the capacity of the parking lot. The number of cars follows a binomial distribution with a probability of success of p = 0.12 and a sample size of n = 50. We can use the binomial probability formula to calculate this probability:
P(X > 30) = 1 - P(X ≤ 30)
where P(X ≤ 30) is the probability that the number of cars is less than or equal to 30. We can use a binomial calculator or software to find this probability:
P(X > 30) ≈ 0.9999999999
How was triangle A translated?
A tree 24 feet tall casts a shadow 12 feet long.Brad is 6 feet tall. How long is Brads shadow
Answer: 6
Step-by-step explanation:
thiss is for a challenge
add or subtract.
[tex] \binom{7 \sqrt{2} }{2} - \binom{ \sqrt{8} }{2} [/tex]
The length of a rectangular prism is 4 feet, and the width is 3 feet. The volume of the prism is 9 cubic feet. In inches, what is the height of the prism?
The purchase price of an IPad is 650. What is the total price oif the sales tax rate is 8%
19.21 is 113% of what number
Can someone solve this please?
Give me an expression that is equal to 4(6j + 5 + 2j). I already got 4(8j + 5), can you get me another expression using the distributive property? Once you got the answer give me the answer you got and translate it into a verbal expression
Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would he have saved? Round the answer to the nearest tenth of a mile.
Pick one;
1.2 miles
1.8 miles
2.5 miles
4.2 miles
(Ps: I can't copy the picture but its a right triangle.)
Answer:
1.8 miles
Step-by-step explanation:
One-third the sum of 6 and 3 (u get 10 points)
Hurry
Final answer:
The sum of 6 and 3 is 9, and one-third of this sum is 3 when you divide 9 by 3.
Explanation:
In mathematics, a sum is the result of adding two or more numbers or quantities together. It represents the total or aggregate of those quantities. The process of finding this total is called addition.
Thus,
To calculate one-third the sum of the numerals 6 and 3, we first find the sum of 6 and 3, which is 9.
Then, we need to take one-third of 9.
To find one-third of a number, you divide the number by 3.
So one-third of 9 is 9 divided by 3, which equals 3.
Therefore, one-third the sum of 6 and 3 is 3.
Determine the equation for the parabola graphed below.
Ms.michaels made an apple pie with a radius of 5in .she cut the pie into 6 equal slices. Fined the approximate area of each slice.
misha has a board that is 17 1/2 inches long that he has to cut into 3 equal pieces how long should each piece be
In a probability experiment, Craig rolled a six-sided die 57 times. The die landed on a number greater than three 36 times. What is the ratio of rolls greater than three to rolls less than or equal to three?
The ratio of rolls greater than three to rolls less than or equal to three is 36:21, which simplifies to 12:7 after dividing both terms by the greatest common divisor of 3.
Since Craig rolled the die 57 times, and it landed on a number greater than three 36 times, then it landed on a number less than or equal to three the remaining number of times. Subtracting the number of greater rolls from the total rolls:
Total rolls: 57
Rolls greater than three: 36
Rolls less than or equal to three = 57 - 36 = 21
Now, we can establish the ratio of rolls greater than three to rolls less or equal to three:
Ratio = Rolls greater than three : Rolls less than or equal to three = 36 : 21
And if needed, we can simplify this ratio by dividing both sides by their greatest common divisor, which is 3:
Simplified Ratio = 12 : 7
Hello i need help on this one and giving away points+ brainiest on the legit answer thanks!
A cylinder shaped water tank has a diameter of 8 m and a height of 20 m. What volume of water does the tank contain when it is 60% full? Use 3.14 to approximate pi. Enter your answer as a decimal to the hundredths place in the box.
____ m³
For each pair of numbers, tell: By what percent of the first number is the second number larger? By what percent of the second number is the first number smaller? 100 and 110
Final answer:
The second number, 110, is 10 percent larger than the first number, 100. Conversely, the first number, 100, is approximately 9.09 percent smaller than the second number, 110.
Explanation:
To find by what percent the second number is larger than the first, we calculate the difference between the two numbers and then divide by the first number, multiplying the result by 100. For the numbers 100 and 110:
Subtract the first number from the second: 110 - 100 = 10.
Divide the difference by the first number: 10 / 100 = 0.10.
Multiply by 100 to find the percentage: 0.10 * 100 = 10 percent.
Now, to find by what percent the first number is smaller than the second number:
Again, find the difference: 110 - 100 = 10.
But this time, divide by the second number: 10 / 110 = ~0.0909.
Multiply by 100 to find the percentage: ~0.0909 * 100 = approximately 9.09 percent.
Therefore, 110 is 10 percent larger than 100, while 100 is approximately 9.09 percent smaller than 110.
the least common denominator of 2 fractions is 12 if you add the two denominators their sum is 7 what are the denominators
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an lg smartphone survey). if 12 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.
Using the binomial probability formula, sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings, which will give you the total probability for fewer than 3.
Explanation:The subject of this question appears to be probability theory, a branch of mathematics that studies the likelihood of different outcomes. The problem presented involves calculating the probability of a certain number of smartphone users behaving in a specified way. In this case, it's about finding the likelihood that fewer than 3 out of 12 selected individuals use their smartphones in meetings or classes.
To solve this, we'll use a binomial probability formula: P(X=r) = (nCr) * p^r * (1-p)^(n-r), where:
n is the number of trials (in this case, 12 smartphone users),r is the desired number of successful outcomes,p is the probability of success on a single trial (54%), andnCr is the combination of n items taken r at a time.
You will need to sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings or classes to get the total probability for fewer than 3.
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A section in a stained glass window is shaped like a trapezoid. The top base is 1 centimeter and the bottom base is 1.5 centimeters long. If the area of the section of glass is 5.5 square centimeters, how tall is the section?
A car traveled 48.36 miles in one hour. What was it's average speed per minute?
0.806 miles per minute
Step-by-step explanation:There are 60 minutes in an hour, so replace the unit "hour" by 60 minutes and recompute.
... 48.36 mi/h = 48.36 mi/(60 min) = (48.36/60) mi/min = 0.806 mi/min
The car's average speed was calculated by dividing the total distance of 48.36 miles by the total time of 60 minutes, resulting in an average speed of 0.806 miles per minute.
Explanation:To compute the car's average speed per minute, we need to divide the total distance covered by the total time in minutes. This is because speed is defined as the rate at which an object covers distance. The distance travelled by the car is 48.36 miles (the total distance), and the time is 1 hour. To transform this hour into minutes, we multiply by 60, as there are 60 minutes in an hour. So,
1 hour = 60 minutes
Therefore, to find the average speed, we take the total distance and divide by the total time in minutes. Using this, we find:
Average speed = Total distance / Total time
Average speed = 48.36 miles / 60 minutes = 0.806 miles per minute.
Therefore, the car's average speed was approximately 0.806 miles per minute.
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How many lines of a reflectional symmetry does a equilateral triangle have?
Answer:
Equilateral triangle has 3 Reflection symmetry.
Step-by-step explanation:
Given : Equilateral triangle.
To find : How many lines of a reflectional symmetry does a equilateral triangle have.
Solution : We have given a equilateral triangle.
Equilateral triangle :triangle which has all three sides and angles are equal.
Reflection symmetry : If we reflect any shape of figure it gives same shape .
Therefore, Equilateral triangle has 3 Reflection symmetry.
The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments with lengths in the ratio 1:2. the length of the altitude is 8. how long is the hypotenuse
The hypotenuse is 17.1 inches long
Given that the scale ratio is 1 : 2.
This means that:
Segment 1 : Segment 2 = 1 : 2
This gives
Segment 1 : Segment 2 = x : 2x
By comparison,
Segment 1 = x
Segment = 2x
Using the Altitude rule, x is then calculated as:
[tex]\frac{Segment\ 2}{8} = \frac{8}{Segment\ 1}[/tex]
Substitute known values
[tex]\frac{2x}{8} = \frac{8}{x}[/tex]
Cross multiply
[tex]2x^2 = 64[/tex]
Divide through by 2
[tex]x^2 = 32[/tex]
Take the square root of both sides
[tex]x = 5.7[/tex]
The length of the hypotenuse (h) is then calculated as:
[tex]h =x + 2x[/tex]
[tex]h =3x[/tex]
[tex]h =3 * 5.7[/tex]
[tex]h =17.1[/tex]
Hence, the hypotenuse is 17.1 inches long
Read more about right triangles at:
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Rachel has 60 scones. She sells them to Robbie, Cameron, Louis, Tom and Charlie in that order. Each customer buys more scones than the last and the increase is the same number in each case. Robbie and Cameron’s combined total number of scones is three sevenths of the total of Louis, Tom and Charlie. How many scones does each boy buy?
What is the value of x?
Enter your answer in the box.
_____ units
Answer:
x=28
Step-by-step explanation:
We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.
x 42
---------- = ----------
x+10 42+15
Simplify
x 42
---------- = ----------
x+10 57
Using cross products
57x = 42 (x+10)
Distribute
57x = 42x+420
Subtract 42x from each side
57x-42x = 42x-42x +420
15x = 420
Divide each side by 15
15x/15 = 420/15
x=28
Answer: The value of x is 28 units.
Step-by-step explanation:
Since we have given that
DC ║ PA
So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.
So, it becomes,
[tex]\frac{RC}{CA}=\frac{RD}{DP}\\\\\frac{x}{10}=\frac{42}{15}\\\\15\times x=10\times 42\\\\x=\frac{420}{15}=28\\\\x=28[/tex]
Hence, the value of x is 28 units.
6. Antonio is a freelance computer programmer. In his work, he often uses 2n, where n is the number of bits, to find the number of ways bits (or units of information) can be arranged. a. Antonio is working on programming a new video game in which the main character, Millie, collects golden keys to help in her quest. Antonio writes a formula to show that Millie can collect one less key than the highest number of bits that can be arranged in the system. What formula can he use? b. If Antonio is working with a 16-bit system, how many golden keys can Millie collect? c. Antonio is also working on a new spreadsheet program. The program takes up 14 tes of memory. If each byte is equal to 8 bits, how many bits is Antonio's program? Show your work.
Final answer:
Antonio can use the formula 2ⁿ - 1 to calculate the number of golden keys Millie can collect in a 16-bit system, resulting in 65,535 keys. For the spreadsheet program taking up 14 TB of memory, this translates to 112 × 10¹² bits, illustrating the vastness of binary encoding in computing.
Explanation:
Understanding Antonio's Formulas and Calculations
In the realm of computer programming and data representation, understanding how information is encrypted and the number of combinations possible for bits is crucial. Here, we'll explore Antonio's approach to calculating the number of golden keys in a video game and translating memory size from terabytes to bits.
a. Formula Creation for Golden Keys
Antonio is developing a video game where the main character collects golden keys. The number of possible arrangements of bits in the system is represented by 2n, where n represents the number of bits. Therefore, to find the maximum number of keys Millie can collect, which is one less than the total number of bit arrangements, Antonio can use the formula 2ⁿ - 1.
b. Calculating Golden Keys in a 16-bit System
At a 16-bit system, the number of possible arrangements is 216 = 65,536. Following Antonio’s formula, Millie can collect 65,536 - 1 = 65,535 golden keys.
c. Bits in Antonio's Spreadsheet Program
For a program taking up 14 terabytes (TB) of memory, with each byte equating to 8 bits, we need to first convert terabytes to bytes then to bits:
One TB equals 1012 bytes.
Therefore, 14 TB equals 14 × 10¹² = 14 × (1012 bytes).
Converting to bits (by multiplying by 8): 14 × 10¹² × 8 = 112 × 10¹² bits.
This calculation illustrates how memory size translates into a vast number of bits, reflecting the exponential nature of binary encoding used in computing and data storage.
A drum of oil has a height of 4ft and a radius of 1.2ft The cost of oil $22 per cubic feet.What is the cost to fill the drum of oil
In a survey, 60 baseball fans were asked whether they thought the designated hitter rule should be changed. Forty-one fans thought the rule should be changed. WHat percent of the fans surveyed said that the designated hitter rule should be changed.
Va doctor prescribes 10 mg of cough syrup. available is 5 mg/5 ml. how many teaspoons would you give?