Answer:
0.599 or 0.6
Step-by-step explanation:
We will be using the alphabets M and N in this solution.
Let M be that one of the number is even
Let N be that the sum is 8
The sample space of these two dice when rolled is 36
Probability of 8 and even numbers is (4,4),(6,2),(2,6)
= 3/36 = 0.08333
Probability of sum of 8 is (4,4),(5,3)(3,5),(6,2),(2,6)
= 5/36 = 0.1389
P(M|N) = 0.08333/0.1389
= 0.599
Approximately 0.6
Answer:
0.6
Step-by-step explanation:
What is an equation of the line that passes through the points (2, -6) and (-1, 6)?
Answer: (Point-Slope) y+6=-1/4(x-2)
Step-by-step explanation:
1. Find slope (y2-y1)/(x2-x1) = -3/12 simplifies to -1/4
2. Point slope form: y-y1=m(x-x1)
Answer:
The equation is y= - 4x+2 .
a company claims that their new bottle holds 25% more laundry soap. If their original container held 53 ounces of soap, how much does the new container hold?
Answer:
25% of 53 is 13.25 so the new bottle should hold 66.25 ounces or 13.25 mor than the regular bottle
Step-by-step explanation:
Fifty people are in a line. The first person in the line to have a birthday matching someone in front of them will win a prize. Of course, this means the first person in the line has no chance of winning. Which person has the highest likelihood of winning? Defend your answer with a statistically sound argument.
Answer:
20th person
Step-by-step explanation:
Before proceeding into problem,assume that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year.
The probability, p(n), of winning a prize when you are the nth person is line is:
(probability that none of the first n−1 people share a birthday)*( probability that you share a birthday with one of the first n−1 people)
So,The first person can't have the same birthday as anyone less by themselves, so lets look at the second person. At the point where we add the second person there is a 364/365 chance of them not sharing a birthday with the previous person. When we add the 3rd person there is there is a 363/365 chance of them not sharing a birthday and so on such that the (n-1)th person when added has a probability of not forming a share of (365 -n -2)/365. We can multiply these together to get the probability that none of first (n-1) people share their birthday.
Therefore the position in line that has highest chance of winning is 20th.
We want to see which position has the largest probability of winning the prize. We will find that the 18th person has the largest probability of winning.
We know that a person only will win the prize if that person has the same birthday that some in front of him/her.
So, the probability that the n-th person wins the prize is given by:
(probability that none of the persons in front share a birthday)*(probability of sharing a birthday with some of the n - 1 people in front).
Let's find the first one.
The first person can have a birthday in any of the 365 days.
The second person must not have the same birthday, so there are 364 options remaining.
The probability of this is just
p₂ = 364/365
For the third person, we have the same thing, this time, 363 remaining options:
p₃ = 363/365
For the (n - 1) person the probability is:
pₙ₋₁ = (365 - n + 2)/365
And the n-th person must share a birthday with some of the n persons in front of him, so there are (n - 1) options to choose, so the probability is:
pₙ = (n - 1)/365
Then, the joint probability is:
P = p₂*p₃*...*pₙ
[tex]P = \frac{364*363*...*(365 - n + 2)*(n - 1)}{365^{n-1}}[/tex]
Now we have the equation, we just need to solve it for n such that we maximize the value of P in the range n ∈ [1, 50]
This is actually a really hard thing to find, but what you can notice, is that each time that n increases by 1, the denominator increases 365 times.
While the numerator increases by a factor:
(365 - n - 1)*n/(n - 1)
So we need to find the value of n such that the thing above is equal or smaller than 365.
Let's solve:
(365 - n - 1)*n/(n - 1) = 365
(365 - n - 1)*n = 365*n - 365
364*n - n^2 - 365*n + 365 = 0
-n^2 - n + 365 = 0
This is just a quadratic equation, the solutions are:
[tex]n = \frac{1 \pm \sqrt{1 + 4*365} }{-2}[/tex]
We only care for the positive solution, so we take:
[tex]n = \frac{1 - \sqrt{1 + 4*365} }{-2} = 18.6[/tex]
So, for the 19th person, the probability of winning will be smaller than for the 18th person, this happens because the numerator increased by a smaller factor than the denominator.
This means that the 18 person has the largest probability of winning.
If you want to learn more, you can read:
Convert 0.119cL to L
Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below.
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
66 + 36 = 3 (22 + 12)
What statement best describes Gary’s error?
Gary did not use correct factors for 66 in the equation.
Gary did not use correct factors for 36 in the equation.
Gary did not use two equivalent expressions in the equation.
Gary did not use the greatest common factor in the equation.
Answer:
Gary did not use the greatest common factor in the expression.
Step-by-step explanation:
Both factors of 36 and 66 are correct.
Gary also used equivalent expressions. I hope this helps.
Answer: Gary did not use the greatest common factor in the equation.
Step-by-step explanation: Gary did not use the Greatest common factor because the greatest common factor would be 33
Holly checked her answer to a division problem by estimating the quotient which is the best estimation of the quotient 23.564 divided by 5.97
Answer: The best estimation is 4
Step-by-step explanation: I rounded 23.564 to 24 and I rounded 5.97 to 6. I did 24 divided by 6. I got 4.
Answer:
A
Step-by-step explanation:
Factor.
9x^4−64y^2
Enter your answer in the box.
Answer:
(3x² + 8y)(3x² - 8y)
Step-by-step explanation:
9x^4 - 64y^2
~Rewrite
(3x²)² - (8y)²
~Apply difference of two squares
(3x² + 8y)(3x² - 8y)
Best of Luck!
can we conclude that any association that is found in the sample
Answer:
yes
Step-by-step explanation:
a square has a side length represented by the expression 2x + 5. write the expression that represents the area of the square
Answer:
4x+25
I hope this helped ;)
Evaluate q - r if q = -14 and r=-6.
Answer:
-8
Step-by-step explanation:
q - r
-14 - (-6)
-14+6
-8
what is the base of the expression 11 12
Answer:
B. 11
Step-by-step explanation:
Edge 2021 :)
What is the slope of the function?
Answer: Your answer should be, (4)
A PAIR OF SHOES IS DISCOUNTED BY 25%. THE DISCOUNTED PRICE WAS $93.75. WHAT WAS THE ORIGINAL PRICE AHHH SOMEONE ANSWER
Answer:
$70.31
Step-by-step explanation:
Hope this helps
Answer:
$117.19
Step-by-step explanation:
93.75 * .25 =23.4375
23.4375+93.75 = $117.1875
(rounded:$117.19)
The perimeter of the rectangle below is 176 units. Find the value of x.
3x + 1
4x + 3
Una sirena y una persona se acercan entre sí con velocidades de 20 m/s cada una. La sirena emite un sonido de 300 Hz de frecuencia. Halle la frecuencia percibida. (Recuerde que la velocidad del sonido es 343 m/s).
Answer:
La frecuencia percibida es 337,2 Hz.
Step-by-step explanation:
Dado que tanto el emisor del sonido como el receptor se están acercando, la frecuencia percibida es:
[tex] f' = f*\frac{v + v_{r}}{v - v_{e}} [/tex] (1)
En donde:
f': es la frecuencia recibida
f: es la frecuencia emitida = 300 Hz
v: es la velocidad del sonido = 343 m/s
[tex]v_{e}[/tex] es la velocidad del emisor = 20 m/s
[tex]v_{r}[/tex] es la velocidad del receptor = 20 m/s
Sustituyendo los valores en la ecuación (1) tenemos:
[tex]f' = f*\frac{v + v_{r}}{v - v_{e}} = 300 Hz*\frac{343 + 20}{343 - 20} = 337,2 Hz[/tex]
Por lo tanto, la frecuencia percibida es 337,2 Hz.
Espero que te sea de utilidad!
Willie left the mall and traveled toward the town hall at an average speed of 40 km/h. Gabriella left two hours later and traveled in the opposite direction with an average speed of 70 km/h. Find the number of hours Gabriella needs to travel before they are 410 km apart.
a) 1 hour
b) 3 hours
c) 4 hours
d) 2 hours
Answer:
b) 3 hours
Step-by-step explanation:
Given;
speed of Willie , s = 40 km/h
speed of Gabriella, s = 70 km/h
when they are 410 km apart:
Willie's time = t
Gabriella's time = t- 2
2 hours later, the position of Willie = 40t
2 hours later, the position of Gabriella = -70 (t-2) (since he is traveling in opposite direction)
the difference in their positions = 410 km
40t - {-70 (t-2)} = 410
40t -{-70t + 140} = 410
40t + 70t - 140 = 410
110t = 410 + 140
110t = 550
t = 550 / 110
t = 5 hours
Gabriella's time = t- 2
Gabriella's time = 5 - 2 = 3 hours
Thus, Gabriella needs to travel 3 hours before they are 410 km apart.
how many sixths are there in 5/12
Answer:
Step-by-step explanation:
There are 20 sixths in 5/12
Use summation formulas to rewrite the expression without the summation notation .
sum i=1 ^ n 2i^ 3 -3i n^ 4
Factor out 1/n⁴, and distribute the sum over each term:
[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac1{n^4}\sum_{i=1}^n(2i^3-3i)[/tex]
[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac2{n^4}\sum_{i=1}^ni^3-\frac3{n^4}\sum_{i=1}^ni[/tex]
Recall the following formulas:
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4[/tex]
So we have
[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac{n^2(n+1)^2}{2n^4}-\frac{3n(n+1)}{2n^4}=\boxed{\dfrac{(n+1)(n^2+n-3)}{2n^3}}[/tex]
Write the following comparison as a ratio reduced to lowest terms.
44 feet to 9898 yards
Answer:
22:4949
Step-by-step explanation:
Convert the mixed number to a fraction and reduce 7 2/8
Answer:
29/4
Step-by-step explanation:
7 2/8
58/8=29/4
Answer:
29/4
Step-by-step explanation:
multiply 7 and 8 which is 56 then add 2 which will be 58 for the numerator, the denominator stays the same. 58/8 simplify by dividing 58 divided by 2 and 8 divided by 2 which will get u the answer as 29/4
Pls mark as brainliest thank you, have a nice day!!!!
إعراب كلمة (الأزهار) في جملة (قطفت
الأزهار من الحديقة) هو
Answer:اين الجملة؟
Step-by-step explanation:
According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of F and a standard deviation of F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within standard deviations of the mean? At least nothing% of healthy adults have body temperatures within standard deviations of F. (Round to the nearest percent as needed.)
Answer:
At least 89% of the data
Minimum = 96.34 F
Maximum= 100.06 F
Step-by-step explanation:
According to the Chebyshev's theorem 89% of the data are within the 3 standard deviations of the mean.
The mean body temperature is 98.20 F and standard deviation is 0.62 F
Mean- 3SD= 98.20 F- 3(0.62)= 98.20 F- 1.86= 96.34 F
Mean + 3SD= 98.20 F + 3(0.62)= 98.20 F+ 1.86= 100.06 F
A bus is known to arrive every 10 minutes on average at a certain bus stop. You arrive at the bus stop, hoping to catch the bus. How long are you expected to wait for the bus
Answer:
10 minutes maximum
Step-by-step explanation:
well, based on the condition/fact that the bus takes and average of 10 minutes to arrive at a bus stop, you can assume that the previous bus just left(that is worst case scenario), so might have to weight for 1o minutes to get a bus.
Hence for the worst case it is expected that you would have to wait for 10 minutes maximum for the next bus to arrive, or you might even wait for a shorter time.
Will give BRAINLIEST
Answer:
b
Step-by-step explanation:
Answer:
(0, 4)
Step-by-step explanation:
g(x)=-3x+4
y intercept is (0, 4)
Please help. (look at image)
Which of the following measurements is
smallest?
a. 12 inches
b. 216 inches
c. 412 inches
d. 12/4 inches
which expression is equalivent 7 - 4(2x - 3)
A sample of 4 different calculators is randomy selected from a group containing 12 that are defective and 36 that have no defects. What is the probability that a least one of the calculators is defective?
Answer: 0.69727
Step-by-step explanation:
Given: Sample size : n= 4
Number of defective calculators = 12
Number of non-defective calculators = 36
Total calculators = 12+36=48
Let X = Number of defective calculators.
The probability that a least one of the calculators is defective will be :
[tex]P(X\geq1)=P(X=1)+P(X=2)+P(X=3)+P(X=4)\\\\=\dfrac{^{12}C_1\times\ ^{36}C_{3}}{^{48}C_4}+\dfrac{^{12}C_2\times\ ^{36}C_{2}}{^{48}C_4}+\dfrac{^{12}C_3\times\ ^{36}C_{1}}{^{48}C_4}+\dfrac{^{12}C_4\times\ ^{36}C_{0}}{^{48}C_4}\\\\=\dfrac{12\times7140}{194580}+\dfrac{66\times\ 630}{194580}+\dfrac{220\times\ 36}{194580}+\dfrac{495\times\ 1}{194580}\approx0.69727[/tex]
Hence, the required probability = 0.69727
Determine if the ordered pair (1,4) is a solution of 5y - 2x = 16
Show work
Answer:
No, it is not
Step-by-step explanation:
5(4) - 2(1) = 16
20 - 2 = 16
18≠16
Elena walked 12 miles and then she walked 1/4 that distance how far did she walk together
Answer:
15 miles
Step-by-step explanation:
1/4 = .25
12 ÷ 4 = 3
12 + 3 = 15
Answer:
12 1/4 miles
Step-by-step explanation: