Answer:
The answer is "[tex]7.21 \times 10^{37}[/tex]".
Step-by-step explanation:
[tex]\to ^{n}_{C_r}=\frac{n!}{r!(n-r)!}[/tex]
[tex]=^{66}_{C_{33}} \times ^{66}_{C_{22}} \times ^{55}_{C_{1}} \\\\=\frac{66!}{33! (66-33)!} \times \frac{66!}{22! (66-22)!} \times \frac{55!}{1! (55-1)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55\times 54!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times 55\\\\= 7219428434016265740 \times 182183167981760400\times 55\\\\[/tex]
[tex]= 7.21 \times 10^{18} \times 1.82\times10^{17}\times 55\\\\= 7.21 \times 10^{35} \times 1.82\times 55\\\\=721.721 \times 10^{35}\\\\=7.21\times 10^{37}[/tex]
The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of 10 minutes and a standard deviation of 3 minutes. Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
Answer:
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 10 minutes and a standard deviation of 3 minutes
This means that [tex]\mu = 10, \sigma = 3[/tex]
Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
This is 1 subtracted by the p-value of Z when X = 15, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 10}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
two sides of a triangle measure 5 in and 12 in what could be the length of the third side
Answer:
b
Step-by-step explanation:
4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?
Answer:
12
Step-by-step explanation:
how did the tempicher change if at first it increased by 5% and then increased by 20 percent
Answer:
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
Step-by-step explanation:
Take a number, x.
Now increase it by 5%.
1.05x
Now increase it by 20%.
1.2 * 1.05x = 1.26x
1.26x = 126% of x = 100% of x + 26% of x
100% of x is the same as x, so it is the same as the original x.
The increase is 26% of the original number.
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
Write 2^60 the expression as a exponent with the base of 4
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]2^{60} =2^{2 \times 30} =(2^{2} )^{30}=4^{30}[/tex]
A box contains 16 large marbles and 18 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 3 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green
Answer:
[tex]P(S&G) =0.7941[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=16+18=>34[/tex]
N0 of Large [tex]L=16[/tex]
N0 of Small [tex]S=18[/tex]
N0 large Green [tex]L_g=9[/tex]
N0 of small White [tex]S_w=3[/tex]
Therefore
Number of green marbles [tex]N0(G)=9+(18-3)[/tex]
Number of green marbles [tex]N0(G)=24[/tex]
Generally the Number of both small and green Marble is
[tex]N0 of (S&G)= 18 - 3 = 15[/tex]
Generally the probability that it is small or green P(S&G) is mathematically given by
[tex]P(S&G) = \frac{(18 + 24 - 15)}{(18 + 16)}[/tex]
[tex]P(S&G) =0.7941[/tex]
Zoe has 4 pounds of strawberries to make pies. How many ounces of strawberries Is this?
64 oz.
60 oz.
68 oz.
72 oz.
Work Shown:
1 pound = 16 ounces
4*(1 pound) = 4*(16 ounces)
4 pounds = 64 ounces
Simplify: (w^3)^8 * (w^5)^5
Answer:
(w^3)^8 * (w^5)^5 = w^49
Step-by-step explanation:
(w^24) * (w^25)
using exponent rule
w^24 • w^25 = w^24+25
w^49
Answer:
Step-by-step explanation:
(W^24)*(W^25)
W^24+25
=W^49
calculate the resistance if V = 220V and I = 3.6amp
Step-by-step explanation:
V= IR --> R = V/I = (220 V)/(3.6 A) = 61.1 ohms
Answer:
61.11 ohms
Step-by-step explanation:
R=V/I
R=220/3.6
R=61.11 ohms
A Food Marketing Institute found that 34% of households spend more than $125 a week on groceries. Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31
Answer:
0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population.
This means that [tex]p = 0.34, n = 124[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.34[/tex]
[tex]s = \sqrt{\frac{0.34*0.66}{124}} = 0.0425[/tex]
What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?
This is the p-value of Z when X = 0.31, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.31 - 0.34}{0.0425}[/tex]
[tex]Z = -0.705[/tex]
[tex]Z = -0.705[/tex] has a p-value of 0.2405.
0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
There is a 60% probability that a home in the United States has a large-screen TV. In a sample of six homes, what is the probability that there will be a large screen TV in:_________a). All 6 homes? b). None of the homes c). At least 5 of the homes? d). At most 2 of the homes? e). More than 3 of the homes? f). Less than 3 of the homes? g). How many homes would you expect to have a large-screen TV in a sample of six homes?
Answer:
faster and smarter Homes its b
Step-by-step explanation:
I did this one
What is the greatest common factor of 16ab3 + 4a2b + 8ab ?
Answer:
2ab(3b^2+2a+4)
Step-by-step explanation:
6ab^3 + 4a^2b + 8ab
2*3*a*b*b^2 +2*2*a*a*b +2*2*2*a*b
Factor out the common terms
2ab( 3*b^2 +2*a +2*2)
2ab(3b^2+2a+4)
AABC-AXYZ. What's the scale factor from
AABC to AXYZ?
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Answer:
(d) 1/4
Step-by-step explanation:
The scale factor is the ratio of lengths of corresponding sides:
XZ/AC = 3/12 = 1/4
_____
Additional comment
I find the wording of the question a bit ambiguous. To transform ΔABC to ΔXYZ, every linear dimension of ΔABC is multiplied by 1/4. This is the sense of "ΔABC to ΔXYZ" that is used in the above answer.
On the other hand, one of the ways ratios are written is using the word "to," as in "12 to 3". Using this idea, we might interpret the question to be asking for ...
ΔABC to ΔXYZ = AC to XZ = 12 to 3 = 12/3 = 4
Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202
Answer:
Kindly check explanation
Step-by-step explanation:
Rounding each number to 4 significant figures and expressing in standard notation :
(a) 102.53070,
Since the number starts with a non-zero, the 4 digits are counted from the left ;
102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2
(b) 656.980,
Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.
656.980 = 657.0 (4 significant figures) = 6.57 * 10^2
(c) 0.008543210,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3
(d) 0.000257870,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4
(e) -0.0357202,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2
Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3? in a test plese help fast
Answer:
Graph (a)
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x+ 6} -3[/tex]
Required
The graph
First, calculate y, when x = 0
[tex]y = \sqrt[3]{0+ 6} -3[/tex]
[tex]y = \sqrt[3]{6} -3[/tex]
[tex]y = -1.183[/tex]
The above value of y implies that the graph is below the origin when x = 0. Hence, (c) and (d) are incorrect because they are above the origin
Also, only the first graph passes through point (0,-1.183). Hence, graph (a) is correct
Answer:
the answer is A
Step-by-step explanation:
22
20
14
22
29
20
Mean
Mode
Medium
Range
Answer:
mean=21.17
mode=20,22
median=3.5
range=15
Step-by-step explanation: MEAN=sum of all observations/ no. of observations
mean=22+20+14+22+29+20/6
mean=127/6
mean=21.17
MODE= most frequent observations
mode=22,20
MEDIAN=1/2(n/2+n+2/2)
=1/2(6/2+6+2/2)
=1/2(3+4)
=1/2(7)
=7/2
=3.5
RANGE=X max -X min
=29-14
=15
I need help ASAP please no links
Answer: D' = (1, -1)
Step-by-step explanation:
When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).
PLEASE HELPPPPPPP #1
Answer:
is the second answer 2x+1/x-1
I need all the help I can get. please assist.
4. The equation of a curve is y = (3 - 2x)^3 + 24x.
(a) Find an expression for dy/dx
5. The equation of a curve is y = 54x - (2x - 7)^3.
(a) Find dy/dx
Answer:
4(a).
Expression of dy/dx :
[tex]{ \tt{ \frac{dy}{dx} = - 2(3 - 2x) {}^{2} + 24}}[/tex]
5(a).
[tex]{ \tt{ \frac{dy}{dx} = 54 - 2(2x - 7) {}^{2} }}[/tex]
The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?
Answer:
B. 28, 32, 36 millions
Step-by-step explanation:
Given:
P(t) = 24 + 0.4t
Where,
P(t) = population in millions
t = number of years
✔️Value of the population when t = 10:
Plug in t = 10 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(10)
P(t) = 24 + 4
P(t) = 28 million
✔️Value of the population when t = 20:
Plug in t = 20 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(20)
P(t) = 24 + 8
P(t) = 32 million
✔️Value of the population when t = 30:
Plug in t = 30 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(30)
P(t) = 24 + 12
P(t) = 36 million
whats the next two terms in order are p+q, p , p-q
Answer:
p - 2q and p - 3q
Step-by-step explanation:
A Series is given to us and we need to find the next two terms of the series . The given series to us is ,
[tex]\rm\implies Series = p+q , p , p - q [/tex]
Note that when we subtract the consecutive terms we get the common difference as "-q" .
[tex]\rm\implies Common\ Difference = p - (p + q )= p - p - q =\boxed{\rm q}[/tex]
Therefore the series is Arithmetic Series .
Arithmetic Series:- The series in which a common number is added to obtain the next term of series .
And here the Common difference is -q .
Fourth term :-
[tex]\rm\implies 4th \ term = p - q - q = \boxed{\blue{\rm p - 2q}}[/tex]
Fifth term :-
[tex]\rm\implies 4th \ term = p - 2q - q = \boxed{\blue{\rm p - 3q}}[/tex]
Therefore the next two terms are ( p - 2q) and ( p - 3q ) .
An item costs $20 and sells for $50.
a. Find the rate of markup based on cost.
b. Find the rate of markup based on selling price.
Step-by-step explanation:
50-20=30 rate of markup
1. What is the theoretical probability that the family has two dogs or two cats?
2.
Describe how to use two coins to simulate which two pets the family has.
3. Flip both coins 50 times and record your data in a table
like the one below.
Frequency
Result
Heads, Heads
Heads, Tails
Tails. Heads
Tails. Tails
Total
50
4
Based on your data, what is the experimental probability that the family has two dogs or
two cats?
5
If the family has three pets, what is the theoretical probability that they have three dogs or
three cats?
How could you change the simulation to generate data for three pets
6
let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. Note that there can be the possible outcomes
h-h, h-t, t-h, t-t.
How this affects the possibility of two dogs & two cats. Note that there are 1/2 a chance of getting those two (with the others being one of each), which means that out of 4 chances, 2 are allowed.
2/4 = 1/2
50% is your answer
Heads represents cats and tails represents dogs. There is two coins because we are checking the probability of two pets. You have to do the experiment to get your set of data, once you get your set of data, you will be able to divide it into the probability for cats or dogs. To change the simulation to generate data for 3 pets, simply add a new coin and category for the new pet.
Hope this helps you out!
Calculate the product below and give your answer in scientific notation.
(3.3 x 10-4) (8.0 x 109) = ?
Show Calculator
Answer:
25288
Step-by-step explanation:
shown in the picture
Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2
Answer:
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
Step-by-step explanation:
We have the mean during the interval, which means that the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Lost-time accidents occur in a company at a mean rate of 0.8 per day.
This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.
10 days:
This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]
What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]
[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]
[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]
So
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
How do I figure this question out
Answer:
Orthocenter would be in the middle of the shape.
Step-by-step explanation:
B.
A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1
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Answer:
(b) x = 1
Step-by-step explanation:
A graph shows the solution to f(x) = g(x) is x = 1.
__
We want to solve ...
g(x) -f(x) = 0
x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0
x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping
(x^2 -1)(x +2) +11/3(x -1) = 0 . . . . . . the difference of squares can be factored
(x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor
(x -1)(x^2 +3x +2 +11/3) = 0
The zero product rule tells us this will be true when x-1 = 0, or x = 1.
__
The discriminant of the quadratic factor is ...
b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3
This is less than zero, so any other solutions are complex.
Two complex numbers have a sum of 14 and a product of 74. Write either of the two numbers.
Answer:
Hello,
Step-by-step explanation:
The 2 numbers are roots of the equation:
U²-14U+74=0
Discriminant=14²-4*74=-100
U=7-5i or U=7+5i
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Answer:
7 +5i or 7 -5i
Step-by-step explanation:
If the two numbers are represented by x and y, then ...
x+y = 14
xy = 74
Substituting for y, we have ...
x(14 -x) = 74
x^2 -14x +49 = -74 +49 . . . . . multiply by -1, complete the square
(x -7)^2 = -25 . . . . . . . . . . . write as a square
x -7 = ±√(-25) = ±5i . . . . take the square root
x = 7 ± 5i . . . . . . . . . . . add 7
One of the numbers is 7 +5i.
if the lines 3x+2ky=0 and 2x+5y+1=0 are parallel, then what is the value of k?
Answer:
k = 15/4
Step-by-step explanation:
Slope of a line = -a/b
slope of the first line = -3/2k
slope of the second line = -2/5
the slope of two parallel lines are congruent
-3/2k = -2/5
-15 = -4K
k = 15/4
find the slope of the line passing through the points (-4, -7) and (4, 3)
Answer:
5/4
Step-by-step explanation:
Use the slope formula which is y2-y1/x2-x1.
1. Plug the given values into the equation: 3-(-7)/4-(-4)=5/4
