Answer:
0.0579
Step-by-step explanation:
P(X≤2) = P(X=0) + P(X=1) + P(X=2)
P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³
P(X≤2) = 0.00032 + 0.0064 + 0.0512
P(X≤2) = 0.0579
Probability of obtaining a success is 0.0579 .
Here,
Binomial distribution formula:
P(x:n,p) = nCx px (1-p)n-x Or P(x:n,p) = nCx px (q)n-x
Substituting the values of n and p
n = 5
p = 0.8
So,
P(X≤2) = P(X=0) + P(X=1) + P(X=2)
P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³
P(X≤2) = 0.00032 + 0.0064 + 0.0512
P(X≤2) = 0.0579
Know more about binomial distribution,
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Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y= -x+5
y=x-3
Answer:
X+5= -x-3
2x = 2
X=1
then y1 is 4
y2 is -1
Answer:
Answer is 4, 1. If you graph the lines, they intersect at 4, 1.
Step-by-step explanation:
Which of the following equations describes the line shown below? Check all
that apply
Answer:
y-7=1/2(x-8)
y-4=1/2(x-2)
Step-by-step explanation:
Slope: 3/6, or 1/2
y-7=1/2(x-8)
y-4=1/2(x-2)
Which expression is equivalent to 24 ⋅ 2−7?
Answer:
41
Step-by-step explanation:
[tex]24*2-7=\\48-7=\\41[/tex]
The area of the sector of a circle with a radius of 8 centimeters is 125.6 square centimeters. The estimated value of is 3.14.
The measure of the angle of the sector is
Answer:
225º or 3.926991 radians
Step-by-step explanation:
The area of the complete circle would be π×radius²: 3.14×8²=200.96
The fraction of the circle that is still left will be a direct ratio of the angle of the sector of the circle.
[tex]\frac{125.6}{200.96}[/tex]=.625. This is the ratio of the circe that is in the sector. In order to find the measure we must multiply it by either the number of degrees in the circle or by the number of radians in the circle (depending on the form in which you want your answer).
There are 360º in a circle, so .625×360=225 meaning that the measure of the angle of the sector is 225º.
We can do the same thing for radians, if necessary. There are 2π radians in a circle, so .625×2π=3.926991 radians.
Answer:
225º
Step-by-step explanation:
divide and simplify x^2+7x+12 over x+3 divided by x-1 over x+4
Answer:
[tex]\dfrac{x^2+8x+16}{x-1}[/tex]
Step-by-step explanation:
In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...
[tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]
The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25 feet.
Answer:
9.233 ft, 23.233 ft
Step-by-step explanation:
If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...
x^2 + (x +14)^2 = 25^2
2x^2 +28x +196 = 625
x^2 +14x = 214.5
x^2 +14x +49 = 263.5
(x +7)^2 = 263.5
x = -7 +√263.5 ≈ 9.23268
The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.
Answer: 9 ft, 23 ft
Step-by-step explanation:
We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.
(x-14)²+x²=25²
(x²-28x+196)+x²=625
2x²-28x+196=625
2x²-28x-429=0
When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].
Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.
A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ a. becomes wider. b. becomes narrower. c. becomes 100.1 to 120.1. d. does not change.
Answer:
b. becomes narrower.
Step-by-step explanation:
Since the 95% confidence interval for a population mean could find out from 100 to 120
And based on this, the coefficient confidence level is declined to 0.90
Therefore the confidence interval for mean should become narrowed
As a 95% confidence interval represents narrower and 99% confidence interval represents wider
Therefore the option B is correct
Using confidence interval concepts, the correct option is:
b. becomes narrower
The margin of error of a confidence interval is given by:
[tex]M = z\frac{s}{\sqrt{n}}[/tex]
In which:
z is the critical value.s is the standard deviation.n is the sample size.The lower the confidence level, the lower the value of z, hence, the margin of error decreases and the interval becomes narrower, which means that option b is correct.
A similar problem is given at https://brainly.com/question/14377677
PLEASE I NEED HELP ASAP sally drives for 2 hours at an average speed of 70 m/h. she then drives for half an hour at an average speed of 40 m/h work ot the total distance that sally has travelled
Answer:
Total Distance = 160 m
Average speed = 64 m/hr
Step-by-step explanation:
For first 2 hours:
Distance = Speed × Time
D = 70 × 2
D = 140 m
For the next half hour:
Distance = Speed × Time
Distance = 40 × 0.5
Distance = 20 m
Now total Distance:
Total Distance = 140+20
Total Distance = 160 m
After that,
Average Speed = Total Distance Covered/ Total Time taken
Average Speed = 160 m / 2.5 hours
Average speed = 64 m/hr
Question from quadratic equation .
solve.
(x-3)(x+7)=0
Answer:
x = 3, -7
Step-by-step explanation:
Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:
x - 3 = 0
x + 7 = 0
x = 3, -7
Answer:
3 or -7
Step-by-step explanation:
For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.
Word related to circle
Answer:
Center, radius, chord, diameter... are Words related to circle
Overweight participants who lose money when they don’t meet a specific exercise goal meet the goal more often, on average, than those who win money when they meet the goal, even if the final result is the same financially. In particular, participants who lost money met the goal for an average of 45.0 days (out of 100) while those winning money or receiving other incentives met the goal for an average of 33.7 days. The incentive does make a difference. In this exercise, we ask how big the effect is between the two types of incentives. Find a 90% confidence interval for the difference in mean number of days meeting the goal, between people who lose money when they don't meet the goal and those who win money or receive other similar incentives when they do meet the goal. The standard error for the difference in means from a bootstrap distribution is 4.14.
Answer:
The 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two means is:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
It is provided that:
[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]
The critical value of z for 90% confidence level is,
z = 1.645
*Use a z-table.
Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
[tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]
Thus, the 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).
A number subtracted from -9
Answer:
x-9
Step-by-step explanation:
An engineering study indicates that 8.5% of the bridges in a large state are structurally deficient. The state's department of transportation randomly samples 100 bridges. What is the probability that exactly 6 bridges in the sample are structurally deficient
Answer:
[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]
Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%
Step-by-step explanation:
Let X the random variable of interest "number of bridges in the sample are structurally deficient", on this case we now that:
[tex]X \sim Binom(n=100, p=0.085)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=6)[/tex]
And if we use the probability mass function and we replace we got:
[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]
Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%
Find sin angle ∠ C.
A. 12/13
B. 1
C. 13/12
D. 13/5
Answer:
A
Step-by-step explanation:
We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:
[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
The opposite side with respect to ∠C is 24 and the hypotenuse is 26.
Hence:
[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]
Our answer is A.
A sample of 8 students was asked how often they used campus dining facilities during the past month. The responses were as follows. 4 1 6 1 2 10 2 6 The sample standard deviation is _____.
Answer:
Your answer is 3.16227766
Step-by-step explanation:
can some one answer this plsss
Answer:
D
Step-by-step explanation:
0.2x+5=8
0.2x=3
x=15
Therefore, the correct answer is choice D. Hope this helps!
(b) How many different groups of children can be chosen from a class of 18 children if the class contains one set of twins who must not be separated?
A population of protozoa develops with a constant relative growth rate of 0.7944 per member per day. On day zero the population consists of two members. Find the population size after six days
Answer:
[tex] y =y_o e^{kt}[/tex]
Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.
For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:
[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]
And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235
Step-by-step explanation:
We can assume that the following model can be used:
[tex] y =y_o e^{kt}[/tex]
Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.
For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:
[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]
And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 30 with a standard deviation of 7 days. Assume the data to be approximately bell-shaped.
Between what two values will approximately 68% of the numbers of days be?
Approximately 68% of the customer accounts have payment made between __________and________________ days
Answer:
Approximately 68% of the customer accounts have payment made between 23 and 37 days.
Step-by-step explanation:
We want to calculate what two values will approximately 68% of the numbers of days be.
For a bell shaped distribution, we can apply the 68-95-99.7 rule, which states that approximately 68% of the data will fall within 1 standard deviation from the mean.
Then, for a mean of 30 and standard deviation of 7, we can calculate the two values as:
[tex]X_1=\mu+z_1\cdot\sigma=30-1\cdot 7=30-7=23 \\\\X_2=\mu+z_2\cdot\sigma=30+1\cdot 7=30+7=37[/tex]
Answer:
The answer is 16 and 44 days.
Step-by-step explanation:
This is the correct answer for this question.
The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes. Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total
Answer:
44.93% probability that the person will need to wait at least 7 minutes total
Step-by-step explanation:
To solve this question, we need to understand the exponential distribution and conditional probability.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Conditional probability:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes
This means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]
Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total
Event A: Waits at least 3 minutes.
Event B: Waits at least 7 minutes.
Probability of waiting at least 3 minutes:
[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]
Intersection:
The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So
[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]
What is the probability that the person will need to wait at least 7 minutes total
[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]
44.93% probability that the person will need to wait at least 7 minutes total
Evaluate the expression 4/15÷x+0.4 for x if: x=1, x=4/9, x=1 1/3. Solve for each X. I need help Will give brainliest!
Answer:
4/15 ÷ x + 0.4
When x = 1
4/15 ÷ 1 + 0.4
x = 2/3
When x = 4/9
4/15 ÷ 4/9 +0.4
x = 1
When x = 1 ⅓ = 4/3
4/15 ÷ 4/3 + 0.4
x = 3/5
Hope this helps.
A biologist conducting an experiment starts with a culture of 300 E. coli bacteria. 72 hours later the culture consists of 600,000 bacteria. What is the average increase in the number of E. coli bacteria per hour
Answer:
2,000
Step-by-step explanation:
if you divide 600,000 by 300 you get 2,000.
Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 4 cm and 6 cm if two sides of the rectangle lie along the legs. webassign cengage
Answer:
[tex]6cm^2[/tex]
Step-by-step explanation:
Let x and y be the sides of the rectangle.
Area of the Triangle, A(x,y)=xy
From the diagram, Triangle ABC is similar to Triangle AKL
AK=4-y
Therefore:
[tex]\dfrac{x}{6} =\dfrac{4-y}{4}[/tex]
[tex]4x=6(4-y)\\x=\dfrac{6(4-y)}{4} \\x=1.5(4-y)\\x=6-1.5y[/tex]
We substitute x into A(x,y)
[tex]A=y(6-1.5y)=6y-1.5y^2[/tex]
We are required to find the maximum area. This is done by finding
the derivative of Aand solving for the critical points.
Derivative of A:
[tex]A'(y)=6-3y\\$Set $A'=0\\6-3y=0\\3y=6\\y=2$ cm[/tex]
Recall that: x=6-1.5y
x=6-1.5(2)
x=6-3
x=3cm
Therefore, the maximum rectangle area is:
Area =3 X 2 =[tex]6cm^2[/tex]
The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it? 10 weeks 13 weeks 15 weeks 21 weeks
Answer: 13 weeks
Step-by-step explanation:
y = -24x + 379
67 = -24x + 379
24x = 379 - 67
x = 312 / 24
x = 13
Answer:
the answer is 13 weeks
Step-by-step explanation:
y = amount left
y = 67
67 = -24x+379
-312 = -24x
x = -312 / -24
x = 13
Please answer this correctly
Answer:
Raspberry: 30%
Strawberry: 15%
Apple: 20%
Lemon: 35%
Step-by-step explanation:
18 + 9 + 12 + 21 = 60 (there are 60 gummy worms)
18 out of 60 = 30%
9 out of 60 = 15%
12 out of 60 = 20%
21 out of 60 = 35%
Please mark Brainliest
Hope this helps
Answer:
Raspberry Worms: 30%
Strawberry Worms: 15%
Apple Worms: 20%
Lemon Worms: 35%
Step-by-step explanation:
Raspberry Worms: [tex]\frac{18}{18+9+12+21}=\frac{18}{60}=\frac{30}{100}[/tex] or 30%
Strawberry Worms: [tex]\frac{9}{18+9+12+21}=\frac{9}{60} =\frac{15}{100}[/tex] or 15%
Apple Worms: [tex]\frac{12}{18+9+12+21} =\frac{12}{60} =\frac{20}{100}[/tex] or 20%
Lemon Worms: [tex]\frac{21}{18+9+12+21} =\frac{21}{60} =\frac{35}{100}[/tex] or 35%
Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.5. (Round your answers to four decimal places.)(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 10 pins is at least 51
Answer:
0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 50, \sigma = 1.5, n = 10, s = \frac{1.5}{\sqrt{10}} = 0.4743[/tex]
What is the probability that the sample mean hardness for a random sample of 10 pins is at least 51
This is 1 subtracted by the pvalue of Z when X = 51. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{51 - 50}{0.4743}[/tex]
[tex]Z = 2.11[/tex]
[tex]Z = 2.11[/tex] has a pvalue of 0.9826
1 - 0.9826 = 0.0174
0.0174 = 1.74% probability that the sample mean hardness for a random sample of 10 pins is at least 51
A lake has a large population of fish. On average, there are 2,400 fish in the lake, but this number can vary by as much as 155. What is the maximum number of fish in the lake? What is the minimum number of fish in the lake?
Answer:
Minimum population of fish in lake = 2400 - 155 = 2245
Maximum population of fish in lake = 2400 + 155 = 2555
Step-by-step explanation:
population of fish in lake = 2400
Variation of fish = 155
it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.
For example
for increase
population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc
but it cannot be beyond 2400 + 155.
It cannot be 2400 + 156
similarly for decrease
population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc
but it cannot be less that 2400 - 155.
It cannot be 2400 - 156
Hence population can fish in lake can be between 2400 - 155 and 2400 + 155
minimum population of fish in lake = 2400 - 155 = 2245
maximum population of fish in lake = 2400 + 155 = 2555
IF UR CLEVER PLEAZE HELP ME OUT I AM ON A LIVE LESSON . NEEDS TO BE ANSWERED STAT!!!!
Answer:
384cm2
Step-by-step explanation:
surface area
12×12=144
10×12/2=60
60×4=240
240+144=384cm2
Jeff's net monthly income is $2550. His monthly expense for rent is $625. What percent of his net monthly income is his rent? (Round your answer to the nearest whole percent.)
Answer:
25%
I cannot really describe how I did it but I am pretty sure it is correct.
Math 7th grade. help please!!!
Answer:
1 .angle S is 90 degree
2. 12
3. 155 degree
1. x = 3
hope it helps .....