Answer:
43.46% probability that the person will need to wait at least 9 minutes total
Step-by-step explanation:
To solve this question, we need to understand conditional probability and the exponential distribution.
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.
Expontial 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]
In this question:
Event A: Waited at least 4 minutes.
Event B: Waiting at least 9 minutes.
The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes.
This means that [tex]m = 6, \mu = \frac{1}{6}[/tex]
Probability of waiting at least 4 minutes.
[tex]P(A) = P(X \geq 4) = P(X > 4)[/tex]
[tex]P(A) = P(X > 4) = e^{-\frac{4}{6}} = 0.5134[/tex]
Intersection:
The intersection between a waiting time of at least 4 minutes and a waiting time of at list 9 minutes is a waiting time of 9 minutes. So
[tex]P(A \cap B) = P(X > 9) = e^{-\frac{9}{6}} = 0.2231[/tex]
What is the probability that the person will need to wait at least 9 minutes total
[tex]P(B|A) = \frac{0.2231}{0.5134} = 0.4346[/tex]
43.46% probability that the person will need to wait at least 9 minutes total
Identify which of these designs is most appropriate for the given experiment: completely randomized design, randomized block design, or matched pairs design. A drug is designed to treat insomnia. In a clinical trial of the drug, amounts of sleep each night are measured before and after subjects have been treated with the drug.
Answer:
Matched pairs design
Step-by-step explanation:
A matched pair design can be used in a case where the same people are being measured in before-and-after comparison. The same set of people are measured for the amount of sleep each night before the administration of the drugs and after the drug administration and this is used to test for a difference.
Bob raked 30 bags of leaves in 3 hours. If he raked the same leaves did he rake per hour
Divide total bags by total hours:
30 bags / 3 hours = 10 bags per hour
What is the common ratio of the geometric sequence below?
-2, 4, 8, 16, -32, ...
-4/2
-2/4
2/4
4/2
Answer:
-4/2
Step-by-step explanation:
just take 4 and divide it by -2 and youll get the common ratio as-2
Hope it helps
The height of a saw tooth in inches after time in seconds is represented by the function y = 0.4sin (15x + 1.5) - 0.2 for t > 0. Without graphing the function, determine the maximum height that the saw tooth reaches.
Answer:
0.2 Inches
Step-by-step explanation:
Given the height of the saw tooth represented by the function
[tex]y = 0.4sin (15x + 1.5) - 0.2$ for $t > 0.[/tex]
Comparing with the general form of a trigonometric equation
[tex]y = A sin(B(x + C)) + D[/tex]
Where:
A =AmplitudePeriod =[tex]2\pi/B[/tex]C=Phase Shift D=Vertical ShiftAmplitude, A=0.4
Vertical Shift (Midline),D = - 0.2
The maximum and minimum height of the sinusoidal function is given by:
[Min, Max]=[D-A, D+A]
=[-0.2-0.4, -0.2+0.4]
=[-0.6,0,2]
The maximum height that the sawtooth reaches is 0.2 inches.
Classify the following triangle as acute, obtuse , or right
Answer:
Acute
Step-by-step explanation:
No angle is bigger than 90 degrees.
Answer:
AcuteAll angles are less than 90 degrees.
Acute = less than 90 degrees
Obtuse = more than 90 degrees
Right = 90 degrees
Hope this helps
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. p(x) = 19x - 15
Step-by-step explanation:
→Set it up, like so:
[tex](25x)-(6x+15)[/tex]
[tex]25x - 6x-15[/tex]
→Add like terms (25x and -6x):
[tex]19x - 15[/tex]
There are five boys and 10 girls in the glee club which ratio represents the number of boys in the club to the total number of students in the club
Answer:
A. 1/3
Step-by-step explanation:
did it on edge, hope this helps :)
To find the ratio, we simply take the amount of boys and put that number first because that is what they asked for first:
5
Then we find the total amount of the students because that is what they ask for next:
5 boys + 10 girls = 15 students
Finally we take those two numbers and put them in a ratio:
5 : 15
(I had to redo my answer cause for some reason my other one was taken down.)
Adrian makes $36.50 per day plus tips. His average tip is 17% of the total amount of money customers spend. Which equation could be used to determine x, the total amount of money customers would need to spend for Adrian to earn a daily income of $150? A. 150 = 36.50 + 17x B. 150 = 0.17 + 36.50x C. 150 = x(17 + 36.50) D. 150 = 36.50 + 0.17x
Answer:
For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:
[tex] y = mx +b[/tex]
Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope m would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:
[tex] 150 = 36.5 +0.17x[/tex]
D. 150 = 36.50 + 0.17x
Step-by-step explanation:
For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:
[tex] y = mx +b[/tex]
Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:
[tex] 150 = 36.5 +0.17x[/tex]
D. 150 = 36.50 + 0.17x
Please answer this correctly
Answer:
Its absolutely cone , it has one triangle face seen from front , and a circular base
Answer:
Rectangular pyramid had a triangular face .
Kyle has decided to start doing crunches as part of his daily exercise routine and is using the bar chart below to keep track of how many he has done each day. How many crunches will he do on day 15?
Answer: 59
Step-by-step explanation:
On 15th day Kyle will do 59 crunches.
What is an Equation?An equation is a statement that consists of algebraic expressions equated with other algebraic expressions by an equal sign.
The crunches Kyle did on Day 1 are 3
The rate by which he is increasing per day is 4 crunches/per day
let t represent the number of days
Let the number of crunches on t day be y
Then the equation formed will be
y = 3 + 4(t-1)
On 15th day, he will do
y = 3+ (15-1) *4
y = 3+56
y = 59
Therefore, on 15th day Kyle will do 59 crunches.
To know more about Equation
https://brainly.com/question/10413253
#SPJ2
helen rolls a dice and flips a coin calculate the probibility that she gets a 4 and tails
Answer:
1/12
Step-by-step explanation:
dice has 6 sides so the prob of getting 4 is 1/6
coin has 2 sides so the prob of getting tails is 1/2
Probability of getting both tails and a four simultaneously is = 1/2×1/6=1/12.
hope this helped!
Please mark as Brainliest!
Answer:
1/12
Step-by-step explanation:
The probability of get a 4 in a die is 1/6 because a die has the following numbers 1,2,3,4,5,6 ; we see each number occurs just once hence; 1/6 is the probability.
The probability of getting a tail is 1/2 because there are one tail and one head in a 2 side face coin.
Hence getting a tail and a four is ;
1/6 × 1/2 = 1/12
The polynomial P(x) = 3 – 2x2 + 5x5 – 7x7 has what order?
Answer:
This, polynomial has order 7.
Step-by-step explanation:
Given the polynomial
P(x) = 3 – 2x2 + 5x5 – 7x7
[tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]
Order for any polynomial is highest exponential value for variables . The exponent for polynomial is also called as degree.
Hence in terms of degree, the term in polynomial which has the highest degree . That degree is the order of the polynomial.
For example ,
in [tex]x^5 + x^8 + x^9[/tex]
here we see that variable x has highest power of 9. Thus, order of the given equation is 9.
Similarly for the polynomial given we see that
in the polynomial [tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]
x has three power 2, 5 and 7 .
As 7 is the highest power of P(x) = 3 - 2x^2+ 5x^5 - 7x^7
This, polynomial has order 7.
The cone-shaped container for the echidna treats holds to 218 cubic centimeters of ants and has a radius of 4 cm. rounded to the nearest whole number, what is the height of the container? use 3.14 for pie symbol
Answer:
13 cm
Step-by-step explanation:
To find the answer, you can use the formula to calculate the volume of a cone and isolate the height:
V= πr^2[tex]\frac{h}{3}[/tex]
V= volume= 218 cubic centimeters
π= 3.14
r= radius= 4 cm
h=height
218= 3.14*4^2*[tex]\frac{h}{3}[/tex]
218*3=3.14*16*h
654=50.24*h
h=654/50.24
h=13
According to this, the height of the container is 13 cm.
Not sure if I got it right...I know it is one of the first 2.
Answer:
Step-by-step explanation:
-6x^2 + x -3 + 2x + 4
________________________
x^2 + 9
-6x^2 + 3x + 1
__________
x^2 + 9
the solution is the first one
Answer:
D.[tex]\frac{-6x^{2}-x-7 }{x^{2}+9}[/tex]
Step-by-step explanation:
since the [tex]x^{2}+9=x^{2} +9[/tex] you just have to add [tex]\frac{-6x^{2}+x-3-2x-4 }{x^{2}+9 }[/tex] so the answer will be: [tex]\frac{-6x^{2}-x-7 }{x^{2}+9 }[/tex]
find the least number divisible by 15,20,24,32and 36
Step-by-step explanation:
I think the first number should be 16
Then these numbers are divisible by 4
SOMEBODY HELP MY FINAL GRADE DEPENDS ON IT THIS IS EASY I JUST FORGOT
Answer:
76
Step-by-step explanation:
The sum of the angles of a triangle add to 180
40+ 3x+10 + 2x+20 = 180
Combine like terms
70 + 5x = 180
Subtract 70
70+5x-70 =180-70
5x = 110
Divide by 5
5x/5 = 110/5
x = 22
We want to find BCA
BCA = 3x+10
= 3(22)+10
= 66+10
=76
Answer:
76
Step-by-step explanation:
The sum of the angles of a triangle add to 180
3x+10 + 2x+20 = 140
5x+30=140
-30 -30
5x=110
x=22
3*22=66+10=76
A construction company buys a bulldozer for $26,000. The company expects the useful life of the machine to be 12 years, at which time its value will have depreciated to $6000. The company uses the declining balances method for depreciation, so the annual depreciation rate r (in decimal form) is given by the formula r=1−(S/C)^1/n . In the formula, n is the useful life of the item (in years), S is the salvage value (in dollars), and C is the original cost (in dollars). What annual depreciation rate (in percent form) did the company use? Round your answer to the nearest tenth.
Answer:
11.5%
Step-by-step explanation:
Put the given numbers in the formula and do the arithmetic.
r = 1 - (6000/26000)^(1/12) = 1 -(3/13)^(1/12) ≈ 1 -0.88498 ≈ 11.5%
The company used a depreciation rate of 11.5%.
A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly?
The student got____problems correct on the test.
Answer:
The student got 16 problem correct
Step-by-step explanation:
Take the number of problems and multiply by the percent correct
20 * 80%
20 *.80
16
The student got 16 problem correct
Answer: The student got 16 problem correct.
Step-by-step explanation: To solve this problem, you first want to take the number of problems that are on the math test and multiply that by the percent the student got correct.
So we have 20 × 80%
Now write 80% as a decimal to get .80.
So we have 20 × .80 which is equal to 16.
So the student got 16 problems correct
and 4 problems incorrect on their test.
A wire with a length of 100 cm is cut into three parts. The length of wire of the first and second parts are the same. The length of the third part of the wire exceeds the sum of the first two parts by 4 cm. Calculate the length of each part.
The first two pieces are the same, let each of those equal x, so you have x + x = 2x
The 3rd piece is the sum of the first two + 4, so this would be 2x + 4
Now you have 2x + 2x + 4 = 100 cm
Combine like terms:
4x +4 = 100
Subtract 4 from both sides
4x = 96
Divide both sides by 4
X = 24
First piece is 24 cm
Second piece is 24 cm
Third piece is 52 cm
Joseph is creating a dilation through point B with a scale factor of 2. Which statements about the dilation are correct? Check all that apply. Triangle A B C. Angle B is a right angle.
Answer:
Options (1), (2) and (4).
Step-by-step explanation:
Given question is incomplete; Find the complete question in the attachment.
Triangle ABC is a right triangle.
ΔABC has been dilated by a scale factor of 2 forming ΔA'B'C'.
These are the observations,
1). A and A' will be co-linear.
2). Since the given triangle has been dilated about a point B therefore, after dilation vertex B and B' will at be same location.
3). Length of B'C' = 2BC
4). AB and BC are the segments which will lie on the sides BA' and BC'.
5). Pre-image ABC will be inside the image A'B'C'.
Therefore, Options (1), (2) and (4) will be the answer.
A B and D
i just took the quiz on edge
ill mark you as brainliest if you get this correct
Answer:
a) 72
b) 9
c) 9
d) 54
Step-by-step explanation:
a) 12 * 6 = 72
b) 3 * 6 = 18. 18 ÷ 2 = 9
c) 3 * 6 = 18. 18 ÷ 2 = 9
d) 72 - 18 = 54
Edith wants to make a paperweight at pottery class. She wants the paperweight to have a pyramid-like shape with a base area of 120120120 square centimeters, and she wants it to weigh 400400400 grams. The density of the clay she is using is 1.61.61, point, 6 grams per cubic centimeter.
What should be the height of the paperweight?
Answer:
Step-by-step explanation:
We would determine the volume of the
pyramid-like paperweight. Formula for volume is expressed as
Volume = mass/density
From the information given,
mass = 400g
Density = 1.61g/cm³
Volume = 400/1.61 = 248.45cm³
The formula for determining the volume of a pyramid us expressed as
Volume = 1/3 × base area × height
From the information given,
Base area = 120 cm²
Volume = 248.45cm³
Therefore,
248.45 = 1/3 × 120 × height
248.45 = 40 × height
height = 248.45/40 = 6.2 cm
the answer to this !!!
Answer: A=12, B=2, C=11
Step-by-step explanation:
With the given problem, you would first expand the numerator.
[tex]\frac{x^1^5y^3z^1^2}{x^3yz}[/tex]. Then you can simply from there. You can subtract the exponents. [tex]x^1^2y^2x^1^1[/tex]
HDTV screens usually have a width-to-heigh ratio of 16:9. Which screen dimensions are in the same proportion?
Answer:
4: 3
Step-by-step explanation:
In this case, we have that there is a relationship between width and height, which is 16: 9, which means that any screen that has the same ratio would be an identical screen.
How would we do this? it must either be raised to a power or rationalized on both sides of the ratio.
If we raise to a power, it would give very large dimensions for an HDTV, therefore, it is best to remove the square root on both sides, since it has more common values for a TV.
[tex]\sqrt{16} :\sqrt{9}[/tex]
4: 3
Therefore, a 4: 3 screen is a good choice for an HDTV with the same ratio.
Answer:
Ideiidididid
Step-by-step explanation:
Cici
If 8-2x<12 is -2 a solution to the inequality
Answer:
no
Step-by-step explanation:
Let's plug in -2 for x.
8 - 2 (-2) <12
8 + 4 < 12
12 < 12
Since this is a false statement, -2 is not a solution to the inequality.
Answer: No
Step-by-step explanation: To determine whether x = -2 is a solution to the inequality, substitute a -2 in for r.
So we have 8 - 2(-2) < 12.
Notice that I used parentheses.
This is a great habit to get into when
substituting numbers in for variables.
So we have 8 - (-4) which can be changed to 8 + (+4) or +12.
Since 12 is not less than 12, -2 is not a solution.
An urn contains 3 red and 7 black balls. Players and withdraw balls from the urn consecutively until a red ball is selected. Find the probability that selects the red ball. ( draws the first ball, then and so on. There is no replacement of the balls drawn.)
Correct question:
An urn contains 3 red and 7 black balls. Players A and B withdraw balls from the urn consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball, then B, and so on. There is no replacement of the balls drawn).
Answer:
The probability that A selects the red ball is 58.33 %
Step-by-step explanation:
A selects the red ball if the first red ball is drawn 1st, 3rd, 5th or 7th
1st selection: 9C2
3rd selection: 7C2
5th selection: 5C2
7th selection: 3C2
9C2 = (9!) / (7!2!) = 36
7C2 = (7!) / (5!2!) = 21
5C2 = (5!) / (3!2!) = 10
3C2 = (3!) / (2!) = 3
sum of all the possible events = 36 + 21 + 10 + 3 = 70
Total possible outcome of selecting the red ball = 10C3
10C3 = (10!) / (7!3!)
= 120
The probability that A selects the red ball is sum of all the possible events divided by the total possible outcome.
P( A selects the red ball) = 70 / 120
= 0.5833
= 58.33 %
PLSSSS HELP!!! what is the slope from 0 to 1 seconds?
Answer:
Since there is no change in the height value over that time, the slope is 0
Find the value of x.
Answer:
x = 98
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
x + 24 = 122
Subtract 24 form each side
x+24-24 =122-24
x =98
Answer:
[tex] x = 98 \: \: degrees \\ [/tex]
Step-by-step explanation:
The exterior angle is equal to sum of opposite interior angles in a triangle.
[tex]24 + x = 122 \\ x = 122 - 24 \\ x = 98 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A coffee shop uses two different-sized bins to store coffee beans. The volume of the smaller bin is x cubic inches and the volume of the larger bin is y cubic inches. The store has S smaller bins and L larger bins. Which expressions represents the total volume of all the bins?
Answer:
Total volume of all the bins = xS + yL
Step-by-step explanation:
Given: x cubic inches represent the volume of the smaller bin and y cubic inches represents the volume of the larger bin. The store has S smaller bins and L larger bins.
To find: an expression that represents the total volume of all the bins
Solution:
The volume of the smaller bin = x cubic inches
The volume of the larger bin = y cubic inches
Also, the store has S smaller bins and L larger bins
So,
Total volume of all the bins = xS + yL
Answer:
xS plus yL
Step-by-step explanation:
A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probabilities of these events:_________.
A. At least one alarm is triggered.
B. More than seven alarms are triggered.
C. Eight or fewer alarms are triggered.
Answer:
a) [tex] P(X \geq 1) = 1-P(X<1) = 1-P(X=0)[/tex]
[tex]P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}[/tex]
And replacing we got:
[tex] P(X \geq 1) =1 -1x10^{-18} \approx 1[/tex]
b) [tex]P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355[/tex]
[tex]P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And adding we got:
[tex] P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992[/tex]
c) [tex] P(X \leq 8) =1 -P(X>8) = 1-P(X=9)[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And replacing we got:
[tex] P(X \leq 8)= 1-0.913517=0.086483[/tex]
Step-by-step explanation:
Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:
[tex]X \sim Binom(n=9, p=0.99)[/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]
Part a
We want to find this probability:
[tex] P(X \geq 1) = 1-P(X<1) = 1-P(X=0)[/tex]
[tex]P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}[/tex]
And replacing we got:
[tex] P(X \geq 1) =1 -1x10^{-18} \approx 1[/tex]
Part b
[tex] P(X \geq 7)= P(X=7) +P(X=8)+ P(X=9) [/tex]
[tex]P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355[/tex]
[tex]P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And adding we got:
[tex] P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992[/tex]
Part c
[tex] P(X \leq 8) =1 -P(X>8) = 1-P(X=9)[/tex]
[tex]P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517[/tex]
And replacing we got:
[tex] P(X \leq 8)= 1-0.913517=0.086483[/tex]
