Answer:
P(X ≥ 125) = 0.9812
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the normal distribution.
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^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.
Normal 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.
The Poisson can be approximated to the normal, with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]
Let μ = 2.5 every minute
This is the mean of the Poisson, so [tex]\lambda = 2.5n[/tex], in which n is the number of minutes.
P(X ≥ 125) over an hour
An hour has 60 minutes, so [tex]n = 60, \lambda = 2.5*60 = 150, \sigma = \sqrt{150} = 12.25[/tex]
Using continuity correction, this is [tex]P(X \geq 125 - 0.5) = P(X \geq 124.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 124.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{124.5 - 150}{12.25}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a pvalue of 0.0188
1 - 0.0188 = 0.9812
So
P(X ≥ 125) = 0.9812
8) What percent of 38 is 15
Answer:
39.4736842105 or 39.47, but in integers is 39
Step-by-step explanation:
38/100=.38
15/.38=39.4736842105
Answer:
39.4736842105% or 39.47%
Step-by-step explanation:
To find what percent of 38 is 15, take 15 divided by 38
15/38 = 0.394736842105
Double check this answer by working backwards
38 x 0.394736842105 = 15
Change 0.394736842105 into a percentage because a percentage is what is needed
0.394736842105 = 39.4736842105% = 39.47%
Suppose ø is an angle in the standard position whose terminal side is in Quadrant I and tan ø = 60/11
Answer:
Following are the ratio to this question:
Step-by-step explanation:
Given:
[tex]\bold{\tan \phi = \frac{60}{11} }\\\\[/tex]
Formula:
[tex]\sin \phi = \frac{Perpendicular}{Hypotenuse}\\\\\cos \phi = \frac{Base}{Hypotenuse} \\\\\tan \phi = \frac{Perpendicular}{Base} \\\\\ cosec \phi = \frac{Hypotenuse}{Perpendicular}\\\\\sec \phi =\frac{Hypotenuse}{Base}\\\\\cot \phi = \frac{Base}{Perpendicular}\\\\[/tex]
[tex]\ Base = 11 \\\ Perpendicular =60\\\ Hypotenuse= 61\\[/tex]
[tex]\sin \phi = \frac{60}{61}\\\\\cos \phi = \frac{11}{61} \\\\\tan \phi = \frac{60}{11} \\\\\ cosec \phi = \frac{ 61}{60}\\\\\sec \phi =\frac{61}{11}\\\\\cot \phi = \frac{11}{60}\\\\[/tex]
The two-way table shows the number of students in a school who have cats and/or dogs as pets.
How many more students have cats than dogs?
Answer:
3
Step-by-step explanation:
43-40=3
As a basketball is bounced, the motion is parabolic. In the graph above, y = 0 represents hand level for a basketball player. Find the focus and directrix of the middle bounce (parabola).
Answer:
A on edge2020
Step-by-step explanation:
A large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $5 each, but only 3,600 shower curtains per month for $10 each. What is the linear demand function for your tie-dye shower curtains
Answer:
q= -40p+c
q= -40p+4,000
Step-by-step explanation:
$5 each for 3800 tye-dye shower curtains
$10 each for 3600 tye-dye shower curtains
Slope of the demand line is
3800-3600/5-10
=200/-5
= -40
Demand function is
q= -40p + c
Where c is a constant
For q=3800 and p=$5
Demand function is
q= -40p + c
3800= -40(5)+c
3800= -200+c
c=3800+200
c=4,000
Linear demand function is
q= -40p+4,000
You own a Roulette Wheel, which has 37 (European Version) equally distributed parts, each has a number number associated. 0 is green, the rest 36 includes 18 red and 18 black. The money you have to pay to the gambler for hitting green, red and black are 10, 1 and 2 dollars respectively. How much you have to charge per play in order to make sure you will make money?
Answer:
To expect a profit in the long run, we have to charge more than $1.73 per play.
Step-by-step explanation:
We hace a roulette wit 37 slots.
One is green, eighteen are red and eighteen are black.
The expected pay for the gambler can be calculated as the sum of the probability of getting green, red or black multiplied by the respective pay.
[tex]E(g)=\sum p_iG_i=p_gG_g+p_rG_r+p_bG_b\\\\\\E(g)=\dfrac{1}{37}(10)+\dfrac{18}{37}(1)+\dfrac{18}{37}(2)\\\\\\E(g)=\dfrac{10+18+36}{37}=\dfrac{64}{37}\approx1.73[/tex]
If $1.73 per play is the expected pay that will receive the gambler, we have to charge at least this amount to make sure we will make a profit in the long run.
What is m ABC?
m ABC = 15°
m ABC = 45°
mABC = 60°
m ABC = 75°
Answer:
C) 60
Step-by-step explanation:
m ABC is 60 degrees
Answer:
The answer is mABC = 60°
After all your hard work studying for Algorithms you, Alice and Bob end up stuck in a room full of deadly zombies! Luckily you have a gun with plenty of ammunition and can reliably shoot one zombie dead every second. Each zombie is di feet away and moving at a speed of si feet per second. If a zombie reaches you then you all die. You are arguing about what order to shoot the zombies so you live as long as possible.
1. State this input and output conditions for this optimization problem.
2. Alice suggests shooting the closest zombie first. Give a counterexample that shows this is incorrect.
3. Bob suggests shooting the fastest zombie first. Give a counterexample that shows this is incorrect.
4. What order should you shoot the zombies?
5. Prove your order will let you live the longest. Grading You will be docked points for errors in your math, disorganization, unclarity, or incomplete proofs.
Answer:
The most important quantity to consider in order to answer this question is the arrival time of the zombies from their initial position, which is the quotient between their distance to the visitors, divided the zombie's speed.
See explanation below.
Step-by-step explanation:
Part 1)
What is crucial to know is what is the time at which each zombie would reach Alice and Bob, and that is given by the quotient between the distance away each zombie is, divided by the zombie's speed:
[tex]speed=\frac{distance}{time} \\time=\frac{distance}{seed} \\t_i=\frac{d_i}{s_i}[/tex]
Then, it is this quotient for each zombie, that one has to estimate given the input values distance and speed, and it is the output "time" ([tex]t_i[/tex]) for each zombie, what we need to analyze so as to prioritize an order regarding which zombie to kill first.
Part 2)
Shooting the closest zombie first is not a good idea, since the speed of that closest zombie may be much slower than another zombie further away, but with much larger speed. Again, the important value to analyze is the time that it would take each zombie to reach Alice and Bob.
Part 3)
Shooting the fastest zombie first is not a good idea either, because that fastest zombie could be located very far away from the visitors, and other zombies closer by may reach them first.
Part 4)
The order that should be used to kill the zombies is given by the value of the time to reach Bob and Alice based on the quotient distance (di) over speed (si) explained in Part 1). The zombie that shows smallest time should be shot first, and then the others in increasing order of time value.
Part 5)
Notice that the individual zombie information is not presented in the question, but the student should be able to calculate the quotients for each zombie, and considering that there could be at most one shot every second, estimate the number of seconds that the time for each zombie in increasing order would allow until the addition of shooting time per second in the appropriate order cannot match the arrival time of the zombies that are left.
One should count number of seconds from the first shot (to the zombie with shortest arrival time), and then increase in one unit (one shot per second), to the following zombie with slightly larger arrival time), and so on, until the addition of seconds (one second per shot and per increasing arrival time of zombie) exceeds the next zombie arrival time.
Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted?
Answer:
876 square feet need to be painted.
Step-by-step explanation:
There are four walls in each bedroom, since she can't paint floors or ceilings. So we calculate the number of square feet of wall there is in one bedroom
(12*8)+(12*8)+(10*8)+(10*8)-60=160+192-60=292
There are 3 bedrooms so
292*3=876
Find the area A of △JKL with vertices J(−4,10), K(0,3), and L(−4,−2).
Answer:
24 sq. u.
Step-by-step explanation:
1)For this triangle area, let's use the classic Euclidean formula:
[tex]\Delta \: area=\frac{b*h}{2}[/tex]
2) Let's measure the lenght of the base, taking the y coordinate of J vertex and L Vertex
[tex]|10-(-2)|=|12|=12[/tex]
3) Similarly to the height, taking the K and its distance to the base
|0-(-4)|=|4|=4
4) Plugging them in:
[tex]\Delta \: area=\frac{12*4}{2}=24[/tex]
Answer:
24 Square Units
Step-by-step explanation:
Write the ratio as a fraction in simplest form.
18
84
Answer:
3/14
Step-by-step explanation:
Please help me !!!!?
Let [tex]n[/tex] be the smallest integer; then, the other two integers are [tex]n+1[/tex] and [tex]n+2,[/tex] so we have the equation [tex]3n+3=63.[/tex] Solving, we have [tex]n=20,[/tex] so the integers are [tex]\boxed{20,21,22}.[/tex]
what is the midpoint between (-3,-2) and (4,7)?
Answer:
1/2, 5/2
Step-by-step explanation:
To find the midpoint add up the x coordinates and divide by 2 and the y coordinates and divide by 2
(-3+4)/2, (-2 +7)/2
1/2, 5/2
Answer:
[tex](\frac{1}{2}, \frac{5}{2} )[/tex]
Step-by-step explanation:
Use the midpoint formula:
[tex](\frac{-3+4}{2} , \frac{-2+7}{2} )[/tex]
The points are:
[tex](\frac{1}{2}, \frac{5}{2} )[/tex]
A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos
Imagine you stick your hand into the refridgerator and pull out a piece of fruit at random. what is the sample space for this process?
a. s={apple, orange, banana, pear, plum, mango}
b. s= {6,5,10,3,7,11,2}c. s= {6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, 2 mangos
Answer:
s={apple, orange, banana, pear, peach, plum, mango} (option A)
Step-by-step explanation:
The sample space of an experiment is the set of all possible outcomes of that experiment.
The sample space is essential in finding the probability of an event associated with a random experiment.
In this question, the set of all possible outcomes of the experiment are apples, oranges, bananas, pears, peaches, plums and mangos.
Therefore the sample space for the process is: s={apple, orange, banana, pear, peach, plum, mango} (option A)
Where s = sample space
Though peach was omitted in the set in option A by mistake, the correct answer:
s={apple, orange, banana, pear, peach, plum, mango}
Given that 5−3x=Px+R, in order to create an equation with no solutions, when R=7, then P= [blank]
Enter the value that correctly fills in the blank, like this: 42
Answer:
p=-3
Step-by-step explanation:
5-3x = Px +7
-7 from both sides
-2-3x=Px+7
add 3x to both sides
-2=Px+3x
P =-3 because it will get rid of variable
Answer:
x= -22.5
Step-by-step explanation:
5–3x=Px + R
r= 7
P= 42
5–3x =42x + 7
-3x -42x = 7- 5
-45x =2
x= -22.5
80% of the students voted for Jane as dass
president she received 112 votes, how
many students voted?
A140
B228
C 152
D 148
Answer:
A
Step-by-step explanation:
140 x 0.8 = 112
Answer:
140 students voted (Answer A)
Step-by-step explanation:
Let v represent the total number of students who voted.
Then 0.80v = 112 votes.
Dividing both sides by 0.80, we get:
v = 140. 140 students voted.
As a check, find 80% of 140 students: that comes out to 112 students (correct)
A frequency distribution for the class level of students in an introductory statistics course is shown. Two students are randomly selected without replacement. Complete parts (a) through (d).
Class
Frequency
Freshman
6
Sophomore
16
Junior
12
Senior
7
a. Determine the probability that the first student obtained is a junior and the second a senior.
Answer: [tex]\dfrac{21}{410}[/tex].
Step-by-step explanation:
Formula : Probability = [tex]\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
From the given frequency distribution for the class level of students in an introductory statistics course, we have
Number of Junior= 12
Number of Senior = 7
Total students = 6+16+12+7 = 41
Probability that the first student obtained is a junior = [tex]\dfrac{12}{41}[/tex]
Probability that the the second student obtained is a senior. [tex]=\dfrac{7}{41-1}=\dfrac{7}{40}[/tex]
Then, the probability that the first student obtained is a junior and the second a senior would be [tex]\dfrac{12}{41}\times\dfrac{7}{40}=\dfrac{21}{410}[/tex]
Hence, the required probability is [tex]\dfrac{21}{410}[/tex].
Gueguen and Jacob asked waitresses to wear different colored T-shirts on different days for a six-week period and recorded the tips left by male customers. The results show that male customers significantly bigger tips to waitresses when they were wearing red. For this study, identify the independent variable and the dependent variable
Answer:
Dependent Variable = tips left by male customers
Independent Variable = T-Shirt color worn by waitresses
Step-by-step explanation:
Dependent variable is the variable that changes when the independent variable changes.
In other words, when the independent variable is varied, the dependent variable changes. The dependent variable is the effect or outcome of the manipulation of the independent variable.
In the study referred to in the question above, the amount of tips given to waitresses is dependent on the color of the T-shirt the waitresses wear.
Therefore, the dependent variable is T-Shirt color, while the independent variable is the amount of tips given.
Fill in the blank.
23 x 6 = (20 + 3) * 6
23 x 6 = 1+ (3x6)
20 * 6
20 * 3
20 * 5
Question:
Fill in the blank.
23 x 6 = (20 + 3) * 6
23 x 6 = _ + (3x6)
Options
20 * 6
20 * 3
20 * 5
Answer:
20 * 6
Step-by-step explanation:
Given
Expression 1: 23 * 6 = (20 + 3) * 6
Expression 2: 23 * 6 = __ + (3 * 6)
Required
Fill in the blank
From Expression 1
23 * 6 = (20 + 3)*6
Using Distributive Property; The expression becomes
23 * 6 = 20 * 6 + 3 * 6
23 * 6 = (20 * 6) + (3 * 6)
By Comparing this with expression 2
23 * 6 = __ + (3 * 6)
The blank position is occupied by 20 * 6.
Hence, the correct option that fills the missing blank correctly is 20 * 6
The correct option that fills the missing blank correctly is 20 * 6.
The blank position is occupied by 20 * 6.
Here, we have,
Given
Expression 1: 23 * 6 = (20 + 3) * 6
Expression 2: 23 * 6 = __ + (3 * 6)
Required
Fill in the blank
From Expression 1
23 * 6 = (20 + 3)*6
Using Distributive Property;
The expression becomes
23 * 6 = 20 * 6 + 3 * 6
23 * 6 = (20 * 6) + (3 * 6)
By Comparing this with expression 2
23 * 6 = __ + (3 * 6)
The blank position is occupied by 20 * 6.
Hence, the correct option that fills the missing blank correctly is 20 * 6.
To learn more on Expression click:
brainly.com/question/14083225
#SPJ6
complete Question:
Fill in the blank.
23 x 6 = (20 + 3) * 6
23 x 6 = _ + (3x6)
Options
20 * 6
20 * 3
20 * 5
Please answer this correctly
Answer:
w = 32
Step-by-step explanation:
Since these triangles are similar, you can set up a proportion like this:
[tex]\frac{24}{w} =\frac{36}{48}[/tex]
Cross multiply:
[tex]\frac{1152}{36w}[/tex]
Divide 1152 by 36:
w = 32
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT
Answer:
I cant see it properly
Step-by-step explanation:
The volume of the triangular prism is 54 cubic units.What is the value of x?
3
5
7
9
Answer:
x=3
Step-by-step explanation:
the volume of the prism with triangular base is 54 unit³
The base is a triangle with, base i.e 4 units and height i.e x units
Also, height of the prism = 3x
So, volume of the prism is,
And
,
[tex]Area_{Triangle}=\dfrac{1}{2}\times base\times Height_{Triangle}=\dfrac{1}{2}\times 4\times x=2x\ unit^2[/tex]
Then,
[tex]V_{Prism}=2x\times 3x=6x^2[/tex]
As the volume is given as 54 unit³, hence
6x²=54
x²=9
x=3
how would i go about this question?
Answer:
x = 48.40'
y = 33.01'
Step-by-step explanation:
These are all segments of a right triangle, so the Pythagorean theorem applies.
x^2 = 46.07^2 +14.82^2 = 2342.0773
x = √2342.0773 ≈ 48.40
__
x^2 = 35.39^2 +y^2
y^2 = 2342.0773 -35.39^2 = 1089.6252
y = √1089.6252 ≈ 33.01
Units are feet for both numbers:
x = 48.40'
y = 33.01'
_____
You always start any question by reading the whole question, identifying the (relevant) given information, and understanding what the question is asking for. You then make an assessment of what you know about the relationships between the given information and what is asked. Finally, you develop a strategy for getting from what you know to what you need to know.
Here, you're given segment lengths of right triangles, and you're asked for other segment lengths. This is not a trig problem--no angles are involved. It is a straight Pythagorean theorem problem. To make use of that theorem, or any formula, you need to have only one unknown. So, you can't start by solving the bottom triangle; you have to start with the upper one where there is only the unknown side x.
After you find x, then you have two known sides in the bottom triangle, so you can find y.
Here, x is an intermediate value in the computation of y. You do NOT use the rounded answer to the question when you're computing y. Rather, you use the full calculator precision for x, so that y can have best accuracy. Only at the end do you round to hundredths.
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
13 l of 15%, 13 l of 25%, 26 l of 70%
Step-by-step explanation:
solutions:
15%, 25% and 70%final solution:
52 l of 45%This includes 0.45*52l= 23.4 l acid
Let's assume:
amount of 15% solution= xamount of 25% solution= yamount of 70% solution= zand we have z=2yso there are 2 equation:
x+y+z=520.15x+0.25y+0.7z=23.4or
x+y+2y= 52 ⇒ x+3y= 52 ⇒ x= 52- 3y0.15x+0.25y+1.4y=23.4 0.15x+1.65y=23.40.15*(52-3y)+1.65y=23.47.8-0.45y+1.65y=23.41.2y=23.4-7.81.2y= 15.6y=15.6/1.2y= 13 l--------
x= 52- 3*13= 13 lz= 2y= 2*13= 26 lA soup can in the shape of a cylinder is 4 inches tall and has a radius of 2 inches. How much soup will fit in the can? Use 3.14
for and round the answer to the nearest tenth.
Recall the formula yr
0 12.6
16.0
25.1
50.2
Answer:
16.0
Step-by-step explanation:
Answer:
b 16.0
Step-by-step explanation:
Please explain as well 4x+3y=24 6x+5y=346x+5y=34 x= y=
Answer:
x = 9 y = -4
Step-by-step explanation:
4x + 3y = 24 . (-5) ------> -20x -15y = -120 (A)
6x + 5y = 34 . (3) -------> 18x + 15y = 102 (B)
(A) + (B) ----------> -2x = -18 ---------> x = 9
4.9 + 3y = 24
3y = 24 - 36
3y = -12
y = -4
The highest temperature ever recorded in a particular city was 105F, and the lowest was -27F. Use absolute values to find the difference between the highest and the lowest temperatures.
PLEASE HELP IM TIMED
Answer:
ΔT =313.5 K - 240.3 K = 73.2 K
Step-by-step explanation:
It's more confortable to work in °C to determine the Absolute value
T°C + 273 = T° K (Kelvin grades)
ΔT = Highest T° in K - Lowest T° in K
We make the conversion to Celsius degree, from Farenheit:
(x F - 32°) . 5/9 = °C
(105 F - 32°) . 5/9 = 40.5°C
(-27 F - 32°) . 5/9 = - 32.7 °C
40.5°C + 273 = 313.5 K
-32.7 °C + 273 = 240.3 K
Answer: 132 Should be your answer.
Step-by-step explanation: I don't know how to explain very correctly, but I do know that is correct, have a nice day.
Find the volume of a cylinder that has a radius of 6 and a height of 10.
607
100 77
3607T
6007
Answer:
360π
Step-by-step explanation:
Put the given numbers in the volume formula and do the arithmetic.
V = πr²h . . . . . r is the radius; h is the height
V = π(6²)(10)
V = 360π
The volume is 360π cubic units.
Nicole has x beads. Together we have 56 beads. How many beads will I have if I lose 1/4 of my beads? WILL GIVE BRANLIEST TO PERSON WHO SOLVES
Answer:
y = 42 - 3/4 * x
Step-by-step explanation:
From the statement we know that the following:
x + y = 56
y = 56 - x
x beads of Nicole and another person's beads, after losing a 1/4 of the beads, it would be:
y = (3/4) * (56 - x)
y = 42 - 3/4 * x
From here on you should know the number of beads that Nicole has or suppose, for example:
x = 12
y = 42 - 3/4 * 12
y = 33
Therefore, you would have 33 beads.
x^2+2x+y^2=20 find the center and radius of the circle
Answer:
Center: (-1,0)
Radius: [tex]\sqrt{21}[/tex]
Step-by-step explanation:
You can complete the square for x:
[tex]x^2+2x+y^2=20 \\\\(x^2+2x+1)-1+y^2=20 \\\\(x+1)^2+y^2=21[/tex]
The standard form for a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where h is the x coordinate of the center of the circle, k is the y coordinate, and r is the radius. Therefore, the center of this circle is at (-1,0), and the radius is [tex]\sqrt{21}[/tex]. Hope this helps!
