a. The probability that a patient experiences relief is 0.9.
b. The probability that at least 10 patients experience relief is 0.9988 (rounded to four decimal places)
c. The probability that at most 7 experience relief is 0.0007 (rounded to four decimal places)
d. The average number of patients who experience relief is 1.14 (rounded to two decimal places)
e. The probability that none of the 15 patients experience relief is 1.0E-15 (rounded to scientific notation)
a. The probability that a patient experiences relief is 0.9. The probability that all 15 experience relief is given by:
P(all 15 experience relief) = (0.9)^15 = 0.2059 (rounded to four decimal places)
b. The probability that at least 10 patients experience relief can be calculated by adding the probabilities of 10, 11, 12, 13, 14, and 15 patients experiencing relief:
P(at least 10 experience relief) = P(10) + P(11) + P(12) + P(13) + P(14) + P(15)
where P(k) represents the probability that k patients experience relief. Each P(k) can be calculated using the binomial probability formula:
P(k) = (15 choose k) * 0.9^k * 0.1^(15-k)
Using a calculator or software, we can find:
P(at least 10 experience relief) = 0.9988 (rounded to four decimal places)
c. The probability that at most 7 patients experience relief is the same as the probability that 8 or fewer patients experience relief. We can use the complement rule to calculate this probability:
P(at most 7 experience relief) = 1 - P(more than 7 experience relief)
To find P(more than 7 experience relief), we can add the probabilities of 8, 9, ..., 15 patients experiencing relief:
P(more than 7 experience relief) = P(8) + P(9) + ... + P(15)
Again, each P(k) can be calculated using the binomial probability formula. Using a calculator or software, we can find:
P(at most 7 experience relief) = 0.0007 (rounded to four decimal places)
d. The average number of patients who experience relief is given by the expected value of a binomial distribution:
E(X) = np
where X is the number of patients who experience relief, n is the sample size (15), and p is the probability of success (0.9). Thus,
E(X) = 15 * 0.9 = 13.5
The standard deviation of a binomial distribution is given by the square root of the variance:
s = sqrt(np*(1-p))
Thus,
s = sqrt(150.90.1) = 1.14 (rounded to two decimal places)
e. The probability that none of the 15 patients experience relief is given by:
P(none experience relief) = 0.1^15 = 1.0E-15 (rounded to scientific notation)
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Drag each number to the correct location on the table. Classify the real numbers as rational or irrational numbers. Please Help I need the answer today!
Answer:
did you ever figure out what the answer was it was because working on this and don't know what to do
Step-by-step explanation:
Answer:
Rational Numbers: √400 | -5/250 | 5.012121212...
Irrational Numbers: √1000 | ^3√30 | 0.01562138411...
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money.
Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Answer:
I think it would be 25m + 10b = 400
In a game, Theodore received a handful of coins (pennies, nickels, dimes, and quarters) as a prize. When he got home, he found that he had managed to get $2.09 in change. He noticed that he had three times as many pennies as dimes, one more nickel than dimes, and twice as many.quarters as dimes. How many quarters did Theodore get in his prize? F. 4 G. 5 9 'H J. 7 K. 8
Answer:
6
Step-by-step explanation:
https://web2.0calc.com/questions/algebra_69756
Theodore get 6 quarters in Prize.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let p the number of pennies, d be the number of dimes, n be the number of nickels and q be number of quarters.
So, the expressions are
p = 3d
n = d+1
= 5(d+1)
d = 10d
and, q = 2d
= 25 (2d)
and, the total is = $209
= 209
Then,
3d + 5(d+ 1) + 10d +25 ( 2d) = 209
68d + 5 = 209
d = 3
Thus, the number of quarters = 2d = 6 quarters.
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I NEED HELP ASAP PLEASE!!! I'LL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!!
Answer:
x = 3
y = 4
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
Find the slope of the line that passes through (4,-5) and (-2,9)
a -2/3
b 5/3
c -7/3
d 2
Answer:
C) -7/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(9-(-5))/(-2-4)=(9+5)/-6=14/-6
simplify -14/6 to -7/3
Salma, joe, and alan sent a total of 106 text messages during the weekend, salma sent 9 fewer messages than alan. Joe sent 3 times as many messages as alan. How many messages did they each send?
Answer:
Salma, joe, and alan sent 14, 69, and 23 text messages respectively
Step-by-step explanation:
Given that Salma, joe, and alan sent a total of 106 text messages during the weekend, it means that
s + j + a = 106 where s, j, and a are the number of messages sent by Salma, joe, and alan respectively
Given salma sent 9 fewer messages than alan
s = a - 9
Joe sent 3 times as many messages as alan
j = 3a
hence
a - 9 + 3a + a = 106
5a - 9 = 106
5a = 106 + 9
5a = 115
Divide both sides by 5
a = 115/5
= 23
s = 23 - 9
= 14
j = 3* 23
= 69
what is the appropriate unit of measure for the mass of a steel cabinet?
Enter the value of 12x-2 when x = 3.
Answer:
34
Step-by-step explanation:
12(3)-2
36-2
34
Answer:
im sorry if this is wrong but i think its 2
Suppose 65% of jurors come to a just decision. In a jury of ten people, what is the probability more than half come to a just decision? 0.7515 0.2485 0.0949 0.8374 0.9051
Answer: 0.7515
Step-by-step explanation:
Binomial probability formula:
[tex]P(X=x)=\ ^nC_xp^x(1-p)^{n-x}[/tex] , where
n = total number of trials.
p= probability of success in each trial.
x= Number of successes.
Let x be a binomial variable that represents the number of jurors come to just decision.
p= 0.65
n= 10
Required probability= [tex]P(x>5)=P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)\\\\ =\ ^{10}C_6(0.65)^6(0.35)^4+ ^{10}C_7(0.65)^7(0.35)^3+ ^{10}C_8(0.65)^8(0.35)^2+ ^{10}C_9(0.65)^9(0.35)^1+^{10}C_{10}(0.65)^{10}(0.35)^0\\\\=0.75149550912\approx0.7515[/tex]
Hence, the probability more than half come to a just decision = 0.7515
PLEASE HELP ME WITH THIS QUESTION!!!!
ILL GIVE 20 POINTS
Answer:
D. This was the first time Judicial Review took action in court.
Step-by-step explanation:
Three quarters of the cars in a parking garage are black, 4/7 of the remaining cars are blue, and the rest are silver. If there are 9 silver cars, how many cars are in the parking garage? * 1 point
Answer:
84 cars
Step-by-step explanation:
Given that 3/4 of the cars in a parking garage are black, let the number of cars in the garage be T, then
number of black cars = 3T/4, other = T - 3T/4 = T/4
If 4/7 of the remaining cars are blue then
the number of blue cars = 4/7 * T/4 = T/7
Remaining cars = T/4 - T/7
= (7T-4T)/28
=3T/28
Given that the remaining cars are sliver and the number of silver cars is 9 then
3T/28 = 9
Cross multiply
3T = 28 * 9
Divide both sides by 3
T = 28 * 9 / 3
= 28 * 3
= 84 Car
5) 15 – 3(x + 2) ??????????????????????
Answer:
-3x + 9
Step-by-step explanation:
Dla każdej z liczb 20, 60, 150, 300, znajdź liczbę : a) o 10% większa, b) o 20% mniejszą, c) o 50% mniejsza,
Odpowiedź:
Prosimy sprawdzić wyjaśnienie
Wyjaśnienie krok po kroku:
Na numer: 20
a.) 10% więcej;
(1 + 10/100) * 20;
1,10 * 20 = 22
b.) 20% mniej
(1 - 20/100) * 20
0,8 * 20 = 16
c.) 50% mniej
(1 - 50/100) * 20
0,5 * 20 = 10
Dla numeru 60:
a.) 10% więcej;
(1 + 10/100) * 60;
1,10 * 60 = 66
b.) 20% mniej
(1 - 20/100) * 60
0,8 * 60 = 48
c.) 50% mniej
(1 - 50/100) * 60
0,5 * 60 = 30
Na numer 150;
a.) 10% więcej;
(1 + 10/100) * 150;
1,10 * 150 = 165
b.) 20% mniej
(1 - 20/100) * 150
0,8 * 150 = 120
c.) 50% mniej
(1 - 50/100) * 150
0,5 * 150 = 75
Dla numeru 300;
a.) 10% więcej;
(1 + 10/100) * 300;
1,10 * 300 = 33%
b.) 20% mniej
(1 - 20/100) * 300
0,8 * 300 = 240
c.) 50% mniej
(1 - 50/100) * 300
0,5 * 300 = 150
f(x) = 5x-3
slove this its is Evaluate functions
Answer:
f(5) = 22
Step-by-step explanation:
When we want to solve for f(x) = 5x - 3 when x is 5, all we have to do is plug in 5 as x into the equation.
f(x) = 5x - 3
f(5) = 5(5) - 3
5 * 5 = 25
25 - 3 = 22
f(5) = 22
I hope this helps you!
Yolanda has 1/6 cup ladle that she uses to pour gravy over potatoes she uses one full ladle for each serving for each server potato
Answer: what is the question
Step-by-step explanation:
solve the problem: -10 + +10 =
Answer:
0
Step-by-step explanation:
-10+ + 10
-10+10
0
HELP PLS!!! make sure to submit a pic of the graph!
Graph the piecewise function.
Answer:
I cant graph on here
Step-by-step explanation:
Answer:
3x-5 if x≤-1 = Green
-2x+3 if -1<x<4 = Orange
2 if x≥4 = Purple
SOMEONE PLEASE ANSWER THIS CORRECTLY AND SHOW HOW THE EQUATION WOULD LOOK LIKE!!!!!!! PLEASE HELP ASAPPPPPPPPP!!!!!!!!!!!!!
Answer:
The answer is C
Step-by-step explanation:
The plumber works $90 per hour and has earned a total of $955, to find the number of hours he worked, you divide the total amount of money by the amount of money he earned every hour. Which would be [tex]\frac{955}{90}[/tex] = H or 90H = 955.
entre 4 grupos de un colegio recolectaron 200kg de papel para reciclarlo.el primer grupo recogio 60 1/4 kg el segundo 13 1/5 y el tercero 45,93 kg cuanto recogio el cuarto grupo?
Answer:
segun yo es asi no confies mucho en mi
Step-by-step explanation:
200 kg total de papel
primer grupo= 60kg
segundo= 13kg
tercero= 45.93
cuarto= x
si sumamos el total recolectado por los tres primero grupos
60+13+45.93
esto nos da
118.93
si en total se recgio 200kg de basura y tenemos que los tres primeros grupos recogieron 118.93, entonces solo queda restar el total menos lo recolectado
200-188.93= cuarto grupo
cuarto grupo=81.07kg
Please help asap I will give you brainliest Find the area of the shaded region
Answer:
36
Step-by-step explanation:
Area of total region = 12 ×5
=60
Area of the small region = 8×3
=24
Area of shaded region = Area of Total region - area of small region
= 60 - 24
= 36
help plssss i give brainliest
Answer:
(7, - 2 )
Step-by-step explanation:
Given the 2 equations
x = - 3y + 1 → (1)
- 3x - 3y = - 15 → (2)
Substitute x = - 3y + 1 into (2)
- 3(- 3y + 1) - 3y = - 15 ← distribute and simplify left side
9y - 3 - 3y = - 15
6y - 3 = - 15 ( add 3 to both sides )
6y = - 12 ( divide both sides by 6 )
y = - 2
Substitute y = - 2 into (1) for corresponding value of x
x = - 3(- 2) + 1 = 6 + 1 = 7
solution is (7, - 2 )
please help solve this but don't spam ( Transposition method )
Answer:
x = -⁷/9
Step-by-step explanation:
[tex] \frac{9x - 8}{3} = \frac{9x - 3}{2} [/tex]
Multiply both sides by 3
[tex] \frac{9x - 8}{3}*3 = \frac{9x - 3}{2}*3 [/tex]
[tex] 9x - 8 = \frac{3(9x - 3)}{2} [/tex]
Multiply both sides by 2
[tex] 2(9x - 8) = \frac{3(9x - 3)}{2}*2 [/tex]
[tex] 2(9x - 8) = 3(9x - 3) [/tex]
[tex] 18x - 16 = 27x - 9 [/tex]
Subtract 27 from each side
18x - 16 - 27x = 27x - 9 - 27x
-9x - 16 = -9
Add 16 to both sides
-9x - 16 + 16 = -9 + 16
-9x = 7
Divide both sides by -9
-9x/-9 = 7/-9
x = -⁷/9
which is bigger or equal 6 gallons or 96 pints
Answer:
96 pints
Step-by-step explanation:
an examination. 30% of the candidates
ailed. If 210 candidatęs passed, how many
Candidates wrote the examination?
1.63 B. 147 C. 210 D. 300 E. 2100
Answer: D
Step-by-step explanation:
If 30% failed then (100-30)% passed
That is 70%
let x be the number of students that wrote the exam
(70/100)x=210
x=21000/70
x=300
y = -3/4x - 2
y = 3/4x + 1
one solution
two solutions
no solution
O infinitely many solutions
Answer:
One Solution
Step-by-step explanation:
Trust me
find a, b (3a- 2) (A+10 ) (3b - 15) (2b +5)
150 miles in 6 gallons
Answer:
uh thanks for the points
Step-by-step explanation:
Answer:
Step-by-step explanation:
For example, suppose it takes you 15 minutes to travel 6 miles. The time elapsed is 15 minutes divided by 60 minutes = 0.25 hours, and your speed is 6 miles divided by 0.25 hours which equals 24 mph.
For an average person:
1 mile = 2,000 to 2,500 walking steps
1 km = 1,250 to 1,550 walking steps
10,000 steps = 4 to 5 miles
Which point satisfies the system of equations y=3x-2 and y=-2x+3?
8
7
B
6
C
5
4
D
9 8 7 6 5 4 3 -2 -1
1
2 3 4 5 6 7
B
9x
-2
-3
4
-5
-5
-7
-9
ΟΑ. Α
ОВ.
B
Occ
ODD
Answer:
27633883532
2732937293739
839364923274693
93730347395393649364
027402649249364
026393473849337
92739262926382
193
19632963286392
92539253925292
9279253285292
2283792
88248935392
926263925392
7363854276393
233
i need help ASAP 6th grade work!!!!! HELP
Answer:
y=7miles
Step-by-step explanation:
The total perimeter is 21 miles and we know two sides of the triangle are 7 miles, or 14 miles together.
We need to know the one other side of the triangle, so we can subtract the 14 miles we know from the total 21 miles.
21-14=7miles
Answer:
y=7 mi
Step-by-step explanation:
If you know that each side of this triangle is 7 and they are each side is the same length, you can make an educated guess that the answer is 7. If you need An easier method 7x3=21. a triangle has 3 sides so your answer would be 7
Which side of DEF is the longest?
A. DE
B. EF
C. DF
D. Cannot be determined
[tex] \huge {\tt{Answer:}} [/tex]
A. DE
Option (A) DE side of the triangle DEF is the longest side.
What is a triangle?A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
The diagram shows the triangle with angles ∠D = 65°, ∠E = 42°.
The sum of the interior angles of a triangle is equal to 180°.
⇒ [tex]\angle D+\angle E+\angle F=180[/tex]
⇒ [tex]65+42+ \angle F=180[/tex]
⇒ [tex]\angle F=180-107[/tex]
⇒ [tex]\angle F=73[/tex]
The side corresponding to the ∠D is EF, ∠E is DF, ∠F is DE
The angle which is greater has the longest side.
⇒ [tex]\angle F > \angle D > \angle E[/tex]
⇒ [tex]DE > EF > DF[/tex]
Thus the side DE has the longest length.
Hence we can conclude that option (A) DE side of the triangle DEF is the longest side.
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