Using the exponential distribution, it is found that there is a:
a) 0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.
b) 0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.
c) 0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.
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) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = e^{-\mu x}[/tex]
In this problem, the mean is of 3.4 days, hence, the decay parameter is:
[tex]\mu = \frac{1}{3.4}[/tex]
Item a:
[tex]P(X \leq 1) = 1 - e^{-\frac{1}{3.4}} = 0.2548[/tex]
0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.
Item b:
[tex]P(X \leq 2) = 1 - e^{-\frac{2}{3.4}} = 0.4447[/tex]
[tex]P(X \leq 3) = 1 - e^{-\frac{3}{3.4}} = 0.5862[/tex]
[tex]P(2 \leq X \leq 3) = 0.5862 - 0.4447 = 0.1415[/tex]
0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.
Item c:
[tex]P(X > 5) = e^{-\frac{5}{3.4}} = 0.2298[/tex]
0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.
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At a particular time, a tree casts a shadow 17 m long on horizontal ground. At the same time, a vertical pole 3 m high casts a shadow 4 m long. Calculate the height of the tree to the nearest tenth of a meter.
Using a system of equations, the height of the tree would be 12.80 meters.
Equating the height and shadows of the tree and pole :
Height of pole / shadow of pole = height of tree / shadow of tree
Representing the equation thus :
Let the height of the tree = h
3/4 = h/17
Cross multiply
4h = 17 × 3
4h = 51
Divide both sides by 4
h = 51/4
h = 12.75.
Hence, the height of the tree to the nearest tenth of a meter is 12.80 meters.
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which could be the function graphed below ??
Answer:
D [tex]\sqrt{x+4}[/tex]
Step-by-step explanation:
Line /1 and line /2 are parallel line
Step-by-step explanation:
1=56⁰
2=56⁰
3=68⁰
4=68⁰
5=56⁰
6=112⁰
7=180-124 Ans=56⁰
8=68+56 Ans=124⁰
9=68⁰
10=112⁰
11=124⁰
12=56⁰
IT TOOK 15MINS mark me BRAINLIEST pls!Prices are going up in the ratio 6:5 Write a 60% decrease as a ratio.
HELP PLSSSSSSSSSSSSSSSSSSSSS
Answer:
To Decrease an amount in a given Ratio, we need to multiply by a fraction that is less than one. For example, in scaling down a recipe for four people into a recipe for 3 people, we would use the ratio of 3 : 4 which means we would multiply all our recipe amounts.
Write the equation of the line that passes through (-2, 4) and is perpendicular to x = 3.
Check the picture below.
Please help with this
==========================================
Explanation:
A) This is true because there are 4 cups of green and 2 cups of white. Each box represents 1 cup.
B) This is false. The ratio 4:2 reduces to 2:1 when describing the ratio of green to white. We have twice as many green compared to white. Choice B describes the other way around. The order is important.
C) This is true. We have 2 cups of white and 4 cups of green.
D) False. There are 6 cups total, but only 2 white (not 4).
E) True. This is a verbal way of describing the ratio 4:2, of green to white.
F) False. The ratio is the other way around. See choice E.
G) False. There are 4 cups of green, not 6. There are 6 cups total, not 4. The ratio of green to total is 4:6.
H) True. We have 2 cups of white and 2+4 = 6 cups total.
If 10 candy cost $35. How much candy can I buy with $20
Answer:
6 candies
Step-by-step explanation:
(find unit rate, cost / quantity)
35/10 = 3.5
20/3.5 = = 5.7142857142857
candies cannot be in decimal so you must round to the nearest whole
Suppose a population is of size N is 1,000,000. Compute the correction factor for the SE of the sample mean, when the sample size, n, is equal to 1,000; 10,000; and 100,000.
Answer:
90081???
Step-by-step explanation:
How can you multiply fractions and mixed numbers?
Step-by-step explanation:
To multiply fractions:
Multiply numerator to numerator and multiply denominator to denominator. Simplify the answer.
To multiply mixed numbers:
Change mixed numbers into improper fraction. Then multiply numerator and denominator just like how you multiply the fractions. Simplify.
Evaluate - (3 ^ - 5) * (3 ^ 3)
Answer:
1 / 3^2 = 1/9
Step-by-step explanation:
3^-5 = 1/3^5
(1/3^5) * (3^3) = 3^3 / 1/3^5 = 3^3 / 3^5 = 1/3^2
The value of the given expression is 1/9 .
Given,
[tex](3^{-5}) (3^{3} )[/tex]
According to the power rule,
[tex](a^{m}) (a^{n} ) = a^{m + n}[/tex]
Now,
[tex](3^{-5}) (3^{2}) = 3^{-5 + 3}\\ \\ (3^{-5}) (3^{2}) = 3^{-2}[/tex]
[tex](3^{-5}) (3^{2}) = 1/3^{2}[/tex]
[tex](3^{-5}) (3^{2} ) = 1/9[/tex]
Thus with the power rule answer will be 1/9.
Learn more about power rule,
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A watch loses 15 seconds every day how many minutes will it lose in 2 weeks.
2 weeks = 14 day
14 * 15 = 210 seconds
210/60=3 hours and 30 minutes or 3.5 hours.
The sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second. What are the numbers?
The numbers are 30, 22, and 66 if the sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the number are x, y and z
Then,
x + y + z = 118 ...(1)
y = x - 8 ...(2)
z = 3y ....(3)
After solving the above three equation by plugging the value of z in the equation (1) then solve this equation with (2) we will get:
x = 30
y = 22
Then z from the equation (3):
z = 3(22) = 66
Thus, the numbers are 30, 22, and 66 if the sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second.
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Solve the equation for x:
4x2 + 15x = 4
Show steps please
Billie bikes 9 miles in 45 minutes. At this rate, how many miles can he bike in 90 minutes?
Answer:
18 miles
Step-by-step explanation:
9 miles : 45 minutes
? miles : 90 minutes
45 x 2 = 90 minutes
9 x 2 = 18 miles
Steven walked 3 miles and drove 24 miles. Maureen walked 3 miles and drove
18 miles. Who has the greater ratio of miles walked/miles driven?
helppppppppppppppppppppppppppppppppppp
Answer:
so the answer is bar graph..
pamelas age is three times jiris age the sum of their age is 32 what is jiris age
Answer:
Jiris age = 8
Step-by-step explanation:
Jiris = j
Pamelas Age = 3j
Pamelas's age + Jiris age = 32
3j + j = 32
4j = 32
j = 32 / 4
= 8
Jiris age = 8
Pamelas age = 3 times Jiris's
Pamelas age = 24
Answer:
8 years old.
Step-by-step explanation:
P = 3I
P + I = 32
Plug P = 3I into the second equation:
3I + I = 32
I = 32/4 = 8
So Jiris's age = 8.
¿Qué fuerza media se requiere para que un objeto de 2 Kg aumente su velocidad de 5 m/s a 12 m/s en una distancia de 8 m?
Answer:
14.87
Step-by-step explanation:
Para conocer cual es la fuerza que necesita el cuerpo para aumentar su velocidad de 5 m/s a 12 m/s en 8 m
Necesitamos conocer la aceleración y para conocer la aceleración debemos saber cuanto tiempo tarda en recorrer los 8m
Vf = Vo +a(t)
12 = 5 +a(t) -------> Vamos a despejar el tiempo.
t = 7/a
X= Vo(t) +1/2a(t²)
X= 5(7/a)+1/2a( 7/a )²
8 = 35/a+49/2a
a = 7.43 m/s²
Ahora que conocemos la aceleración podemos calcular la fuerza como:
F = m*a
F = 7.43 * 2 kg.
F = 14.87
Given the functions,
f(x) = x^3 - 4x^2 + 5
g(x) = x^2 + 6x - 7
h(x) = x + 6
Find f(g(-3)).
Answer:
f(g(- 3) ) = - 5115
Step-by-step explanation:
Evaluate g(- 3) then substitute the value obtained into f(x)
g(- 3) = (- 3)² + 6(- 3) - 7 = 9 - 18 - 7 = - 16 , then
f(- 16) = (- 16)³ - 4(- 16)² + 5
= - 4096 - 4(256) + 5
= - 4096 - 1024 + 5
= - 5115
Find the value of x.
(8x + 2)°
60°
Y
70°
Z
Here according to angle sum property all angles sum u up 180°
So,
[tex]8x + 2 + 60 + 70 = 180 \\ 8x + 132 = 180 \\ 8x = 180 - 132 \\ 8x = 48 \\ x = \frac{48}{8} \\ x = 6[/tex]
- BRAINLIEST answerer
The owner of Get-A-Away Travel has recently surveyed a random sample of 496 customers to test the mean age of the agency's customers is over 24 . The appropriate hypotheses are H0: μ ⤠24, Ha: μ > 24 If he concludes the mean age is over 24 when it is not over 24, he makes a _error.
Using error concepts for hypothesis tests, it is found that there is a Type I error.
A Type I error happens when a true null hypothesis is rejected.
A Type II error happens when a false null hypothesis is not-rejected.
In this problem, the null hypothesis is:
[tex]H_0: \mu = 24[/tex]
The alternative hypothesis is:
[tex]H_1: \mu > 24[/tex]
He concludes that the mean age is over 24 when it is not, that is, a true null hypothesis is rejected, hence there is a Type I error.
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Shawn has $20.00 to spend. He wants to save $5.00. He buys two ice creams for $1.65 each, what is the maximum number of packets of chocolate can he buy at a cost of $3.45 for each packet and still have at least $5.00 left over
(solve as an inequality)
Answer:
3
Step-by-step explanation:
3.45x+2*1.65+5>=20
3.45x+8.3>=20
3.45x>=11.7
after rounding
x>=3
Select the number line that shows that two opposite numbers have a sum of 0.
[tex]Hiya![/tex]
Sokka is here to help!
I believe it is A..
Hopefully, this helps you!!!
[tex]Sokka[/tex]
Answer:
Option B is correct.
Step-by-step explanation:
The question said "Opposite numbers and the sum of those numbers is 0". Let's see if Option B has these abilities.
3 - 3 = 0 ✔Are they opposites of each other? ✔=> Therefore, Option B is the correct answer.
PLEASE ANSWER ASAP (no links please)
Solve for the indicated variable
g/h = e - 10 for g
Answer:
g = he - 10h
Step-by-step explanation:
help me pls help me
Answer:
Well I’m not sure what Answers do you want
Step-by-step explanation:
Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist. how many miles does the second cyclist bike in 45 mins?
Answer:
Step-by-step explanation:
45 minutes is 3/4 hr.
(3/4)(12 + b) = 9 + 3b/4 miles
Which of these situations can be represented by this graph?
Answer:
Step-by-step explanation:
On Monday, Elsbeth’s bank account balance was -$16.75. On Tuesday, she deposited a check for $5.72. On Thursday, she deposited $16.75. What is her new balance?
-16.75 + (5.72 + 16.75)
Use the commutative property to get:
-16.75 + (16.75 + 5.72)
Use the associative property to get:
(-16.75 + 16.75) + 5.72
Answer:
5.72
Step-by-step explanation:
(-16.75 + 16.75) = 0
0 + 5.72= 5.72
Therefore, the answer is 5.72
I’m confused on this question
Answer:
[tex]\lim_{x \to 5}f(x)=-5\\\lim_{x \to 1^-} f(x)=3\\\lim_{x \to 1^+} f(x)=3\\\lim_{x \to 1} f(x)=4\\[/tex]
Step-by-step explanation:
[tex]\lim_{x \to 5}f(x)[/tex]
This means "the limit of f(x) as x approaches 5"
In this case, f(x) is a basic linear function while x > 1, so a limit is not necessary but it can still be used as it is here. For this one, you can just calculate f(5), and that is:
[tex]f(x)=5-2x[/tex]
[tex]f(5)=5-2(5)=5-10=-5[/tex]
[tex]\lim_{x \to 5}f(x)=-5[/tex]
===================
[tex]\lim_{x \to 1^-} f(x)[/tex]
This one is a little different. It means "the limit of f(x) as x approaches 1 from the negative (left) direction"
The negative direction of course means x will be less than 1, so we'll use this function:
[tex]f(x)=4-x[/tex]
It's easier if you graph it, but you can also do it like this:
[tex]f(0)=4+0=4\\f(0.5)=4-0.5=3.5\\f(0.75)=4-0.75=3.25\\f(0.9)=4-0.9=3.1\\f(0.99)=4-0.99=3.01[/tex]
There's a clear pattern there. You can see that f(1) should be 3, but this function only applies while x is less than 1 so it can never reach 3. It will get infinitely close, and that can be shown with the limit:
[tex]\lim_{x \to 1^-} f(x)=3[/tex]
===================
[tex]\lim_{x \to 1^+} f(x)[/tex]
This one works the same way, but from the positive (right) direction.
[tex]f(2)=5-4=1\\f(1.5)=5-3=2\\f(1.25)=5-2.5=2.5\\f(1.1)=5-2.2=2.8\\f(1.01)=5-2.02=2.98\\f(1.001)=5-2.002=2.998[/tex]
It will also get infinitely close to 3 when x = 1, but won't ever reach it because this function only applies when x is greater than 1.
[tex]\lim_{x \to 1^+} f(x)=3[/tex]
===================
[tex]\lim_{x \to 1} f(x)[/tex]
Here, the function for x=1 is just:
[tex]f(x)=4[/tex]
It's given already, so the limit is just:
[tex]\lim_{x \to 1} f(x)=4[/tex]
HELP!!!!! FAST!!!!! !!!!!!!!!!!!!!!!!!!!!!
Answer:
37
Step-by-step explanation:
I don't know if this is totally correct
ATQ,
★⤿ 8(x+9) ≥ 224
★⤿ x+9 ≥ 224/8
★⤿ x +9 ≥ 28
★⤿ x ≥ 28-9
★⤿ x ≥ 19
Hence , option A is correct ✓