Molecules of a toxic chemical eventually decompose into inert substances. Suppose the decomposition time is exponentially distributed with a mean of 1/lambda. The half-life of such a persistent poison is that time beyond which the probability is .50 that a particular molecule will remain toxic. Find the half-life for chemicals whose molecules have an average decomposition time of
Answer:
a)4.15 years
b)22.18 years
c)188.53 years
d)3027.66 years
Step-by-step explanation:
Formula : [tex]P(X\leq t)=1-e^{\frac{-t}{\lambda}}[/tex]
So, [tex]P(X>t)=1-(1-e^{\frac{-t}{\lambda}})[/tex]
[tex]P(X>t)=e^{\frac{-t}{\lambda}}[/tex]
We are given that The half-life of such a persistent poison is that time beyond which the probability is .50 that a particular molecule will remain toxic i.e. P(X>t)=0.5
So, [tex]e^{\frac{-t}{\lambda}}=0.5[/tex]
Taking natural log both sides
[tex]ln(e^{\frac{-t}{\lambda}})=ln(0.5)\\\frac{-t}{\lambda}=ln(0.5)\\t=-\lambda ln(0.5)[/tex]
a)
[tex]\lambda =6[/tex]
t=-(6) ln(0.5)=4.15 years
b)
[tex]\lambda =32[/tex]
t=-(32) ln(0.5)=22.18 years
c)
[tex]\lambda =272[/tex]
t=-(272) ln(0.5)=188.53 years
d)
[tex]\lambda =4368[/tex]
t=-(4368) ln(0.5)=3027.66 years
What is the value of the unknown in the equation 3m + 7 = - 23?
Answer:
Step-by-step explanation:
3m + 7 = - 23
we pass the -7 to the right with a positive sign
3m = -23 - 7
we perform the sum of negative numbers
3m = -30
we pass the -3 to the right to divide
m = -30/3
we perform the division
m = -10
Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 12 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Charles, Margaret, and Sean are chosen?
Using the combination formula, it is found that the probability that you, Charles, Margaret, and Sean are chosen is:
[tex]p = \frac{1}{495}[/tex].
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 people will be chosen from a set of 12, hence the number of ways to choose them is:
[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
The desired combination is only one, hence the probability is:
[tex]p = \frac{1}{495}[/tex].
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Golfing
A golfer is aiming for a hole that is 120 feet away and, when he hits the golf ball off the ground, its highest point
reaches 80 feet up in the air
3
Step-by-step explanation:
Using vertex form of a parabola:
y = a (x − h)² + k
where (h, k) is the vertex.
If we say the vertex is (0, 80), then:
y = a (x − 0)² + 80
y = ax² + 80
The roots of the parabola are (-60, 0) and (60, 0). If we plug this in:
0 = a (60)² + 80
-80 = 3600a
a = -1/45
Noemi's team's answer is incorrect.
A group of students formed a circle during a game. The circumference of the circle was about 43.96 feet, and the diameter of the circle was 14 feet.
Which expression best represents the value of
π
?
A.
43.96
7
B.
43.96
14
C.
7
43.96
D.
14
43.96
Answer:
pi = pi
Step-by-step explanation:
Circumference = 2 * pi * r
Equation you need:
43.96 = 2 * pi * 7
43.96 = 2 * 7 * pi
43.96 / 14 = pi
pi = 3.14
drag and drop each expression to correctly classify if it as having a positive or negative product just put them in order from positive to negative. WHOEVER GIVES ME THE RIGHT ANSWER I WILL MAKE BRAINLIEST
Answer:
The two in the middle are the negatives and the two that are on the sides are positive.
Find DF
Segment addition
Answer:
mDF = 18
Step-by-step explanation:
DE and EF must add up to DF.
Step 1: Set up equation
mDE + mEF = mDF
x + 7 + 7 = 4x + 2
Step 2: Solve for x
Combine like terms: x + 14 = 4x + 2Subtract x on both sides: 14 = 3x + 2Subtract 2 on both sides: 12 = 3xDivide both sides by 3: 4 = xRewrite: x = 4Step 3: Find mDF
mDF = 4x + 2
mDF = 4(4) + 2
mDF = 16 + 2
mDF = 18
blank times blank = 1.5
Answer:
12
Step-by-step explanation:
Answer:
Your answer is:
1) 0.75 * 2
2) 0.3 * 5
Step-by-step explanation:
Hope any of these helped you : )
Jackson can lay 6000ft of tile in 3 hours.
What is Jackson's rate?
A.200ft/h
B.1500ft/h
C.2000
D.18000f/h
Answer:
It's 2000ft/h
Step-by-step explanation:
6000/3 = 1 hour rate
what is the product of 2(-4)
Answer:
-8
Step-by-step explanation:
First, write it out in standard form:
2 x (-4)
Then multiply!
Answer:
-8
Step-by-step explanation:
it is basically 2 x -4 and a negative times a positive is a negative which makes it -8
8 less than the product of 7 and -10.
The expression is
The value of the expression is 1
Answer:
um i dunna
Step-by-step explanation:
uuuuhhghhhh
Li counts 203 stars in the sky. The next night, she counts 178 stars. How many stars in all did she see on the two nights?
Answer:
203 + 178 = 381
Step-by-step explanation:
Answer:
381
Step-by-step explanation:
i added
203
+178
381
NB: NOT HOW I WANTED IT TO TURN OUT
SORRY IF IT'S WRONG
What is the m
R
(x + 2)°
(3x – 6°
S
Q
P
m
If a ray QT bisects ZPQR, what will be the measure of one of the resulting angles?
The value of measure ∠RQS would be,
⇒ ∠RQS = 48°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
A ray QT bisects ∠PQR.
Now, We get;
⇒ ∠PQR + ∠RQS = 180°
⇒ (3x - 6) + (x + 2) = 180
⇒ 4x - 4 = 180
⇒ 4x = 184
⇒ x = 46
Thus, The value of measure ∠RQS would be,
⇒ ∠RQS = x + 2 = 46 + 2 = 48°
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Given the following functions: f(x) = x2 – 5 and g(x) = x - 3.
Find f(g(x))
Answer:
f(g)x))= x^2 -6x +4
Step-by-step explanation:
first, plug in g(x) into f(x): f(g)x)) =(x-3)^2 -5
then, you simplify the (x-3)^2 into (x-3)(x-3): f(g)x))= (x-3)(x-3) -5
when you distribute the two (x-3) you end up with: f(g)x))= x^2 -6x +9 -5
finally, you combine like terms and subtract 5 from 9 and your final answer is : f(g)x))= x^2 -6x +4
note: x^2 is x squared or exponent of 2
why does the graph of a proportional relationship must pass through the origin (0,0)
Answer:
Directly proportional relationships always pass through the origin (0,0). There are other linear relationships that do not pass through the origin.
The graph of a proportional relationship must pass through the origin (0,0). Because of the value of k, the ordered pair (0, 0) satisfies this equation.
What is a graph?
The relation between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and connecting lines. It doesn't matter how long the lines are or where the points are located. A node is specified for each element in a graph.
A ray is used to describe any proportional relationship using an equation of the form y = kx. The ordered pair (0, 0) satisfies this equation regardless of the value of k, hence the ray or line must traverse the origin.
Thus, the graph of a proportional relationship must pass through the origin (0,0). Because of the value of k, the ordered pair (0, 0) satisfies this equation.
Learn more about the graph here,
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Estimate by rounding the first factor to the nearest ten. Then enter the product.
77 × 5
The estimate is _______
The product is ________
Answer:
estimate - 400
product - 385
Step-by-step explanation:
estimate - 77 rounds up to 80
80*5=400
product - 70*5=350
7*5=35
350+35=385
Answer:
The estimate is 390 while the real product is 385
answers please.......
Answer:
$69.375
Step-by-step explanation:
To find the total cost: you will add the actual cost of the rug, $64 and the additional shipping and handling cost, $5.375.
[tex]64 + 5.375 = 69.375[/tex]
The total cost of the rug, including shipping and handling is $69.375
Answer:
$69.38
Step-by-step explanation:
64 plus 5 is 69. Add 375 for 69.375. Round the decimal up to get $69.38
Show the solution in each linear inequality in system of linear inequalities by graphing y>-7/2x+3
Answer: When you graph it, put a dot on 3, and then count down 7 spaces, and 2 spaces to the right, put a dot there. Use a straight edge to draw a line through the two dots, that continues on the graph. You can continue to got down 7, over 2 if needed.
Step-by-step explanation:
Cna someone help me plzz
simplify 7^6 x 7^5
(A) 49^11
(B) 49^35
(C) 7^11
(D) 7^35
Answer:
The answer is C) 7^11
Need help ASAP have 30 minutes
Answer:
1 box of paper will cost $7.25.
Step-by-step explanation:
14.50 divided by 2 is 7.25, therefore one box of paper will be 7.25
Bags of flour at a local grocery store have a mean weight of 83 ounces with a standard deviation of 2 ounces. Which weight represents the 65th percentile?
A.82.2 ounces
B.82.5 ounces
C.83.5 ounces
D.83.8 ounces
Answer:
D.83.8 ounces
Step-by-step explanation:
The z score for 65th percentile = 0.385
Mean weight of 83 ounces with a standard deviation of 2 ounces
The formula for calculating a z-score is z = (x-μ)/σ
where x is the raw score
μ is the population mean
σ is the population standard deviation
x = ??
Hence:
0.385 = (x - 83)/2
Cross Multiply
0.385 × 2 = x - 83
0.77 = x - 83
x = 83 + 0.77
x = 83.77 ounces
Approximately = 83.8 ounces
Answer:
D.83.8 ounces
Step-by-step explanation:
The z score for 65th percentile = 0.385
Mean weight of 83 ounces with a standard deviation of 2 ounces
The formula for calculating a z-score is z = (x-μ)/σ
where x is the raw score
μ is the population mean
σ is the population standard deviation
x = ??
Hence:
0.385 = (x - 83)/2
Cross Multiply
0.385 × 2 = x - 83
0.77 = x - 83
x = 83 + 0.77
x = 83.77 ounces
Approximately = 83.8 ounces
A kilometer is 1,000 meters because kilo is a prefix that means 1,000. The prefix mega means 1,000,000 and giga (as in gigabyte) means 1,000,000,000. One byte is the amount of memory needed to store one letter of the alphabet. About how many of each of the following would fit on a 1-gigabyte flash drive?
Answer: 10 megabytes
10,000 kilobytes
Step-by-step explanation:
I can't solve this problem: 47 x 98= ( ? x 47)-(2 x 47)
Answer:
The answer to your question is:
2 and -49
Step-by-step explanation:
2 x -49 = -98
2 + (-49) = -47
x2 - 47x - 98 = 0
The solution to factor the quadratic equation above is:
(X + 2 ) (X - 49)
Since 2 and -49 multiply to -98 and add up -47, you know that the following is true:
x2 - 47x - 98 = (X + 2 ) (X - 49)
?+7,785= $12,603
please help, I'm completely lost.
Answer:4818
Step-by-step explanation:7785-12603=4818
Answer this for my sister again
Please help me. Will give brainliest.
Answer:
b.) (6,7)
Step-by-step explanation:
the figure is translated 2 units to the left
What is the value of 4x – 3y if x = 3 and y = 6?
Answer:
The value is -6.
Step-by-step explanation:
First, you use subsitution.
4(3) - 3(6)
Then, you multiply.
12 - 18
Do the subtraction and you're left with -6 as your answer.
does this graph represent a function?Hint: use vertical line test.
if i get £20 pounds at week and I need £470 pounds how many weeks do I have to save for
Answer:
23.5 weeks.
Step-by-step explanation:
470/20 is 23.5
Answer:
23.5 weeks or 24 weeks
Step-by-step explanation:
470/20 = 23.5
If you are not rounding to the next week, then its 23.5.
If you are rounding to the next week, then it should be 24.