Answer: 15 and 14
Step-by-step explanation:
Use the exponential decay model, A=A o e^kt. The half-life of thorium-229 is 7310 years. How long will it take for a sample of this substance to decay to 20% of its original amount? Round six. decimal places
The time it will take for a sample of this substance to decay to 20% of its original amount
t=16973.294years
This is further explained below.
What is half-life?The amount of time needed for a quantity to decrease to half of its original value is referred to as its half-life.
In nuclear physics, this word is often used to define the rate at which unstable atoms undergo radioactive decay or the amount of time stable atoms are able to persist.
Additionally, the phrase may be used in a broader sense to define any form of exponential decline.
Generally,
A = A0e^{-kt}
Therefore
A(t) = A0e^{[ln(0.5) / 7310 t}, t in years
0.20 = e^{ln(0.5) / 7310 ]t}
Solve for t.
ln(0.20) = [ln(0.5) / 7310 ]t
t = 7310 [ln(0.20) / ln(0.5)]
t=16973.294years
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I need help
1/2 + 1/3
Answer:
5/6
Step-by-step explanation:
1/2x3= 3/6
1/3x2=2/6
3/6+2/6=5/6
Is 4(7-1) and 28-1 equal?
Answer:
fasdfjahlskfhkajshf
Step-by-step explanation:
jfdlhgkdfhgldfhg lsdfjhgsdhflhg klsfdhgjdsfhgkdfhgh
∑⊥⇆Ф↑↓∩¬║⊅α∨∧
(testing answer, sorry for that)
Hello Please help me.
Answer:
Step-by-step explanation:
1) D
2) B
3) no solution
y ≤ 0.5x - 4 is area C including the red line
y ≥ 0.5x + 5 is area A including the blue line
Maths question help pls !!!!!
Can I have help please thank u
Answer:
A = 30 cm
B = 14 cm
C = 15 cm
D = 41 cm
Step-by-step explanation:
You can find A by multiplying 10 times 6 (because the other side of the square is ten and the side of A already has that 4 there it would be 6) which would be 60, then since it is a right triangle, you can divide that by two and get 30.
You can find B by multiplying 4 by 7 (because the other part of that side of the square is 3 so that part would be 7) which would be 28, then since it is a right triangle, you can divide that by two and get 14.
You can find C by multiplying 10 times 3 and getting 30, then since it is a right triangle, you can divide that by two and get 15.
You can find D by multiplying 10 by 10 (because it is a square) then you'll get 100 from that. Then you can subtract the rest of the triangles from it which would be 100 minus 30 minus 14 minus 15 and you would get 41 which would be triangle D.
Hope this helps!! Let me know if you need more explanation
On what interval(s) of x is f(x) positive?
On what interval(s) of x is f(x) negative?
Answer:
Positive: (-2,1)
Negative: (-∞,-2) U (1,∞)
Step-by-step explanation:
The graph of the function f(x) is given in the figure. We can see some points like (-2,0), (-1,1), (2,-2), and many others.
Note the second value of each point (the value of y) is positive or negative. When it's positive, the graph is above the x-axis, when it's negative, the graph is below the x-axis. When it's 0, the graph crosses the x-axis.
To find the intervals of x where the function is positive, we only have to look into the zone where the graph is above the x-axis. It can be identified as the interval (-2,1).
Similarly, the function is negative in the interval (-∞,-2) U (1,∞)
The function f(x) is positive in the interval [-2, 1].
The function f(x) is negative the interval (-∞, -2) U (1, ∞).
The positive regions of a function f(x) are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero).
To find the intervals of x where the function is positive,
In the interval [-2, 1] , the function f(x) is positive.
The negative regions of a function f(x) are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).
In the interval (-∞,-2) U (1,∞) , the function f(x) is negative.
y-values that are on the x-axis are neither positive nor negative. The x-axis is where y = 0.
when y = 0, x = -2, 1
Therefore, the function f(x) is positive in the interval [-2, 1] and negative in the interval (-∞,-2) U (1,∞).
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___________ are the four main units of length in the U.S.
Inch, foot, yard, and mile are the four main units of length in the U.S.
What is the meaning of units?The units can be described as the means that measurement is been performed on a particular objects, it should be noted that the measurements is a way that help most of the work to be accomplished.
In this case we can come into conclusion that units such as the length help us to know how long or how short a particular object which help us to be able to perform modification on the the object, and in the U.S it can be measured using:
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Find m and c for this line
Y+3x=1
Answer:
m = -3 ; c = 1
Step-by-step explanation:
y = -3x + 1
y = mx + c
m = -3
c = 1
Which is the solution to this system of equations?
Answer:
E empty set
Step-by-step explanation:
The answer is empty at
The theater was full when the movie began. Seventy-six people left
before the movie ended. One hundred twenty-four people remained.
How many people were in the theater when it was full?
The number of people were 200 in the theater when it was full.
What is a theater?
In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.
Given that, the theater was full when the movie began.
76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.
Apply algebraical operation that is addition to find the required answer.
Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.
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What is the markup rate of an item originally priced at $40 that is now selling for $55.60? Round your answer to the nearest percent.
Answer:
Ayo, why are you cheating, I'll have to send this to Ms. Walsh and Mr. Walston.
Step-by-step explanation:
Ayo, why are you cheating, I'll have to send this to Ms. Walsh and Mr. Walston.
factor and solve
x^2-4x=5
Let’s solve the equation x^2 - 4x = 5 by factoring:
First, we’ll move all the terms to one side of the equation:
x^2 - 4x - 5 = 0
Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:
(x - 5) (x + 1) = 0
Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:
x - 5 = 0 or x + 1 = 0
Solving each equation separately, we find that x = 5 or x = -1.
So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.
What is 98 in exponential form
We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.
To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.
Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:
We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.
To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.
98 ÷ 10 = 9.8
Since 9.8 is still greater than 1, we need to continue dividing by 10.
9.8 ÷ 10 = 0.98
Now, we have reached a value less than 1, so we stop dividing.
From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:
98 =\(10^1\) + 2
Therefore, we can write 98 in exponential form as:
98 = \(10^3\)
In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.
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Please Help ASAP PLEASE !!!!!!!
Which mathematical property is demonstrated?
If y=−7 and −7=z, then y = z.
A. symmetric property of equality
B. closure property of multiplication
C. closure property of addition
D. transitive property of equality
Answer:
transitive property of equality
Step-by-step explanation:
I know cus i took the test also sorry it took so long dude
Jillian and her friend went shopping. They were both looking for some new CD's. Jillian went to Music Matrix and spent $25.56 on 4 CD's. Her friend
spent $18.45 on 3 CD's. Who got the better deal? Show your work for each person. Answer who got the better deal and explain your reasoning,
Answer:
Her friend got the better deal.
Step-by-step explanation:
For Jillians equation look at
$22.56/4 = $6.39 per CD
For her friends equation look at
$18.45/3 = $6.15 per CD
Jillian's friend got the better deal because she paid less per CD as shown in the equations above.
The box is a rectangular prism. He covered all the sides with the of the box with special wallpaper that cost a total of $504. How much wallpaper cost per square foot length is 6 feet width is 5 feet and height is 3 feet.
The cost of the wallpaper per square foot is $4.
To find the cost per square foot of the wallpaper, we first need to calculate the total surface area of the box. A rectangular prism has six faces, and each face is a rectangle.
The front and back faces have dimensions 6 feet by 3 feet, so their combined area is 6 ft * 3 ft * 2 = 36 square feet.
The top and bottom faces have dimensions 5 feet by 3 feet, so their combined area is 5 ft * 3 ft * 2 = 30 square feet.
The left and right faces have dimensions 6 feet by 5 feet, so their combined area is 6 ft * 5 ft * 2 = 60 square feet.
The total surface area of the box is 36 + 30 + 60 = 126 square feet.
Since the cost of the wallpaper is $504, we divide the total cost by the total surface area to find the cost per square foot: $504 / 126 sq ft = $4 per square foot.
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The probability distribution for a random variable x is given in the table. -5 -3 -2 0 2 3 Probability .17 .13 33 16 11 10 Find the probability that -2< x <2
The probability that -2 < x < 2 is given as follows:
P(-2 < x < 2) = 0.16.
How to obtain the probabilities?From the table given in this problem, the probability distribution is defined as follows:
P(X = -5) = 0.17.P(X = -3) = 0.13.P(X = -2) = 0.33.P(X = 0) = 0.16.P(X = 2) = 0.11.P(X = 3) = 0.10.The desired interval in this problem is given as follows:
-2< x <2.
It is an open interval, meaning that the only outcome that satisfies this interval is X = 0, and thus the probability is given as follows:
P(-2 < x < 2) = 0.16.
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Which set of ordered pairs represents a function?
o{(1,3) (2,5) (4,9) (4, 13)}
o{(1,3) (1,5) (4, 9) (6,3)}
o {(1, 3) (2,5) (2, 9) (6, 13)}
O {(1,3) (2,5) (4, 9) (6,5)}
Answer:
The answer is D
Step-by-step explanation:
The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the _____________.
a. probability of incorrectly accepting the null hypothesis decreases
b. probability of Type II error decreases
c. probability of incorrectly accepting the null hypothesis increases
d. probability of incorrectly rejecting the null hypothesis increases
The probability of a Type I error is the probability of incorrectly rejecting the null hypothesis. When the probability of a Type I error decreases, the probability of a Type II error, It decreases the likelihood of choosing the null hypothesis wrongly.
When conducting a hypothesis test for a given sample size, a Type I error is the probability of incorrectly rejecting the null hypothesis. This means that the null hypothesis is true, but the hypothesis test incorrectly rejects it. A Type II error is the probability of incorrectly accepting the null hypothesis. This means that the null hypothesis is false, but the hypothesis test incorrectly accepts it. When the probability of a Type I error decreases, it means that the hypothesis test is more accurate in correctly rejecting the null hypothesis when it is false. This in turn means that the probability of a Type II error also decreases, as the test is more accurate in correctly accepting the null hypothesis when it is true. In other words, when the probability of a Type I error decreases, the probability of a Type II error decreases as well.
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solve ((-3) x (10 + (-7))) to the power of 2 divided by 3 - (-9) to the power of 2)
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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Based on the graph below, what is f(2)?
0
1
2
-2
Answer:
the answer is 2 or c good luck
Answer:
C. 2
Step-by-step explanation:
A student solves the following equation and determines that the solution is −2. Is the student correct? Explain. 3/a + 2 − 6a/a2 − 4 = 1 /a − 2
The value of a is mathematically given as a=1.68989794. Both sides of the equation are unequal with -2 , Hence No, the student is not correct
What is an equation?An Equation is simply defined as an mathematical statement, where two mathematical expressions are made equal to one another.
Was the solution of -2 given by the student to the equation correct?Question Parameter(s):
. 3/a + 2 − 6a/a2 − 4 = 1 /a − 2
Firstly, for the student to be correct the value -2 as a value of a must render the equation equal to zero
Generally, the equation is mathematically given as
3/a + 2 − 6a/a2 − 4 = 1 /a − 2
Subbing -2
3/(-2) + 2 − 6(-2)/(-2)2 − 4 = 1 /(2) − 2
-15.5-1.5
In conclusion, both sides are unequal
therefore, student, a is not correct
The correct value of a=1.68989794
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Answer:
No, the student did not check the solution to the derived equation in the original equation.
No, a possible solution is a = –2, but it does not check in the original equation because it makes two of the denominators equal to zero.
No, a = –2 is an extraneous solution, and there is no solution to the original rational equation.
Step-by-step explanation:
edge 2023
Nao and Arban drive to work.
Nao drives 95 miles in 2.5 hours.
Arban drives 128 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h.
1 mile = 1.6 km
Thank You.
Answer:
41.6 km/h
Step-by-step explanation:
Nao drives 95mi/2.5hr or 38 miles per hour, or 60.8 km/h
1 hr 15 min is the same as 1.25 hours
Arban drives 128km/1.25hr or 102.4 km/h
The difference is 102.4-60.8 = 41.6
Find the value of θ from the following equation.(θ≤90°)
Answer: 10°
__________________________________________________________
We are given:
Sin(6θ) = Cos(3θ)
Solving for θ:
Simplifying Cos(3θ):
We know that:
Cos(θ) = Sin(90-θ)
So, we can say that:
Cos(3θ) = Sin(90 - 3θ)
Finding the value of θ:
Sin(6θ) = Cos(3θ)
Sin(6θ) = Sin(90 - 3θ) [Since Cos(3θ) = Sin(90 - 3θ)]
6θ = 90 - 3θ [If Sin(θ) = Sin(A) ; θ = A]
9θ = 90 [adding 3θ on both sides]
θ = 10° [dividing both sides by 9]
. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:
a. Bert gets a Jack and Ernie rolls a five.
b. Bert gets a heart and Ernie rolls a number less than six.
c. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.
d. Bert gets a red card and Ernie rolls a fifteen.
e. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.
Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.
What is probability, exactly?The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.
Here,
a.
P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)
= (4/52) * (1/12)
= 1/78
b.
P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)
= (13/52) * (5/12)
= 65/624
c.
P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)
= (12/52) * (6/12)
= 1/4
d.
P(Bert gets a red card and Ernie rolls a fifteen) = 0
e.
Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:
A regular 52-card deck contains 48 cards that are not Jacks,
so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.
On a 12-sided dice with 11 possible outcomes,
Ernie rolls a non-12th-number (1, 2, 3, etc.).
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Find the value of each variable. (x and y)
Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)
Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).
You have $1,900 in savings for retirement. If your investments earn 8% annually, how much will you have in your retirement account in 6 years?
Answer:
$3,015
Step-by-step explanation:
To determine the amount that you will have in 6 years, you have to use the formula to calculate the future value:
FV=PV*(1+i)^n
FV= future value
PV= present value= $1,900
i= interest rate= 8%
n= number of periods of time= 6 years
FV=1,900*(1+0.08)^6
FV=1,900*(1.08)^6
FV=3,015
According to this, the answer is that in 6 years you will have $3,015 in your retirement account.
The balance on a credit card, that charges a 12%
APR interest rate, over a 1 month period is given in
the following table:
Days 1-3:
$150 (initial balance)
Days 4-20: $200 ($50 purchase)
Days 21-30: $50
($150 payment)
What is the finance charge, on the average daily
balance, for this card over this 1 month period?
finance charge =$[?]
Round to the nearest hundredth.
Answer:
Step-by-step explanation:
25-34-56-=10