It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.
In the given statement is:
λ = 2.5 x 10^-2 [tex]min^{-1}[/tex]is the rate constant of the nucleus
To solve this problem, we use
N(t) = [tex]N_{0}[/tex]e^-λt
and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set
N(t) = 1/4 [tex]N_{0}[/tex] = 0.25[tex]N_{0}[/tex]
We can substitute this in the decay equation:
0.25[tex]N_{0}[/tex] =[tex]N_{0}[/tex] e^-λt
Cancel the like terms
0.25 = e ^-λt
Take the natural logarithm of both sides:
㏑(0.25) =㏑(e^-λt)
㏑(0.25)= -λt
Solve for the time t:
t = - ㏑(0.25)/λ
Substitute the given rate constant :
t = ㏑(0.25) / 2.5 x 10^-2 [tex]min^{-1}[/tex]
t = -1.3863 /2.5 x 10^-2 [tex]min^{-2}[/tex]
t = 55.452mins
It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.
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Help pleaseeeeeeeeeeeee
The equation that can be used to find x, which is the width of the walkway will be (16 + 2x)(12 + 2x) = 396.
How to illustrate the information?It should be noted that an expression is used to show the relationship that's exists between the variables.
The equation that can be used to find x, which is the width of the walkway will be:
= (16 + x + x) (12 + x + x) = 396
= (16 + 2x)(12 + 2x) = 396
In conclusion, the correct option is C.
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Find all sides to the right triangle
Answer: 22, 15.4, 26.857
Step-by-step explanation:
sin 55=0.819
22/0.819=26.857
sin 35=0.5736
26.857*0.5736=15.4
sin 90=1
26.857*1=26.857
22, 15.4, 26.857
Select the correct answer.
Which expression is equivalent to 4x²√5x4 3√5x8, if x=0?
OA. 12x¹0 √5
OB. 60x8
OC.
35x18
O D. 7x¹⁰ √5
The expression 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] is equivalent to 60 [tex]x^{8}[/tex] if x≠ 0 which is option B
We have to simplify the given equation 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] in order to find its equivalent
Which can be simplified using the basics of square and square roots
Square and square root gets cancelled for example [tex]\sqrt{x^{2} }[/tex] = x and powers get added when same bases are multiplied for example x² × x³ = [tex]x^{2+3}[/tex] =[tex]x^{5}[/tex]
Also √25 can be written as 5
At x = 0 the whole expression can be written as zero
4x² ×√[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex]
12x²×[tex]x^{2} \sqrt{5}[/tex] ×[tex]x^{4} \sqrt{5}[/tex]
12[tex]x^{8}[/tex] ×√25
60 [tex]x^{8}[/tex]
Hence, The expression 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] is equivalent to 60 [tex]x^{8}[/tex] if x≠ 0 which is option B
The correct question is Select the correct answer.
Which expression is equivalent to 4x²√5x4 3√5x8, if x≠0?
OA. 12x¹0 √5
OB. 60x8
OC.35x18
O D. 7x¹⁰ √5
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You purchase tickets to a rock concert for you and 5 friends. You paid a total of $483.30. Write an equation and solve to find out how much each concert ticket cost. You must have your equation, the work to solve the equation and your answer in sentence form.
Answer:
to figure out the total for each person what you need to do is divide 483.30 by 5
483.30 / 5= 96.66
Step-by-step explanation:
Hey guys i need help with numbers 3-7
Answer:
I don't know what u wanted me to solve for but here you go
Step-by-step explanation:
can u please use an explanation, i need it for my answer please.
======================================================
Work Shown:
[tex]a^2 + b^2 = c^2 \ \ \text{ ... pythagorean theorem}\\\\12^2 + 9^2 = c^2\\\\144 + 81 = c^2\\\\225 = c^2\\\\c^2 = 225\\\\c = \sqrt{225}\\\\c = 15\\\\[/tex]
New York State energy consumption (2008)
Transportation sector 28%
Residential sector 30%
Commercial sector 32%
Industrial sector 10%
The total energy consumption in New York State in 2008 was about 4,000 trillion btu. About how many trillion btu was consumed by the residential sector?
The energy consumes by the residential sector in 2008 was 1200 trillion btu. This is a problem from percentage.
Here, the energy consumption in different sector in New York State (2008) is
Transportation sector 28%
Residential sector 30%
Commercial sector 32%
Industrial sector 10%
So, the total energy consumption is = 28% + 30% + 32% + 10% =100%.
Therefore, the power consume by Residential sector is 4000x30% = 1200 trillion btu.
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number; it has no unit of measurement.
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mr. lopez is spreading pebbles around a water garden. he spreads 2 cubic yards of pebbles in 3 4 hour. at this rate, how many cubic yards of pebbles can he spread in one hour? cubic yards in one hour answer
Mr. Lopez spread the stones at a pace of 0.059 cubic yards per hour.
What is rate of change?
A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
"Per unit of time" is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).
The word "per" is used to denote the division of the units of the two measurements that make up a rate when discussing its units (for example a heart rate is expressed "beats per minute"). A rate that is defined using two numbers of the same units will provide a dimensionless quantity that can be stated as a percentage (for instance, the global literacy rate in 1998 was 80%), fraction, or multiple. Examples of these rates include tax rates and literacy rates.
2/34 = 0.0588 equals to 0.059 ( approximately).
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The roof and exterior walls of a house represent intersecting planes. Using the image, name all the lines that are formed by the intersecting planes. (i dont have the picture but if you know which question im talking about please help me)
In the possible diagram of the house, the lines formed by intersecting planes are; [tex] \overline{AG}[/tex], [tex]\overline{ AB}[/tex], [tex]\overline{AH}[/tex], [tex]\overline{GF}[/tex], [tex]\overline{ BH}[/tex], [tex]\overline{HF}[/tex], [tex]\overline{BC}[/tex], [tex]\overline{ HD}[/tex], and [tex]\overline{FE} [/tex]
What are the planes and the lines formed by them on the building?The diagram found in a similar question has points A, G, B, H, and F on the roof.
The points on the walls of the house are; B, H, F, C, D, and E
A plane in Euclidean geometry is a surface that is flat, such that a line that connects two points on it lie completely on the plane.
A plane can be identified by three non collinear points that lay on it.
A line is a figure that does not have a curvature, width or depth, and it is infinitely long.
The planes on the roof are; ABH and AGHF
The planes on the walls of the house are; BCDH, and HDCF
The lines that are formed by the intersecting planes are therefore;
On the roof;
[tex] \overline{AG}, \overline{ AB}, \overline{AH}, \: \overline{GF},[/tex]Between the roof and the walls of the house;
[tex]\overline{BH}, \overline{HF}[/tex]Between the two sides of the walls;
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The Alden Middle School girls' soccer team won 80% of its games this season. If the team won 12 games,how many games did it play?
Answer:
15 games
Step-by-step explanation:
Since the team won 80% of the games and won 12, we can put these into an equation.
80% is also 0.8 so:
x * 0.8 = 12
To find x we can simply do 12 divided by 0.8 which equals =
15
The sum of three consecutive integers is 303. If n is the smallest of the three, which equation represents this situation?
The equation that best represents a the given situation is: 3n + 3 = 303., as found by number system.
What is number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Given: Sum of three consecutive integers is 303.
n = smallest integer.
According to question, the other two integers are: n + 1, and n + 2.Since the sum of the three consecutive integers is 303, addition operation on the values of number system
n + n + 1 + n + 2 = 303
3n + 3 = 303.
Hence, The equation that best represents a the given situation is:
3n + 3 = 303., as found by number system.
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HELPPP QUESTION three
The image of D surely lies on the ray BA ,as ray BA is antiparallel to the ray BD.
Consider D’ to be the image of point D obtained ,when D is rotated 180 degrees anti-clockwise(or counter-clockwise),with B as center of rotation.
From the image above,it is clear that the rays BA and BD are antiparallel.
A ray is a segment of a line with a starting point and an infinite length in one direction.
Antiparallel rays are the rays which are parallel but oppositely directed.The angle between such rays is 180 degrees.
Hence,D’ must lie on the ray BA, as ray BA is antiparallel to BD(i.e the angle between the rays is also 180 degrees).
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-2x+3y >=1 -5x+6y<=1
Answer:
x = 1 and y = 1
Step-by-step explanation:
Find the circumference of the largest circle that will fit inside of a square that has an area of 144 square feet?
Answer:
6
Step-by-step explanation:
The square's side will be √144 = 12
The largest circle will have diameter of 12 so it's radius will be 12/2 = 6
Solve the inequality and express your answer in interval notation.
x^2-6x+7 < 0
Solution:
A. [tex](3-\sqrt{2}, 3+\sqrt{2})[/tex]
Hope this helps!
is 9817 completely divisible by 3
Answer:
No
Step-by-step explanation:
To know if a number is completely divisible by 3, you can add up its digits. If its digits equal a number divisible by 3, then the number itself is divisible by 3.
9817
9 + 8 + 1 + 7
= 25
2 + 5
= 7
Since 25 isn't divisible by 3, 9817 isn't completely divisible by 3 either.
Have a lovely rest of your day! :)
in a reaction time study involving 12 participants, the number of participants whose average time is between 400 and 600 milliseconds
Using the concepts of continuous and discrete variables it is found that the reaction time of students would be a continuous variable.
What is the missing information?This problem is incomplete, but researching it on a search engine, it asks to classify the variable reaction time of students as discrete or continuous.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …A reaction time of 500.5 milliseconds is a valid reaction time, hence a decimal value is accepted, meaning that the reaction time of students would be a continuous variable.
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How many cubes are in the box? What fraction of the entire box do the 7 cubes represent? Explain you answer. 10*10*10
Answer:
7/10 %
Step-by-step explanation:
what is the soluton to the equation e^3x=12
Answer:
[tex]x=\frac{ln(12)}{3}[/tex]
Step-by-step explanation:
We can solve this equation by taking the natural log of both sides.
This gives us the equation: [tex]ln(e^{3x})=ln(12)[/tex]
And the definition of natural log is basically, "what do I have to raise e to, to get this result"
The result is just e^3x, so I have to raise e to what? Well that's just 3x, you could also use log properties to bring the exponent in front and realize ln(e) = 1
So this gives us: [tex]3x=ln(12)[/tex]
Now divide both sides by 3: [tex]x=\frac{ln(12)}{3}[/tex]
george’s average bowling score is 180; he bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. bill’s average bowling score is 190; he bowls in a league where the average is 160 and the standard deviation is 15. who ranks higher in his own league, george or bill?
If k equals 42 in [tex]x^{2}[/tex] + [tex]y^{2} + z^{2}[/tex] = k, what is x?
The value of x is ±√(42 - y² - z²).
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.
Given:
x² + y² + z²=k
As, it is given that k = 42.
So, x² + y² + z²=k
x² + y² + z²= 42
x² = 42 - y² - z²
x=±√(42 - y² - z²)
Hence, the value of x is ±√(42 - y² - z²).
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How are defined terms and undefined terms related?
Answer:
"Defined items" are defined in terms of "undefined terms".
Step-by-step explanation:
None.
the median player salary for the new york yankees was $1.5 million in 2007 and $1.7 million in 2013. write a linear equation giving the median salary y in terms of the year x. (let y be in millions of dollars and let x
(a) The linear equation giving the median salary "y" in terms of the year "x" is y = 0.034x + 1.266.
(b) The median player salary in the year 2048 will be approximately $2.9.
We are given the years to be 2007 and 2013, so the corresponding "x" values are 7 and 13 respectively.x1 is 7 and x2 is 13.We are given the median player salaries to be $1.5 million and $1.7 million, so the corresponding "y" values are 1.5 and 1.7.y1 is 1.5 and y2 is 1.7.In the form of corresponding points, we can write (7, 1.5) and (13, 1.7).(a) To form a linear equation, we use the equation of a line.(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)y - 1.5 = [(1.7 - 1.5)/(13 - 7)]*(x - 7)y - 1.5 = (0.2/6)*(x-7)y = (0.2/6)*(x-7) + 1.5y = 0.034x - 0.234 + 1.5y = 0.034x + 1.266(b) For the year 2048, the "x" value is 48.y = 0.034(48) + 1.266y = 1.632 + 1.266y = 2.898Thus, the median player salary in the year 2048 will be approximately $2.9.To learn more about linear equations, visit :
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A truck can be rented from Company A for $40 a day plus $0.30 per mile. Company B charges $20 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
The number of miles in a day at which the rental costs for Company A and Company B are the same is 200 miles per day
Let the truck is driven X miles per day
Charges of company A will be = 90+0.4X
Charges of company B will be =30+0.7X
Let us find out value of X when charges of both companies are same
which means that 90+0.4 X= 30+0.7X
90-30 = 0.7X-0.4X
60 = 0.3X
60/0.3 = X
X= 200
The charges of both companies will be same if truck is driven 200 miles per day
Company A will have better deal if truck is driven more than 200 miles per day ( because per mile rate of company A is less than company B)
A mile is defined as 1760 yards, or around 1.6 kilometers, in length. They traversed the desert for 600 km by car. She's only a half-mile away. singular noun. A large distance is indicated by the word "miles," particularly in the phrase "miles distant."
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Help please!! I would appreciate it:)
[tex]2A +B = -2 \cdot (2z +8 -2z-4) = -2 \cdot 4 = -8[/tex]
what is the simplest form of 3/7 of 6/1
3/7 of 6/1 means [tex]6(\frac{3}{7})=\frac{18}{7} =2\frac{4}{7}[/tex]
hope this helped
angie, a student in an advanced statistics course, was given an algebra test and she scored 80%. is this an accurate predictor of how well students in the algebra class will perform on the test? (2 points) yes, because angie is representative of the population in the algebra class yes, because angie scored high on the test so it must be easy no, because angie is not representative of the population in the algebra class no, because angie scored too high on the test
No, this is not an accurate predictor because angie is not representative of the population in the algebra test.
Here,
Angie, a student in an advanced statistics course, was given an algebra test and she scored 80%.
We have to find is this an accurate predictor.
What is Accurate predictor?
Accurate predictor describes whether the predicted values match the actual values of the target field within the incertitude due to statistical fluctuations and noise in the input data values.
Here,
Angie is the student of an advanced statistics course but she gives the algebra test and scored 80%.
We know that the advanced statistics is the higher level of math so it is not an accurate predictor.
Because, An accurate predictor should be applied when the person is 100% confirmed to the related thing. So in the given situation, the student is not 100% confirm.
Hence, this is not an accurate predictor because Angie is not representative of the population in the algebra test.
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If a - b = b = c = 2, what is the value of: (a − b)² + (b − c)²/(a - c)² ihx-ezjm-mww
Answer:
Step-by-step explanation:
If a - b = b = c = 2, what is the value of: (a − b)² + (b − c)²/(a - c)² ihx-ezjm-mww
Solve 4x + 3y = 2 for y. Question 18 options: A) y = –4∕3x + 2∕3 B) y = –4x + 2 C)
Answer:
i think its answer is A or D
Answer:
y =2/3 =4/3x
Step-by-step explanation:
simplify
5/8 divide by 5/6
Answer: 3/4
Step-by-step explanation:
See attached work. Remember when dividing fractions, you must multiply by the reciprocal of the second fraction.