The speed that will martin need to drive, if he wants to take the 512 hours is 0.537 mph.
What does proportionality's constant look like?Students determine the rate of change, often referred to as the constant of proportionality (k = y/x), which is the consistent ratio between two proportional values (y/x) indicated by the symbol k, which may be a positive rational integer. The x value and the y value are directly proportional, as in the equation y = kx.
Speed and travel time vary in opposite directions.,
So v ∝ 1/t.
speed = v
time = t
So
=> v = k/t, k=constant of proportionality.
Since it takes Kris 5 hours when driving at 55 mph,
=> v = 55mph and t = 5 hours.
=> 55 = k/5
by doing cross multiply
=> k = 55*5
=> k = 275
Hence, to calculate for Martin to drive for 5 hours, we will take k = 275 and t = 5 into v = k/t
=> v = 275/512
=> v = 0.537 mph
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(HELP)
Which triangle Congruence postulate or theorem proved that these triangles are congruent?
Answer: If it is one of your choices it should be angle angle side(aas)
The circle below has center K, and its radius is 7 in. Given that m
The length of the major arc is (203/18)π.
What is a length of an arc?
The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.
Here, we have
The circle with center K has an arc with a radius of 7 inches and an angle subtended at the center which measures 70 degrees.
The major arc LNM would have its central angle measured as:
Angle ∅ = 360 - 70 (Sum of angles on a point equals 360)
Angle ∅ = 290
The calculation for the length of an arc is given as;
Length of arc = (∅/360) x 2πr
Where ∅ = 290, and r = 7, the length of the major arc becomes;
Length of arc = (290/360) x 2 x π x 7
Length of arc = (29/36) x 14π
Length of arc = (29 x π x 14)/36
Length of arc = 203π/18
Hence, the length of the major arc is (203/18)π.
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What are the agile 4 types?.
The four types of agile are:
Scrum, Kanban,
Extreme Programming (XP),
Lean Development, and Cryst.
What is the Agile cycle?
The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.
The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.
The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.
Hence,
The four types of agile are:
Scrum, Kanban,
Extreme Programming (XP),
Lean Development, and Cryst.
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The area A, in square meters, of a rectangle with a perimeter of 140 meters is given by the equation A = 70w - w², where w is the width of the rectangle in meters. What is the width of a rectangle if its area is 600 m²?
The width of the rectangle is 60 meters
The area A, in square meters, of a rectangle is given by the equation
A = 70w - w²
where w is the width of the rectangle in meters.
70w - w² = 600
70w - w²- 600 = 0
w²-70w+600 = 0
w²-60w-10w+600 = 0
(w-60)(w-10) = 0
w =60
w =10
the width of the rectangle is 60 meters
Subtraction:
The act of removing elements from a collection is represented by subtraction. Subtraction is symbolized by the negative symbol. The stack will now include five oranges rather than nine if, for instance, four of the nine oranges that are stacked together (as in the figure above) are then moved to a basket. As a result, 5 is the difference between 9 and 4, which is the same as 9 less 4. Subtraction can be applied to other types of numbers in addition to natural numbers. Subtraction is represented by the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.
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One leg of a right triengle is decreasing at a tate of 5 kilometers per hour and the other leg of the triangle is increasing at a rete of 14 kilometers per hour. Ara certain anstant the decreasing leg is 3 kilometers and the increasing leg is 9 kilometers. What is the rate of change of the area of the right triangle at that instant (in square kilometers per hour)? 11 e 111 01.5 -1.5 Stuck? Watch a video or use a hint
The rate of change of the area of the right triangle at that instant is -1.5 sq km/h.
Let ABC be a right triangle, right-angled at B.
the side decreasing be, BC = x
and the increasing side be, AB = y
then, AC = z = √(x² + y²) (using Pythagoras theorem)
It is given that, dx/dt = - 5km/h and dy/dt = 14 km/h
x = 3, y= 9 at certain instant
now, the area of the triangle = 1/2 xy
A = 1/2 xy
dA/dt = 1/2 (y).dx/dt + x/2.dy/dt
at x = 3, y = 9, substituting the values,
(dA/dt) = 1/2 (9)(-5) + 3/2 (14)
= -1.5
therefore, the rate of change of the area of the right triangle at the instant when x=3 and y= 9 is -1.5 sq km/h.
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In quadrilateral $abcd$, we have $ab=3,$ $bc=6,$ $cd=4,$ and $da=4$. If the length of diagonal $ac$ is an integer, what are all the possible values for $ac$? explain your answer in complete sentences.
{4, 5, 6, 7} total 4 values which diagonal can take constraint is it must be an integer.
What is quadrilateral ?It is the shape enclosed by 4 line segments. So, it has 4 vertices as well as four angles with the total of 2 diagonals.
What is triangle ?It is the shape enclosed by the 3 lines and have 3 vertices with 3 angles and constitute no diagonals.
The triangle inequality applies.
In order for ACD to be a possible triangle, the length of the AC must lie between CD-DA=0 and CD+DA=8.
In order for ABD to be a possible triangle, the length of AC must in range between BC-AB=3 and BC+AB=9.
The values common to both these restrictions are numbers between 3 and 8. Assuming that we don't want the diagonal to be coincident with any of the sides, its integer length will be one of the ...
{4, 5, 6, 7}
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a couple plans to have no more than three children, and they will keep having children until they have a girl. so, if their first child is a girl, they will stop and have only one child. however, if their first child is a boy, they will try again and have a second child. as it turns out, the probability of having a boy is slightly greater than having a girl. here is the probability distribution for the number of boys the couple could have. boys 0 boys 1 boy 2 boys 3 boys probability 0.490 0.250 0.127 0.133 what is the probability the couple will have at least two boys? do not round.
The probability the couple will have at least two boys is 0.26.
How to calculate the probability?This type of probability is independent probability. Independent probability can only occur if the events are independent or not dependent on previous event and also this event doesn't affect the next event.
For probability the couple will have at least two boys is equal to probability they have two boys plus probability they have three boys. Mathematically is,
P(x≥2) = P(x=2) + P(x=3)
P(x≥2) = 0.127 + 0.133
P(x≥2) = 0.26 or 26%
Thus, the couple will have at least two boys has a probability of 0.26 or 26%
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the following data are from a simple random sample. 6 8 10 8 10 6 what is the point estimate of the population standard deviation?
The point estimate of the population standard deviation is 2.82
Since the given simple random sample is 6 8 10 8 10 6. considering the data of the sample be denoted by X. the mean of the sample is
X'=1/n ∑X, where n is the number of data points
=6+ 8 +10+ 8+ 10+ 6/ 6 = 6
Since the formula for The point estimate of the population standard deviation is:
s= [tex]\sqrt{}[/tex](1/(n-1)* ∑(X−X')^2, where X' is the sample mean and n is the
s=[tex]\sqrt{}[/tex]( 1/(6-1)*{(6-6)^2+(8-6)^2+(10-6)^2+(8-6)^2+(10-6)^2)
= [tex]\sqrt{}[/tex](1/5 *(4+16+4+16)
= [tex]\sqrt{}[/tex](1/5 *(40))
=[tex]\sqrt{}[/tex](8)
=1.41*2
=2.82
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Coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 20 in^3/min. a. How fast is the level in the pot rising when the coffee in the cone is 4 in. deep? b. How fast is the level in the cone falling then?
When the coffee in the cone is 5 inches high, we need to determine how quickly the level in the pot is rising. deep and how quickly is the cone's level falling? Use the equation for the volume of a cone and a cylinder pot. Make use of it to achieve your goals.
We know that a conical filter with "r" as the radius and "h" as the height will have a volume of V conical 1/3 πr²h (2)
The coffee is draining from a conical filter at a rate of dVdt=10in3/min, and the volume of the cylindrical coffeepot will be Vcylindrical=r2h.
The term "rate of change" (ROC) describes the rate at which something changes over time. Therefore, it is not the magnitude of individual changes but rather the acceleration or deceleration of changes (the rate). Rate of change is used in finance to understand price returns and determine trend momentum.
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using the va/linear foot method, the total va that must be used in a service calculation for a 50' show window is?
The total VA( volt-ampere ) that must be used in a service calculation for 50' show window is 125000VA.
What is VA linear foot method?A volt-ampere (SI symbol: VA or V A, abbreviated as VA) is the unit of perceived power in an electrical circuit. The apparent power is equal to the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are commonly used to analyze alternating current (AC) circuits. In direct current (DC) circuits, this product equals the real power in watts. The volt-ampere is dimensionally identical to the watt: 1 VA = 1 W in SI units).
The total VA that must be used in a service calculation for 50' show window is, Therefore, by using VA linear foot method,
200 VA per linear foot×50'=10000VA10000VA×1.25
=125000VA
Hence, the total VA that must be used in a service calculation for 50' shadow is 125000VA.
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How do you expand a binomial to the 6th power?.
We can expand a binomial to the 6th power by simplifying each of the expansion's terms.
Define binomial.An algebraic expression with two non-zero terms is called a binomial. Binomial expression examples: The binomial with two variables, a and b, is a2 + 2b. A binomial in two variables, x and y, is 5x3 - 9y2. A binomial is a polynomial in algebra that is created by adding two terms, each of which is a monomial. After monomials, it is the most basic type of sparse polynomial.
Given,
We can expand a binomial to the 6th power in following steps:
From the nth row of Pascal's triangle, count the number of terms and their coefficients.
Start with the first phrase that has no b terms and only an an.
With each term of the expansion, a loses power.
With each term of the expansion, b's power grows.
Simplify each of the expansion's terms.
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a process of observation that has an uncertain outcome is referred to as a(n) ________.
Answer: experiment
Step-by-step explanation:
A course of perception that has an unsure result is alluded to as an experiment.
What is an experiment?The study of mathematical objects by computing in order to discover their properties and patterns is known as experimental mathematics. It has been described as "that mathematical theory that concerns itself ultimately with both the convention and transmission of insights within the mathematical neighborhood through the use of experimental investigation of conjectures and also more irregular beliefs and just a careful analysis of the information acquired in this endeavor (in either the Galilean, Baconian, Aristotelian or Kantian sense).
The nineteenth century saw the reemergence of experimental mathematical concepts as a distinct field of study as the range of calculations that could be performed was greatly expanded by the development of the electronic computer, which could perform calculations at speeds and with levels of precision that were unimaginable to earlier generations of mathematicians.
A course of perception that has an unsure result is alluded to as an experiment.
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To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map of the forest. A ground survey visited a sample of 10% of the plots selected using this method: 1. Number the plots from 1 to 1410. 2. Use a random number generator to select 141 different integers from 1 to 1410. 3. Select the corresponding 141 plots. If you used the method described to generate a random sample of 3 plots, which of the following plots could be a legitimate random sample? 298, 772, 772 All of these are proper random samples. 40,825, 1470 8.902, 148, 533 115.540, 876
115, 540, and 876 are legitimate random samples.
An irregular example is an example that is picked haphazardly. It might be more appropriate to refer to it as a sample chosen at random. In order to avoid bias and other undesirable effects, random samples are used.
Three distinct values between 1 and 1410 will constitute a legitimate random sample. As a result, the first sample cannot be random because 772 are being repeated.
Because 1470 is greater than 1410, the third sample cannot be random.
Because there are four values, the fourth sample cannot be random.
Thus, 115, 540, and 876 are accurate plots.
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Write two expressions that are equivalent to 4.8n-5.
please help
Answer:
Well, since your answer is 4.8n-5, It could be 2+2.4+4n.3+2
Step-by-step explanation:
it's probably wrong but I'm only doing this for points so get rekt
Step-by-step explanation:
just for points
The two expressions can be -5 + 4.8 n and 4.8n + (-5).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
4.8n-5.
We can write the expression as
-5 + 4.8 n
or, using the integers
4.8n + (-5)
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The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let x = the number of sick days they took for the past year. Should the personnel team believe that the mean number is ten?
The personnel team should not believe that the mean number is ten
How to determine what the personnel team should believe?From the question, we have the following parameters that can be used in our computation:
x = the number of sick days they took for the past year
Also, we have the following representation of the values of x
x = 12; 4; 15; 3; 11; 8; 6; 8
The mean of a set of observations can be calculated using the following equation
Mean = Sum of observations/Count of observations
Substitute the known values in the above equation, so, we have the following representation
Mean = (12 + 4 + 15 + 3 + 11 + 8 + 6 + 8)/8
Evaluate the sum in the above equation
So, we have the following representation
Mean = 67/8
Evaluate the quotient in the above equation
So, we have the following representation
Mean = 8.375
8.375 does not approximate to 10
So, the mean number is not ten
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Given f(x) = 2x - 1 and g(x) = x² + 5, find i)fg(x)
ii) gf(x)
Answer:
see explanation
Step-by-step explanation:
(i)
substitute x = g(x) into f(x) , that is
f(g(x))
= f(x² + 5)
= 2(x² + 5) - 1
= 2x² + 10 - 1
= 2x² + 9
--------------------------------------
(ii)
substitute x = f(x) into g(x) , that is
g(f(x))
= g(2x - 1)
= (2x - 1)² + 5 ← expand factor using FOIL
= 4x² - 4x + 1 + 5
= 4x² - 4x + 6
Weight Not Over (lbs.) Price
0 $0
1 $2.69
2 $3.17
3 $3.65
4 $4.13
5 $4.61
6 $5.09
7 $5.57
8 $6.03
9 $6.49
10 $6.95
What is the domain and range of this function?
The domain of the given function is {0, 1, 2 3.... 10}.
The range of the function is: {0, 2.69, 3.17, 3.65, 4.13, 4.61, 5.09, 5.57, 6.03, 6.49, 6.95}
What is the Range and Domain of a Function?A function has a set of input values (x-values) that are corresponding to a set of output values (y-values).
The set of these input values (x-values) is what is referred to as the range of a function, while the set of the corresponding output values (y-values) is the domain of the function.
Given the graph above, all the set of weight are input values which make up the domain of the function, while the set of corresponding prices is the range of the function.
The domain is therefore: {0, 1, 2 3.... 10}.
The range is therefore: {0, 2.69, 3.17, 3.65, 4.13, 4.61, 5.09, 5.57, 6.03, 6.49, 6.95}
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Can u help me with this it would be alot helpuful
Answer:
y=2x-5
Step-by-step explanation:
1 u must calculate the slop then the amount of b
by -3=1×2-b
-5=b
so after we find the number if y we will make an equation y=2x-5
an inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 4 cm, and the height is 11 cm. find the rate at which the water level is rising when the water level is 4 cm.
The rate at which the water level is rising when the water level is 5 cm is; dh/dt = 1.6 cm/s
We are told that;
length of square side; s = 4 cm
height of pyramid; h = 11 cm
volumetric rate; dV/dt = 35 cm³/s
Since the base is square shaped and we know that area of a square = s², then we can say that;
Volume of pyramid = ¹/₃s²h
The pyramid has a height of 11 cm and length of its' square base side is 11 cm.
Now, regardless of the water height, the surface of the water will always be square shaped. This implies that the ratio of the height to the top side of square will always be the same. Thus, we can say that; s = 4/8 h = h/2
Thus, Volume is;
V = ¹/₃ × (h/2)² × h
V = ¹/₃ × h³/4
V = h³/12
dV/dt = (3h²/4) dh/dt
Plugging in the relevant values gives;
30 = (3 × 5²/4) dh/dt
120 = 75 dh/dt
dh/dt = 120/75
dh/dt = 1.6 cm/s
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how many four letter strings can be formed from the letters a,b,c,d,e if the first letter must be a vowel and the last letter must be a consonant?
Number of ways to form four letters strings formed using a, b, c, d, e with the given conditions is equal to 150ways.
As given in the question,
Given letters are a, b, c, d, e has
Number of vowel = 2
Number of consonant= 3
Number of letter strings to be formed = 4
Condition:
First letter must be vowel
Last letter must be consonant
First place filled in 2 ways
Second and Third place filled in 5ways
Last place filled in 3 ways
Total number of ways to form four letters strings
= 2 × 5 × 5 × 3
= 150
Therefore, number of ways to form four letter string is 150 ways.
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Find the average value of the function over the given interval.
f (t) = te312
on [1,3]
The average value of the function f(t) is [tex]4.433*10^{10}[/tex] .
Given,
[tex]f(t)=te^{3t^2}[/tex] over interval [1,3]
To find average value of the function use formula,
[tex]f(x)_{avg} =\frac{1}{b-a}\int\limits^a_b {f(x)} \, dx[/tex] over the interval {a,b}
[tex]f(x)_{avg} =\frac{1}{3-1}\int\limits^3_1 {te^{3t^2}} \, dt\\\\\\f(x)_{avg} =\frac{1}{2}\int\limits^3_1 {te^{3t^2}} \, dt\\[/tex]
let
[tex]u=3t^2\\\\du=6tdt \\\\tdt=\frac{du}{6}[/tex]
replacing u and du ,
[tex]f(x)_{avg} =\frac{1}{2*6}\int\limits^3_1 {e^{u}} \, du\\\\f(x)_{avg} =\frac{1}{12}\ e^u\|\limits^3_1\\ \\f(x)_{avg} =\frac{1}{12}\ e^{3x^2}\|\limits^3_1\\\\f(x)_{avg} =\frac{1}{12}\ [e^{3(3)^2}-e^{3(1)^2}]\\\\f(x)_{avg} =\frac{1}{12}\ [e^{27}-e^{3}]\\\\f(x)_{avg}=4.433*10^{10}[/tex]
Thus, the average value of the function f(t) is [tex]4.433*10^{10}[/tex] .
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How do you simplify complex fractions with LCD?.
To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD
Given,
LCD;- Least Common Denominator
When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.
We have to find the method of simplification of complex fractions with LCD;
Here,
Multiply each term in the numerator and denominator by the LCD to simplify this complicated fraction. It doesn't matter how complicated these fractions are; all you need to do is discover the LCD to convert the complicated fraction into a simpler one. The technique is done more frequently the more fractions there are in an issue
That is,
To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD
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When a number is decreased by 8%, the result is 79. What is the original number to the nearest tenth?.
A number is decreased by 8%, the result is 79. So the original number to the nearest tenth is 85.8.
How to determine the original number to the nearest tenth?These are the specified parameters:
a number is decreased by 8%, the result is 79.
Suppose, a number = x
a number - 8% a number = 79
x - 8/100 x = 79
100/100 x - 8/100 x = 79
92/100 x = 79
x = 79 × 100/92
x = 7900/92
x = 85.8
So these numbers are 85.8.
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9. A local Pennysaver paper charges f dollars weekly for a five-line classified ad. Each additional line
costs a dollars. Express algebraically the cost of a four-line ad that runs for a year.
The algebric expression represents the cost of a four-line ad that runs for a year will be $(192/5)f.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
Expression is very useful to determine the end or root value of constraint.
The constraint of expression is represented as = or <, >.
As per the given,
A local Pennysaver paper charges f dollars weekly for a five-line classified ad.
Cost of five-line ad = $ f / week
Cost of one line ad = $ f/5 / week
Cost of four line ad = $ (4/5) f / week
It is known that,
1 year = 12 x 4 = 48 weeks
Cost of four line ad for one year = $ (4/5)48 f
⇒ $(192/5)f
Hence "The algebric expression represents the cost of a four-line ad that runs for a year will be $(192/5)f".
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PEASE HELP ASAP
ACB~ EFD
What is x equal to?
Enter your answer in decimal form.
The value of x in the similar triangles is 11.4.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
Therefore,
ΔACB ~ ΔEFD
Hence,
AC / EF = CB / FD = AB / ED
Therefore, let's find x
x = AB
ED = 3.8
BC = 15
FD = 5
x / 3.8 = 15 / 5
cross multiply
5x = 15 × 3.8
5x = 57
divide both sides of the equation by 5
x = 57 / 5
x = 11.4
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The value of t0.10 with 5 degrees of freedom is greater than the value of t0.10 with 10 degrees of freedom.
true, since t0.10 with 5 d.f. = 2.015 > t0.10 with 10 d.f. = 1.812
By using t test, it can be concluded that
The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom
What is t test?
If the observations are from a normal population and the population standard deviation is not known, the distance between the sample mean and the population mean can be calculated by using t test
By using t- table
The value of t at level of significance = 0.10 with 5 degree of freedom = 2.015
The value of t at level of significance = 0.10 with 10 degree of freedom = 1.812
Since 2.015 > 1.812,
The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom
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a right circular cone has a radius of 2 x 3 and a height of 5 units less. express the volume of the cone as a polynomial function. the volume of a cone is v
Volume of the cone as a polynomial function., Radius of cone = x + 4 units.
What is a Polynomial Function?Polynomial functions are the simplest, most commonly used, and most important mathematical functions. These functions represent specific conditional algebraic expressions and cover a wide variety of functions. Due to its wide range of applications, it is important to study and understand polynomial functions.This article details the definition of polynomial functions, their types, and graphs with solved examples.Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants. Here are some examples of polynomial functions.According to our question-
Radius of cone = x + 4 units,
Height of cone = 5 units less than radius,
Volume formula.
Solution
We are given the volume formula:
V = (1/3)πr²h
Find the height:
h = r - 5
h = x + 4 - 5 = x - 1
Substitute all into formula:
V(x) = (1/3)π(x + 4)²(x - 1)
You may keep it as is or simplify:
V(x) =
(1/3)π(x² + 8x + 16)(x - 1) =
(1/3)π(x³ + 8x² + 16x - x² - 8x - 16) =
(1/3)π(x³ + 7x² + 8x - 16)
Hence, Volume of the cone as a polynomial function., Radius of cone = x + 4 units.
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What is the common ratio of 3 12 48 and the next 3 terms?.
The common ratio is 4.
The next 3 terms are 192,768, 3072
What is common ratio?
In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.
Here, 48/12 = 12/3 = 4 ( it is a constant ratio )
Hence it is a geometric sequence and common ratio is 4.
Next 3 terms can be found by multiplying the common ratio with the previous term.
48*4=192
192*4=768
768*4=3072
So, the next 3 terms are 192,768, 3072
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If there are 4.8 grams of a radioactive substance present initially and 0.4 grams remain after 13 days, what is the half life?
Half life of the radioactive substance is 3.6 days
How to calculate the half life of the substanceThe half life of the element is calculated from the formula
N(t) = N'(1/2)^(t/t')
N(t) = quantity of the substance remaining
N' = initial quantity of the substance
t = time elapsed
t' = half life of the substance
0.4 = 4.8 (0.5)^13/t'
0.4 / 4.8 = (0.5)^13/t'
take natural logarithm of both sides
㏑(0.4/4.8) = 13/t' ㏑(0.5)
divide through by natural log of 0.5
-2.4849 / ㏑(0.5) = 13/t'
13/t' = 3.58496
t' = 13 / 3.58496
t' = 3.626 days
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There are 1.67 x 1021 molecules in a drop of water. How many molecules are in 100 drops of water? Write in scientific notation.
Answer:
1.70507 x 10^5
Step-by-step explanation:
First, we multiply 1.67 x 1021:
1.67 x 1021 = 1705.07.
So, 1705.07 is for one drop of water. We need to find 100 drops of water. To do this, we can set up this equation:
1705.07 x 100 = 170,507
Now, we have to convert this number into scientific notation. How do we do this? The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number:
1.70507 x 10^5 is our answer.
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