[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & 2\\ P=\textit{initial amount}\dotfill &18\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases}[/tex]
[tex]2=18(1 - 0.04)^{t}\implies \cfrac{2}{18}=(1 - 0.04)^{t}\implies \cfrac{1}{9}=0.96^t \\\\\\ \log\left(\cfrac{1}{9} \right)=\log(0.96^t)\implies \log\left(\cfrac{1}{9} \right)=t\log(0.96) \\\\\\ \cfrac{\log\left(\frac{1}{9} \right)}{ ~~ \log(0.96) ~~ }=t\implies 53.82\approx t\qquad \textit{about 53 years and 301 days}[/tex]
It will take approximately 54 years for the element to decay from 18 grams to 2 grams at a rate of 4% per year.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
To determine how long it takes for an element to decay from 18 grams to 2 grams, you can use the formula:
t = (ln(A/B)) / (-r)
where:
t is the time it takes for the decay to occur
A is the initial amount of the element, in this case 18 grams
B is the final amount of the element, in this case 2 grams
r is the decay rate, in this case 4% per year
Plugging these values into the formula gives you:
t = (ln(18/2)) / (-0.04)
t = (ln(9)) / (-0.04)
t = (2.1972) / (-0.04)
t = -54.30
Hence, It will take approximately 54 years.
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Use the table below to find d/dx[5f(x)-4x] x=2
The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
From the table:
At x=2,
f'(x) = 4
f(x) = 4x
= d/dx(5*4x - 4x)
= d/dx(20x - 4x)
= d/dx(16x)
= 16
Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
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Need help with question
a) The decay formula for the mass of Strontium-90 is m(t) = 75 · [tex]e^{-t /40.395}[/tex].
b) The sample of Strontium-90 has a mass of approximately 13.258 miligrams after 70 days.
c) The sample of Strontium-90 takes a time of approximately 146.405 days.
How to model the mass decay of a sample of Strontium-90
The mass of Strontium-90 decays exponentially in time, whose model is described below:
m(t) = m' · [tex]e^{- t /\tau}[/tex]
Where:
m' - Initial mass of the isotope, in miligrams. m(t) - Current mass of the isotope, in miligrams. τ - Time constant, in days.And the time constant can be estimated by the following formula:
τ = t' / ㏑ 2
Where t' is the half-life of the isotope.
a) If we know that m' = 75 mg and t' = 28 d, then the expression for the mass of the sample is:
τ = 28 / ㏑ 2
τ ≈ 40.395 d
m(t) = 75 · [tex]e^{-t /40.395}[/tex]
b) And the mass of the isotope after 70 days is:
m(70) = 75 · [tex]e^{- 70 / 40.395}[/tex]
m(70) ≈ 13.258 mg
The current mass is approximately 13.258 miligrams.
c) If we know that m(t) = 75 · [tex]e^{-t /40.395}[/tex] and m(t) = 2 mg, then the time needed for the decay is:
75 · [tex]e^{-t /40.395}[/tex] = 2
[tex]e^{-t /40.395}[/tex] = 2 / 75
- t / 40.395 = ㏑ (2 / 75)
t = - 40.395 · ㏑ (2 / 75)
t ≈ 146.405 d
The needed time is approximately 146.405 days.
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According to a recent survey of 43 million citizens in the United States, 8 million were planning to start a new degree program or continue their education in the next year. According to this data, what is the probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year? (Round to four decimal places.)
The probability of people not planning a new degree = [tex]\frac{35}{43}[/tex]
What is probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
And while solving these type of question we calculate the probability of a particular event.
The survey has 43 million people
Given is 8 million were planning to start a new degree program
Thus the probability of people planning a new degree program = 8 million divided by 43 million
Thus the probability of people not planning a new degree = 1 - [tex]\frac{8 million}{43 million}[/tex]
which is equal to [tex]\frac{35,000,000}{43,000,000}[/tex]
which on solving further will give us:
P ( people not planning a new degree ) = [tex]\frac{35}{43}[/tex]
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An x-ray machine for animals costs 125,000. If the loan is for 10 years, and the interest paid is $65,625, what is the interest rate on the loan?
The interest rate on the loan is 5.25%.
How to calculate the rate?It should be noted that the formula for calculating the simple interest is given as:
Interest = (Principal × Rate × Time) / 100
In this case,
Interest = 65625
Principal = 125000
Time = 10
Interest = (Principal × Rate × Time) / 100
65625 = (125000 × R × 10)/100
Cross multiply
6562500 = 1250000R
Divide
R = 6562500 / 1250000
R = 5.25
The rate is 5.25%
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The function f(x) is graphed below. What is true about the graph on the interval from point e to point f?
Answer: It is positive and increasing
Step-by-step explanation:
From point e to f it is clearly going up, and is part of the positive side of the graph.
please help me due today
Answer: B
Step-by-step explanation: I believe this is correct. The arrows on both run all trough the x-axis, so it would be negative infinity to positive infinity. Then, you go from open circle ( ( ) -3 to closed circle ( } ) 4.
One way that a company can raise money for expansion is to sell stock. When you buy a share of a company's stock, you become a shareholder, or part owner, of that company. The cost of a share is often represented in points, where each points represents one dollar. When a stock gains points, its shares increase in value, and when a stock loses points, its shares decrease in value. For instance, if a stock gains three points one day, each share of its stock is worth three dollars more than it was the day before. Positive decimal numbers are used to represent gains, and negative decimal numbers are used to represent losses.
On Monday, the closing value of a share of stock in Company ABC, was 74.01. On Tuesday, it closed at 73.67, and on Wednesday, it closed at 74.32. On Thursday, the change in stock value was -1.48. And, on Friday, Company ABC's stock gained 0.89 points. Answer the following questions based on Company ABC's stock performance this week.
One shareholder owns 13 shares of Company ABC's stock. What was the total value of their stock in this company at the close of Tuesday? $
equation if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68 of his share hope this helped there a lot of extra information in the question
An equation is written as expressions, connected by an equals signal ("=").[2] The expressions on the two facets of the equals signal are referred to as the "left-hand side" and "right-hand side" of the equation. Very regularly the right-hand side of an equation is assumed to be zero. Assuming this doesn't lessen the generality, as this can be realized through subtracting the right-hand side from each facets.
The most common sort of equation is a polynomial equation (commonly known as also an algebraic equation) wherein the 2 facets are polynomials. the edges of a polynomial equation incorporate one or greater terms
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2009
Evaluate x y for the following values of x and y.
value of x value of y value of xy
1
5
-205
1
67
1
-1
11
.
-1
-7.93
-1
-11
Answer:meh
Step-by-step explanation:good enough
Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. The z score corresponding to a woman with a height is 2.56. How tall is the woman?
Answer:
70
Step-by-step explanation:
Had this question too ;)
14. Reflection: in the line y=x
Rotation: 180 about the origin
The image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
Given, a line segment with end points X(-3 , 1) and Y(4 , -5)
We have to find the image of the points after the given composition,
Reflection in the line y = x.
Rotation 180° about the origin.
After the reflection the image of the points X and Y be,
X' = (1 , -3) and Y' = (-5 , 4)
Now, after the rotation of the points of 180° about the origin be,
X'' = (-1 , 3) and Y'' = (5 , -4)
Hence, the image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
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What is the simplified form of |-10-(-20)|-|-6+2|+|12-6|
Answer:
12
Step-by-step explanation:
|-10+20| - |-4| + |6|
10 - 4 + 6
12
On a map, 2 inches equals 180 miles. The distance that a family travels is 3.5 inches on the map. Represent the scale as two different ratios. What is the actual distance the family travels?
Answer:
315
Step-by-step explanation:
2/180=3.5/x
2x=630
x=315
hey please solve this
Answer:
∴ x = 70°, y = 70°, z = 40°
Step-by-step explanation:
x = 180° - 110° (adjacent angles on a straight line)
= 70°
Since triangle PQR is an isosceles triangle,
∴ y = x = 70°
∴ z = 180° - 70° - 70° (angle sum of a triangle)
= 40°
Please help. Find x and y. NEED ASAP
Answer:
x=10
y=5
Step-by-step explanation:
you have to find the length
See the question above. I don’t understand how I was wrong to do the LCM of 50 and 60, which is 300, so that’s the distance where the friends will meet, and d/s = time, so 300/50 and 300/60 are 6 and 5, and the average of that is 5.5, but the real answer seems to be approx. 18.2? Please solve the question AND explain my mistake.
Answer:
Step-by-step explanation:
so this is a combined work problem, both of the people are moving towards each other. They are both doing some of the work to move towards each other.
one is moving at 50 , the other at 60 , directly towards each other. Now change the problem to one moving at 50+60 =110 at a destination 200 away
now you can solve this pretty easily , i'm guessing
200/110 = 1.818181
or approx. 1.82 hours
got it?
NO LINKS!! Please help me with this symmetry part 2
Functions that are symmetric with respect to the x-axis are those with even degree of y, i.e y², y⁴ etc.
Correct choices are:
x = 1/8y²x = - y² + 9
Answer:
[tex]x=\dfrac{1}{8}y^2[/tex]
[tex]x=-y^2+9[/tex]
Step-by-step explanation:
Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:
f(x, y) = f(x, −y)To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Therefore, any function that includes the term y² will be symmetric with respect to the x-axis since (-y)² = y².
[tex]\begin{aligned}&\textsf{Given}: \quad& x&=\dfrac{1}{8}y^2\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=\dfrac{1}{8}(-y)^2\\&\textsf{Simplify}: \quad &x&=\dfrac{1}{8}y^2\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.
[tex]\begin{aligned}&\textsf{Given}: \quad& x&=-y^2+9\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=-(-y)^2+9\\&\textsf{Simplify}: \quad &x&=-y^2+9\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.
Simplify the power (3x^2 y)^4
Answer:
(3x^2 y)^4
first apply the index power to all the numbers.
3^4= 81
then you multiply the two indices.
x^2 x 4= x^8
y^4
the answer is:
81 x^8 y^4
Suppose that the volume of water in the rain barrel decreased by 4
58
gallons in 4 minutes. What will be the change in the volume of water after 1 minute.
The change in the volume of water after 1 minute is 1 5/32 gallons.
How to calculate the change in volume?Given that the volume of water in the rain barrel decreased by 4 5/8 gallons in 4 minutes.
The change after 1 minute will be:
= Total volume of water / Number of minutes
= 4 5/8 ÷ 4
= 37/8 ÷ 4
= 37/8 × 1/4
= 37 / 32
= 1 5/32
The change is 1 5/32 gallons.
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IXL Help Fast Please!
The equation of the line d that is parallel to line c is y = -5x + 4.
How to find the equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, c has an equation y = -5x + 3. Line d is parallel to line c. Therefore, they have the same slopes. Parallel lines have the same slope.
Hence, let's find the equation of line d passing through (2, -6)
Let's find the y-intercept
-6 = -5(2) + b
-6 = -10 + b
b = -6 + 10
b = 4
Therefore, the equation of the line d is y = -5x + 4
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A restaurant has 33,500 gallon aquarium and a 500 gallon aquarium. How many times greater is the capacity of the larger aquarium than the smaller aquarium?
Answer:
67
Step-by-step explanation:
33,500/500 = 67
To check our work:
67 x 500 = 33,500
Answer:
67 percentStep-by-step explanation:
The sum of two numbers is 42. The sum of 5 times the 1st number and 9 times the 2nd number is 190. What are the two numbers?
Step-by-step explanation:
x + y = 42
5x + 9y = 190
x = 42 - y
5(42 - y) + 9y = 190
210 - 5y + 9y = 190
210 + 4y = 190
4y = -20
y = -5
x = 42 - y = 42 - -5 = 42 + 5 = 47
How much money must be deposited today to become $2250 in 20 years at 5.5%
compounded continuously?
The deposit must be $
(Round to the nearest cent as needed.)
The amount of money that must be deposited today is $749 .
In the question ,
it is given that ,
the amount that is need to be made (A) = $2250
time (t) = 20 years
rate percent (r) = 5.5% = 0.055
let the amount that must be deposited today be P .
The amount that is needed to be deposited today at 5.5% compounded continuously can be calculated using the formula .
A = P×[tex]e^{r\times t}[/tex]
Substituting the values , we get
2250 = P × [tex]e^{0.055\times 20}[/tex]
2250 = P × [tex]e^{1.1}[/tex]
P = 2250/ [tex]e^{1.1}[/tex]
P = 748.9599
P ≈ 749
Therefore , The amount of money that must be deposited today is $749 .
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If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to
support your answer.
Answer:
[tex] \binom{?}{?} [/tex]
Step-by-step explanation:
$40 Pam use type diagram
$45. bro
Factor 3x+11y if the expression cannot be factored
The expression 3x+11y cannot be factorized.
What is factorization?
To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.
Here the given expression 3x+11y didn't have any common factors.
The given expression has two variables 3x and 11y and they didn"t have any common terms.
Hence the expression 3x+11y cannot be factored.
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How many values of x must be excluded in the expression (x+9)(x-5)?
The number of values of x to be excluded is 2.
To find out the values of x that must be excluded in the expression
(x+9)(x-5) as follows:
The value of x is 2.
We are given to find the number of value of x that must be excluded in the expression below:
E = (x+9)(x-5)
We have to exclude those values of x for which the expression E becomes undefined.
Since E is a rational expression, so the becomes undefined only when the denominator becomes 0.
That is,
(x+9)(x-5) = 0
= x+9 = 0 x-5 = 0
= x = -9 x = 5
Therefore, we need to exclude the values x = -9 and x =5.
So, there are two values of x to be excluded from the given expression.
Hence the answer, the number of values of x to be excluded is 2.
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Which expression shows the distance on the number line between -12 and negative one
Answer: (-12,-1)
Step-by-step explanation: Point A=-1 and Point B=-12
:)
Consider triangle XYZ with altitude WZ. What is XZ?
X
W
N
28
21
Y
The value for the side of rectangle XZ is equal 14, using the trigonometric ratios of cosine and sine of angles.
What is trigonometric ratios?The trigonometric ratios concerns the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the triangle WYZ, the cosine of angle Y;
cos(Y) = 21/YZ {adjacent/hypotenuse}
YZ = [21/cos(Y)] {cross multiply}
Considering the triangle XYZ, the cosine of angle Y;
cos(Y) = YZ/28
YZ = 28 × cos(Y)
Therefore,
28cos(Y) = [21/cos(Y)]
cos²(Y) = 21/28 {cross multiply}
cos(Y) = √(21/28) {take the square root of both sides}
cos(Y) = 0.8660
Y = cos^(-1)(0.8660) {cross multiply}
Y = 30°
To get the side XZ, considering the triangle XYZ the sine of 30°;
sin30° = XZ/28 {opposite/hypotenuse}
by cross multiplication
XZ = 28 × sin30°
XZ = 14
Therefore, by proper application of the trigonometric ratios of cosine and sine of the angle for the given triangle, the side XZ = 14.
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Julie had $20.00 in her pocket. She spent $7.40. About what percent of her money does she still have?
63%
First, we have to take 20.00 - 7.40 which gets us 12.60.
Then, we use the formula where we put the 12.60 on top of a fraction bar, and the 20.00 on bottom.
We do 12.60 x 100 which makes 1260.
Lastly, we divide that by the 20.00 which gets us 63.
So, Julie has 63% of her money left.
I hope this helped!!!
3. Use the graph of f(x) below to answer the following questions. Approximate answers are okay.
Answer:
Step-by-step explanation:
f(0) = 4
f(x)=0 when x = 0.75
f(x) =5 when x =3
A{ x ∈ R ║ 3≤x}
4.5÷0.9= what is 4.5 divided by 0.9 equal to .explain
Answer: The answer is 5.
Step-by-step explanation:
4.5 ÷ 0.9 = 450/90.
Convert decimal 4.5 to fraction 45/10
Convert decimal 0.9 to fraction 9/10
Divide 450/90
Simply 450/90 = 5
Answer:
5
Step-by-step explanation: