Answers
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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Related Questions
Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) = x^(-1), a = 0.9
Answers
A linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate is L(x)=-6 -4x .
What is function ?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Nearest integer is x =-1
Centre of linearization as x =-1
f(x)=3x2 +2x -3
f(-1)=3(-1)2 +2(-1) -3
f(-1)=-2
f(x)=3x2 +2x -3
f '(x)=6x +2
f '(-1)=6(-1) +2
f '(-1)= -4
L(x)=f(-1) + f '(-1) (x-(-1))
L(x)=-2 -4(x+1)
L(x)=-2 -4x -4
L(x)=-6 -4x
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find the mean weight and variance of the following students in kilograms 50,70,58,62,66,53 and 76
Answers
Answer:
The answer is 62 and 86
Step-by-step explanation:
Mean
(50 + 70 + 58 + 62 + 66 + 53 + 76) ÷ 7
435/7 = 62.1 ≈ 62
Variance
(50 - 62)² + (70 - 62)² + (58 - 62)² + (62 - 62)² + (66 - 62)² + (53 - 62)² + (76 - 62)²
(144 + 64 + 16 + 0 + 16 + 81 + 196)/(7 - 1)
517/6 = 86
Thus, The mean of the given data is 62 and Variance is 86
Which is equivalent to 64 1/4 ?
O24^4
04
O 16
O 1644
Help me pls !! Being timed !
Answers
The value equivalent to [tex](64)^{1/4}[/tex] is [tex]2\sqrt[4]{4}[/tex].
What is meant by an expression?An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.
A formula and an expression are often distinguished by authors, with the former designating a mathematical entity and the latter a statement about such a thing.
But in contemporary mathematics, and particularly in computer algebra, formulas are seen as expressions that can be evaluated as true or false, depending on the values given to the variables present in the expressions.
Given expression is [tex](64)^{1/4}[/tex]
The number 64 can be written as 2 × 2 × 2 × 2 × 2× 2 =2⁶
So, the above given expression becomes,
[tex](64)^{1/4}[/tex]=[tex](2^{6}) ^{1/4}[/tex]
2⁶=2⁴.2²
So,
[tex](2^{6}) ^{1/4}[/tex]=[tex](2^{4} 2^{2})^{1/4}[/tex]
By simplifying we get,
[tex](64)^{1/4}[/tex]=[tex]2\sqrt[4]{4}[/tex]
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Show the optimal binary search tree for the following words, where the frequency
of occurrence is in parentheses: a (0.18), and (0.19), I (0.23), it (0.21), or (0.19).
Answers
The optimal binary search tree for the given frequency is attached below.
Binary search tree:
Binary search tree refers the value of left node must be smaller than the parent node, and the value of right node must be greater than the parent node.
Given,
Here we have to plot the optimal binary search tree for the following words, where the frequency of occurrence is in parentheses: a (0.18), and (0.19), I (0.23), it (0.21), or (0.19).
In order to plot the binary search tree, we have to do the following steps,
First, we have to insert 0.18 into the tree as the root of the tree.Now, then read the next element; if it is smaller than the root node, insert it as the root of the left subtree, and move to the next element.Whereas, if the element is larger than the root node, then insert it as the root of the right subtree.Then we get the binary search tree like the following.
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consider the following method. public int pick(boolean test, int x, int y) { if (test) return x; else return y; }
Answers
If P is the minimum number of tests to achieve full statement coverage for f(x) and Q is the minimum number of tests to achieve full branch coverage for f(x), then (P,Q) =(3, 4)
Branch coverage: During program testing, every branch in a statement must be run at least once.
Coverage of the statement:
This means that during testing, every statement in the computer code must be run at least once.
All of the statements must be executed in order to obtain complete statement coverage.
Statement coverage is calculated as (statement executions divided by total statement executions).
To obtain complete statement coverage in the code above, two test cases are necessary.
Case 1: If the if condition is satisfied,
{
int res=0;
if(m<0) {res=n-m;}
return res;
}
These commands will be carried out.
Case 2: All remaining statements will also be put into effect when the other two cases of else do. Full statement coverage is attained after three tests.
Branch coverage: It includes both true and false situations and is decision-based.
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Inequalities in the real world
Pls help
Answers
WHat is 64% as a fraction
Answers
Answer:
64/100
Step-by-step explanation:
Answer: 16/25or64/100
Step-by-step explanation: 64/100 and divide it by 4 . To change a percent to a fraction, put the percentage over 100 (after removing the % sign) and simplify if necessary
What are the zeros of this function?
Answers
Answer:
B. x = 0 and x = 5
Step-by-step explanation:
The zeros of this function are x = 0 and x=5
_________________
Have a great day!
Consider the function f(x)=x³+7 x²-36
1. Consider the function f(x)=x³+7 x²-36.
a. [1 pts] Find f(2).
b. [4 pts] Factor f(x). Show all your work. (Hint: You can use the fact that if f(a)=0, then the f(x) must have (x-a) as a factor.
2. Miguel decided to invest some of his money in an account gaining $3 % interest compounded semiannually. He ultimately would like to purchase a 560,000 car.
a. [5 pts] How much would he have to invest initially to have the necessary money in 4 years? Round your answer to the nearest whole dollar
Answers
By using the concept of factorization and compound interest, it can be calculated that-
1a) f(2) = 0
b) f(x) = (x - 2)(x + 6)(x + 3)
2) Miguel must initially invest 497118.23
What is factorization and compound interest?
Factorization is the reduction of an algebraic expression into two or more algebraic expressions of smaller degree
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.
1) a) f(x) = x³+7 x²-36
f(2) = 2³+7(2)²-36
f(2) = 36 - 36 = 0
b) Since f(2) = 0, (x - 2) is a factor of f(x)
f(x) = x²(x - 2) + 9x(x - 2) + 18(x - 2)
f(x) = (x - 2)(x² + 9x + 18)
f(x) = (x - 2)(x² + 6x + 3x + 18)
f(x) = (x - 2){x(x + 6) + 3(x + 6)}
f(x) = (x - 2)(x + 6)(x + 3)
c) Let the principal be $p
Rate = 3%
Time = 4 years
[tex]560000 = p(1 + \frac{3}{200})^{4 \times 2}\\\\560000 = p(\frac{203}{200})^8\\\\\\p = 560000 \times (\frac{200}{203})^8\\\\p = 497118.23[/tex]
Miguel must initially invest 497118.23
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Which sequence of transformations could demonstrate the similarity of the two shapes from Part 1?
A. a rotation and then a reflection
B. a dilation and then a reflection
C. a rotation and then a dilation
D. a translation and then a reflection
Answers
SUPER URGENT!
20 points!!
picture required
Answers
So the sun angle = 90
Two people receive an e-mail. Every day, the number of people who receives the e-mail triples. If people continue to receive the e-mail at this rate, how long will it take until 4,374 people receive the e-mail?
Choose the equation for the number of people who receive the e-mail, E, in terms of the number of days since the first e-mail was sent, d, and the correct solution.
PLS HELP
Answers
Answer:
Step-by-step explanation:
First, you will multiply 2 times 4,374 and get 8,748 then you will divide 8748 by 7 which is a week, and get 1249.7 then you will divide it by 356 which is a year approximate, and get 10.51 days.
5/6 q - 1/3 q = 2/5
Please explain step by step on how I could get this answer
Answers
Answer:
4/5
Step-by-step explanation:
5/6q-1/3q=2/5
We change the coefficient’s denominators to 6 so we can subtract them
5/6q-2/6q=2/5
3/6q=2/5
1/2q=2/5
Now divide both sides by 1/2 or multiply both sides by 2
1/2q=2/5
/1/2. /1/2
q=2/5/1/2
q=2/5*2/1
q=4/5
Hopes this helps please mark brainliest
Find the cost of installing a fence around all sides of a rectangular
yard that is 50 feet by 90 feet. The fence that is being used costs
$8.50 per foot.
$1,190.00
$2,380.00
$3,825.00
$38,250.00
Answers
The total cost of installing a fence around all sides of the rectangular yard would be $38250.
What is the area of the rectangle?
For the dimensions of the rectangle of length 'l' and breadth 'b', the area can be computed by using the formula,
Area = Length × Breadth
Given data:
The length of the yard is 90 feet. and the breadth is 50 feet.
Area of the yard = length * breadth
= 90 * 50
= 4500 square foot
Now per square foot, the cost is $8.50 so the total cost of installing a fence around all sides of the yard would be = 4500 * 8.5
= $38250.
Hence, the total cost of installing a fence around all sides of the rectangular yard would be $38250.
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Find the angle between 0 and 2π in radians that is coterminal with the angle -25π/6
Answers
Hi,
I hope you and your family are doing well!
An angle is coterminal with another angle if it has the same terminal side as the other angle, but may have a different degree measure. In other words, coterminal angles are angles that are measured around the same point on the unit circle, but may start at different points.
To find the angle between 0 and 2π in radians that is coterminal with the angle -25π/6, we can add or subtract multiples of 2π to -25π/6 until we get an angle between 0 and 2π.
For example, adding 2π to -25π/6 gives us:
-25π/6 + 2π = -π/6 + 2π = 7π/6
This angle is between 0 and 2π, so it is coterminal with -25π/6.
Alternatively, subtracting 4π from -25π/6 gives us:
-25π/6 - 4π = -29π/6 = -π/2
This angle is also between 0 and 2π, so it is coterminal with -25π/6.
Therefore, the angle between 0 and 2π in radians that is coterminal with -25π/6 is either 7π/6 or -π/2.
Please give this answer 5 stars and brainliest if you find it helpful.
Happy Holidays & New Year!
Let f(x)= -4x-1 and g(x)= x^2 +3. Find (f o g)(-6).
Answers
The value of (f o g)(-6) will be;
⇒ (f o g)(- 6) = - 157
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ f (x) = - 4x - 1
And, g (x) = x² + 3
Now,
Since, The values are,
⇒ f (x) = - 4x - 1
And, g (x) = x² + 3
Hence, The value of function (f o g)(x) is,
⇒ (f o g)(x) = f (g (x) )
= f (x² + 3)
= - 4 (x² + 3) - 1
= - 4x² - 12 - 1
= - 4x² - 13
Thus, (f o g)(- 6) = - 4 (-6)² - 13
= - 4 × 36 - 13
= - 144 - 13
= - 157
So, The value of (f o g)(-6) will be;
⇒ (f o g)(- 6) = - 157
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3y^2 + 3(4y^2 - 2) please help
Answers
The roots of the quadratic equation 3y² + 3(4y² - 2) is ± √(1/7).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, 3y² + 3(4y² - 2).
3y² + 12y² - 2.
14y² - 2.
Let 14y² - 2 = 0.
14y² = 2.
y² = (2/14).
y = ± √(2/14) Or ± √(2/2×7) Or ± √(1/7).
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Find the value of $x$ so that $3^x = (-27)^{-6}$.
Answers
[tex]3^x=(-27)^{-6} \\ \\ 3^x=(-3^3)^{-6} \\ \\ 3^x=(3^3)^{-6} \\ \\ 3^x=3^{-18} \\ \\ \boxed{x=-18}[/tex]
Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 1 + cos - SXST, with n = 3, 4, and 6. Illustrate each case with a sketch similar to the figure shown below.
Answers
The upper and lower sums for f(x) = 1 + cos - SXST, with n = 3, 4, and 6 is 10.1913798 and 10.19913798.
What is upper and lower sums?
Using rectangles that are both enscribed in and circumscribed by a curve, we may approximate the area under a curve. The total area of the rectangles that are inscribed is the lower sum, while the total area of the rectangles that are circumscribed is the higher sum.
[tex]$n=6: \quad \Delta x=\frac{2 \pi}{6}$[/tex]
[tex]\begin{aligned}& \text { Lower sum }=\frac{2 \pi}{6}\left[f(-\overline{4})+f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)\right] \\& c_6=\frac{2 \pi}{6}[1+1.5+1.8660256+2+1.8660254+1.5] \\& c_6=10.1913798\end{aligned}[/tex]
upper sum:
[tex]\begin{aligned}& =\frac{2 \pi}{6}\left[f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)+f(\pi)\right] \\R_6 & =\frac{2 \pi}{6}[1.5+1.8660254+2+1.8660254+1.5+1] \\R_6 & =10.1913798]\end{aligned}[/tex]
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What is the correct to this answer ???? ( answers only)
Answers
Answer:
x>9
Step-by-step explanation:
2x-5>13
2x>13+5
2x>18
x>18/2
x>9
Answer:
x > 9
Step-by-step explanation:
To find the solution to this inequality we need to follow these steps:
2x - 5 > 13
add 5 to both sides2x > 18 (-5 will be eliminated by +5 on the left side while 13 will be 18 when 5 added to it)
divide both sides by 2x > 9
Your business has conducted five market research surveys in the past year. The cost per survey is as follows: Survey 1: $725 Survey 2: $850, Survey 3: $1,250, Survey 4: $1,350, Survey 5: $900. What is the median cost of the market research surveys?
a) $900
b) $1,015
c) $1,092
d) $1,250
Answers
The median cost of the market research surveys is $900 so option (a) is correct.
What are the mode and median?Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.
As per the given surveys,
Survey 1: $725 Survey 2: $850, Survey 3: $1,250, Survey 4: $1,350, Survey 5: $900.
Write the surveys in the increasing format as
$175,$850,$900,$1250,$1350
The median will be the middle value thus $900 will be correct.
Hence "The median price of the surveys for market research is $900".
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Todd orders pictures from a photographer. Each picture costs $7.50 A one time shipping fee of
$3.25 is added to the cost of the order.
Write an algebraic expression that reflects this situation.
Answers
Answer:
1.25 es la respuesta
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given:
Each picture costs $7.50
One time shipping cost = $3.25
Total cost of the order = $85.75
To FInd:
An equation to determine the number of pictures ordered.
Solution:
Define x:
Let x be the number of pictures bought.
Let y be the total amount of money collected.
Form the equation:
The $3.25 one time shipping cost is a fixed cost.
The $7.50 is a variable cost depending on the number of pictures ordered.
Therefore the equation:
⇒ y = 3.25 + 7.5x
Find the number of pictures bought.
The total cost is $85.75
3.25 + 7.5x = 85.75
7.5x = 82.50
x = 11
Answer: The equation is y = 3.25 + 7.5x and Todd bought 11 pictures.
Ima needs an at least B help me out here Please.
What number makes the expressions equivalent?
−1.1−1.4m + 0.4 = ? − 1.4m
Answers
By using the concept of algebraic expression, it can be calculated that
The number that makes the expressions equivalent is -0.7
What is algebraic expression?
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
The given algebraic expression is
−1.1−1.4m + 0.4
On simplifying −1.1−1.4m + 0.4
−1.1−1.4m + 0.4
-0.7 - 1.4m
So the number that makes the expressions equivalent is -0.7
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graph and label (-3.25,3)
Answers
Answer
hello I have provided a picture of the answer
Step-by-step explanation:
ur welcome and have a nice day
Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
Answers
In 11.61 years the given principal amount of $ 900 will be double.
What is Compound interest:Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.
The formula for the Amount when compound interest is calculated is given by
Amount, A = P(1+r/n)^ntP = Principal amount
r = Rate of interest
n = Number of compounds
t = Time period in years
Here from the given data,
Principal amount = $ 900
Rate of interest = 6% = 6/100 = 0.06
Number of compounds = 12 [ ∵ compounded monthly]
Here we need to find the time period
Assume that after 't' years the amount will be doubled
From the given data and formula,
Amount, A = 900(1+0.06/12)^12t
= 900(1+0.06/12)^12t
= 900(1 + 0.005)^12t
= 900 (1.005)^12t
As we assumed after 't' years the amount is double
=> 900 (1.005)^12t = 2 × 900
=> (1.005)^12t = 2
Applying log on both sides
=> log (1.005)^12t = log 2
=> 12t log(1.005) = log 2
=> 12t = log 2/log(1.005)
[ we can use a calculator for log (1.005) and log 2]
=> 12t = 0.30108/ 0.00216
=> 12t = 139.888
=> t = 11.61
Therefore,
In 11.61 years the given principal amount of $ 900 will be double.
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Any help on this question
Answers
Using trigonometric relations we will see that:
a = 5*√3
b = 5
The correct option is the one you marked.
How to get the values of a and b?For a right triangle with a known hypotenuse H and a known angle x, we can use the trigonometric relations:
cos(x)= (adjacent cathetus)/h
sin(x) = (opposite cathetus)/h
Here the hypotenuse measures 10 units, and the known angle is x = 30°.
The adjacent cathetus to that angle is a, so we can write:
cos(30°) = a/10
a = cos(30°)*10 = 10*√3/2 = 5*√3
And b is the opposite cathetus:
sin(30°) = b/10
b = 10*sin(30°) = 5
Then the correct option is the one you marked.
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A credit card company determines a card holder's minimum monthly payment by adding all new interest to 1.5% of the outstanding principal. The credit card company charges an interest rate of % per day. On November , a customer used his credit card to pay for the following business expenses: van repairs ($), equipment maintenance ($), office supplies ($), and dinner with clients ($). Use the given information and the rule that minimum payments are rounded up to the nearest dollar to answer parts a and b below.
a. Assuming the card holder had no new interest, determine his minimum payment due on December 1, his billing date.
The card holder's minimum payment due on December 1 is ___$.
Answers
(a) Minimum payment to be paid is $22
(b) Minimum payment to be paid is $35
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.
The formula for simple interest is:
Simple Interest=P×R×T
where:
P=Principal Amount
R=Daily interest rate
T=Number of days between payments
(a)The minimum monthly payment is calculated by taking 1.5 percent of the outstanding principle
(0.015) ×$ (677+452+139+141) = $21.135
as there is no additional interest due.
The minimum monthly payment required on December 1 is $22, rounded up to the nearest whole dollar.
(b) The minimum monthly payment will be equal to 1.5 percent of the outstanding principle plus the new interest charges.
We will apply the simple interest formula, S.I = p×r×t, to get his new interest costs.
Because Dec contains 31 days, the
Principle amount, p = (677+452+139+141) - 300 = 1109,
the rate, r = 0.05163% each day
Time, t = 31 days.
S.I =p×r×t=1109×0.0005163×31= $17.75
0.015×1109 = 16.64, which is 1.5 percent of the outstanding amount.
To reach $17.75 + $16.64 = $34.39, we must now add the additional interest to 1.5 percent of the outstanding principal.
The minimum monthly payment required on January 1 is $35, rounded up to the next whole dollar.
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Pls answer free brainliest
Answers
The expression that is a factor of the polynomial x³ + 2x² - 9x - 18 is (x + 2).
How to find the factors of a polynomial?Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
For example x² - 4 can be broken as (x - 2) and (x + 2).
Therefore, the expression that factor the polynomial x³ + 2x² - 9x - 18 is as follows:
Therefore,
x³ + 2x² - 9x - 18 = (x - 3)(x² + 5x + 6)
Let's break (x² + 5x + 6) down
x² + 5x + 6
x² + 2x + 3x + 6
x(x + 2) + 3(x + 2)
(x + 3)(x + 2)
Therefore, the factors are (x + 3)(x + 2) and (x - 3)
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Answer:
The answer is C, (x+2).
what is the equation of the line that passes through the point (3, -4) and had an undefined slope
Answers
The equation of the line that passes through the point (3,4) and has an undefined slope is y = 3
What is an Undefined Slope?An undefined slope is an infinite slope. This is the slope of a vertical line. The x values never changes no matter the changes in the y values.
The equation of a line in slope intercept form can be represented as follows:
y = mx + c
where
m = slope
c = y-intercept
Since the slope, m is undefined, the expression that has an undefined slope is a vertical line
Therefore,
y = 3
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Music Company A charges a 15$ membership fee and 0.75$ each to download a song. Music Company B charges 0.90$ each to download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
_________ Songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money? Justify your answer using mathematics.
________ (Type Company A or Company B)
Answers
a. Using linear equations in one variable we get the number of songs at which both companies would charge the same amount is 100 songs.
b. Company B would be a better choice as the total charges for 150 songs would be $127.5.
Explain linear equations in one variable.
A straight line with only one variable is a linear equation. the single variable's power is 1. Simple algebraic methods are used to solve these equations, which have the form ax+b=0.
a) Assume the number of songs downloaded is 'x'.
Now according to the question,
Total charges by company A is 15+0.75x
Total charges by company B is 0.90x
For equal charges, both must be equal,
Hence equating the 2 expressions we get,
15+0.75x=0.90x
15=0.15x
x=100
Hence total number of songs to reach the charge of the same amount is 100.
b)Let us take 150 songs from company A, we get the total charge to be
15+0.75*150=$127.5
Taking for company B, we get
0.90*150=$135.
We see that for 150 songs, the charges of company A is less compared to company B. Therefore I would choose company B over company A.
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