Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.
What is the half-life of a substance?
Half-life is the time required for the amount of something to fall to half its initial value. The converse of half-life is doubling time.
The half-life of a substance is the time it takes for half of the initial mass of the substance to decay.
Since the half-life of Palladium-100 is 4 days, after 4 days, the mass of the sample will be reduced to half of its initial value. After 8 days, it will be reduced to a quarter of its initial value, and after 12 days it will be reduced to an eighth of its initial value.
We are given that after 12 days, the mass of the sample is 6 mg. This means that the initial mass of the sample was 8 * 6 mg = 48 mg.
After 7 weeks (7 * 7 = 49 days), the mass of the sample will be reduced by a factor of
= [tex]8^{(49/4) }[/tex]
= [tex]8^{12.5}[/tex] =
approximately [tex]2.6 * 10^6[/tex]. The mass of the sample after 7 weeks will be approximately [tex]\frac{6 mg }{2.6 * 10^6}[/tex] = approximately [tex]2.3 * 10^{-6}[/tex] mg.
Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.
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The diameter of a circle is 18m.Eugene claims that the circumference of the circle is about 113.04m.
Answer:
formula. for circumference of a circle is. : 2πR. if you have the radius.
As the diameter is twice the radius, then circumference is. diameter π
then : 18*π≈ 56.52
the mistake was to take the diameter as the radius.
Step-by-step explanation:
check answer
A survey of 2000 subscribers to a certain news paper revealed that 1800 people subscribe to the daily morning edition and 1000 subscribe to both the daily and the sunday editions. how many subscribe to the Sunday edition? how many subscribe to the Sunday edition only?
1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that A survey of 2000 subscribers to a certain news paper revealed that 1800 people subscribe to the daily morning edition
And 1000 subscribe to both the daily and the sunday editions.
Let x denote the number who subscribe to the Sunday edition.
Then the addition rule with overlap tells us that is;
1800 + x – 1000 = 2000
800 + x = 2000
x = 1200
so, 1500 subscribe to the Sunday edition and 1200 – 1000 = 200 subscribe to the Sunday edition only.
Hence, 1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.
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Finding slope given the graph of a line on a grid
Find the slope of the line graphed below.
Systolic blood pressure for a group of women is normally distributed, with a mean of 115 and a standard deviation of 9. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.) (a) greater than 130 (b) less than 108 (c) between 108 and 122
The probability that the blood pressure of woman is more than 130 by given normal distribution is 0.9505
What is z-value?
The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean.
We are given a normal distribution with a mean value 115 and standard deviation 9
And we are asked to find the probability that a woman selected at random has blood pressure greater than 130
We first find the z-value
z= (x-μ)/σ
z= (130-115)/9
z= 15/9
z= 1.6666
Now the corresponding value is
Probability is 0.95
Hence the probability is 95%
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eg=72. if ef = 4x-3 and fg = 6x+9 then x+?
The value of x has been solved as 6.4
How to solve for xWe would have EG = EF + FG
where EG = 70
EF = 4x-3
FG = 6x+9
We would have to put these values in the equation that we have above, such that we would have, To the respective variables, connect the related terms:
70 = (4x-3) + (6x+9)
Separate the x variable. Because of the equal symbol, everything you do on one side also affects the other.
Open the brackets
70 = 4x + 6x -3 + 9
70 = 10x + 6
70 - 6 = 10x
64 = 10x
divide through by 10
x = 64 / 10
x = 6.4
Hence the value of x would be given as 6.4
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On July , the billing date, Marvin Zug had a balance due of $265.72 on his credit card. His card charges an interest rate of 1.25% per month. The transactions he made are to the right.
a) Find the finance charge on August , using the previous balance method.
b) Find the new balance on August 7.
(see photo)
Answer:
475$
Step-by-step explanation:
12. Electricity Company A charges 14 € per unit for the first 100 units in a quarter, and 11 % per unit after that. Electricity Company B charges a flat rate of $12 per unit. How many units must a customer use per quarter for Company A to be the cheaper option?
13 Taxi company A charges a minimum of $ 2.25 for each journey of up to 2 miles, plus per mile for every mile over that. Taxi company B has no minimum fare, but charges 95 per mile. Which of the following is the minimum number of miles over which taxi company A is cheaper than taxi company B ?
A 4
12. The customer should use 120 units in a quarter for company A to be cheaper.
What is cost management?
Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.
Solution:
Company A charges $14 for first 100 units = 14×100
= $1400
After that 11% of 14 = 1.54 per unit
Company B charges $12 per unit so for 100 units = $12×100
= $1200
For company A to be cheaper, customer must use 120 units of electricity from company B as expense for 120 units from company B will be $12×120 = $1440
and,
For 120 units of electricity from company A would be
$14×100 + 1.54×20 as after 100 units company A will charge 11%.
∴ for 120 units = 1400 + 30.8
= $1430.8
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13. For taxi company A to be cheaper customer must travel a minimum of 6 miles.
What is cost management?
Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.
Solution:
Given:
Company A charges $2.25 for a minimum of 2 miles journey and after that 85 cents per mile.
Company B charges 95 cents per mile without any minimum mile condition.
Let's assume
no. of miles = 4
fare from A = $2.25(2 miles) + 85 cents(1 mile) + 85 cents(1 mile)
= $3.95
fare from B = 95 cents × no. of miles
= 95 cents × 4
= $3.8
∵ Fare of company A is greater than B, minimum number of miles should be greater than 4.
now,
Let's assume
no. of miles = 5
fare from A = $2.25 + 85 cents + 85 cents + 85 cents
= $4.8
fare from B = 95 cents × no. of miles
= 95 cents × 5
= $4.75
∵ Fare of company A is greater than B minimum number of miles should be greater than 5.
now,
Let's assume
no. of miles = 6
fare from A = $2.25 + 85 cents + 85 cents + 85 cents + 85 cents
= $5.65
fare from B = 95 cents × no. of miles
= 95 cents × 6
= $5.7
∵ Fare of company A is less than B.
∴ Minimum number of miles should be 6.
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Multiple choice: Select the best answer for Exercises 49 to 52. Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (a) 0.008. (b) 0.02. (c) 0.03. (d) 0.04. (e) 0.208.
The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04
The margin of error is a statistic that describes how much random sampling error there is in survey results.
Given in question,
n = 400
p = 317/400
= 0.7925
Confidence Level = 95%
= 0.95
Formula for margin error, E = [tex]z\sqrt{\frac{p(1-p)}{n} }[/tex]
Confidence level corresponding to 95 % confidence interval, z = 1.96
Therefore,
Margin Error, E = [tex]1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }[/tex]
= 0.0397
≈ 0.04
Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.
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Consider the graph of the function.
Which best represents the graph of the function?
Responses
f(x)=x−8−−−−√+2
f
(
x
)
The equation of the function represented by the graph is (d) g(x) = √(x + 9) - 1
How to describe the transformed equation from the parent function?From the question, we have the graph that can be used in our computation:
The parent function of the graph is a square root function
This is represented as
f(x) = √x
First, we have the transformation to be:
The function is translated left by 9 units
Next, we have:
The function is translated down by 1 unit
Mathematically, this can be represented as
g(x) = f(x - 9) - 1
When represented as an equation, it is
g(x) = √(x + 9) - 1
Hence, the transformation is (d) g(x) = √(x + 9) - 1
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What is C ?
⁸ ⁶
A. 10
B. 28
C. 35
D. 14
Answer:
B
Step-by-step explanation:
assuming you mean [tex]8C_{6}[/tex]
using the definition
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n! = n(n - 1)(n - 2) × 3 × 2 × 1
then
8[tex]C_{6}[/tex]
= [tex]\frac{8!}{6!(8-6)!}[/tex]
= [tex]\frac{8!}{6!(2!)}[/tex]
= (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (6 × 5 × 4 × 3 × 2 × 1 × 2 × 1
cancel (6 × 5 × 4 × 3 × 2 × 1 ) on numerator / denominator
= (8 × 7 ) / 2 × 1
= 56 ÷ 2
= 28
Apologies for formatting.
What is the complete factorization of the polynomial below?
x³-2x²+x-2
A. (x-2)(x + 1)(x-1)
B. (x + 2)(x + 1)(x-1)
C. (x + 2)(x-1)(x-1)
D. (x-2)(x-1)(x-1)
Answer:
(x-2)(x^2+1)
do not exist the answer, so check your question
Step-by-step explanation:
(x^3-2x^2)+(x-2) = x^2(x-2)+(x-2)
= (x-2)(x^2+1)
somebody please help!!
Step-by-step explanation:
I just answered this with all explanations.
the 2 solutions are
x = 6
x = -12
If y varies inversely as x2 and y=38 when x=18, find y if x=20.
The required value of y for the given inverse relation is 30.78
What is the inverse variation?
Inverse variation occurs when one variable varies inversely with respect to another. It represents the inverse relationship between two quantities are two quantities.
In mathematics, inverse variation refers to the relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value. It states that if the value of one quantity rises, the value of the other quantity falls.
Given, y varies inversely as [tex]x^{2}[/tex]
That is, y∝ 1/ [tex]x^{2}[/tex]
or, y = k/ [tex]x^{2}[/tex]
or, [tex]x^{2}[/tex]y = k
And, y=38 when x=18
Then, [tex]18^{2}[/tex]*38 = k
k = 12312
Now, if x=20 then y=?
[tex]x^{2}[/tex]y = 12312
or, [tex]20^{2}[/tex]*y = 12312
or, 400y = 12312
or, y = 12312/400 = 30.78
Hence, the required value of y is 30.78
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The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function: R(x) = -3x^2 +53x
a. How many hearing aids need to be produced and sold in order to maximize the revenue? Round to the nearest whole number. ______ hearing aids must be produced and sold to maximize revenue.
b. What is the revenue? Use the fraction from (a) then round answer to the nearest dollar. The maximum revenue is $ ________.
Answer:
9 ; $234
Step-by-step explanation:
the maximum revenue is the vertex of the parabola
a) -53/(2*-3)
-53/-6
53/6
8.833333
9
b
-3(53/6)^2 + 53(53/6)
-3(2809/36) + 2809/6
-2809/12 + 2809/6
(-2809 + 5618)/12
2809/12
234.083333
234
Which relation is a function?
Answer:
i think A is a function because when you search what it looks like it looks kind of like A so i am sure it is A
Step-by-step explanation:
Find the value.
4³ =
A
12
с
B
81
64
Answer: 64
Step-by-step explanation:
43 = (4)(4)(4)
=64
OR
4x4x4=64
At the July 1980 Olympics, the record for the women's shot put was 22.41 meters, which was 5.09 meters less than double the 1948 Olympic winning distance. What was the women's winning shot put distance in the 1948 Olympics?
The graph of a line y = 2x -1 is shown below. Find the Slope and y-intercept of the function.
Answer:
Slope = 2
y-intercept = -1
Step-by-step explanation:
In the slope-intercept form of the equation of a line (y=mx+b), m equals the slope and b represents the y-intercept.
So, for this problem, m=2 and b=-1. This means the slope is 2 and the y-intercept is -1.
What is the image of (7, 8) after a reflection over the line y = -x?
Answer:
If you connect the 2 dots it will give a X image.Both lines will cross each other forming the X
A ball is thrown from an initial height of 4 feet with an initial upward velocity of 18/fts. The ball's height h (in feet) after t seconds is given by the following.
=h+4−18t16t2
Find all values of t for which the ball's height is 8 feet.
All values of t for which the ball's height is 8 feet are 0.82 or 0.305.
What is quadratic equation?
Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.
Main Body:
The actual equation is
h= 4- 18t +16t²
initial height of ball = 4 ft
The problem asks for a time when the ball's height will be 8 ft. To find these times, I plug 8 in for h and solve for t:
8 = 4+18t -16t²
16t² - 18t +4 =0
Using the quadratic equation:
t = {18 ±√((18)² - 4*16 *4 )}/2*16
t = 18 ± √(324 - 256)/32
t = (18 ± √68) /32
t = (18±8.24)/32
t = 0.82 or 0.305
Hence ,all values of t for which the ball's height is 8 feet are 0.82 or 0.305.
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Andrea started out the day with 2 quects and sold some each hour. Lee started the day with 12 quects and sold some each hour. The graph below represents the number of quects each person has after x hours. Estimate the number of quects each person will have when they have the same amount.
Each person will have 3 quects when they have the same amount
How to estimate the number of quects each person will have when they have the same amount?
Given that:
Andrea started out the day with 2 quects and sold some each hour. Lee started the day with 12 quects and sold some each hour.
The equation of a line is of the form y = mx+c
where m is the slope and c is the y-intercept
For Lee
y =mx+c
c = 12
m = 12-8/0-1 = 4/( -1) = -4
y = -4x+12
For Andrea
y =mx+c
c = 2
m = 2-1/0-1.5 = 1/(-1.5) = -2/3
y = -2/3 x + 2
At the same amount y = -4x+12 is equal to y = -2/3 x + 2. Thus:
-4x+12 = -2/3 x + 2
4x-2/3 x = 12-2
10/3 x = 10
10x = 30
x = 30/10 = 3
Therefore, at 3 quects each person will have when they have the same amount
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Solve F = MGH for H. G=?
The value of G = F/MH for H
What is expression ?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent all of the numerical constants, variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
According to the given information
F = MGH
we need to find the value for G
Dividing the above equation by MH
F/MH = MGH/MH
SO
G = [tex]\frac{F}{MH}[/tex]
So the value of G = F/MH for H
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14,032.8/ 1,000 this is my q and a i nedd this to colm
Answer: 14.0328
Step-by-step explanation:
Answer: 14.032
Step-by-step explanation: you just have to move the decimal point
Help me plssss I dead don’t get this asap
Answer:
i don't know but its not B or D and my guess is A
Step-by-step explanation:
On a standardized exam, the scores are normally distributed with a mean of 135 and a standard deviation of 20. Find the z-score of a person who scored 115 on the exam.
The value of z-score of a person who scored 115 on the exam will be;
⇒ z - score = - 1
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The scores are normally distributed with a mean of 135 and a standard deviation of 20.
Now,
Since, The scores are normally distributed with a mean of 135 and a standard deviation of 20.
We know that;
⇒ z - score = X - μ / σ
Substitute all the values, we get;
⇒ z - score = 115 - 135 / 20
⇒ z - score = - 20/20
⇒ z - score = - 1
Thus, The value of z-score of a person who scored 115 on the exam will be;
⇒ z - score = - 1
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6 divided by 0.528 long division (answer QUICKLY)
Answer: 11.36
Step-by-step explanation:
↓ Please look in the screenshot below...
Write a quadratic equation in a such that the sum of its roots is -8 and the product
of its roots is -15
The equation is x^2-8 x-15=0.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Given, sum of the roots of a quadratic equation is 8 and their product is 15 We know that the quadratic equation is given as [tex]$\mathrm{x}^2-$[/tex](Sum of the roots) [tex]$\mathrm{x}+$[/tex] (product of the roots)[tex]$=0$[/tex] [tex]$\Rightarrow x^2-8 x-15=0$[/tex]
Hence, the equation is x^2-8 x-15=0.
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Answer:
x² +8x -15 = 0
Step-by-step explanation:
You want a quadratic such that the sum of the roots is -8 and their product is -15.
CoefficientsWhen the roots of a quadratic are p and q, its factored form is ...
(x -p)(x -q) = 0
The expanded form of this is ...
x² -(p+q)x +pq = 0
That is, the coefficient of x is the opposite of the sum of the roots, and the constant is the product of the roots.
ApplicationHere, we want the sum of roots to be -8, so the x-coefficient will be the opposite of that: 8. The constant will be the product of the roots: -15. That makes the desired quadratic be ...
x² +8x -15 = 0
__
Additional comment
The attachment shows the quadratic, its roots, and their sum and product.
raise the fraction to higher terms as indicated. 2/3 to twenty-fourths
Answer:
16/24
Step-by-step explanation:
To raise a fraction, we have to multiply by 24/3, which is 8:
2 * 8 / 3 * 8 =
16/24
Part of your job as manager is to count the cash for the daily bank deposit. When you count thecash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9dimes and 15 quarters. What is the total amount of the deposit?
Answer:
$592.92
Step-by-step explanation:
Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9dimes and 15 quarters. What is the total amount of the deposit?
47 ones = $47
22 fives = $110
9 tens = $90
17 twenties = $340
67 pennies = $0.67
12 nickels = $ 0.60
9 dimes = $0.90
15 quarters = $3.75
$47 + $110 + $90 + $340 + $0.67 + $ 0.60 + $0.90 + $3.75 = $592.92
What is the y-intercept of the
grouph of the line whose equation is
y = -2/5 x +4?
Answer:
b = 4
Step-by-step explanation:
y = mx + b represents the equation of a line
m represents the slope
b represents the y-intercept
Based on what we're given, we could determine that 4 is our y-intercept or b.