Radiocarbon dating is effective on specimens up to 40,000 years old. In 1953, a nuclear chemist was trying to determine the age of some scrolls that were recently found. Carbon-14 has a half-life of 5730 years. If he found 79.5% of the original carbon-14 still present, in about 1908 year were the scrolls made.
What is decay constant?Disintegration constant is another name for the decay constant. It is the ratio of the number of radioactive atoms that break down quickly to the number of the same sort of atoms that were there at the beginning.
Given data:
Carbon-14 has a half-life = 5730 years
So, formula for decay constant:
= log 2/half life
= 0.693/5730
=0.0001209
exponential decay equation:
N(t) = N₀[tex]e^{kt}[/tex] ............ (i)
where N₀ is initial amount ;
N(t) = final amount ;
t = time;
k =decay constant
Given that,
N(t) =0.794 N₀
Now, putting the values in equation (i), we get -
0.794 N₀ = N₀ [tex]e^{-0.0001209t}[/tex]
0.794 = [tex]e^{-0.0001209t}[/tex]
take on natural log on both sides:
ln 0.794 = -0.0001209 t
t = 1907.95 years
t = 1908 years
Therefore, it took 1908 years.
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(-20, 12)
(17, 2)
(-11, 8)
(17, 8)
(11, 2)
Is this relation a function?
Answer:
No because x-coordinate 17 appears twice.
Step-by-step explanation:
In a function, no two ordered pairs can have the same x-coordinate.
Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.
need help! can't figure it out :/
Answer:
please tell me if you get the answer. I need it too!
Fifty students in the seventh grade are trying to raise at least $2,000 for sports supplies. They have already raised $750. How much should each student raise, on average, in order to meet the goal?
On average the 50 students need to raise $25 each.
What is average?
In plain English, an average is a single number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
Given: Fifty students in the seventh grade are trying to raise at least $2,000 for sports supplies. They have already raised $750.
To find the number of students should each student raise, on average, in order to meet the goal.
Let, $2000 - $750 = $1250
So,
$1250/50 = 25
Hence, on average the 50 students need to raise $25 each.
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For which situation does one quantity change at a constant rate per unit interval relative to another quantity?
Responses
For every day that passes, a person drives 54 miles.
.
For every month that passes, a savings account earns interest at a rate of 1.5%
For every week that passes, a vine doubles in length 2 times a week.
.
For every year that passes, a population of insects increases by 6%
Answer:
(a) For every day that passes, a person drives 54 miles
Step-by-step explanation:
You want to know the situation in which one quantity changes relative to another at a constant rate.
DrivingThe rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.
SavingsWe assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.
VineIf the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.
PopulationAs with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.
The situation with a constant rate of change is ...
For every day that passes, a person drives 54 miles.
__
Additional comment
When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.
<95141404393>
It's a mean and median frequency table
Pls answer
a) The mode is 2.
b) 32 Students were there altogether.
c) 15 dinners were served during the week.
d)The mean number of dinners is 2.5.
What is mode?This refers to the value that appears most often in a set of data values.
What is mean?
This refers to the average of the given set of numbers. It is calculated by dividing the sum of given numbers by the total number of numbers.
Given in the question:
a)The number of school dinners 2 has a frequency of 12.
Hence, the mode is 2.
b) To calculate the number of students altogether, we add then frequencies
Total number of students = 0 + 8+ 12 + 6+ 4 + 2
Total number of students = 32
c) To get the number of dinners served during the week, we add the number of dinners together.
Number of dinners served during the week= 0 + 1 + 2 + 3 + 4 + 5
Number of dinners served during the week = 15
D) The mean number of dinners =
1+1+1+1+1+1+1+1+2+2+2+2+2+2+2+2+2+2+2+2+3+3+3+3+3+3+4+4+4+4+5+5
32
The mean number of dinners = 80
32
The mean number of dinners = 2.5
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Given the side measures, which of the following could form a right triangle?
A. 61 m, 60 m, 11 m
B. 24 in, 34 in, 28 in
C. 55 ft, 45 ft, 35 ft
D. 48 cm, 46 cm, 15 cm
The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
What is the right triangle is triangle?
A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using this information, we can determine which of the given sets of side measures could form a right triangle:
A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:
(61 m)² = (60 m)² + (11 m)²
61² = 60² + 11²
61² ≠ 60² + 11²
Since the left side does not equal the right side, these sides cannot form a right triangle.
B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(34 in)² = (24 in)² + (28 in)²
34² = 24² + 28²
34² = 24² + 28²
The left side equals the right side, so these sides could form a right triangle.
C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(55 ft)² = (45 ft)² + (35 ft)²
55² = 45² + 35²
55² = 45² + 35²
The left side equals the right side, so these sides could form a right triangle.
D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:
(48 cm)² ≠ (46 cm)² + (15 cm)²
48² ≠ 46² + 15²
Since the left side does not equal the right side, these sides cannot form a right triangle.
Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
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A quadratic function has roots at 2 and 4 and a vertex at (3, −2). What is the equation of the function in vertex form?
Answer:
Step-by-step explanation:
Which of the following statements is correct for a triangle?
A. triangle can have two obtuse angles
B.The difference of two sides of a triangle is greater than any other side of the same triangle.
C.A triangle can have an obtuse angle and a right angle.
D.None of these
Sonny has 2x + 3 dollars. Allan has 6x + 4 dollars. How much money did Sonny have if they both had $407 all together?
Answer:
$103
Step-by-step explanation:
In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:
2x + 3 + 6x + 4 = 4078x + 7 = 407Now we can solve the equation for x.
8x = 400x = 50We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.
2(50) + 3 = 100 + 3 = 103Sonny has $103.We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.
6(50) + 4 = 300 + 4 = 304CHECK: $103 + $304 = $407A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
Answers: 7 units
14 units
25 units
26 units
answer : 26
steps
get hypotenuse
a² + b² = c²
7² + 8² = c²
49 + 64 = c²
113 = c²
square root of c is √113 which 10.63
7 + 8 + 10.63 = 25.63
7. Use the Division Property of Equality to write an equation that is
equivalent to 5x = 14.
Answer: x = 14/5 or x = 2.8
Step-by-step explanation:
Step 1: Divide both sides of the equation by five: a common nonzero real number.
(5x)/5= 14/5
Step 2: Simplify
x = 14/5
What are the slope and Y intercepted of the relationship?
The slope of the equation 10x+5y-15=0 is -2 and the y-intercept is 3.
What is the slope-intercept form of the line?
The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y-intercept (0, b). In the formula, b represents the y value of the y-intercept point.
To find the slope of the equation, we need to put it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we can first divide both sides of the equation by 5 to get:
2x + y - 3 = 0
Then, we can add 3 to both sides to get:
y = -2x + 3
Now comparing the equation with y = mx + c, we can say that
the slope is -2 and the y-intercept is 3.
Hence, the slope of the equation 10x+5y-15=0 is -2 and the y-intercept is 3.
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Help I don’t understand this
Answer:
A
Step-by-step explanation:
the the direction of the graph is increased that means slope of the graph is positive.
You mix 1 fourth cup of crisp wheat cereal with 1 1 half cups of crisp rice cereal. Find and interpret the value of the ratio of crisp wheat cereal to crisp rice cereal.
The amount of crisp wheat cereal is _____ the amount of crisp rice cereal
Response:
Answer:
The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.
Step-by-step explanation:
Please help if possible.
Answer:
$1020.00000$1020.15050$1020.18436$1020.19742$1020.20078Step-by-step explanation:
You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...
1 per year4 per year12 per year52 per year365 per yearCalculatorThe attached calculator display shows the result:
yearly: $1020.00000quarterly: $1020.15050monthly: $1020.18436weekly: $1020.19742daily: $1020.20078What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
A school is arranging a field trip to the zoo. The school spends 546.53 dollars on passes for 40 students and 3 teachers. The school also spends 351.60 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
There are $21.5 money was spent on a pass and lunch for each student.
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 amount spent by school on pass of 40 students and 3 teachers = $546.53
And, the amount spent for the lunch only for students = $351.60
Now,
The money spent for pass of 43 person = $546.53
Then, The amount of pass for each person = 546.53/43
= $12.71
Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40
⇒ $8.79
Therefore, amount of pass and lunch for each student = 12.71 + 8.79
= $21.5
Thus, $21.5 is the required answer.
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A bakery used `25\%` less butter this month than last month.
The bakery used `240` kilograms of butter this month.
How much did it use last month?
In linear equation, The amount of butter used is an illustration of equivalent ratio.
The amount of butter used last month is 300kg.
What is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Because the bakery used 25% more last month, the amount they used is then calculated using
Amount = ( 1 + 25%) * last month
Substitute 240kg for Last Month
Amount = ( 1 + 0.25) * 240
Remove brackets
Amount = 1.25 * 240kg
= 300 kg
Hence, the amount of butter used last month is 300kg.
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By identifying the vertical asymptote, one can determine the denominator of this
function is
The denominator of function is -x/2 - 1 and vertical asymptote x = -2.
What is vertical asymptote?A vertical line that is not a part of the function's graph but serves as a guide is known as a vertical asymptote. Because it occurs at an x-value outside of the function's domain, the graph cannot cross it. There may be more than one vertical asymptote for a function.
Given graph
the function of graph is F(x) = [tex]2\frac{\left(-\frac{x}{2}\ +\ 1\right)}{\left(\frac{x^{2\ }}{4}-1\right)}[/tex] = 2(1- x/2)/(x²/4 - 1)
reducing the equation
F(x) = 2/(-x/2 - 1)
denominator is -x/2 - 1
for vertical asymptote -x/2 - 1 = 0
x = -2
Therefore for function is -x/2 - 1 and vertical asymptote at x = -2.
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member c: works 7 hours per week at $7.25 per hour member d: works 9 hours per week at $6.35 per hour a. a and b b. a and c c. b and c d. b and d
Only member B and D will reach their goal.
Given;
Amount to be saved = $285
Total time to save money = 5 weeks
Now,
For member A:
Working hours = 8 per week
per hour earnings = $6.15
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hour
= 8 × 5 × 6.15
= $246
For member B:
Working hours = 10 per week
per hour earnings = $5.85
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 10 × 5 × 5.85
= $292.5
For member C:
Working hours = 7 per week
per hour earnings = $7.25
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 7 × 5 × $7.25
= $253.75
For member D:
Working hours = 9 per week
per hour earnings = $6.35
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 9 × 5 × $6.35
= $285.75
Since, the amount earned by member B and D is greater than the goal amount and the amount earned by member A and C is less than the goal amount
therefore,
Only member B and D will reach their goal
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Your question is incomplete. Please find the missing content below:
To be able to go on the band trip, four band members each get a part-time job. Each person has 5 weeks in which to save his or her money. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $285? Member A: Works 8 hours per week at $6.15 per hour Member B: Works 10 hours per week at $5.85 per hour Member C: Works 7 hours per week at $7.25 per hour Member D: Works 9 hours per week at $6.35 per hour
HELP PLEASEEEE ASAP
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $29,521. The variable costs will be $12 per book. The publisher will sell the finished product to bookstores at a price of $25.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer:
2,228
Step-by-step explanation:
Each unit will make 13.25 in profit before incorporating the one time cost. This means that 29,521/13.25= the amount needed to break even.
how to find the standard deviate and variance of a discrete random variable in ap stats organic chem tutor
Calculation the variance and standard deviation of the discrete random variable is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation is the square root of Variance 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
As given in the question,
Variance is used to represent the dispersion of the values in the data from the calculated mean.[tex]( x_{i} - \bar{x})[/tex] represent the dispersion of the given data values from the mean.Variance is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] Standard deviation is the square root of the variance it represents the amount of dispersion of all the given data values.Standard deviation is given by 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].Therefore , the variance and standard deviation of the discrete random variable is calculated with the help of the following formulas:
Variance 'σ²' = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
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Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. In how many weeks will Rufus have a total of 400 pounds of cans?
Answer: 12
Step-by-step explanation:
What does 43,589 + 12,641 equal
Also, what does
63,274+ 97,047 and what does 41,805- 26,426 equal and my last question what does 82,004-11,534
Equal
Answer:
1st one is 160,321
2nd one is 15,379
3rd one is 70,470
Step-by-step explanation:
63,274+ 97,047 = 160,321
41,805- 26,426 = 15,379
82,004-11,534 = 70,470
Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. What is the compound interest?
The compound interest received by Matthew Westhoven is $51.80
What is compound interest?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.
Given, the principal amount (P) = $925
Compound interest percentage (r) = 5.5% = 0.055
Time period (t) = 1
Since, it is semiannually compounded (n) = 2*t = 2
Amount (A) = P(1 + r/n)^nt
= 925(1 + 0.055/2)^2
= 925(1.0275)^2
= 925(1.056)
= 976.80
Thus, Interest amount (CI) = A - P
= $976.80 - $925
= $51.80
The compound interest received by Matthew Westhoven is $51.80
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For what values of x, y, and z is this a parallelogram?
The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
What are the Properties of Angles of a Parallelogram?
A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.
The opposite angles of a parallelogram are congruent (equal). All the angles of a parallelogram add up to 360°. All the respective consecutive angles are supplementary.The consecutive angles are supplementary then,
5y + 7y - 24 = 180
12y = 180 + 24
12y = 204
y = 204/12
y = 17
The opposite angles of a parallelogram are congruent (equal) then,
5y = 4x + 7
5(17) = 4x + 7
85 = 4x + 7
85 -7 = 4x
4x = 78
x = 78/4 = 19.5
x = 19.5
the consecutive angles are supplementary, then
4x + 7 + 3z = 180
4(19.5) + 7 + 3z = 180
78 + 7 + 3z = 180
85 + 3z = 180
3z = 180 - 88
3z = 92
z = 92/3
z = 30.6
All the angles of a parallelogram add up to 360°, then:
4x + 7 + 3z + 5y +7y - 24 = 360
To check is this a parallelogram? put the values of x, y, and z in the above equation:
4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360
356.8 ≠ 360
hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
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Tires A mechanic checked the tire pressures on each car that he worked on
for one week. The random variable x represents the number of tires that
were underinflated.
0
P(x) 0.30
1
2
0.25 0.25
3
0.15
4
0.05
The expected value for the given problem is E(x) = 1.4.
What is expected value?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
A projected average value for an investment at some point in the future is known as the expected value (EV).
Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.
The formula for to find the expected value is given as,
E ( X ) = μ = ∑ x P ( x ) .
E(x) = 0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05
E(x) = 1.4
Hence, the expected value for the given problem is E(x) = 1.4.
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14x+17.5<−66.5 can you guys help me
Answer: < -6
Step-by-step explanation:
r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
