Answers
N=N0e^(-kt)
where
N is amount of C-14 at time t
N0 is the initial amount
k is the constant
t is the time taken
given that the amount found was 30% percent of the initial amount, the age of the mammal will be found as follows:
let N=x, N0=0.3x, k=0.0001, t=?
Plug in the formula we get:
0.3x=xe^(-0.0001t)
x will cancel and we shall remain with:
0.3=e^(-0.0001t)
introducing natural logs we get:
ln 0.3=-0.0001t
hence
t=ln0.3/(-0.0001)
t= 12039.7 years
Related Questions
Choose the graph that represents the time for which the velocity of the ball will be between –90 and –58 ft/s.
Answers
The answer is c because t must be less than 2.5 and more than 1.5.
Find this by separating the inequality into:
-90 < -32t - 10
&
-32t - 10 < -58
Simplify and you get 2.5 and 1.5
Graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have:
The velocity of the ball will be between –90 and –58 ft/s.
Let v be the velocity of the ball:
v lies between -90 and -58
-90 < v < -58
The above expression represents the inequality:
Or
-90 < -32t - 10
t < 2.5
And
-32t - 10 < -58
t > 1.5
The number line will be:
Open the circle on the number 1.5 and open circle at 2.5 and a line was drawn between this point.
Thus, graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
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Which multiplication expression that does not belong based on scaling. Explain.
Choose an expression
6 x 2 1/2
6 x 3 3/5
1/2 x 6
2 2/5 x 6
Answers
Use the diagram of the right triangle above and round your answer to the nearest hundredth. If m
Answer choices:
A) 17.32 m
B) 6.83 m
C) 14 m
D) 9.99 m
Answers
Answer:
b. 6.93 m.
Step-by-step explanation:
We have been given triangle ABC and we are asked to find the measure of a.
We will use law of sines to solve our given problem.
[tex]\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are opposite sides of angle A, B and C respectively.
First of all, we will find the measure of angle B using angle sum property.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]30^{\circ}+\angle B+90^{\circ}=180^{\circ}[/tex]
[tex]\angle B+120^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-120^{\circ}[/tex]
[tex]\angle B=60^{\circ}[/tex]
Upon substituting our given values in law of sines we will get,
[tex]\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}[/tex]
[tex]\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}[/tex]
[tex]\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5[/tex]
[tex]a=\frac{12}{\sqrt{3}}[/tex]
[tex]a=6.9282032302755\approx 6.93[/tex]
Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.
What is 30 divided by half plus 10
Answers
15 + 10
25 is your answer. Hope its helps! :)
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Answers
However, tables/software have been developed to give the areas under the normal curve to the left of particular values of z. The function is the probability of Z<z, or P(Z<z).
The area between two values z1 and z2 (where z2>z1) is therefore
P(Z<z2)-P(Z<z1).
For example, to find the area between z1=1.5, z2=2.5
is
P(Z<2.5)-P(Z<1.5)
=0.99379-0.93319
=0.06060
(above values obtained by software, such as R)
For example, the value P(Z<2.5) can be calculated using
P(Z<2.5)=erf(2.5/sqrt(2))/2+1/2
where erf(x) is a mathematical function that does not have an explicit formula (calculated by summation of series, or tabulated).
We have that for the Question, it can be said that the area under the standard normal curve between z 1.5 and z 2.5 is
P(1.5 &2.5) =0.06
From the question we are told
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Generally the equation for the probability is mathematically given as
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
Where
P(Z < 2.5) = 0.99
P(Z < 1.5) = 0.93
From Z Table
Therefore
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
P(1.5 &2.5) =0.06
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Cream filled chocolates are $3.59 a pound Billy bought 1/2 pound of vanilla creams what was the cost round your answer
Answers
how many miles will you go if you ride your bike for t hours at 9 miles per hour?
Answers
r = rate = 9 miles / hour
t = t hours
d = ???
d = 9 * t <<<<==== answer.
A pendulum travels 30 inches on its first swing. During each of its subsequent swings, it travels 90 percent of the previous swing.
Answers
Answer:
a1= 30 and r=0.9
Step-by-step explanation:
edge
In a line of students ,Jenna is number 8.The teacher says the rule for a number pattern is add4.The first term 7.What number should Jenna say?
Answers
2. Let's call "n" to the number in the line where each student is. Then, you can express this as below:
4n+7
3. So, you have:
Student N°1=4(1)+7=11
Student N°2=4(2)+7=15
Student N°3=4(3)+7=19
Student N°4=4(4)+7=23
Student N°5=4(5)+7=27
Student N°6=4(6)+7=31
Student N°7=4(7)+7=35
Student N°8=4(8)+7=39
What number should Jenna say?
The answer is: 39
This list shows the age at which 43 U.S. Presidents began their terms. 57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46 Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?
Answers
The best way to group these ages into six intervals is from 40-44 to 65-69.
What is a Frequency Distribution Table ?A frequency distribution table gives an idea about the data point or interval and its frequency.
The age of the Presidents given as
57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46
The smallest number ( age) is 42 and the largest number (age ) is 69
To make 6 intervals in this gap of 27 , each interval should be of length 5
Therefore the intervals will be
40-44
45-49
50-54
55-59
60-64
65-69
This is the best way to group into intervals.
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Final answer:
The best way to group the ages of U.S. Presidents into six intervals for a frequency table is by intervals of five years each, starting at age 42 and ending at age 71, to cover the entire range and maintain equal width for all intervals.
Explanation:
When grouping ages into intervals for a frequency table, it's best to have intervals that are of equal width and cover the entire range of data without overlap. For the ages of U.S. Presidents starting their terms, which range from 42 to 69, we could divide this range into six intervals in a way that makes sense for this data set.
First, find the range by subtracting the youngest age from the oldest: 69 - 42 = 27. Next, divide this range by the number of desired intervals (6), which gives us 4.5. We can round this to 5 to make the intervals more practical. Thus, each age interval will span 5 years. Starting at 42, the six intervals would be: 42-46, 47-51, 52-56, 57-61, 62-66, and 67-71.
This grouping covers all the ages and each interval is of equal width, making it easy to interpret the frequency table.
Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that the average salary of a group of 16 randomly selected ph.d. students is more than $13,000.
Answers
Mike drew a quadrilateral with four right angles. What shape could be drawn?
Answers
A rectangle, or a square.
All of their angles are 90° angles, which are right angles.
Hope this helped!
they knew that they could 3 miles in 20 minutes. how far can they ride in 45 minutes?
Answers
To find out how far the student can ride in 45 minutes, we calculate the speed of 0.15 miles per minute from the given 3 miles in 20 minutes, then multiply this speed by 45 minutes, resulting in a distance of 6.75 miles.
Explanation:The student has stated that they can travel 3 miles in 20 minutes. To find out how far they can ride in 45 minutes, we need to calculate their riding speed and then apply it to the longer time period.
Step 1: Calculate the riding speed
The speed can be calculated by dividing the distance (3 miles) by the time (20 minutes), which gives us a speed of 0.15 miles per minute.
Step 2: Use the speed to determine the distance in 45 minutes
Now that we know the speed, we can multiply it by the new time period (45 minutes) to find the distance they can ride. That calculation is 0.15 miles/minute × 45 minutes = 6.75 miles.
When we check whether the answer is reasonable, we can notice that 45 minutes is a little more than twice 20 minutes, and since they can ride 3 miles in 20 minutes, it makes sense that they could ride more than twice that distance in 45 minutes, so our answer of 6.75 miles seems reasonable.
They can ride 6.75 miles in 45 minutes.
Explanation:To find how far they can ride in 45 minutes, we can use the concept of average speed.
Given that they can ride 3 miles in 20 minutes, we can calculate their average speed as:
Average Speed = Distance / Time
Average Speed = 3 miles / 20 minutes
Average Speed = 0.15 miles per minute
Now, we can find how far they can ride in 45 minutes:
Distance = Average Speed x Time
Distance = 0.15 miles per minute x 45 minutes
Distance = 6.75 miles
Therefore, they can ride 6.75 miles in 45 minutes.
find the domain of
[tex]f(x) = \frac{ \sqrt{x + 2} }{ {x}^{2} - 25 } [/tex]
Answers
A university is trying to determine what price to charge for tickets to football games. At a price of $18 per ticket, attendance averages 40,000 people per game. Every decrease of $3 adds 10,000 people to the average number. Every person at the game spends an average of $4.50 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?
Answers
Final answer:
To maximize revenue from football game ticket sales and concessions, we create a revenue function based on ticket price adjustments and evaluate changes in quantity demanded. The optimal price and attendance are found by analyzing the combined revenue function, deriving it with respect to the number of price decreases, and finding the maximum value of this function.
Explanation:
To determine the ticket price that should be charged by the university to maximize revenue from football game attendance, we need to analyze the effect of price changes on the quantity demanded. We can create a revenue function based on the given figures and the assumptions that a decrease of $3 in ticket price increases attendance by 10,000 people, and each person spends an average of $4.50 on concessions.
Let x represent the number of $3 decreases in price from the original $18. The ticket price can then be expressed as P = 18 - 3x, and attendance as A = 40000 + 10000x. The revenue from ticket sales is R1 = P × A, which gives us R1 = (18 - 3x) × (40000 + 10000x). The concession revenue per person is $4.50, so total concession revenue is R2 = 4.50 × A, which gives us R2 = 4.50 × (40000 + 10000x).
To maximize total revenue R = R1 + R2, we need to find the maximum of the function R = (18 - 3x) × (40000 + 10000x) + 4.50 × (40000 + 10000x). To find this, we can use calculus to take the derivative of R with respect to x and find the value of x that makes this derivative zero. This will be the critical point which we can then test to confirm it provides a maximum.
if c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE
Answers
-6. -6
__________
3x=8x-55
-8x. -8x
________
-5x=-55
x=11,
3(11)+6=39
8(11)-49=39
Answer:
[tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Step-by-step explanation:
As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.
Remember that a bisector is a line that equally divides an angle.
So,
[tex]\angle AMC = \angle DMC\\3x+6=8x-49[/tex]
Solving for [tex]x[/tex], we have
[tex]6+49=8x-3x\\5x=55\\x=11[/tex]
Then, we substitute this value in each expression to find the angles.
[tex]\angle AMC = 3x+6 = 3(11)+6=33+6=39[/tex]
[tex]\angle DMC = 8(11)-49=88-49=39[/tex]
Therefore, the measures of those angles are [tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Write the epxressions for the equivalent capacitance of two capacitors write your answers in terms of c1 and c2
Answers
.. Ceq = (C1*C2)/(C1 +C2)
Connected in parallel:
.. Ceq = C1 +C2
^4sqrt6/^5sqrt6 I don't have square root signs
Answers
[tex] = \dfrac{ 6^{\frac{1}{4}} }{ 6^{\frac{1}{5}} } [/tex]
[tex] = 6^{\frac{1}{4} - \frac{1}{5}} [/tex]
[tex] = 6^{\frac{5}{20} - \frac{4}{20}} [/tex]
[tex] = 6^{\frac{1}{20}} [/tex]
[tex] = \sqrt[20]{6} [/tex]
Answer:
6^1/20
Step-by-step explanation:
you multiply the two exponents
A polynomial that is written as a product has been ______.
Answers
The polynomial has been factored completely.
Hope this helps!
A polynomial that is written as a product has been "factored completely."
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
In the expression Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Since we know that factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
A polynomial which can be written as a product has been "factored completely."
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8pints compared to 15 cups
Answers
First we need both in the same unit of measurement.
1 pint= 2 cups
Convert 15 cups to pints:
=15 cups ÷ 2 cups per pint
=7.5 pints
STEP 2:
Find percentage:
=8 pints ÷ 7.5 pints
=1.0666 decimal percent of 8 pints
STEP 3:
Convert to %:
=1.06666 x 100
=106.66% percent 8 is of 7.5 pints
*TIP: if you know you're changing to a percentage from a decimal, you will always move the decimal two places to the right.
ANSWER:
8 pints is 106.66% of 7.5 pints.
Hope this helps! :)
NEED HELP ASAP What is the simplified form of the following expression? 4 sqrt 3/2x Assume x>0
Answers
Answer:
[tex]\frac{4\sqrt{6x}}{2x}[/tex]
Explanation:
The problem we are given is
[tex]4\sqrt{\frac{3}{2x}}[/tex]
We can write the square root of a fraction as a fraction with a separate radical for the numerator and denominator; this gives us
[tex]4\times \frac{\sqrt{3}}{\sqrt{2x}}[/tex]
We can write the whole number 4 as the fraction 4/1; this gives us
[tex]\frac{4}{1}\times \frac{\sqrt{3}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}}{\sqrt{2x}}[/tex]
We now need to "rationalize the denominator." This means we need to cancel the square root in the denominator. In order to do this, we multiply both numerator and denominator by √(2x); this is because squaring a square root will cancel it:
[tex]\frac{4\sqrt{3}}{\sqrt{2x}}\times \frac{\sqrt{2x}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}\times \sqrt{2x}}{2x}[/tex]
When multiplying radicals, we can extend the radical over both factors:
[tex]\frac{4\sqrt{3} \times \sqrt{2x}}{2x}\\\\=\frac{4\sqrt{3\times 2x}}{2x}\\\\=\frac{4\sqrt{6x}}{2x}[/tex]
Answer:
The correct answer is ^4sqrt24x^3/2x or B on edge.
Step-by-step explanation:
Find the fifth term of A n = 2n
Answers
Let n = 5.
[tex] A_5 = 2(5) = 10 [/tex]
Given a circle with a diameter of 4, which equation expresses π as the ratio of the circumference of a circle to its diameter?
Answers
is the formula (d*pi=C)
C /4 = π
Took the test myself, this is the answer.
A fourth as much as the product of two thirds and 0.8
Answers
The product of is the answer to a multiplication problem, so it would be 2/3 x 0.8. One fourth of this means that we are finding that part of the answer. To show this we would multiply 1/4 by that answer. Please see the attached picture for the written out problem and the work. The answer is 2/15.
A fourth as much as the product of two thirds and 0.8 is ²/₁₅
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
First, we will translate this word problem into a mathematical equation.
The product of two thirds and 0.8
[tex]\frac{2}{3} \times 0.8[/tex]
A fourth as much as the product of two thirds and 0.8
[tex]\frac{1}{4} (\frac{2}{3} \times 0.8)[/tex]
[tex]= \frac{1}{4} (\frac{2}{3} \times \frac{4}{5})[/tex]
[tex]= \frac{1}{4} (\frac{2 \times 4}{3 \times 5})[/tex]
[tex]= \frac{1}{4} (\frac{8}{15})[/tex]
[tex]= \frac{1}{4} \times \frac{8}{15}[/tex]
[tex]= \frac{1 \times 8}{4 \times 15}[/tex]
[tex]= \frac{8}{60}[/tex]
[tex]= \frac{8 \div 4}{60 \div 4}[/tex]
[tex]= \boxed {\frac{2}{15}}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
in fifteen minutes greg sailboat went 3/6 miles, gina sailboat went 6/6 miles, and stuart sailboat went 4/6 miles. whose sailboat went the longest distance in fifteen minutes?
Answers
Tickets for the movies are $7 for adults and $4 for children. Fourteen people paid a total of $68 for tickets. How many were adults and how many were children?
Answers
7a+4c=68
sincr it was 14 ppl,
let a+c=14
so, system of equations.
multiply a+c= 14 all by 4 to get
4a+4c=56 subtract this from the other
7a+4c=68
-3a=-12
a=4
plug in to either. for a
4+c=14
c=10
plug into other equation to check.
7(4)+4(10)=68
28+40=68
Using the zero product property to find the solutions to the equation x^2-9=16
Answers
Answer:
x=-5, 5
Step-by-step explanation:
To find the solutions, use inverse operations to rearrange the equation to be equal to 0.
[tex]x^2-9-16=16-16\\x^2-25=0[/tex]
Factor the equation and then set each equal to 0 to solve for x.
[tex]x^2-25=0\\(x+5)(x-5)=0[/tex]
x+5=0
x=-5
x-5=0
x=5
Cheryl paid $3.00 for a pair of socks and eight times as much for a pair of shoes. Her brother Kevin also bought socks and shoes but paid twice as much as Cheryl did for each. How much money did they spend together ?
Answers
Kevin: 2(3) + 2(24) = 6 + 48 = 54
27 + 54 = 81
They spent $81.00 all together.
Find the slope of the line that passes through (-95, 31) and (-94, 6).
Answers
Answer:
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Step-by-step explanation:
The equation of a line has the following format:
[tex]y = ax + b[/tex]
In which a is the slope.
Passes through the point (-95, 31).
When [tex]x = -95, y = 31[/tex]
[tex]y = ax + b[/tex]
[tex]31 = -95a + b[/tex]
Passes through the point (-94, 6).
When [tex]x = -94, y = 6[/tex]
[tex]y = ax + b[/tex]
[tex]6 = -94a + b[/tex]
We have to solve the following system:
[tex]31 = -95a + b[/tex]
[tex]6 = -94a + b[/tex]
We want to find a.
From the first equation
[tex]b = 31 + 95a[/tex]
Replacing in the second equation:
[tex]6 = -94a + 31 + 95a[/tex]
[tex]a = -25[/tex]
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number?
Answers
we have that
the value of the digit in the hundreds place in the number 653,841 is------> 800
case A) 748,917
the value of the digit in the thousands place------> 8000
1/10 the value of the digit is-------> (1/10)*8000=800
800=800---------------> is ok
case B) 749,817
the value of the digit in the thousands place------> 9000
1/10 the value of the digit is-------> (1/10)*9000=900
900 is not 800
case C) 784,817
the value of the digit in the thousands place------> 4000
1/10 the value of the digit is-------> (1/10)*4000=400
400 is not 800
case D) 797,481
the value of the digit in the thousands place------> 7000
1/10 the value of the digit is-------> (1/10)*7000=700
700 is not 800
the answer is the option A) 748,917
The answer is 0.5.
To find the answer, understand the place value system in numbers.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number.
To find the answer, we need to understand the place value system. In the number 653,841, the digit in the hundreds place is 8, and the digit in the thousands place is 5. Therefore, 1/10 of the digit in the thousands place is 0.5.
So, the answer is 0.5.