A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14. A hiker in Africa discovers a skull that contains 72 % of its original amount of C 14 .
Answers
If the 72% of its original amount of C-14. Then the number of years will be 3285.
The complete question is attached below.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14.
Then the function is given below.
[tex]\rm N= N_0 \ e^{-kt}[/tex]
Where, N₀ is the initial amount of C - 14, t is the number of the years, k is constant that is 0.0001, and N be the amount of the C - 14 at t years.
[tex]\rm N= N_0 \ e^{-0.0001 \times t}[/tex]
We have N = 0.72N₀, the time will be
[tex]\rm 0.72N_0 = N_0 \ e^{-0.0001 \times t}\\\\\rm 0.72 \ \ \ \ = \ e^{-0.0001 \times t}[/tex]
Take log on both side, then we have
ln 0.72 = -0.001 × t × ln e
-0.33 = -0.001 × t
t = 3285 years
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Related Questions
Which statement describes the quadratic inequality in factored form that represents the relationship greater than or equal to the quadratic equation containing the point (6, -8) on the boundary and zeros -4 and 10?
Answers
In the equation given, the quadratic inequality that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).
What is the quadratic inequality about?Note that a quadratic function exist in factored form is as:
y = a(x - a)(x - b)
The zeros of the equation is seen at x = (-4, 10)
Therefore, one need to write an expression for the quadratic inequality and so it will be:
y ≥ a(x - a)(x - b)
Also note that at At point (6, -8), we also have:
-8 = a(6 - (-4))(6 - 10)
-8 = a(6 + 4)(6 - 10)
-8 = a(10)(-4)
-8 = -a(40)
a = 0.2.
Therefore, In the equation given, the quadratic inequality that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).
See full question below
Which statement describes the quadratic inequality in factored form that represents the relationship greater than or
equal to the quadratic equation containing the point (6, -8) on the boundary and zeros-4 and 10?
Oy2-0.2(x + 4)(x - 10)
Oy≥ 0.2(x + 4)(x - 10)
O y 20.2(x-4)(x + 10)
Oy2-0.2(x-4)(x + 10)
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I WILL GIVE BRAINIEST
The measure of angle N is (3x + 18) degrees . The measure of angle B is (2x + 142) degrees. If angle N is the supplement of angle B, what is the measure of the two angles?
Answers
Answer:
N: 30 B:150
Step-by-step explanation:
Supplementary angles add up to 180 meaning their equations must also add up to 180:
(3x + 18) + (2x + 142) = 180
Solve for x:
5x + 160 = 180
5x = 20
x = 4
Substitute 4 in all values of x to obtain the measure of the two angles:
N: 3(4) + 18 = 30
B: 2(4) + 142 = 150
Consider the circle represented by this equation.
x² + 4x + y2 - 2y - 4 = 0
Which features are features of the circle?
Answers
Answer:
See below
Step-by-step explanation:
arrange to standard form (x-h)^2 + (y-k)^2 = r^2 h,k = center r = radius
x^2 - 4x + y^2 + 2y = 4 complete the square for 'x' and 'y'
(x-2)^2 - 4 + (y-1)^2 -1 = 4
(x-2)^2 + ( y-1)^2 = 4 + 4 + 1 = 9 '9' is equal to r^2 so r = 3
center = 2,1 radius = 3
Answer:
you're welcome!!!
Step-by-step explanation:
Find the measure of one interior angle of a regular 21-gon.
A. 160
B. 162.9
C. 165.6
D. 165
Answers
(21-2)180
=3420
3420 is the measure of the sum of a regular 21-gon, and to find the measure of only one angle, we need to divide the sum by the number of sides, so
3420/21
= 162.9
the answer is B
The gravel path is 5.6 cm long
Answers
i need help what's 8*3^2 i will mark brainiest if someone can answer it in 72-minute s
Answers
Answer:
72
Step-by-step explanation:
8 x 3² = 8 x 3 x 3
= 8 x 9
= 72
[P.S. If you meant (8 x 3)² the answer is:
(8 x 3)² = (24)²
= 24 x 24
= 576 ]
the area of square ABCD is 10cm2 show that x^2+6x=a where a is a constant to be found
Answers
The value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
The question is incomplete.
The question is:
The area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant to be found.
The missing figure is attached; please refer to the picture.
As we can see in the figure we have given a rectangle.
Area of rectangle = (3 + x)(3 + x)
10 = (3 + x)(3 + x)
or
10 = (3 + x)²
10 = 9 + 6x + x²
After rearranging:
x² + 6x = 1
We have equation:
x² + 6x = a
After comparing:
a = 1
Thus, the value of a is 1 if the area of square ABCD is 10 cm² showing that x²+6x=a where a is a constant.
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Given the function h of x equals negative 5 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (–∞, 0).
The function is decreasing on the interval (0, ∞).
The function is increasing on the interval (0, ∞).
Answers
Answer:
The function is decreasing on the interval ( 0,∞)The function h(x) = -5√x is decreasing on the interval (–∞, 0) is true, Option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function h of x equals negative 5 times the square root of x.
h(x) = -5√x
The value of h(x) decreases as the value of x increases.
The function h(x) is a decreasing function over the interval (–∞, 0) because it is a negative function over the interval.
Hence, the function is decreasing on the interval (–∞, 0) is true.
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1) Which situations are BEST modeled by an exponential function?
es
A) The yearly depreciation of a car.
B) An investment compounded annually.
C) The cost of screws sold by the pound.
D) The amount of sugar to make a pound of fudge.
E) The annual growth rate of a city's population.
Answers
A function assigns the values. The correct options are A, B, and E.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The situations that can be best modelled by exponential functions are:
A) The yearly depreciation of a car.
B) An investment compounded annually.
E) The annual growth rate of a city's population.
Hence, the correct options are A, B, and E.
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The sum of ages of Clayman and Ato is 25 years. In five years' time, the age of Ato will twice the age of Clayman now. a. How old is Clayman? b. How old is Ato?
Answers
Clayman is 10 years old and Ato is 15 years old
Word problems leading to equationsLet the age of Clayman be x
Let the age of Ato be y
If the sum of ages of Clayman and Ato is 25 years. then;
x + y = 25
x = 25 - y ...... 1
In five years time;
Age of Clayman = x + 5
Age of Ato = y + 5
If in five years' time, the age of Ato will twice the age of Clayman now, then;
y+5 = 2x ............. 2
Substitute equation 1 into 2
y +5 = 2(25-y)
y + 5 = 2(30 - y)
y + 5 = 50 - 2y
3y = 45
y = 15
Since x + y = 25
x = 25 - 15
x = 10
Therefore Clayman is 10 years old and Ato is 15 years old
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Gcf of 24x^5 - 56x^3 + 16x
Answers
Answer:
8x
Step-by-step explanation:
Greatest common factor is the factor of 24, 56 and 16. Since 16x only has the power of 1, then then the answer should be on power of 1.
Answer:
Given the 24x⁵ - 56x³ + 16x contains numbers and variables, there are two steps to finding the GCF. Find the GCF for the numeric part, then find the GCF for the variable part.
Steps to find the LCD of 24x⁵ - 56x³ + 16x
Find the LCD for the numerical part 24, - 56, 16x Find the LCD of the variable part x⁵, x³, x¹.Multiply the values with each otherFind the common factors of the numerical part: 24, −56, 16
The factors for 24 are −24,−12,−8,−6,−4,−3,−2,−1,1,2,3,4,6,8,12,24.
The factors for −56 are−56,−28,−14,−8,−7,−4,−2,−1,1,1,2,2,4,4,7,7,8,8,14,14,28,28,56,56.
The factors for 16 are −16,−8,−4,−2,−1,1,2,4,8,16.
List all the factors 24,−56,16 to find the common factors.
24:−24,−12,−8,−6,−4,−3,−2,−1,1,2,3,4,6,8,12,24−56:−56,−28,−14,−8,-7,−4,−2,−1,1,1,2,2,4,4,7,7,8,8,14,14,28,28,56,5616:−16,−8,−4,−2,−1,1,1,4,8,16The common factors for 24,−56,16 are −8,−4,−2,−1.−8,−4,−2,−1
The GCF of the numerical part is 8.
[tex]\bf{GCF_{Numerical}=8 }[/tex]
Then find the common factors for the variable part:
x⁵, x³, x
The factors for x⁵ are:
x · x · x · x · x
The factors for x³ are:
x · x · x
The factors for x¹ are:
x
List all the factors x⁵, x³, x¹ to find the common factors.
x⁵ = x · x · x · x · x
x³ = x · x · x
x¹ = x
The common factor of the variables x⁵, x³, x¹ is x.
The LCD of the variable part is x.
[tex]\bf{GCF_{Numerical}=x }[/tex]
Multiply the LCD of the numerical part 8 and the GCF of the variable part x.
8x
i need helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
sorry. thats a hard one. math isn't. my area best of luck
If Bob sells each fish at a profit of $1.25, how much money will he have after selling all 24 fish? Show your calculation.
Best answer receives brainliest
Answers
Answer: $30
Step-by-step explanation:
So if Bob sells his fish at a profit of $1.25 and he has 24 fish to sell then 1.25*24= 30
(I'm assuming what you mean by "how much money he will have" is profit)
Answer:
The answer is $30. remove the decimal from the price and multiply it by the amount of fish. then when you finish multiplying add the decimal back in.
Step-by-step explanation:
125
× 24
--------
500
+ 2500
-----------
30.00
Simplify this expression.
[tex]\\\\(\sqrt{2} + \sqrt{3})(\sqrt{5} - \sqrt{7} \\A: \sqrt{5} + \sqrt{-2} \\B: \sqrt{10} + \sqrt{15} - \sqrt{14} - \sqrt{21} \\C: 2\sqrt{5} - 2\sqrt{7} \\D: 2\sqrt{5} + 3\sqrt{5} - 2\sqrt{7} - 3\sqrt{7}[/tex]
Answers
By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)
How to simplify a product of two binomials with radical numbers
Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:
(√2 + √3) · (√5 - √7) Given(√2 + √3) · √5 + (√2 + √3) · (- √7) Distributive property√2 · √5 + √3 · √5 + √2 · (- √7) + √3 · (- √7) Distributive property√10 + √15 - √14 - √21 (- a) · b = - a · b/ √a · √b = √a · b/ResultBy applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)
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Answer:
B is correct
Step-by-step explanation:
Cus I said so
Kevin earns $240,000 a year as a surgeon. He contributes $20,500 to
his pre-tax 401(k) retirement account and pays the government 28% of his
remaining salary per year. How much is his net pay?
Answers
Using proportions, it is found that his net pay is of $158,040.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
His first discount is for the retirement account, hence the taxable amount is:
T = 240000 - 20500 = $219,500.
He pays 28% of that in taxes, hence his net pay is of 100 - 28 = 72% of $219,500, hence:
N = 0.72 x 219500 = $158,040.
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Laboratory tests show that the lives of
light bulbs are normally distributed with
a mean of 750 hours and a standard
deviation of 75 hours. Find the
probability that a randomly selected
light bulb will last between 750 and 825
hours.
Answer in percentage!!!
Answers
This result is approximate.
=========================================================
Explanation:
mu = 750 = mean
sigma = 75 = standard deviation
The raw scores or x values are x = 750 and x = 825
Let's compute the z score for each x value
z = (x - mu)/sigma
z = (750 - 750)/75
z = 0
and
z = (x - mu)/sigma
z = (825 - 750)/75
z = 1
Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.
Use a z score table to determine that
P(z ≤ 0) = 0.5
P(z ≤ 1) = 0.84314 approximately
So,
P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)
P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)
P(0 ≤ z ≤ 1) = 0.84314 - 0.5
P(0 ≤ z ≤ 1) = 0.34314 approximately
The value 0.34314 then converts to 34.314% which rounds to 34%
Or you could use the empirical rule as shown below. The pink section on the right is marked 34% which is approximate. This pink section is between z = 0 and z = 1.
A fishing gear shop from boulder, co bought $23,000 worth of fishing rods from a liquidator in pasadena, ca. the shop sold the fishing rods for $49,000, making a profit of $250 per fishing rod. there were __?__ fishing rods involved.
Answers
Subtraction is a mathematical operation that reflects the removal of things from a collection. The boulder.co bought 104 fishing rods.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given the cost price of all the fishing rods is $23,000, also the selling price of all the fishing rod is $49,000. Therefore, the total profit from this transaction is,
Profit = $49,000 - $23,000 = $26,000
Since the profit on a single fishing rod is $250, while the total profit is $26,000. Therefore, the number of fishing rods can be written as,
Number of Fishing rod = Total profit/ Profit per rod
= $26,000 / $250
= 104
Hence, the boulder.co bought 104 fishing rods.
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If j is 53 degrees and l is 29 how much is k?
Answers
Answer:
98
Step-by-step explanation:
There are 180 degrees in a triangle.
180 - 53 - 29 = 98
How much of a radioactive kind of francium will be left after 44 minutes if you start with 2,616 grams and the half-life is 22 minutes?
Answers
Step-by-step explanation:
sorry but I dont know
Answer: 654 grams
Step-by-step explanation:
that's the answer it gave it when I got it wrong.
Which figures are polygons?
x
Figure A
Select each correct answer.
Figure B
O Figure A
O Figure B
O
Figure C
O
Figure D
Figure C
Figure D
Answers
Answer:
The answer is figure A, B, C, D.
Step-by-step explanation:
Because, polygon means a shape with more then 1 side, and in your pic all of the figures have more than one side, so that's the answer.
6root27+root243 simplify
Answers
Answer:
6√27 + √243
6√9 x 3 + √81 x 3
6 x 3 √3 + 9√3
18√3 + 9√3
27√3
the cost of kg of apples is $262.50. find the cost of 25 kg of apples
Answers
Answer:
Step-by-step explanation:
cost of 25 kg =262.50x25
=6562.5
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. Consider the given table. x -2 2 5 9 f(x) 5 17 26 ?
The "?" in the table represents the number_because the average rate of change on every interval of the function is_ .
Answers
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The value of f(x) when the value of x is 9 is 38.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The given data points are in a linear relation, therefore, if we find the slope of the line on which these data points will be located. Then the slope will be,
m = (17-5)/(2+2) = 3
Now, equate any point and the slope in the general equation of line, therefore, the equation will be,
y = 3x + c
17 = 3(2) + c
17 - 6 = c
c = 11
Further, the value of f(x) when the value of x is 9 will be,
f(x) = 3x + 11
f(9) = 3(9) + 11
f(9) = 38
Hence, the value of f(x) when the value of x is 9 is 38.
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What is this Simplify as √16y¹6
Answers
Answer:
[tex]6y^1^6[/tex]
Step-by-step explanation:
I hope this has Helped :)
The vertex of this angle is:
R
T
S
Answers
The vertex of this angle is point S.
the inverse of f(x)=2x-10
Answers
The inverse of the function f(x) = 2x - 10 is f-1(x) would be x/2 + 5.
Lets try to solve it,
We will be using the inverse function to solve this.
f(x) =[tex]2x - 10[/tex]
Replace f(x) with y.
[tex]y = 2x - 10[/tex]
Interchange x and y
[tex]x = 2y - 10[/tex]
Solve for y
[tex]y = (x + 10) / 2[/tex]
Replace y with f-1(x).
[tex]f-1(x) = x/2 + 5[/tex]
Thus, the inverse of the function f(x) = 2x - 10 is f-1(x) = x/2 + 5
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what is the factor each expression of x2 - 2x
Answers
Answer:
x(x - 2)
Step-by-step explanation:
x² - 2x ← factor out x from each term
= x(x - 2)
The figure below shows a square ABCD and an equilateral triangle DPC:
ABCD is a square. P is a point inside the square. Straight lines join points A and P, B and P, D and P, and C and P. Triangle D
Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC:
Statements Justifications
In triangles APD and BPC; DP = PC Sides of equilateral triangle DPC are equal
In triangles APD and BPC; AD = BC Sides of square ABCD are equal
In triangles APD and BPC; angle ADP = angle BCP Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 60°
Triangles APD and BPC are congruent SAS postulate
What is the error in Ted's proof? (1 point)
He writes the measure of angles ADP and BCP as 60° instead of 45°.
He uses the SAS postulate instead of AAS postulate to prove the triangles congruent.
He writes the measure of angles ADP and BCP as 60° instead of 30°.
He uses the SAS postulate instead of SSS postulate to prove the triangles congruent.
Answers
Answer:
Which of the following completes Ted's proof?
In square ABCD; angle ADC = angle BCD
In square ABCD; angle ADP = angle BCP
In triangles APD and BPC; angle ADC = angle BCD
In triangles APD and BPC; angle ADP = angle BCP\
J
Question 1 of 10
Each equation given below describes a parabola. Which statement best
compares their graphs?
x = 5y²
x=3y²
OA. Both parabolas open upward, and x = 3y2 is wider than
x = 5y².
B. Both parabolas open to the right, and x = 3y² is wider than x = 5y².
OC. Both parabolas open upward, and x = 5y2 is wider than
x = 3².
OD. Both parabolas open to the right, and x = 5y² is wider than x = 3y².
SUBMIT
Answers
Answer:
D
Step-by-step explanation:
x = 5y²
x = 3y²
Here x is a function of y and so the parabola is open either to right or left.
The coefficient of y² is positive. So the parabola is open to right.
Both parabolas are open to right and x = 5y² is wider than x = 3y².
The most efficient first step in the process to factor the trinomial 2x^3 - 18x^2 + 40x is:
A. Factor out 2
B. Factor out -1
C. Factor out 2x
D. Factor out (x-5)
Answers
Considering the common factor, the most efficient way to factor the expression 2x³ - 18x² + 40x is given by:
C. Factor out 2x.
How to factor an expression?The most efficient way to factor the expression is factoring out the common factor.
In this problem, the expression is:
2x³ - 18x² + 40x
We have that:
The common factor of 2, -18 and 40 is 2.Of x³, x² and x, it is of x.Hence the common factor is of 2x, which means that option C is correct.
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