Final answer:
The age of the mammal hide can be determined by using carbon-14 dating. By comparing the remaining amount of carbon-14 to the initial amount and knowing the half-life of carbon-14, the age of the hide can be calculated. In this case, the hide is approximately 778 years old.
Explanation:
The age of the mammal hide can be determined using carbon-14 dating. Carbon-14 (or C-14) is an isotope that is present in all living organisms. When an organism dies, the amount of C-14 in its remains begins to decay.
Based on the information provided, the mammal hide contains 54% of its original amount of C-14. Knowing that the half-life of C-14 is 5,730 years, we can calculate the age of the hide.
To do this, we can set up the following equation: Remaining amount of C-14 = Initial amount of C-14 × (0.5)^(number of half-lives)
Since the hide contains 54% of its original amount of C-14, the remaining amount is 0.54 times the initial amount.
By substituting the known values into the equation, we can solve for the number of half-lives:
0.54 × Initial amount of C-14 = Initial amount of C-14 × (0.5)^(number of half-lives)
Dividing both sides of the equation by the initial amount of C-14 and taking the logarithm of both sides, we can find the number of half-lives:
ln(0.54) = number of half-lives × ln(0.5)
Using a logarithmic calculator, we find that the number of half-lives is approximately 0.136.
Since each half-life spans 5,730 years, we can calculate the age of the hide:
Age of hide = Number of half-lives × Half-life duration
Age of hide = 0.136 × 5,730 years
Therefore, the age of the mammal hide is approximately 778 years.
Answer: 5621
Step-by-step explanation:
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A band wants to create a CD of their last concert. To create the CD’s, the cost will be $350 advertisement fee plus $3 per CD. Write an inequality that represents how many CD’s they can buy with maximum of $1225. Solve the inequality
A factory worker packs 32 mugs into the bottom layer of a box for shipping. If each box can hold 6 layers of mugs, how many mugs can be packed into each box?
Is my math answer correct or no?
estimate the value of this expression by rounding each number to the nearest
whole unit. (1.94)(7.51)(3.74)
A. 21
B. 42
C. 56
D.64
A right triangle is drawn on a coordinate plane. Two vertices of the triangle are points A(−2,4) and B(3,−2) . The third vertex of the triangle is point C, which lies in the third quadrant of the coordinate plane.
What is the distance from point A to point C?
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Which of the following represents the most accurate estimation of 388 - 212?
Lexie needs to buy 105 vases for a party each package has 6 vases how many packages should lexi buy
I would rather to help 6th and 7th grade math
whats a prime number
Your cell phone company charges $40 per month for one phone, plus an additional $5 per moth for each extra phone. Write an expression to represent the cost of a plan with x phones.
BRAINLIEST if right!
A cone has a diameter of 9 inches and a height of 12 inches. Find the volume of the cone to the nearest cubic inch.
972 in³
113 in³
324 in³
254 in³
△ABC is similar to △DEF .
AB=5 inches, BC=9 inches, and DE=7.5 inches.
What is EF ?
I need help figuring out when to use law of sine or law of cosine?
These are some examples of problems.
Please Help!
Final answer:
Use the law of sines when you have two angles and one side, or two sides and a non-inclusive angle. Use the law of cosines when you have two sides and the included angle or all three sides. Apply trigonometric identities for vector addition and resolving forces.
Explanation:
Deciding when to use the law of sines or the law of cosines depends on the information given in a triangle problem. The law of sines is most useful when you know either two angles and one side (AAS or ASA) or two sides and a non-enclosed angle (SSA). The law states that the ratio of the length of a side to the sine of its opposing angle is consistent for all sides and angles in a triangle, often written as a/sin A = b/sin B = c/sin C.
The law of cosines is handy when you have either two sides and the included angle (SAS) or when you have all three sides (SSS). This law relates the lengths of the sides of a triangle to the cosine of one of its angles, following the formula c² = a² + b² - 2ab cos C.
For vector addition problems or when decomposing forces into components, trigonometric identities involving sine and cosine are employed. If you're resolving a weight into components, you may use sine to find the component opposite the angle and cosine for the component adjacent to the angle.
What is the square root of 25p^3 expressed in simplified form?
State a true conclusion.
1) If it is June, then it is summer.
2) It is summer.
Conclusion:
In the conditional logic given, 'If it is June, then it is summer' and 'It is summer', we can infer the conclusion 'It can be June'. However, it is important to note this is a potential conclusion and not a definite one since other months exist in the summer. This kind of conclusion is an example of the converse fallacy, or affirming the consequent.
Explanation:The question provided presents a logical statement in the form of a conditional statement. In logical reasoning and mathematics, a conditional statement is a statement of the form 'if P then Q', where P and Q are both statements. Here, the statement 'If it is June, then it is summer' is the given condition. The statement 'It is summer' is the second statement. A conclusion can be drawn using both of these statements. According to the rules of the logic, we can conclude that 'It can be June.' Remember, we cannot definitively say it 'is' June because there could be other months during the summer. This type of conclusion comes under the inference rule known as the 'converse fallacy' or 'affirming the consequent', where if the consequent (Q - the 'then' clause) is true, the antecedent (P - the 'if' clause) might also be true, but it could also possibly be false due to other factors.
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It takes 24 cups of chicken broth to make chicken soup recipe. How much is this in quarts?
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what is negative 3 times negative one half
Margaret has been told to draw up plans for a 48 square foot flower bed. How many different size flower beds (using whole foot dimensions) can Margaret draw?
A 48
B 24
C 12
D 5
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Is the answer b? I'm not sure.
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"Our customer retention rate has decreased 10% from last quarter's goal of 250 consumers retained. We need to increase our current rate by at least 16% to meet this quarter's goal."
Employee: "That means our target is __________ consumers retained."
Using proportions, it is found that the correct sentence is:
"That means our target is 261 consumers retained."Decreased 10% from last quarter's goal of 250 consumers retained, hence, the number of customers is:
[tex]0.9(250) = 225[/tex]
The current rate has to be increased by 16%, hence, the goal is:
[tex]1.16(225) = 261[/tex]
Hence, the sentence is:
"That means our target is 261 consumers retained."
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for which data representation is the median the better measure of center
The median is the better measure of center when dealing with data sets that have outliers or extreme values.
The median is the better measure of center when a data set contains several outliers or extreme values. It is less sensitive to measurements with extreme values, providing a more robust estimation of central tendency. The median can be thought of as the middle number in a series, where 50% of the measurements are above it and 50% are below.
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What is the measure of AC ?
Enter your answer in the box.
Yesterday it rained 5/8 inch. Today it rained 1/8 inch. What is the total amount of rain for the two days?
The total amount of rain for the two days is 2/3 inch.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Yesterday it rained 5/8 inch.
and, Today it rained 1/8 inch.
So, in two days the amount of rain fall
= 5/8+ 1/8
= 6/8
= 2/3
Hence, total amount of rain is 2/3 inch.
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An old road was 3.95 miles long. After a renovation it was 3.81 times as long. How long was the road after the renovation?
If a polynomial has one root in the form a - √b, it has the second root on the form of a _√b?
The second root will be a + √b the missing sign is positive because the roots are always in the pair.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
The quadratic formula:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
Here the roots are in pairs:
One root is a - √b
The second root will be a + √b
Thus, the second root will be a + √b the missing sign is positive because the roots are always in the pair.
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△ABC has interior angles with measures x°, 100°, and 70°, and △DEF has interior angles with measures y°, 70°, and 50°.
Using the given information, which statement is true?
The two triangles are not similar because y=60 so it is impossible to have three congruent angles.
The two triangles are not similar because the interior angles are congruent but the side lengths are different.
The two triangles are not similar because x≠y .
The triangles are similar because they each have an interior angle with a measure 70°.
The two triangles are not similar because y=60 so it is impossible to have three congruent angles.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In △ABC has interior angles with measures x°, 100°, and 70°,
And, △DEF has interior angles with measures y°, 70°, and 50°.
Hence, Measure of x is,
x + 100 + 70 = 180
x + 170 = 180
x = 180 - 170
x = 10
And, Measure of y is,
y + 70 + 50 = 180
y + 120 = 180
y = 180 - 120
y = 60
Thus, The two triangles are not similar because y=60 so it is impossible to have three congruent angles.
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A rectangle has vertices at these coordinates.
(1, 7), (1, 3), (9, 3)
What are the coordinates of the fourth vertex of the rectangle?
Enter the coordinates in the boxes.