A bone fragment that has 10% of the parent Pb-210 remaining with half-life of Pb-210 is 22 years, the bone fragment is approximately 51 years old.
To determine the age of the bone fragment, you need to calculate the number of half-lives that have elapsed since the bone was formed. The age of the bone can be calculated using the formula:
age = number of half-lives * half-life
To calculate the number of half-lives, you need to determine how much of the original Pb-210 has decayed. If a bone fragment has 10% of the parent Pb-210 remaining, then 90% has decayed.
You can calculate the number of half-lives by taking the natural logarithm of the ratio of the remaining amount of Pb-210 to the original amount:
number of half-lives = ln(0.10) / ln(0.5)
Using the half-life of Pb-210, which is 22 years, you can now calculate the age of the bone fragment:
age = number of half-lives * 22 years
Substituting the values and calculating the number of half-lives and the age of the bone fragment, you get:
number of half-lives = ln(0.10) / ln(0.5) = 2.302
age = number of half-lives * 22 years = 51.064 years
So, the bone fragment is approximately 51 years old.
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Find three consecutive positive integers such that
twice the product of the first and third is 2 less
than twenty times the second.
The three consecutive positive integers satisfying the statement are
9, 10, and 11.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The three numbers be n, (n + 1), and (n + 2).
Therefore, the numerical expression of the given statement is,
2(n)(n + 2) + 2 = 20(n + 1)
2n² + 4n + 2 = 20n + 20.
2n² - 16n - 18 = 0.
n² - 8n - 9 = 0.
n² - 9n + n - 9 = 0.
n(n - 9) + 1 (n - 9) = 0.
(n - 9)(n + 1) = 0.
n = 9 is the positive integer.
So, The numbers are 9, 10, and 11.
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Guys please help
Find the intersection of y = 2(x+2) and y = 4(x-4).
Answer:
(10, 24)
Step-by-step explanation:
First equate both the equations,
2(x+2) = 4(x-4)
Then expand the brackets,
2x + 4 = 4x - 16
Collect like terms in each sides,
4 + 16 = 4x - 2x
Simplify and solve,
20 = 2x
20 ÷ 2 = x
x = 10
Then substitute 10 for x in one of the equations,
y = 2(x + 2)
y = 2(10 + 2)
y = 24
Therefore, the point of interssection is (10, 24).
you can solve this using the simultaneous equation
so y = y
4(x-4) = 2( x + 2)
4x - 16 = 2x +4
4x - 2x = 4+16
2x/2=20/2
therefore x=10
y=2 (x+2)
y=2(10+2)
y=2(12)
y=24
In the xy-plane, a line with equation 2y = 4.5 intersects a parabola at exactly one point. If the parabola has equation y = −4x2 + bx, where b is a positive constant, what is the value of b ?
Answer: b=6
Step-by-step explanation:
While visiting your friend in the city, you see two roads that intersect as shown. Your friend tells you that the angle between the roads on the north side is 69° and the angle between the roads on the south side is (3x)°. Find the value of x.
Answer and Step-by-step explanation:
Let's call the angle between the roads on the south side "y" for simplicity. Since the two roads intersect, the sum of the two adjacent angles on one side must add up to 180 degrees. Therefore, we can set up an equation:
y + 69 = 180
Solving for y, we get:
y = 180 - 69 = 111
We also know that y is equal to 3x, so we can set up another equation:
3x = 111
Solving for x, we get:
x = 37
Therefore, the value of x is 37.
Hope it helps! : )Pleeeeeeeeeeeease answer this for me I’ll give brainly pls pls pls pls
Answer: S=V cubed
Step-by-step explanation:
Answer: A. S = cube of V
Step-by-step explanation:
Cube both sides of the equation to single s out
Express 20cm to 15m
to the lowest form
Answer:
Step-by-step explanation:
To convert 20 cm to meters, we divide by 100, because 1 meter = 100 centimeters.
So, 20 cm = 20/100 m = 0.2 m
To convert 0.2 m to meters in the lowest form, we divide by 15, because 1 meter = 15 units.
So, 0.2 m = 0.2/15 m = 0.013 m
So the final answer is 0.013 m.
Melissa ate 1/2 of her salad for lunch and ate 4/9 of he salad for dinner. How much of her salad did she eat?
Answer:
17/18
Step-by-step explanation:
We know
Melissa ate 1/2 of her salad for lunch and ate 4/9 of the salad for dinner.
How much of her salad did she eat?
We take
1/2 + 4/9 = 9/18 + 8/18 = 17/18
So, Melissa ate 17/18 of her salad.
Mrs Ananaya is buying pencils in packs of 12, notebooks in packs of 16, and red pens in packs of 20. She needs to buy the same number of pencils, notebooks, and red pens. What is the least number of packs of each item that she can buy?
Answer:
Below
Step-by-step explanation:
You need to find the LCD of 12 16 and 20
Using Prime Factorization:
12 = 2 * 2 * 3
16 = 2 * 2 * 2 * 2
20 = 2 * 2 * 5
2 2 2 2 3 5 so LCD will be 2 * 2 * 2 * 2 * 3 * 5= 240
so she will need 240 / 12 = 20 packs of pencils
240 / 16 = 15 packs of notebooks
240 / 20 = 12 packs of pens
for each positive integer n, what is the largest value of p such that zero is the most likely number of successes in n independent trials with success probability p?
The largest value of success probability p with zero as most likely number of success with n independent trials is equal to 1 / ( n + 1 ).
Probability of success is equal to p
Probability of failure is equal to ( 1 - p)
Number of trials is positive integer n
Condition for 'n' independent trials :
Zero is most likely number of success
⇒ P(0) ≥ P(1)
⇒ ⁿC₀ p⁰ ( 1 - p )ⁿ⁻⁰ ≥ ⁿC₁ p¹ ( 1 - p )ⁿ⁻¹
⇒ ( 1 - p )ⁿ ≥ np ( 1 - p )ⁿ⁻¹
⇒( 1 - p ) ≥ np
⇒ np + p ≤ 1
⇒ p ≤ 1 / ( n + 1 )
Largest value of p is equal to 1 / ( n + 1 ).
Therefore, the largest value of success probability p with n independent trials is equal to 1 / ( n + 1 ).
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Can someone please explain how to solve this step by step so I could learn how to do this, if I don’t figure this out I’m literally gonna shoot myself
[tex]2x+2y=-8 \implies x+y=-4 \implies y=-4-x[/tex]
We can substitufe this result into the second equation.
[tex]-10x-5(-4-x)=-5 \\ \\ -10x+20+5x=5 \\ \\ -5x+20=5 \\ \\ -5x=-15 \\ \\ x=3 \implies y=-4-3=-7[/tex]
[tex]\therefore[/tex] The solution is [tex](3,-7)[/tex].
Given f(x) = 4* and its inverse f-¹ (z) = log4z. If f (6) = 4096, then f-¹ (4096) = |
-L
(Just type answer, no spaces)
help please
The numeric value of the inverse function at x = 4096 is given as follows:
f-¹ (4096) = 6.
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
The transformation rule for each point on the inverse function, compared to the original function, is given as follows:
(x,y) -> (y,x).
f(6) = 4096, hence the point on the function is:
(6, 4096).
Then the point on the inverse will be of:
(4096, 6).
Meaning that:
f-¹ (4096) = 6.
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A group of volunteers tagged and released 29 owls as part of a research project. Later, the researchers counted 902 owls, 11 of which had tags. To the nearest whole number, what is the best estimate for the owl population?
The best estimate for the owl population is 2,378.
The population of the owl can be estimated using the concept of proportion. Proportion refers to a mathematical comparison between two numbers. According to the concept, if two sets of given numbers are increasing or decreasing in the same ratio, hence the ratios are said to be directly proportional to each other.
Based on the provided information, 29 owls are tagged and released as part of a research project. Assume that the total number of owl populations is x. At the later time, researchers counted 902 owls and found the 11 were tag. Hence, there are 18 tagged owls which are not accounted for. Assuming that the proportional of tagged owls to number of owls counted applies to the remaining population, the total number of owls can be best estimated as:
x = (902/11)*29 = 2,378
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WRITING Write the
Parallelogram Opposite
Sides Theorem and the
Parallelogram Opposite
Sides Converse as a
biconditional statement.
The Parallelogram Opposite Sides Theorem and the Parallelogram Opposite Sides Converse as a biconditional statement is, If the opposite sides of a parallelogram are equal in length, then the parallelogram is a rectangle and If the parallelogram is a rectangle, then the opposite sides are equal in length.
What is a parallelogram?
Parallelogram is a quadrilateral with opposite sides parallel and equal and opposite angle are equal.
The Parallelogram Opposite Sides Theorem and the Parallelogram Opposite Sides Converse can be stated as a biconditional statement as follows:
For any parallelogram, the opposite sides are equal in length if and only if the parallelogram is a rectangle.
In other words,
(1) If the opposite sides of a parallelogram are equal in length, then the parallelogram is a rectangle.
(2) If the parallelogram is a rectangle, then the opposite sides are equal in length.
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20% of all the children in a class are left-handed. 4 children are left handed. How many children are there in a class altogether?
Answer: 20 children in total.
Step-by-step explanation: If you do 20% of 20 you get 4.
20
let the total children be x
therefore 20/100 × x =4
x = 400/10
x =20
The maximum weight, w, that a stepladder can hold is 250 pounds. Which inequality represents this situation?
O w ≥ 250
w > 250
O w ≤ 250
w < 250
Answer: C
Step-by-step explanation:
Just look for the less than or equal to sign
A motorboat can maintain a constant speed of 23 miles
per hour relative to the water. The boat makes a trip
upstream to a certain point in 52 minutes; the return trip
takes 40 minutes. What is the speed of the current?
The speed of the current is
mile(s) per hour.
Naomi is using pairs of numbers from the set below to find sums, differences, products, and quotients
-6 2.7 -2/3 4 1/5 -5.1
Determine whether each statement about Naomi's calculations is true.
Select True or False for each statement.
The greatest possible sum of two numbers is 6.9.
The least possible difference of two numbers is -11.1. 0
The greatest possible product of two numbers is 11.34
The least possible quotient of two numbers is -6.3
The greatest possible sum of two number is 6.7. Naomi's statement is false.
The least possible difference between two number is -10 Naomi's statement is false
The greatest product of two number in the set is 30.6. Naomi's statement is false
The least possible quotient of two numbers from the set is -6. Naomi statement is false
What are mathematical operations?In mathematics, an operation is a function which takes zero or more input values to a well-defined output value. The number of operands is the arity of the operation.
The greatest possible sum = 4+2.7 = 6.7
The least possible difference = -6-4 = -10
The greatest possible product = -6×-5.1 = 30.6
The least possible quotient = 4÷ -2/3 = -12/2 = -6
Therefore all Naomi's statement are false.
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help, need answer asap
The area of the triangle is 1 square foot.
Waht is the area of the triangle?Remember that the area of a triangle of base B and height H is:
A =B*H/2
Here we can see that:
B = 3ft
H = (2/3) ft
Replacing that in the area formula we will get:
A = (3ft)*(2/3)ft/2 = 1 ft²
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The ratio of a rectangle's length to the rectangle's width is 6:11. If
the perimeter of the rectangle is 510 units, then what is the length of
the rectangle?
Answer:
Step-by-step explanation:
90
By solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.
What are equations?
It primarily consists of a variable, sometimes with a numerical constant in addition.
Take the following illustration into consideration to quickly grasp this idea. 3x – 4 = 5. It is a simple equation of class 7.
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
So, we know that the ration is 6:11 and the perimeter is 510 units.
Then, form and solve the equation as follows:
510 = 2(6x + 11x)
510 = 12x + 22x
510 = 34x
x = 510/34
x = 15
Then, the length will be:
6x
6(15)
90 units
Therefore, by solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.
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25 POINTS. HELP W THE EQUATION TYSM
Step-by-step explanation:
cubing on both sides,
(-4)³= ³√(9x-1)³
-64=9x-1
-64+1=9x
-63=9x
-63/9=x
x=-7
Do u know what this is
Answer:
248
Step-by-step explanation:
Find the volume of each box, then add them up.
Volume = l x w x h
Top: 5 x 2 x 5 = 50
Middle: 6 x 4 x 3 = 72
Bottom: 9 x 7 x 2 =126
Total = 50 + 72 + 126 = 248 cubic feet
Can someone please explain how to group terms in maths (I'm really struggling here )
Answer:
Step-by-step explanation:
Grouping terms in mathematics refers to the process of combining like terms, which are terms that have the same variable raised to the same power.
For example, consider the expression 2x + 3x. The terms 2x and 3x are like terms because they both have the variable x, so they can be grouped together:
2x + 3x = (2 + 3)x = 5x
When grouping terms, it's important to simplify each group of like terms before combining them. For example, consider the expression 2x^2 + 3x^2 + 4x^3. The terms 2x^2 and 3x^2 are like terms because they both have x raised to the power of 2, but they are not like terms with 4x^3 because it has x raised to a different power. To group the terms correctly, we simplify each group of like terms first:
2x^2 + 3x^2 = (2 + 3)x^2 = 5x^2
2x^2 + 3x^2 + 4x^3 = 5x^2 + 4x^3
Once all like terms are grouped and simplified, the expression can be simplified further by combining the groups of like terms:
5x^2 + 4x^3 = 5x^2 + 4x^3
This final expression is the simplified form of the original expression.
Given the set of data below, which measure(s) will change if the outlier is removed?
4, 7, 9, 9, 10
mode
median
mean
range
If the outlier is removed, the following measures will change:
mean
range
Understanding mean and rangea) Mean: Mean is the average of a set of numerical values. It is calculated by summing up all the values in the set and then dividing the sum by the number of values. The mean is a measure of central tendency and represents the typical value of a set of data.
b) Range: Range is a measure of dispersion and represents the difference between the largest and smallest values in a set of numerical data. It provides a quick and simple way to understand the spread of the data, and the difference between the extreme values. The range is calculated by subtracting the smallest value in the set from the largest value.
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The speed, s, of the current in a certain whirlpool is modeled by x = StartFraction 300 Over d EndFraction, where d is the distance from the center of the whirlpool. Which statement is true?
As you move closer to the center of the whirlpool, the speed of the current approaches 0.
As you move closer to the center of the whirlpool, the speed of the current approaches 1.
As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
As you move closer to the center of the whirlpool, the speed of the current approaches 300
The correct statement regarding the function is given as follows:
As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
How to interpret the function?The function for this problem is defined as follows:
s = 300/d.
In which:
s is the speed of the current.d is the distance to the center.As d approaches 0, the equation has the following format:
s = 300/0.
The division by a number that is very close to zero means that the output assumes a value close to infinity, hence the third option is the correct option in the context of this problem.
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Find the slope and y-intercept of the graph of the equation.
Answer:
The slope: 4
Y-intercept: 9
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
In this case y = 4x + 9
m = 4
b = 9
So,
The slope: 4
Y-intercept: 9
Answer:
Slope: 4/1 or 4
Y-Intercept: 9
Step-by-step explanation:
y = mx + b is the Slope Intercept Formula. 'm' in the formula stands for rate of change in y/x, which is practically slope. 'b' in the formula is where the line crossed the y line. It's where it intercepts with y.
What is the midpoint of the segment shown below O A (-7/2, 3/2) O B. (-7,3) O c. (-7/2, 3) O D. (-7,3/2)
Answer:
B.
Step-by-step explanation:
The midpoint of a line segment is found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the segment.
The midpoint of segment AB can be found as follows:
Midpoint of AB = ((-7/2 + -7)/2, (3/2 + 3)/2) = (-7, 3)
Since the midpoint of AB is the same as point B, we can conclude that the midpoint of segment AB is (-7, 3).
a large Ghirardelli bar is 30cm long and 12cm wide. a smaller Ghirardelli bar is 10cm long. If the bars are similar, what is the width of the smaller Ghirardelli's bar?
Answer:
Step-by-step explanation:
if the bars are similar, they are proportional.
make a proportion: length = 30 = 10
width 12 x
cross multiply: 12 times 10 = 120
divide by the number that ids left - 120 ÷ 30 = 4 cm
The width of the smaller bar is 4 cm.
80% of 25$
…………………….
$20
there is two ways to solve this.
ratio form:
80% / 100% = X / $25
---> 2000 / 100 = X
---> X = 20
Decimal form:
80% --- move decimal two places to the left.
80% = 0.8 --- now multiply decimal by total value
0.8 x 25 = 20
$20.
(5x + 14)°
(8x-10)
Pls help me
I am stoopid
explain in your own words why it takes more to prove that quadrilaterals are similar
Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°
Explaining quadrilaterals?
With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.
What is quadrilateral formula?
When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.
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The complete question is -
Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.