geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately 3.7973 × 10⁹ years old is the sample.
What is decay constant?The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.
According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.
t1/2 of U₂₃₈ is 4.5 × 10⁹ years
moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles
moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles
Now, U₂₃₈ → Pb₂₀₆
As Pb₂₀₆ comes from U₂₃₈ hence,
moles of U₂₃₈ decayed = moles of Pb₂₀₆
= (0.686 × 10⁻⁶ / 206) moles
Therefore, initial moles of U₂₃₈:
N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles
and N = (1 × 10⁻⁶ / 238) moles
Now, λ (decay constant) = 0.693 / (t1/2)
= 0.693 / ( 4.5 × 10⁹ years)
So,
t = 2.303 / λ × log (N₀ / N)
t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]
t = 14.95 × 10⁹ × 0.254
t = 3.7973 × 10⁹ years.
Thus, the sample is: 3.7973 × 10⁹ years old.
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the degree to which an instrument appears to measure what it is supposed to be measuring is referred to as:
22) The function y = -16t² + 56t+ 4 must have a root between
which of the following x- values?
A) 0 and 1
B) 1 and 2
C) 2 and 3
D) 3 and 4
E) 4 and 5
t = 3.750 and t = 0.070 are, the following x- values, between A) 0 and 1 and D) 3 and 4
What is quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable (x) using the formula ax² + bx + c = 0 and a≠0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.
According to question.
y = -16t² + 56t+ 4
⇒ -16t² + 56t + 4
⇒ -4t² + 14t + 1
⇒ t = [-14 ±√((14)² - 4*(-4)*1)]/-8
⇒ t = [-14 ±√(212)]/-8
⇒ t = [-14 ± 14.560]/-8
⇒ t = [-14 ± 14.560]/-8
⇒ t = -(28.56)/-8 and t = 0.560/-8
⇒ t = 3.750 and t = 0.070
hence, t = 3.750 and t = 0.070 are, the following x- values, between A) 0 and 1 and D) 3 and 4
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Which is the domain of the function f(x) = negative five-sixths (three-fifths) superscript x?all real numbersall real numbers less than 0all real numbers greater than 0all real numbers less than or equal to 0.
The function's domain is (a) all real numbers.
What is the domain in math?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set. A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
How do you identify the domain?The formula for the function is: f(x) = Negative 5/6. X in superscript?
The function mentioned above is exponential
There are no input value restrictions for exponential functions
Consequently, the function's domain is (a) all real numbers.
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b) Mrs. Maharjan can do part of a work in 1 day. She worked for 2 days and left. The remaining parts of the work is done by Mrs. Rai. (i) How much work did Mrs. Maharjan do in 2 days? (ii) How much work was left to do? (iii) How much work was done by Mrs. Rai?
i) The amount of work that Mrs. Maharjan did in 2 days is; ¹/₃ parts
ii) The amount of work that was left to do is; ²/₃ parts
iii) The amount of work that was done by Mrs. Rai is; ²/₃ parts
How to solve fraction word problems?We are told that Mrs. Maharjan can do ¹/₆ part of a work in 1 day.
Thus;
i) Amount of work done in two days = ¹/₆ + ¹/₆ = ¹/₃ part
This represents the amount of work that Mrs. Maharjan did in 2 days.
(ii) Since Mrs. Maharjan did ¹/₃ part of the work in 2 days, then it means that the amount of work that was left to do is;
1 - ¹/₃ = ²/₃ parts
(iii) Since we are told that Mrs. Rai did the remaining works, the the amount of work that was done by Mrs. Rai is as calculated in ii above.
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Complete question is;
Mrs. Maharjan can do ¹/₆ part of a work in 1 day. She worked for 2 days and left. The remaining parts of the work is done by Mrs. Rai.
(i) How much work did Mrs. Maharjan do in 2 days?
(ii) How much work was left to do?
(iii) How much work was done by Mrs. Rai?
An organic food company need to paint it new ilo. The ilo i a cylinder with a height of 24 yard and a bae 3 yard in diameter. The paint the company ha elected will cover 150 quare feet per gallon. How many gallon of paint will be needed to paint the top and lateral urface of the ilo?
To calculate the total area of the cylinder, we need to use the formula for calculating surface area; SA = 2πr² + 2πrh. In this case, r is equal to 1.5 yards and h is equal to 24 yards:
SA = 2(3.14)(1.5^2) + (2)(3.14)(1.5)(24)
= 28 ft² + 144 ft²
= 172 ft²
Therefore, we need 172/150 gallons of paint in order to cover both sides of the ilo with one coat each - approximately 1 gallon and 14 fluid ounces or about 1 3/4 gallons of paint will be needed in total
What is Surface Area?
The area is the area occupied by a flat, two-dimensional surface. It is expressed in square units. The surface area of a three-dimensional object is the space taken up by its exterior surface.
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pls answer the question in the image :)
The system of equations that to be used to calculate the number of chicken wings (x) and sliders (y) in the combination meal:
55x + 275y = 1100 and y = 8x.
What is system of equations?A system of equations is a collection of one or more equations with multiple variables.
Let x represent each onion ring.
Allow each slider to be represented by y.
That is what we are told;
The calorie count for each onion ring is 55.
The number of calories in each slider is 275.
A combination meal of both contained 1100calories.
Thus;
The equation formed wiil be,
55x + 275y = 1100
It also shows that there are 8 more onion rings than as many sliders.
Thus;
The equation formed is,
y = 8x
Therefore the system of equations in the combination meal are as follows: 55x + 275y = 1100 and y = 8x.
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The area of a right Triangle is 30 sq.cm and it’s perimeter is 30cm. If it’s hypotenuse is 13cm, what are the lengths of the other two sides?
Answer:
either h=12, b=5
or h=5, b=12
Step-by-step explanation:
We'll use a system of equations to solve this. We'll have 2 equations and 2 unknowns. Our 2 unknowns are the 2 other sides, and our 2 equations are as follows:
look for any information given. I see that the area is 30 sq.cm and the perimeter is 30cm. There are our pieces of information.
Our first equation will be the one about how the area is 30 sq.cm (we'll use b for base and h for height:
(1/2)×b×h=30
Our second equation will be the one about how the perimeter is 30cm:
13+b+h=30
These equations both have to be true at the same time, and there are a few techniques for solving a system of equations, but in this case, this way is probably the simplest. We'll get one variable on one side of an equation and then plug it into the other equation using the transitive property.
13+b+h=30
b=30-13-h
b=17-h
now we'll plug in (17-h) for all the b in the first equation:
(1/2)×(17-h)×h=30
17h-h²=60
-h²+17h-60=0
now we'll use quadratic formula (or factor) to find h:
[-17±√(289-240)]/-2
(-17±7)/-2
-24/-2 or -10/-2
12 or 5
h=12
h=5
we'll try both of them in this equation:
13+b+h=30
25+b=30
or 18+b=30
therefore;
either h=12, b=5
or h=5, b=12
6. The coordinates of point A are given. The midpoint of AB is (3,-5). Find the coordinates of point B.
a. A(4,-8)
b. A(2.5, -6.5)
The tide, or depth of the ocean near the shore, changes throughout the day. The depth of the bay can be modeled by d = 35 - 28 cos (π/6. 2 t)
where d is the depth in feet and t is the time in hours. Consider a day in which t = 0 represents 12:00 A. M. At what time is the water depth 14 feet.
(please include explanation)
The exists no solution for which the water depth 14 feet in the ocean near the shore.
Explain the term time period?A time period (T) is the length of time it takes for one complete vibration cycle to pass over a certain location. As the frequency of a wave rises, so does its period. The length of time is expressed in "seconds."We determine the function's period since that is the number of it takes hours for the ocean to return to its original depth of a specific number of feet.
The function's duration is 2π/ (π/6.2) = 12.4 hours.
When t = 0, midnight, or 12:00AM, it is low tide.
As a result, the next low tide will occur at 12:24 PM, or t = 12.4, 12.4 hours from now.
A high tide will occur halfway between those two low tides, at t=6.2 hours after midnight, or at 6:12AM.
Another high tide will occur at t=18.6 hours after midnight, or at 6:36 PM, 12.4 hours later.
If t = 0 is used in the equation, the low tide occurs at that time;
d = 35 - 28cos(pi/6.2)t
d = 35-28cos(pi/6.2)0
d = 35-28cos(0)
d = 35-28(1)
d - 35-28
d = 7
Therefore, there will never be 4 feet there because the lowest depth that may exist is 7 feet.
Thus, the exists no solution for which the water depth 14 feet in the ocean near the shore.
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originally, What is the estimated age of the artifact? (The half-life of 7. An archeologist finds an artifact that contains 44% of the carbon-14 that it would have had carbon-14 is 5,730 years.)
Answer: To determine the estimated age of the artifact, we can use the half-life of carbon-14 and the percentage of carbon-14 that is present in the artifact.
The half-life of carbon-14 is the amount of time it takes for half of the carbon-14 in a sample to decay. In this case, the half-life of carbon-14 is 7,730 years.
The percentage of carbon-14 that is present in the artifact is 44%. This means that the artifact contains 44% of the carbon-14 that it would have had when it was originally made.
To determine the age of the artifact, we can use the formula:
age = (half-life / log(2)) * log(percentage of carbon-14 / 100)
Substituting the values from the problem into the formula, we get:
age = (7,730 years / log(2)) * log(44% / 100)
age = (7,730 years / 0.693) * log(0.44)
age = 11,095 years * (-0.847)
age = -9,432 years
Therefore, the estimated age of the artifact is -9,432 years.
It is important to note that this is just an estimate, and the actual age of the artifact may be different. Carbon-14 dating is only accurate up to a certain point, and the accuracy of the age determination depends on several factors, including the initial concentration of carbon-14 in the sample and the presence of any contaminants.
can anyone please help me on my bell ringer
Answer:
y= 20x+50
Step by Step:
Which inference is incorrect?
The analysis of the logical statement from among the options indicates that the inference that is not true is the option;
If not p, not q. q therefore not not qWhat is a logical statement?A logical statement is one which draws a conclusion based on an hypothesis.
The logical statement which is incorrect can be found by examining the specified statements as follows;
If p then q,
The converse statement , found by switching the positions of the hypothesis and the conclusion is therefore;
q therefore p
The inference is correct
The statement, if not p, not q . q therefore not not p
According to the law of contraposition, a conditional statement is true when the contrapositive statement is also true.
The statement if not p, not q. which is the contrapositive of the statement if q then p
The inference, q, therefore not not q is incorrect
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The time,
T
(seconds), it takes for a pot of water to boil is proportional to the amount,
A
(litres), of water.
It takes 200 seconds to boil 2.7 litres of water.
Work out how much water is in the pot if it boils in 220 seconds.
The relationship between the time it takes to boil a pot of water, T (in seconds), and the amount of water, A (in litres),
T ∝ A,
setting up the equation and solving:
2.96 liters of water will boils in 220 seconds.
what is equation?An equation is a mathematical statement that shows that two expressions are equal.
what is proportionality constant?A proportionality constant is a coefficient that relates two quantities that are proportional to each other. In other words, if two quantities are proportional, their ratio is always the same, and this constant ratio is the proportionality constant.
This proportionality can be written as an equation by introducing a constant of proportionality, k:
T = k * A
We are given that it takes 200 seconds to boil 2.7 litres of water, so we can set up an equation using this information:
200 = k * 2.7
Solving for k, we find that k = 200/2.7 = 74.07407407407407.
Now that we know the value of the constant of proportionality, we can use it to find the amount of water in the pot if it boils in 220 seconds. We can set up the following equation:
220 = 74.07407407407407 * A
Solving for A, we find that the amount of water in the pot is A = 220 / 74.07407407407407 = 2.962962962962963 litres.
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PLS HELP ME DUE NOW!!!!!!!!!!!!
The new coordinate for point B is (0,2). Hence option B is the correct option.
What is coordinate of a point?
A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x,y) the x-value and y-value.
Given that the coordinate of point A and B are (3,0) and (0,4).
The line AB is dilated by 1/2.
This means the scale factor is 1/2.
The x coordinate of point B is 0.
The y coordinate of point B is 4.
Multiply 1/2 with the x coordinate and y coordinate of point B to find the new coordinate of point B:
The new x coordinate of point B is (0 × 1/2) = 0
The new y coordinate of point B is (4 × 1/2) = 2.
The new coordinate of point B is (0,2).
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Aisha models a can of ground coffee as a right cylinder. She measures its height as 5 and 1/2 and its radius as 1/2 in. Find the volume of the can in cubic inches. Round your answer to the nearest tenth if necessary.
how to simplify radical expressions
The way to simplify radical expressions include:
Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.Use the product rule to rewrite the radical as the product of two radicals.Simplify the root of the perfect power.What is a radical expression?Any expression with the radical symbol is referred to as a radical expression. This symbol, which is frequently used to calculate the square root of a number, is frequently called the "square root" symbol by mistake.
But it can also refer to a cube root, a fourth root, or something higher. Radical equations are equations that contain radicals.
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Evaluate
-1/3 - (-6/5)
SIMPLEST FORM
Answer:
13/15
Step-by-step explanation:
Step 1) Convert to -5/15 - (-18/15)
Step 2) -5/15 - (-18/15)= 13/15
hurrryyyyy please
What is the solution for p in the equation?
1/3 P + 1/2 P + 7 = 7/6 p + 5 + 4
A. p=1
B. p=-1
C. p=6
D. p=-6
Answer:
D. p = -6
Step-by-step explanation:
1. combine like terms
5/6 P + 7 = 7/6 P + 9
2. subtract 7/6 P from both sides
-2/6 P + 7 = 9
3. subtract 7 from both sides
-2/6 P = 2
4. multiply both sides by -6/2
Answer:
p = -6
Answer: D
Step-by-step explanation:
you roll a 6-sided die two times. what is the probability of rolling a 6 and then rolling a 4
Step-by-step explanation:
the same as every other individual outcome of a roll of 2 dice : 1/6 × 1/6 = 1/36
Line H is represented by the following equation: 2x + 2y = 8
What is most likely the equation for line K so the set of equations has infinitely many solutions
O a
Ob
O c
Od
x + 2y = 2
x+y=4
2x + y = 6
x-y=8
Question 2 (4 points)
x+y=4 is most likely the equation for line K so the set of equations has infinitely many solutions.
Define equation.Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.
Given
There must be identical lines made up of the same points for there to be an endless number of solutions. This implies that when expressed in the simplest terms, their equations are also identical.
As a result, x+y Equals 4. Equation here corresponds to B.
2x + 2y = 8
Dividing equation by 2
x + y = 4
As a result, x+y Equals 4. Equation here corresponds to B.
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A line has a slope of 1 and passes through the point (–12, –17) What is its equation in slope intercept form?
Equation of the line in slope intercept form is y = x - 5, when slope is 1 and a point on the line is (-12, -17).
What is Slope?Slope of a line is the degree of inclination of that line.
In other words, slope of a line can be calculated by taking the change in y coordinates to the change in x coordinates when x coordinate and y coordinate of two points are given.
Equation of a line in slope-intercept form is,
y = mx + c
where, m is the slope and c is the y-intercept.
y- intercept is the y-coordinate of a point where the line touches with the Y-axis. x coordinate will be zero at this point.
We have m = 1 and a point (x, y) = (-12, -17)
Substituting these values in the equation,
-17 = (1 × -12) + c
-17 + 12 = c
c = -5
Substituting m = 1 and c = -5, equation in slope intercept form can be written as,
y = x - 5
Hence, the equation of the line in slope intercept form when slope = 1 and passing through the point (-12, -17) is y = x - 5.
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When we reject the null and the null is true, we have a made a _________ __________.
When we reject the null and the null is true, we have a made a type I error
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.
null hypothesis is denoted as H₀
Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. When you can reject the null hypothesis, your results are statistically significant.
when the p-value is greater than your significance level, you fail to reject the null hypothesis.
Sometimes , we reject our null hypothesis even when its true
there we made a type I error in hypothesis
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The interest rate on your loan is lowered from 3.5% to 3%
A) What is the percentage change
B) what is the percentage point of change
I NEED HELP ASAP!! ITS URGENT
If the interest rate on your loan is lowered from 3.5% to 3%:
A) The percentage change is 14.28%
B) The percentage point of change is 0.5%
What is meant by interest rate?A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe. An interest rate is the percentage of a loan, deposit, or borrowing that must be paid in interest each period (called the principal sum). The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.
Let the capital will be 100
For interest rate 3.5% then the loan amount will be:
100×(3.5/100)=3.5
For interest rate 3% then the loan amount will be:
100×(3/100)=3
A) Percentage change=((-3.5+3)/3.5)×100
=(-0.5/3.5)×100
=14.28%
B) Percentage point of change=3.5%-3.0%
=0.5%
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Suppose you are trying to find your longitude and start looking for when the shadows are shortest at your house. You discover that this happens at 1:31:45 PM EDT (Eastern Daylight Savings Time).
What is this time in GMT?
Remember that EDT = GMT – 4.
Practice
A
1:31:45 PM
B
5:31:45 PM
C
9:31:45 AM
D
4:31:45 PM
The time calculation which involve calculating the time in GMT when it is 1:31:45 PM EDT (Eastern Daylight Savings Time) is
B 5:31:45 PMHow to convert from Eastern Daylight Savings Time to GMTThe conversion given in the problem is
Eastern Daylight Savings Time = Greenwich mean time GMT - 4
Eastern Daylight Savings Time + 4 = Greenwich mean time GMT
Solving for the time equivalence in Greenwich mean time
Greenwich mean time GMT = Eastern Daylight Savings Time + 4
substituting known values
Greenwich mean time = 1 : 31 : 45 PM + 4
Greenwich mean time = 5 : 31 : 45 PM
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The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of "-0.5" . See the figure below. Suppose that the height of the candle after 19 hours is 16.5 centimeters. What was the height of the candle after 11 hours?
The height of the candle after 11 hours is 20.5 if the slope is -0.5.
What is a slope?The ratio of "vertical change" to "horizontal change" between any two separate points on a line, or any two points, is used to compute slope. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line. The line may be practical, as determined by a road surveyor, or in a diagram that represents a roof or a road as a description or a design.
The absolute value of the slope serves as a proxy for a line's steepness, incline, or grade.
Given, slope m= -0.5
(y-y₁)=m(x-x₁)
Also given that,
x=19, y=16.5 cm
(y-16.5)=m(x-19)
y-16.5= -0.5(x-19)
y-16.5= -0.5x+9.5
0.5x+y-26=0
After 11 hours, the height of the candle is:
x=11
0.5(11)+y-26=0
y=26-5.5
y=20.5
Therefore, the height of the candle after 11 hours is 20.5
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a polynomial function of degree n has at most real zeros and at most relative extrema. t or f
A polynomial function of degree n has at most n real zeros and at most n-1 turning points.
What is polynomial function ?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
What isa Zeros of Polynomials?
Every polynomial will have as many zeros as its degree if we are able to factor it over the entire set of complex numbers, though some of these zeros are repeated and therefore counted more than once. As the function might not be fully factorable over the set of real numbers, if we limit ourselves to the set of real numbers, we might or might not be able to identify this many zeros.
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w+13=27
what is answer
Answer: w=14
Step-by-step explanation: The way I solve it is if you take 27 and subtract 13 from it, you'll get 14. Hope this helps!
Answer:
w=14
Step-by-step explanation:
hope this helps...
25^x = 5^4x+1
what is the value of x? pls help me :(
Answer:
x = -0.5
Step-by-step explanation:
[tex]factors \: of \: 25 \\ 25 = 5 {}^{2} \\ 5 {}^{(2)x} = 5 {}^{4x + 1} \\ since \: bases \: are \: equal \: \\ hence \: exponents \: are \: equal \\ 2x = 4x + 1 \\ collect \: like \: term \\ 2x - 4x = 1 \\ - 2x = 1 \\ divide \: by \: - 2 \: both \: sides \\ x = - 0.5[/tex]
During the holiday, students went swimming in a local rectangular pool. The pool measures 20 feet by 35 feet. It is surrounded by a patio that is uniform width. Find the width of the patio if the total area of the pool and patio is 1350 sqr feet. Write a quadratic equation to solve the problem.
Answer:
The width of the patio is 3/2 feet.
Step-by-step explanation:
following equation to solve for w:
(20+2w) * (35+2w) = 1350
Expanding the equation, we get:
700 + 140w + 70w^2 = 1350
Subtracting 700 from both sides, we get:
140w + 70w^2 = 650
Dividing both sides by 10, we get:
14w + 7w^2 = 65
We can now solve for w using the quadratic formula:
w = (-b +/- sqrt(b^2-4ac)) / 2a
where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:
w = (-14 +/- sqrt(14^2-47(-65))) / 2*7
w = (-14 +/- sqrt(196+1820)) / 14
w = (-14 +/- sqrt(2016)) / 14
w = (-14 +/- 44) / 14
To find the width of the patio, we need to find the area of the pool and the area of the patio. Let's call the width of the patio "w". The area of the pool is 20 * 35 = <<20*35=700>>700 square feet. The area of the patio is (20+2w) * (35+2w) = 1350 sqr feet. We can set up the following equation to solve for w:
(20+2w) * (35+2w) = 1350
Expanding the equation, we get:
700 + 140w + 70w^2 = 1350
Subtracting 700 from both sides, we get:
140w + 70w^2 = 650
Dividing both sides by 10, we get:
14w + 7w^2 = 65
We can now solve for w using the quadratic formula:
w = (-b +/- sqrt(b^2-4ac)) / 2a
where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:
w = (-14 +/- sqrt(14^2-47(-65))) / 2*7
w = (-14 +/- sqrt(196+1820)) / 14
w = (-14 +/- sqrt(2016)) / 14
w = (-14 +/- 44) / 14
This means that the width of the patio is either 3/2 or -5/2 feet. Since the width cannot be negative, the width of the patio must be 3/2 feet.
The quadratic equation we can use to solve this problem is:
w^2 + 14w - 65 = 0
(b) Let M be the function defined by M (x) = f(x) + h (x). Find M' (3).
Answer:
You will need to use information from (a)