Answers
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
What is meant by isotope?Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.
If we start with 180 g of the isotope, after one half-life the quantity will diminish to 180 g/2 = 90 g which exists half the original quantity.
This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]
After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]
After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]
But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.
The original quantity can then be rapidly computed for six half-lives using the formula below:
[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
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Related Questions
Which problem could be solved with the expression 3 (5 – 2) - 1?Choose 1 answer:Stephanie had 3 apples. She then found 5 more but immediately ate 2 of them. Several minuteslater, she ate 1 more. How many apples does she still have?Orlando had 5 action figures but decided to give 2 of them to his younger brother. His parents wereso impressed with his kindness that they tripled the action figures he had left. Since he got so manynew action figures, he then gave 1 more to his brother. How many action figures does he now have?Of Ralph's 5 toy cars, he gave 2 to his sister. After that, he found 1 more toy car. Then, he decidedto go to the store and triple his number of cars. How many toy cars does Ralph have now?Stuck? Review related articles/videos or use a hint.Report a problem
Answers
The given expression is 3 x (5-2)-1
From the options
If Orlando has 5 actions figures.
He decides to give 2 of them to his younger brother, then he will have (5-2) action figures left
His parents were happy with him and tripled what he had left
3 x ( 5 -2 ) action figures.
If he had so many actions figures after that and he gave his brother 1 more action figure then he will have
3 x ( 5-2) - 1 action figures left.
The right answer is therefore option B
Silvia has 20 tomato plants and 30 bean plants. She wants to put the plants in rows so that each row has the same number of tomato plants and the same number of bean plants. What is the greatest number of rows Silvia can plant?
Answers
The greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.
As given in the question,
Silvia is going to plant 20 tomato plants and 30 bean plants.
Total tomato plants = 20
Total bean plants = 30
If Silvia would like to plant, the plants in rows where each row has the same number of tomato plants and each row has the same number of bean plants.
Then, the greatest number of rows Silvia can plant is equal to greatest common factor of 20 and 30.
20 = 2×2×5
30 = 2×3×5
Greatest common factor of 20 and 30 = 2×5 = 10
Therefore, the greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.
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Use the conditional statement "If it is January, then there is snow." for questic
17. Identify the hypothesis:
18. Identify the conclusion:
Answers
Hypothesis: It is January and Conclusion: There is snow
What is hypothesis and conclusion?The initial clause, or "if," of a conditional statement is the hypothesis. The second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.
An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. As indicated, this is pq. Read this: if p, then q. If the hypothesis is correct but the conclusion is untrue, a conditional statement is false.
Conditionals are in the form if P, then Q.
P is the hypothesis.
Q is the conclusion.
If It is January, then there is snow.
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How many solutions does this equation have?
-7k 2k= -9k
no solution
one solution
infinitely many solutions
Submit
Answers
Answer:
1 answer
Step-by-step explanation:
when the terms are collected
[tex]4k = 0[/tex]
[tex]k = 0[/tex]
A parabola can be drawn given a focus of (-5, -1) and a directrix of y=7. Write the equation of the parabola in any form.
Answers
A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² = 8 (y - 3)
How to write the equation of parabola with directrix of y = 7 and focus of (-5, -1)Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The focus
F (h, k + p) = (-5,-1)
h = -5
k + p = -1
P in this problem, is the midpoint between the focus and the directrix
P = (-1 - 7) / 2 = -4
p = -4
the vertex
v(h, k)
h = -5
k + p = -1, k = 3
v(h, k) = v(-5, 3)
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -5)² = 4 * 2 (y - 3)
(x + 5)² = 8 (y - 3)
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Find length between AC-3,8) and B(5,-4) in simplest radical form:
Answers
The Points are in the form (x,y), and they are A(-3,8) and B(5,-4).
The length between two points is:
[tex]\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]In this case:
[tex]\text{length = }\sqrt[]{(-3-5)^2+(8-(-4))^2}=\sqrt[]{(-8)^2+(12)^2}=\sqrt[]{64+144}[/tex][tex]\text{length =}\sqrt[]{208}\text{ = }\sqrt[]{16\cdot13}=4\sqrt[]{13}[/tex]The correct anser is:
[tex]\text{length = 4}\sqrt[]{13}[/tex]A graph of a linear function has a slope of -1/3 and contains the point (0, 2). Which of these represents the equation of this function?
Answers
slope intercept equation is represented below
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 2=-\frac{1}{3}(0)+b \\ b=2 \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]3potniIn a right triangle, the altitude drawn to the hypotenuse divides the hypotenuse into two segments of equal lengths 8 cm and 2 cm. What is the length of the altitude?O 10 cm
Answers
Answer:
[tex]\text{The altitude is 4cm.}[/tex]Step-by-step explanation:
Let's illustrate the situation in a diagram to understand.
In a right triangle if the altitude drawn divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.
Therefore,
[tex]\begin{gathered} \frac{8}{a}=\frac{a}{2} \\ 2\cdot8=a^2 \\ 16=a^2 \\ a=\sqrt[]{16} \\ a=4\text{ cm} \end{gathered}[/tex]Two 50 foot tall radio towers are 3000 feet apart. Find the angle of depression from the top of one tower to the base of the other.
Answers
Answer:
Explanation:
The diagram representing the two towers is given below:
3(x+3)= x +13 ansewr!
Answers
Answer: x=2
Step-by-step explanation:
1. Distribute
2. Subtract 9 from both sides
3. Simplify
4. Subtract x from both sides
5. Simplify
6. Divide both sides by the same factor
7. Simplify
Use the table to answer the question. Number of cases ordered Number of rolls of paper towels 1 12 3 36 5 60 10 120 A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair
Answers
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls. 1:12 ratio does the proportionality constant appear at in the data table.
Given that,
There is a table.
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls.
We have to find what ratio does the proportionality constant appear at in the data table.
The table is
Number of cases ordered | Number of rolls of paper towels
1 | 12
3 | 36
5 | 60
10 | 120
Therefore, 1:12 ratio does the proportionality constant appear at in the data table.
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Determine the missing number in the equation.
The equation 4 times 7 equals 4 times 10 in parentheses minus 4 times blank
Answers
Answer:
The missing number is 3.
Step-by-step explanation:
1. For the sake of the equation, let's represent the missing number as y. Then write the equation: 4*7=(4*10)-4*y
2. Follow according to the order of operations, then you should get the result of 28=40-4y
3. Swap -4y and 28 in the equations: 4y=40-28 which goes to 4y=12.
4. Find y by dividing the rest of the equation by 4: y=3
what is an equation of the line that passes through the points (5,-6) and (-5,-2)
Answers
The equation of line is 11y + 3x + 37 = 0
What is Equation of Line ?
The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
The given points are, (5, -6) and (-5, -2)
To find slope we have formula ,
m = (y2 - y1 ) / (x2 - x1)
where,
(x1, x2) = (5, -6) and,
(y1, y2) = (-5, -2)
Put the values in given formula of slope,
m = (-2 - (-5) ) / (-6 - 5)
m = (-2 + 5) / (-11)
m = - (3/11)
we get the slope, now to find the equation of line.
We know, the equation of the line with slope intercept is
y = mx + b
Now, for x and y value take any point and put it into this equation and find 'b'
let's take (-5, -2)
-2 = -(3/11) * -5 + b
-2 = 15/11 + b
-2 = (15 + 11b) / 11
-22 = 15 + 11b
-22 - 15 = 11b
-37 = 11b
b = -37/11
We got m = - 3/11 and b = -37/11
Now put these value in equation of line and form the equation
y = mx + b
y = -3/11 x - 37/11
11y = -3x - 37
3x + 11y + 37 = 0
Hence, the equation of line is 11y + 3x + 37 = 0
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Jenny love to plant flowers.she has $30 to spend on flower plant flats .find the number of flats she can buy of the cost $4.98 each
Answers
Answer:
6
Step-by-step explanation:
We can round $4.98 up to $5.
Then do $30 / $5 = 6
Go back and check if 6 works:
$4.98 × 6 = $29.88 which is less than $30.
So the answer is 6
find a polynomial f(x) of degree 3 with real coefficients and the following zeros -1, 3-i
Answers
The least polynomial that contains the roots - 1 and 3 - i is x³ - 5 · x² + 4 · x + 10.
What is the least polynomial that contains a given set?
In this case we need to find a polynomial that contains a set of roots, a real root and a complex root. In accordace to the quadratic formula, the root 3 - i must be accompanied by its conjugate, that is, 3 + i to guarantee that all coefficients of the polynomial are real.
Then, the factor form of the cubic equation is:
f(x) = (x + 1) · (x - 3 + i) · (x - 3 - i)
f(x) = (x + 1) · [x² - (3 - i) · x - (3 + i) · x + (3 - i) · (3 + i)
f(x) = (x + 1) · (x² - 3 · x + i x - 3 · x - i x + 9 - i²)
f(x) = (x +1) · (x² - 6 · x + 10)
f(x) = x³ - 6 · x² + 10 · x + x² - 6 · x + 10
f(x) = x³ - 5 · x² + 4 · x + 10
The least polynomial is x³ - 5 · x² + 4 · x + 10.
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PLEASE ANSWER ALL THE QUESTIONS FOR 50 POINTS!!!!!
Answers
b. 72.1 - 45.6 = 26.5
c. 82.2 - 41.3 - 29.2 = 11.7
d. 17.1 - 11.7 - 0.8 = 4.6
e. 29.2 - 12.5 - 0.9 = 15.8
f. 21 - 14 = 7
g. 71 - 37 - 18 = 16
h. 50 - 19 - 8 = 23
i. 92 - 57 - 16 = 19
Answer:
a. 4.2 - 2.8 = 1.4
b. 72.1 - 45.6 = 26.5
c. 82.2 - 41.3 - 29.2 = 11.7
d. 17.1 - 11.7 - 0.8 = 4.6
e. 29.2 - 12.5 - 0.9 = 15.8
f. 21 - 14 = 7
g. 71 - 37 - 18 = 16
h. 50 - 19 - 8 = 23
i. 92 - 57 - 16 = 19
j. 44 - 18 - 9 = 17
Select the correct answer from each drop-down menu. a cash card has a starting value of $25. if the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month. the relationship between the number of months after the first year and the amount remaining on the card is . the independent variable is the . the dependent variable is the .
Answers
The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)
a) the independent variable is the: Number of month after the first year
b) the dependent variable is the: Amount remaining on the card
To solve this problem, we have to state the equation using the information of the problem.
Information about the problem:
Starting value= $25Decrease= $2.50 per monthWriting the equation according to the information gave, we have:
y = 25 - (2.50x)
Where:
Amount remaining on the card = yNumber of month after the first year = xThe relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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Find the distance between C & D. C = (8, -3) and D = (-9, -6) CD= [?] Round to the nearest tenth. Hint: Use the distance formula.
Answers
The distance between C and D is 17.26 units
What is meant by distance?
Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.
Distance CD = √{(-9-8)² + (-6+3)²}
= √{(-17)² + (-3)²}
= √{289 + 9}
= √298
= 17.26 units
Hence, the distance between C and D is 17.26 units
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Answer: 17.3
Step-by-step explanation:
In the diagram below line FG is // to line HI, and line segments BC and AD intersect at E.
The measure of angle GBE = 3x+20, and the measure angle ECD = x.
Answers
The values of the angle x in the line segments is 40 degrees.
How to find the measure of angle?When parallel lines are are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the line FG is parallel to line HI. The line segment BC and AD are the transversal lines that cut across the parallel lines FG and HI.
Therefore,
3x + 20 + x = 180 (Same interior angles)
Same interior angles are supplementary. That is the angles sum up to 180 degrees.
Therefore,
3x + 20 + x = 180
4x + 20 = 180
4x = 160
divide both sides by 4
x = 160 / 4
x = 40 degrees
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Problem
Grandma baked 96\ cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received ccc fewer cookies than she would have received had all of the cookies been evenly divided among the 8 grandchildren.
How many cookies did Cindy receive?
Write your answer as an expression.
I Need a VERY clear answer please
Answers
The expression to show the number of cookies that Cindy receive is 96/8 - c.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, 96 cookies were shared among 8 people and Cindy has c fewer cookies. This will be:
= 96/8 - c
This illustrates the concept of expression.
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given circle K with diameter IJ and radius KG. GH is tangent to K at G. If GH =6 and KH =8, solve dor KG. Round your answer to the nearest tenth if necessary. If the answer cannot be determined click cannot be determined.
Answers
EXPLANATION:
We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.
Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.
We can now extract the following triangle from the diagram provided;
We now have a right triangle which we shall solve by use of the Pythagorean theorem;
[tex]a^2+b^2=c^2[/tex]Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;
[tex]\begin{gathered} a^2+b^2=c^2 \\ KG^2+6^2=8^2 \\ KG^2+36=64 \end{gathered}[/tex]Subtract 36 from both sides;
[tex]\begin{gathered} KG^2+36-36=64-36 \\ KG^2=28 \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{KG^2}=\sqrt[]{28} \\ KG=5.2915 \end{gathered}[/tex]Rounded to the nearest tenth, the answer is;
ANSWER:
[tex]KG=5.3[/tex]m=p*Vwe have
p=m/V
Solve for m
That means-----> isolate the variable m
Multiply both sides by V
p*V=(m/V)*V
Simplify
p*V=m
rewrite
m=p*V
Answers
Using the properties of equality, the value for m in the equation is: m = pV.
How to Apply the Properties of Equality to Solve for a Variable?For any given equation, to solve for a variable in the equation, we have to isolate the variable to one side of the equation in order to determine its value. To do this, several properties of equality need to be applied to isolate the variable to one side of the given equation.
Given the equation, p = m/V, we need to isolate the variable m to one side of the equation in order to solve for m.
p = m/V
Multiply both sides of the equation by V
p × V = m/V × V [multiplication property of equality]
Simplify the equation:
pV = m
m = pV
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17. What are the roots of the equation s² - 7 = 74?
18. One of the roots of x² - 8x = 0 is 8. What is the other root?
paanswer po ngaun
w solution if meron po sana
Answers
Answer:
17. s = 9
18. x = 8x^(½)
Step-by-step explanation:
s² - 7 = 74?
s² = 74 + 7
s² = 81
√(s²) = √(81)
s = 9
x² - 8x = 0
x² = 0 + 8x
x² = 8x
√(x²) = √(8x)
x = 8x^(½)
OR by factoring
x²−8x=0
x(x−8)=0
x=0 or x−8=0
x=0 or x=8
I need your help please
Answers
In order to calculate the price for each brand, calculate the quotient in between the price for n forks over the number of forks, just as follow:
Brand A:
3.89/72 = 0.05
Brand B:
6.62/96 = 0.07
Hence:
Unit price for brand A:
$0.05
Unit price for brand B:
$0.07
9. The density of an
object can be found by taking its mass and dividing by its volume.
equation to represent the relationship between
the three quantities
Write an (density, mass, and volume) in each situation. Let the density, D, be measured in
grams/cubic centimeters (or g/cm'3).
a. The mass is 500 grams
and the volume is 40 cubic centimeters.
b.
The mass is 125 grams and the volume is u cubic centimeters.
C.
The volume is 1.4 cubic centimeters and the density is 80 grams per cubic
centimeter.
d bnt
d. The mass is m grams and the volume is v cubic centimeters.
(From Unit 2, Lesson 2
Answers
When the mass is 500 grams and the volume is 40 cubic centimeters then density is 12.5 gm per cc.
When the mass is 125 grams and the volume is 1.4 cubic centimeters then density is 89.28 gm per cc.
What is a simple definition of density?The amount per unit of length, area, or volume as. a: a substance's mass per unit volume. b: the distribution of an amount (such as mass, electricity, or energy) per unit, typically of space.
D = M/V
a) M = 500 gms
V = 40 cubic cm
D = 500/40
D = 12.5 gm per cc
b) M = 125 gms
V = 1.4 cubic cm
D = 125/1.4
D =89.28 gm per cc
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Percy has $200 in a savings account that earns annually.
How much will he have in total in 1 year?
Answers
Hi may you please help me
Answers
The value of x is 85° when a pair of parallel lines intersects another pair of parallel lines.
According to the question,
We have the following information:
A pair of parallel lines intersects another pair of parallel lines.
We have a figure where an angle is given as 85°.
Now, the following theorems would be helpful in finding the value of x:
When a pair of parallel lines is intersected by another line then the sum of two consecutive interior angles is 180°. (1)
When a pair of parallel lines is intersected by another line then the alternate interior angles are equal. (2)
Vertically opposite angles are equal. (3)
(Now, we will refer to these theorems by the number given in the brackets.)
Now, by theorem 3, we have vertically opposite angle as 85°.
Now, its alternate interior angle will also be 85°.
Now, 85° and x° are vertically opposite angles.
So, by theorem 3, we have the value of x as 85°.
Hence, the value of x is 85°.
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Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for bagels, then walks the rest of the way home. What does the X axis represent. What does the y-axis represent?
Answers
Based on the information provided about Arthur, we have the following:
The x-axis of the graph would represent the amount of time that Arthur spends on his way home.The y-axis of the graph would represent the distance covered by Arthur from a reference position (home).What is a graph?In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate).
What is distance?Distance simply refers to the amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of the physical object's direction, starting point, or ending point.
In conclusion, the distance covered by a physical object (body) over a particular period of time can be plotted by using a position-time graph as shown in the image attached below.
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Below is the change received by Julia after buying a magazine.She paid for the magazine using a £10 note. Work out the price of the magazine.
Answers
pls provide the picture below, because of that its an incomplete answer
Jayden multiples -4yx 1/5y and gets an answer of -4/5y. How can you tell without multiplying that his answer is incorrect
Answers
Multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, -4y × 1/5y:
The answer to this multiplication is -4/5y.Which is a wrong answer.We can easily observe in the second term that the denominator is 5y and in the 1st term there is no denominator, so 1 will be represented as a denominator.And y will not be present.Hence, multiplication is not possible with so similar variables in the denominator, in the given situation.Theefore, multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.
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