The complete question is:
A certain element has a half life of 4.5 billion years.
You find a rock containing a mixture of the element and lead. You determine that 30% of the original element remains; the other 70% decayed into lead. How old is the rock?
Answer:
Age of rock = 7.82 billion years
Step-by-step explanation:
For a first order decay, fraction remaining is given by the formula 0.5n where n = number of half lives elapsed.
We are given that;
fraction remaining = 30% = 0.3
Thus;
0.3 = 0.5n
To find n, we have to use the log function;
log 0.3 = n log 0.5
-0.5229 = -0.301 n
n = -0.5229/-0.301
n = 1.737
We are given that;
Half life = 4.5 billion years
So, 1.737 half lives would give;
1.737 × 4.5 = 7.82 billion years
So, age of rock = 7.82 billion years
PLZ PLZ PLZ PLZ HELP HELP HELP HELPFind the area of the shape.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answer:
3.14
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi r^2[/tex], where r is the radius. In this circle, the area would therefore be [tex]3.14\cdot 2^2=12.56[/tex]. However, since this is only a quarter circle, you need to divide the area by 4, meaning that the area of this shape is 3.14 square units. Hope this helps!
Answer:
π
Step-by-step explanation:
calculate the the full circle: A = π*[tex]r^{2}[/tex] = π*[tex]2^{2}[/tex] = π*4 (the area of the full circle)
you've got 1/4 or the circle according to the picture, so divide the area of the full circle with 4:
(π*4)/4 = π
The distance around the edge of a circular pond is 88 m. The radius, in
metres. 19
Answer:
14
Step-by-step explanation:
look at the other answer as the person is taking a very long time to write it
Answer: radius = 14.01 m
Step-by-step explanation:
Circumference = 2πr
88 = 2πr
r = 88/2π = 14.01m
The proof that TriangleMNG ≅ TriangleKJG is shown.
Given: AngleN and AngleJ are right angles; NG ≅ JG
Prove: TriangleMNG ≅ TriangleKJG
What is the missing reason in the proof?
a) the reflexive property
b) ASA
c) AAS
d) the third angle theorem
Answer:
b) ASA
Step-by-step explanation:
If you were to look at both triangles the marked angles are rothe other same for the side and also the angle of G which connects both triangles together.
The missing reason in the question is option B which is ASA that is ANGLE SIDE ANGLE.
What are congruent triangles?Triangles are congruent when they have three corresponding sides and exactly the corresponding three angles are equal to other.
What are similar triangles?If two triangles can be superimposed on each other then it is said to be similar triangles.
How to check similarity between triangles?Two triangles are said to be similar if two angle and a side, one angle and two sides are equal to other.
If we look at the figure we found that both triangles the marked angles are same for the side and also the angle of G which connects both triangles together.
Hence the correct option for the problem is ASA (Angle Side Angle)
Learn more about congruent triangles at https://brainly.com/question/2938476
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Benjamin has 3 gallons of punch. He adds another 1··2gallon of juice to the punch. How many gallons of punch does he have now? How many cups? Explain your reasoning.
Answer:
4.2 gallons
67.2 cups
Step-by-step explanation:
He had 3 gallons of punch.
He added another 1.2 gallons.
The number of gallons of punch he has now is:
3 + 1.2 = 4.2 gallons
1 gallon = 16 cups
=> 4.2 gallons = 4.2 * 16 = 67.2 cups
He has 67.2 cups
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!
Answer & Step-by-step explanation:
In the problem, we are given an equation. h(t) = -20 + 11t
In the equation, t represents an unknown value. So, if we are given a number that is in the replacement of t, then we can plug that number in to where t is at.
t = 11
h(11) = -20 + 11(11)
h(11) = -20 + 121
h(11) = 101
So, h(11) is equal to 101
Answer:
101
Step-by-step explanation:
h(t)= -20+11t
h(11)= -20+11(11)
h(11)= -20+121
h(11) = 101
PLZ HLP MEEEEEEEEEEEEEEE
the table shows the distribution of students in Mrs boxer's sixth-grade class. what is the ratio of the number of boys to the number of girls? 10= boys 18= girls OPTIONS: A. 9/5 B. 5/4 C. 4/5 D. 14/9 E. 5/9 F. 9/14
Answer: 5/9
Step-by-step explanation:
Because you are looking for the ratio of BOYS to GIRLS you put those numbers in that order so it would be 10boys/18girls simplified that is 5/9
Answer:
Haaave youuu ever seen a troll
digging a hole
down by the bay?
Step-by-step explanation:
May I have brainliest please? :)
if ten coins are spun together, the probability of four or more heads is 0.83. the probability of eight or more is 0.05. find the probability of:
I) less than four. II)fewer than 8
Answer:
a. 0.17
b. 0.95
Step-by-step explanation:
The key to answering both questions is that we should understand that the probability of an event happening = 1 - the probability of the event not happening
Firstly, we want to calculate the probability of less than four
Probability of less than four = 1 - probability of four or more heads
that is 1 - 0.83 = 0.17
Probability of less than 8 = 1 - probability of 8 or more = 1-0.05 = 0.95
Which one of the following solids can produce this two-dimensional shape when sliced vertically?
Choose 1 answer:
A rectangle has an area of k2 + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural numbers, which statement about the rectangle could be true? The length of the rectangle is k – 5 inches. The width of the rectangle is k + 4 inches. The length of the rectangle is k – 20 inches. The width of the rectangle is k + 10 inches.
Answer:
The width of the rectangle is k+4 inches
Step-by-step explanation:
you have [tex]k^{2}+19k+60[/tex] which can be factorized to (k+4)(k+15)
if the length of the rectangle is k-5 that would mean that we can write [tex]k^{2}+19k+60[/tex] as (k-5)n which we know is false, so the only one that applies is k+4
The true statement is:
"The width of the rectangle is k + 4"
Which statement is true?
Remember that for a rectangle of length L and width W, the area is given by:
A = L*W
So we want to factorize the area equation, which is a quadratic equation, into a product of two terms.
A = k^2 + 19k + 60
The two zeros are given by Bhaskara's formula:
[tex]k = \frac{-19 \pm \sqrt{19^2 - 4*1*60} }{2} \\\\k = \frac{-19 \pm 11 }{2}[/tex]
So we have two zeros, these are:
k = (-19 - 11)/2 = -15
k = (-19 +11)/2 = -4
So we can factorize the area as:
A = (k - (-15))*(k - (-4)) = (k + 15)*(k + 4).
From this, the only statement that can be true is:
"The width of the rectangle is k + 4"
If you want to learn more about quadratic equations, you can read:
https://brainly.com/question/1480401
A 3-column table with 4 rows. The first column is labeled Currency and entries Canadian dollar, Euro, Japanese yen, Indian rupee. The second column is labeled U S D/1 Unit and entries 0.97071, 1.35261, 0.01007, 0.01594. The third column is labeled Units/1 U S D and entries 1.03069, 0.73935, 99.90487, 62.72053.
Mitchell travels from the US to Canada, where he exchanges 150 US dollars for Canadian dollars. He then spends 20 Canadian dollars, returns to the US, and exchanges the remaining money back to US dollars. How many US dollars does Mitchell have remaining?
129.46
130.00
130.66
134.59
Answer: 130.66
Step-by-step explanation:
Answer:
$31.88
Step-by-step explanation:
on edge 2020
in parallelogram ABCD, diagonals AC and BD intersect at E. Which statement proves ABCD is a rectangle?
Answer:
AC ≅ BD
Step-by-step explanation:
A parallelogram is a shape that have two pairs of parallel sides with opposite sides having the same length and opposite angles having the same size.
A rectangle is a shape that have two pairs of parallel sides with opposite sides having the same length and each of the four angles is 90°.
A parallelogram is said to be a rectangle if the diagonals of the parallelogram are of the same size (congruent). Therefore in parallelogram ABCD, ABCD is a rectangle if AC is equal to BD. where AC and BD are the diagonals
AC ≅ BD or say Measure of AC = Measure of BD diagonal.
Given that:
ABCD is a parallelogram
AC and BD intersect at E.
A parallelogram is defined as a closed geometric figure that has got 4 straight sides and opposite sides are parallel to each other.
Set of all parallelogram is superset of set of all rectangles.
There is a property about diagonals of a parallelogram that states as;
" A parallelogram is a rectangle if and only if both of its diagonals are equal in size".
Now given parallelogram is ABCD thus its diagonals are AC and BD.
Thus for ABCD to be rectangle we need:
magnitude of AC = magnitude of BC
or
AC ≅ BD
Learn more here:
https://brainly.com/question/1563728
what is the volume of a cylinder with a height of 10 cm and a radius of 2 cm ?
Answer:
20 =10X2cm
20
answer answer
Step-by-step explanation:
First you need to find the area of the base and then multiply that by the height. The base of the cylinder is equal to pi times the radius squared or πr² which in this case is π·2². We then multiply the base times the height which gives us 10·π·2^2. I will let you simplify the result on your own.
PLEASE HELP!! Rick uses this exponential expression to determine what the value of his bank account will be in three years. Select the value in the expression that represents the number of times per year that interest is compounded on the account.
5,000(1+0.04/12)^12t
Answer:
12
Step-by-step explanation:
A compound interest equation is represented as A = P(1 + r/n)^nt, where n=the number of times per year the interest is compounded. In the given equation, n=12.
Answer:
12
Step-by-step explanation:
this is my question -- solve x^2+5x+6=0
Answer:
x = -2,-3
Step-by-step explanation:
Solve the equation by factorizing.
To factorize this equation, you have to find the two numbers that adds up to 5 and multiplies to 6.
This one is obvious, but for others you may use trial and error.
After finding the 2 numbers: 2 and 3.
Present them in this format:
(x+3) ( x+2) = 0
You may check if this is correct using the distribution method.
After this,
you have to solve it individually.
for example:
x+3 = 0
x = -3
x+2 = 0
x = -2.
Thus, x has 2 different values: -3, -2.
You may check this by substituting x with either of these values.
Please mark brainiest
What is 15% of 80kg????
Answer:
12 kg
Step-by-step explanation:
15%×80 =
= 15×80/100
= 15×8/10
= 120/10
= 12 kg
Please help! Correct answer only!
You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 1 to 10. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is odd, you win $25. If the number the ball lands on is even, you win nothing. If you play the game, what is the expected payoff?
$___
Answer:
$12.5
Step-by-step explanation:
Since there is a 50% chance of landing on an odd number, the expected payoff is 0.5*25=12.5. Hope this helps!
What is the value of 0?
Answer:
It is 0
Step-by-step explanation:
The equation of the line which passes
through the point(0,2) and has a gradient
of 1/3 is?
Answer:
Using point (0,2) and gradient 1/3
Equation of the line is
y - 2 = 1/3(x -0)
Multiply through by 3
You'll get
3y - 6 = x
3y = x - 6 or y = 1/3x - 2
Hope this helps.
The library is 3.56 kilometers from Maria's house and 1.38 kilometers from Simon's house. How much farther does Maria live from the library than Simon?
Answer: 2.18 kilometres
Step-by-step explanation:
First we take down the information given to us
Maria's house to library (distance) = 3.56 km
Simon's house to library (distance) = 1.38 km
Now to get how farther Maria lived from the library compared to Simon, we subtract the distance between the library and Simon's house from the distance between the library and Maria's house
i.e
3.46km - 1.38km = 2.18km
there for Maria lived 2.18 kilometres farther from the library compared to Simon.
Please help someone help me! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
what is slope intercept form?
Mr. Singer's choir is going to New York City for a choir competition. He wants them to look their best, so he buys new music folders for all of the members. Each music folder costs $7.99. If Mr. Singer buys 23 music folders, how much does he spend? (Please enter your answer without units.)
Answer:
the answer is 183.77
Step-by-step explanation:
if you know the price was 7.99 for each one he bought you work multiply 23 by 7.99 and you get 183.77.
the square root of 7/16
Answer:
[tex] \sqrt{7} [/tex]
over 4
square the top and bottom separately and 16 squared is four but seven can't square. leave the top as seven squared and the bottom as just four
If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm
Answer:
16kgStep-by-step explanation:
This problem is borers on elasticity of materials.
according to Hooke's law, "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."
[tex]F= ke[/tex]
where F is the applied force in N
k is the spring constant N/m
e is the extension in meters
Given data
mass m= 24kg
extensnion=15cm in meters= [tex]\frac{15}{100}[/tex]= [tex]0.15m[/tex]
we can solve for the spring constant k
we also know that the force F = mg
assuming [tex]g=9.81m/s^{2}[/tex]
therefore
[tex]24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\[/tex]
We can use this value of k to solve for the mass that will cause an extension of [tex]10cm= 0.1m[/tex]
[tex]x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg[/tex]
John goes to a restaurant and has a bill of $ 32. 57. He uses a 10% off coupon on the cost of his meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied. How much does he spend?
Answer: $36.97
Step-by-step explanation:
The cost of the meal was $32.57 and he used a 10% off coupon. You can make 10% equal to 0.1 because [tex]\frac{10}{100}=0.1[/tex]. Now do [tex]0.1 *32.57=$3.26[/tex]. This is the discount, so you want to subtract this from the original to get the actual price of the meal, [tex]32.57-3.26=29.31dollars[/tex].
The tax was 8% so this means he is adding it to his total cost instead of subtracting it. Do 0.08 of $29.31 to get $2.34. Add $2.34 to the now $29.31 to get $31.69.
The tip is also adding to the total cost, so do 0.18 of $29.31 to get $5.28. Add $5.28 to $31.69 to get $36.97
Answer:
$37.51
Step-by-step explanation:
Original cost of meal is $32.57.
Since he has a coupon for 10% off, he pays for 90% of the cost of the meal.
90% of $32.57 = 0.9 * $32.57 = $29.31
Now he pays tax on the new discounted total. Let the new total be called 100%. Since he pays 8% tax, he needs to pay 108% of the new total.
108% of $29.31 = 1.08 * $29.31 = $31.65
He adds a tip of 18% of $32.57.
The tip amount is
18% of $32.57 = 0.18 * $32.57 = $5.86
The total is: $31.65 + $5.86 = $37.51
the point slope form of the equation of the line that passes through (-9,-2) and (1,3) is y-3=1/2(x-1). What is the slope-intercept form of the equation for this line
Answer:
y= 1/2x + 2.5
Step-by-step explanation:
We already have the point-slope form of the line.
Convert into Slope Intercept form:
y-3=1/2(x-1)
[tex]y-3=\frac{1}{2}x -0.5\leftarrow \text {Distribute}\\y-3+3=\frac{1}{2}x-0.5+3\leftarrow \text {Subtraction Property of Equality} \\\boxed{y=\frac{1}{2}x+2.5} \text { OR } \boxed{y=\frac{1}{2}x+\frac{5}{2}}[/tex]
May you help please
Answer:
Option A
Step-by-step explanation:
We are given the inequality 4x + 6 [tex]\leq[/tex] 18;
[tex]4x + 6 \leq 18,\\4x \leq 12,\\\\x \leq 12 / 4,\\x \leq 3,\\\\Conclusion - Option A[/tex]
As you can tell, the second step was derived through the subtraction of 6 from either side of the inequality sign. 18 - 6 is 12, which resulted in the simplified inequality [tex]4x \leq 12[/tex]. Dividing 4 on either side, we derived [tex]x \leq 3[/tex], which is Option A
A 38 gram sample of a substance that is used to sterilize surgical instruments has a k-value of 0.113. Find the substance's half-life in days, round to the nearest tenth.
Answer:
6.13 days
Step-by-step explanation:
Hello,
This question directly relates to radioactivity of a substance.
Data,
k = 0.113
Initial mass (No) = 38g
Half life of the substance (T½) = ?
To solve this question, we don't need the value of the initial mass because the variables in half life (T½) formula does not require it.
T½ = ln2 / k
Note : ln2 is a constant derived while k is the decay constant of the substance
T½ = 0.693 / 0.113
T½ = 6.13 days
The half life of the substance is 6.13 days
Please answer correctly !!!!!!!! Will mark brainliest answer !!!!!!!!!!!!!
Answer & Step-by-step explanation:
Since you looking for the width and you are given the length and the area, then you will divide the area by the length.
(10x² + 5x) ÷ 5x
You can also turn this into a fraction so you can know what you are dividing.
[tex]\frac{10x^2+5x}{5x}[/tex]
So, your width is 2x + 1
Answer:
2x + 1 is the width.
Step-by-step explanation:
Length times width equals the area, which means that the area divided by the length equals the width. In this case, 10x^2 + 5x divided by 5x equals the width.
10x^2 / 5x equals 2x.
5x / 5x equals 1.
The width equals 2x + 1.
Yang–Mills existence and mass gap. Solve that ur a genius
Answer: DescriptionIn mathematical physics, the Yang–Mills existence and mass gap problem is an unsolved problem and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution. The problem is phrased as follows: Yang–Mills Existence and Mass Gap.