Answer:
First problem: 89.07 grams
Second problem: 3910.15 days
Step-by-step explanation:
We can solve these problems with the exponencial equation:
P = Po * (1+r)^t
Where P is the final value, Po is the inicial value, r is the rate and t is the time.
In the first problem, the half-life is 119.77 days and Po = 100, so we have that:
P = 100 * (1-0.5)^(t/119.77)
So after 20 days, we will have:
P = 100 * (1-0.5)^(20/119.77) = 89.07 grams
For the second problem, we have the half-life of 5730 days, and the final value over the inicial value is 62.31%, so:
P/Po = (1-0.5)^(t/5730)
0.6231 = 0.5^(t/5730)
log(0.6231) = log(0.5^(t/5730))
-0.4730 = (t/5730)*log(0.5)
-0.4730 = (t/5730)*(-0.6931)
(t/5730) = 0.6824
t = 0.6824 * 5730 = 3910.15 days
Using the formula for half-life calculation, approximately 82.57 milligrams of Selenium left after 20 days. Based on the amount of Carbon-14 left, the last eruption of the volcano occurred approximately 3896 years ago.
Explanation:The calculation of remaining amount of a given isotope relies on the understanding of what is called a half-life. In the case of selenium, with a half-life of 119.77 days, we are looking at 20 days had passed. This would be a fraction of the half-life (20/119.77 = 0.167). The amount left can be calculated by the formula N = N0 * (1/2)^(t/T), where N is the final amount, N0 is the initial amount, t is the elapsed time, and T is the half-life. This becomes 100 * (1/2)^(0.167) which results in approximately 82.57 milligrams of Selenium left.
For the interval of carbon-14 relating to the volcano eruption using a half-life of 5730 years, we know from the sample that 62.31% of the original amount remains. This relates to 0.623 as the fraction of half life that has passed. Using the formula log2(1/0.623) we get approximately 0.68 half-lives. From this, we can find the time passed, which is half-life times the number of half-lives. This results in 5730 * 0.68 = approximately 3896 years ago for the last eruption.
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Does someone knows the correct answer?? I think is d but I don’t know
Answer:
I think you are right
Step-by-step explanation:
Answer:
YES I AM PRETTY SURE ITs :D GOOD LUCK HAVE A GREAT DAY
Step-by-step explanation:
Find the equation of the line. Use exact numbers.
y = __x + __
Answer:
y = 3x+3
Step-by-step explanation:
We know the y intercept since it crosses the y axis at (0,3) and we know the x intercept since it crosses the x axis at (-1,0)
We can fidn the slope
m = (y2-y1)/(x2-x1) (0,3) (-1,0)
=(0-3)/(-1-0)
= -3/-1
=3
The equation for the line is in the form
y = mx +b where m is the slope and b is the y intercept
y = 3x+3
Consider triangle ABC and triangle ACD in the diagram below. Which of the following complete the proof above?
Options
- AB =AD
- AC=AC
- AC=BD
- BC=DC
Given:
AC is perpendicular bisector of BD
AB ≅ AD
To prove:
ΔABC ≅ ΔACD
Solution:
In triangle ABC and triangle ACD,
Step 1: Given
AC is perpendicular bisector of BD and
AB ≅ AD (Side)
Step 2: By perpendicular bisector definition,
BC ≅ CD (Side)
Step 3: By reflexive property,
AC ≅ AC (Side)
Step 4: By SSS congruence criterion,
ΔABC ≅ ΔACD
Hence proved.
Answer:
BC=DC
Step-by-step explanation:
I did the test yourself and got it right :)
The table shows the height of a tree for various years after it was planted. Using the line of best fit, how tall would the tree be 30 years after it was planted?
A) 22 Feet
B) 36 Feet
C) 37 Feet
D) 23 Feet
Which points are on the graph of g(x)=(1/5)^x ? Select each correct answer. (3, 1/125) (−2, 1/25) (1, 0) (−1, 5)
Answer:
(3,1/125) and (-1,5)
Step-by-step explanation:
plug in the first coordinate (x-coordinate) in each pair for x in the original equation and the second coordinate (y-coordinate) for g(x)
What is the answer to this problem -34=m-16
Answer:
m = -18
Step-by-step explanation:
-34=m-16
+16. +16
-18 = m
Answer:
m = -18
Step-by-step explanation:
to evaluate for the correct answer of this problem , we would simply combine the like terms together.
solution
-34=m-16
-34 + 16 = m
-18= m
m = -18
Find the value of x
Options being
A) 27
B) 4
C) 2
D) 8
Answer:
B
Step-by-step explanation:
81 = 9 × 9 = 3 × 3 × 3 × 3 = [tex]3^{4}[/tex]
Thus the [tex]\sqrt[4]{81}[/tex] = [tex]\sqrt[4]{3^{4} }[/tex] = 3
Hence x = 4 → B
Mrs. Vamer deposited q dollars in a bank account that has been earning annual interest The total value of the
account is based on the function f(x) = 1.025%, where x represents the number of years the money has been in the account If no deposits or withdrawals are made after the initial deposit, which equation represents the total value of
the account 5 years from now?
Answer:
the answer is b
Step-by-step explanation:
nun
what does a subtraction sign mean
Answer:
If you take a number and 'subtract" it with another number, it means that you take your second number and remove that amount from the first number
If this helped, say thanks on my profile ;)
Answer:
Definition of subtraction sign. : a mathematical symbol used to indicate that a particular quantity is to be subtracted from another to which it is joined by the symbol : a symbolic representation of the relation of subtrahend and minuend —symbol −
Step-by-step explanation:
1) Find f(0) when f(x) = x2 - 4x - 4.
A) 16
B) -8
C) -4
D) 4
Answer: -4
Step-by-step explanation:
If you replace x for 0 it will eliminate the variable. The only remaining term without a variable is -4
A pot of piping hot stew has been removed from the stove and left to cool.
The relationship between the elapsed time, m, in minutes, since the stew was removed from the stove, and the
temperature of the stew. T(m), measured in C is modeled by the following function.
T(m) = 20 + 50 - 10-0.0477
How many minutes will it take for the stew to cool to a temperature of 30°C?
Round your answer, if necessary to the nearest hundredth.
minutes
Answer: 17.47 minutes
Step-by-step explanation:
To find the number of minutes it will take for the stew to cool to a temperature of 30°C, solve the given nonlinear equation or graph it to find the intersection point.
Explanation:The given function that models the relationship between the elapsed time, m, in minutes, and the temperature of the stew, T(m), is:
T(m) = 20 + 50 - 10^(-0.0477m)
To find the number of minutes it will take for the stew to cool to a temperature of 30°C, we need to solve the equation:
30 = 20 + 50 - 10^(-0.0477m)
By isolating the unknown variable, m, we can solve for it using logarithms or graphing. However, since the equation is nonlinear, graphing is a more intuitive approach. Graph the equation and find the x-coordinate at which the graph intersects with the y-coordinate 30. This value of m will give you the number of minutes it will take for the stew to cool to 30°C.
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Have three witches each holding a broom and a spoon. Witches say witch plus witch plus witch =45. Three brooms say broom plus broom plus a broom =21 and three spoons say spoon plus spoon plus spoon = 12 then final question is a plain witch plus broom x spoon equal a ? What’s answer?
Answer:
Either 43 or 88
Step-by-step explanation:
45/3 = 15 (one witch)
21/3 = 7 (one broom)
12/3 = 4 (one spoon)
PEMDAS:
Equation: 15 + 7 x 4
if there are parenthesis and the equation looks like:
(15 + 7) x 4
the answer is 88.
if there is NOT parenthesis and the equation looks like:
15 + 7 x 4
the answer is 43.
Answer:
31
Step-by-step explanation:
witch with spoon and wand equals 15 each...wand = 7 spoon =3
b and a win some money and share it in a ratio of 3:4 person b gets 39 how much does person a get?
Answer:52
Step-by-step explanation:
To find this
Total ratio=3+4
=7
Find the amount share
7/4×39
=91
So, to get a share's
3/7×91
=52
is 8, 10, 12 a Pythagorean Triples ?
Answer:
No
Step-by-step explanation:
You use the formula a^2 + b^2= c^2. The biggest number is c.
So 8 ^2 + 10^2 has to equal 12^ 2
64 + 100= 144
164=144
That is not true.
Answer:
No, they are not
Step-by-step explanation:
If you simplify all 3 numbers, you get 4, 5, 6
If you graph the triangle on graph paper, it wouldn't work and there would be a gap.
3, 4, 5 triangles do work though!
How many centimeters is Campsite 3 from the canoe rental office?
Answer:
hi
Step-by-step explanation:
u need to give more information plz thanks
Answer:5 centimeterts
Step-by-step explanation:it right
If a pool table measures 4 ft by 8 ft , what is the diagonal length from the bottom right pocket to the nearest tenth?
Answer:
8.9 ft
Step-by-step explanation:
Use Pythagorean theorem,
a² + b² = c²
√(a² + b²) = c
The diagonal is the hypotenuse of the rectangular pool table.
So,
√(4² + 8²) = c
√(16 + 64) = c
√(80) = c
8.944... = c
Nearest tenth:
8.9
Arrange these numbers from least to greatest: -2.5, 2/5, 5/2, -5.2
Answer:
-5.2, -2.5, 2/5, 5/2
Step-by-step explanation:
Arrange it
Genevieve works on her scrapbook from 11:27 am to 11:58 am. How many minutes does she work on her scrapbook
Answer:
31
Step-by-step explanation:
time is tricky due to the 60 minute interface. In those questions add to the lower number until you hit a rounded number.
Fortunately you don't need to use this in this problem, and can just subtract 58-27 to get 31
Can someone help me with this question?
Answer:
C). 30 I just learned about this!
Step-by-step explanation:
If the smaller diamond is 12 and the bigger one is 36 then its times 3 and whatver you do to the top you do to the bottom so it would be 10 times 3 which would equal 30! (:
Answer:
C - 30
Step-by-step explanation:
Since one side of the smaller diamond is 12 and the side on the bigger diamond is 36 it is 3 times the perimeter on each side so since the side on the small diamond is 10 then you would times it by three to get the perimeter of the side on the bigger diamond , which is 30 .
8. sin 38 = x/16 what does x equal
2.375
Answer:
if the slash (/) is dividing then your answer would be
608
if the slash (/) means to multiply your answer would be
2.375
Step-by-step explanation:
if you were dividing then you have to do the opposite equation.In this case the opposite of dividing is multiply. Multiply the numbers you have then it will give your missing factor.
(Same goes with multiplying)
The center of a circle is (5,-3) and its radius is 4. Which point lies outside of the circle?
Answer:
-1
Step-by-step explanation:
The equation of a circle gives the positions of points inside or on its circumference. A point is outside the circle if the substitution in the equation results in a value greater than the square of the circle's radius.
Explanation:To understand this, we need first to understand the equation of a circle which is defined in the format (x-a)² + (y-b)² = r², where (a,b) is the center of the circle and r is the radius.
In this case, (a,b) = (5,-3) and r = 4. So, the equation of the circle becomes (x-5)² + (y+3)² = 16. Any point (X,Y) that satisfies this equation is inside or at the circumference of the circle. If the computation yields a result greater than 16, the point is outside the circle.
Let's take a point for example: (3,-1). Substituting the values gives (3-5)² + (-1+3)² = 4 + 4 = 8 which is less than 16, hence, lies inside the circle. But for a point like (10,0), it results in (10-5)² + (0+3)² = 25 + 9 = 34 which is greater than 16, so the point (10,0) is outside the circle.
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What is the maximum recommended slope for straight-run stair?
A) 7-1/2" riser, 10" tread
B) 7' riser, 10" tread
C) 7-3/4" riser, 10-1/2" tread
D) 10" riser, 7-1/2" tread
PLS HELP ME IF YOU WANT A BRAINLIEST IM DOING THIS NOW and IDU, Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in each school day for a month were divided by quartiles and summarized in the box plot. Use the drop-down menus to choose the median, interquartile range, and range.
>Median:
>Interquartile range:
>Range:
Answer: Median: 18
Interquartile range: 4
Range: 18
Step-by-step explanation: The median line is at 18, the interquartile range is the difference between the ends of the box, 20 - 16 = 4. The range is the difference between the ends of the line, 28 - 10 = 18. Let's take a look at how the data can be compared, from the two schools using the box plot.
From the information provided, it is clear that the
Median = 18Interquartile range = 4Range = 18How do we arrive at the following above?By observation, the median line is at 18. Note that the median of a distribution is the quantity that lies at the midpoint of a frequency distribution.
The interquartile range is the variance between the quantity at the end of the box, 20 - 16 = 4. The interquartile range (IQR)is defined as the mid 50% of the values in distribution when arranged from the lowest to the highest.
The range is defined as the difference between the quantities at the terminal points of the line. Hence, 28 - 10 = 18.
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The dimensions of a garden are shown.
Write an expression to find the perimeter.
Answer:
P=3x-14
Step-by-step explanation:
P=2(x+1/2 x-7)
=2x+x-14
or P=3x-14
The perimeter of the garden will be;
⇒ 3x - 7/2
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The garden is shown in figure.
Width of garden = 1/2x - 7
Length of garden = x
Now,
Since, Width of garden = 1/2x - 7
Length of garden = x
Hence, The perimeter of garden = 2 (Length + Width)
⇒ The perimeter of garden = 2 (x + 1/2x - 7)
⇒ The perimeter of garden = 2 (3/2x - 7)
⇒ The perimeter of garden = 3x - 7/2
Thus, The perimeter of the garden will be;
⇒ 3x - 7/2
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shape 2
shape 1
8
10
12
14
16
Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true?
A.
Shape 1 is congruent to shape 2, which can be shown using a sequence of dilations and translations.
B.
Shape 1 is not congruent to shape 2 because the shapes do not have the same absolute coordinates.
C.
Shape 1 is congruent to shape 2, which can be shown using a translation
D.
Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 ontos
Answer:
a)shape 1 is congruent to shape 2 which can be shown using a sequence of dilutions and translations
A hot air balloon descended 2,250 feet in 15 minutes. Find the change in altitude per minute (show the process).
Answer:
150 ft/min
Step-by-step explanation:
The change in altitude per minute will have the units of ft/min.
We see that we are given the number of feet: 2250 ft, as well as the number of minutes: 15 min.
So, to get ft/min, we can divide 2250 ft (the distance) by 15 min (time) to get the rate: 2250/15 = 150 ft/min
Thus, the change in altitude per minute is 150 ft/min.
Hope this helps!
Answer:
-15 per minute
Step-by-step explanation:
2250/15 = 150
Since it's descending, height is decreasing.
Hence rate of change of height is -15 per minute
Samuel needs 2 boards to make a shelf. One board is 84 centimeters long
and the other is 45 centimeters long.
What is the total length of the shelf?
centimeters
What would your answer be in millimeters?
millimeters
Answer:
The length of the shelf is 129 cm or 1290 mm.
Step-by-step explanation:
Since Samuel will use the two boards to make the shelf, then the total length of the shelf is the sum of the lengths of each board. So in order to solve this problem we must do as shown bellow:
length shelf = length board1 + length board2
length shelf = 84 + 45 = 129 cm
In order to convert this to milimeters we must multiply the answer above by 10. So we have:
length shelf = 129*10 = 1290 mm
The length of the shelf is 129 cm or 1290 mm.
Answer: 129 cm = 1290 mm
Step-by-step explanation:
Hi, to answer this question we simply have to add the length of both boards.
Mathematically speaking:
Total length = 84 cm + 45 cm = 129 centimiters
Since:
1 cm = 10mm
To convert 129 cm to mm we have to multiply it by 10.
129 cm x 10 mm/cm =1290 mm
Feel free to ask for more if needed or if you did not understand something.
Factor each trinomial completely.
4x^2 - 25b^2 and x^2 - 81
Step-by-step explanation:
4x2 - 25b2
We can solve it by the squares so
(2x - 5b) (2x + 5b)
2) x2 - 81
The same case is here so
(x - 9) (x + 9)
The factorization of the trinomial are;
a. 4x² - 25b² = (2x + 5b)(2x - 5b)
b. x² - 81 = (x + 9)(x - 9)
What is the factorization of the trinomial?To factor the trinomial 4x² - 25b², we can use the difference of squares formula, which states that a² - b² can be factored as (a + b)(a - b).
Applying this formula to 4x² - 25b², we have:
4x² - 25b² = (2x)² - (5b)²
Now, we can rewrite the trinomial as a difference of squares:
4x² - 25b² = (2x + 5b)(2x - 5b)
Therefore, the trinomial 4x² - 25b² can be factored as (2x + 5b)(2x - 5b).
To factor the trinomial x^2 - 81, we can use the difference of squares formula once again:
x² - 81 = x² - 9²
This can be written as a difference of squares:
x² - 81 = (x + 9)(x - 9)
Thus, the trinomial x² - 81 can be factored as (x + 9)(x - 9).
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Choose 1 answer:
A. Vertical angles
B. Complementary angles
C.Supplementary angles
D. None of the above
Answer:
A
Step-by-step explanation:
vertical are always opposite each other
complementary are 180
supplementary are 90
At 6: 00 a.m., Buffalo, NY had a temperature of 10℉. At noon, the temperature was −10℉, and at midnight it was −20℉.
write a statement comparing -10 and -20
Answer:
It got colder Because some nights it gets colder?