Answer:
a) [tex]S(t) = 42(0.9995)^t[/tex]
b) It will take 10,692 years.
Step-by-step explanation:
Exponential function to determine the amount of substance:
An exponential function to determine the amout of substance after t years is given by:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
(a) Write an equation to determine the amount of substance, S, left after t years.
Half-life of 1300 years means that [tex]A(1300) = 0.5A(0)[/tex].
We use this to find r. So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]0.5A(0) = A(0)(1-r)^{1300}[/tex]
[tex](1-r)^{1300} = 0.5[/tex]
[tex]\sqrt[1300]{(1-r)^{1300}} = \sqrt[1300]{0.5}[/tex]
[tex]1 - r = 0.9995[/tex]
[tex]r = 0.0005[/tex]
Sample of 42 grams means that [tex]A(0) = 42[/tex]. So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
Replacing A by S, just for notation purposes
[tex]S(t) = 42(0.9995)^t[/tex]
(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?
This is t when [tex]S(t) = 0.2[/tex]. So
[tex]S(t) = 42(0.9995)^t[/tex]
[tex]0.2 = 42(0.9995)^t[/tex]
[tex](0.9995)^t = \frac{0.2}{42}[/tex]
[tex]\log{(0.9995)^t} = \log{\frac{0.2}{42}}[/tex]
[tex]t\log{0.9995} = \log{\frac{0.2}{42}}[/tex]
[tex]t = \frac{\log{\frac{0.2}{42}}}{\log{0.9995}}[/tex]
[tex]t = 10692[/tex]
It will take 10,692 years.
Plz help with the problem in the picture. Thanks
Answer: x(0,0)y(0,0) tell me more I don't really understand it
x=3.4
Step-by-step explanation:
Evaluate the expression when x-=12.5 and y=6 12x-3y^2
Answer:
Step-by-step explanation:
Expresión x--12.5*y-612*x-3*y-2 = 9.5*y-611.0*x-2.0
find the product 27x3
Answer:
81
Step-by-step explanation:
2
27
x 3
------
8 1
Answer:
81
Step-by-step explanation:
27 × 3
81
Find the slope of the line passing through the points (-2,3) a
and
(-9,6).
===================================================
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (6-3)/(-9-(-2))
m = (6-3)/(-9+2)
m = 3/(-7)
m = -3/7
This means each time you go down 3 units, you go to the right 7 units.
Slope = rise/run = -3/7
rise = -3 and run = 7
Poru
1. It is a relationship that compares two or more quantities
A. quantity
B ratio
C. fraction
D. colon
Solve 81^x= 27^x + 2
Answer:
x=6
Step-by-step explanation:
Create equivalent expressions in the equation that all have equal bases then solve for X.
Hope this helped have a good one.
I NEED HELP PLSSSSSSS
a pack of pens cost $3. Prisha spent $12 on pens. Each pack has 5 pens How many packs did Prisha buy?
Answer: 4
Step-by-step explanation: I think
The accompanying specific gravity values describe various wood types used in construction. 0.32 0.35 0.36 0.36 0.37 0.38 0.40 0.40 0.40 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.48 0.48 0.49 0.53 0.54 0.54 0.55 0.58 0.61 0.66 0.66 0.67 0.68 0.76 Construct a stem-and-leaf display using repeated stems. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Stem
Answer:
Follows are the responses to the given question:
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]Stem\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Leaf\\\\[/tex]
[tex]3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5,6,6,7,8\\\\4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0,0,0,1,1,2,2,2,2,2,3,4\\\\4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5,6,6,7,8,8,8\\\\5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1,4,4\\\\[/tex]
[tex]5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5,8\\\\6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6,6,7,8\\\\7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ NONE\\\\7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6\\[/tex]
The stem & leaf show demonstrates that 0.55 for both the data is indeed a reasonable value.
The probable outlier is the data value 0.76.
The variability of the techniques is relatively large.
It show isn't symmetrical and seems to be optimistic.
find the value of 2xy+3yz-xyz, when x=2, y=-2, z=4
Answer:
-16
Step-by-step explanation:
2xy + 3yz - xyz
x = 2, y = -2, z = 4
First, plug these values into the equation.
2(2)(-2) + 3(-2)(4) - (2)(-2)(4) = ?
Next, multiply the parentheses.
(-8) + (-24) - (-16) = ?
When you add a negative, you are actually subtracting the number. And when you subtract a negative, you are actually adding the number. Apply this to the equation.
-8 - 24 + 16 = ?
Now, simplify from left to right.
-32 + 16
-16
Your answer is -16.
Hope this helps!
ABCD is a parallelogram. If m/CDA = 63, then m/ABC = ? . The diagram is not to scale
it’s 63 because the sides are equal on both sides
2(-4y-7)+3=11 solve for y
Answer:
y = -11/4
Step-by-step explanation:
2 ( -4y - 7) + 3 = 11
-8y - 14 + 3 = 11
-8y - 11 = 11
-8y = 22
y = -11/4
Answer:
12
Step-by-step explanation:
-4 + 12 =7
I choose a card at random from a well-shuffled deck of 52 cards. There is a 1/4 probability that the card chosen is a spade, a 1/4 probability that the card is a heart, a 1/4 probability that the card is a diamond, and a 1/4 probability that the card is a club. Both spades and clubs are black cards, whereas hearts and diamonds are red. The events card is a heart and card is a club are
Answer:
The answer is "disjoint events".
Step-by-step explanation:
Please find the complete question in the attached file.
In this question, the Disjointed events were not connected, throughout this, Some other approach to disorganized events was its lack of common outcomes. When it can come at the same time, two events are exclusive to each other. A whole term, that implies excluding each other is disjoined. If had some are united, the chance of them both happening on one is 0, throughout this question, both heart and club can't be cards at the very same time.
x + 5 x < -2 4 – x2 -2
x2 < −6x − 26
x < -x2/6 - 13/3
What is the height of a trapezoid whose bases have lengths of 11 units and 18 units and whose area is 87 square units?
its either
Question 1 options:
5 units,
3 units, or
6 units
Answer:
6 units is answer for it may be correct check it
Answer:
6
Step-by-step explanation:
Took the test on k12
James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply.
7 x + 4 and 3 x + 5 + 4 x minus 1
-When x = 2, both expressions have a value of 18.
-The expressions are only equivalent for x = 4 and x = 6.
-The expressions are only equivalent when evaluated with even values.
-The expressions have equivalent values for any value of x.
-The expressions should have been evaluated with one odd value and one even value.
-When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
-The expressions have equivalent values if x = 8.
Answer:
When x=2, both expressions have a value of 18.
The expressions have equivalent values for any value of x.
The expressions have equivalent values if x=8
Step-by-step explanation:
f(x) = -x + 2, find f(6)
Answer:
f(6)=-(6)+2=-4
........................
[tex] \frac{ \sqrt{40} }{ \sqrt{3} } [/tex]
Answer:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
Step-by-step explanation:
Given
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Required
Simplify
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Rationalize:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40} }{ \sqrt{3} }*\frac{ \sqrt{3} }{ \sqrt{3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40*3} }{ \sqrt{3*3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ \sqrt{9} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ 3 }[/tex]
Expand the numerator
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4*30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4}*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ 2*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
Where would the shape be located after a rotation of 90 degrees clockwise about the origin?
Answer:
It should be the first quadrant
Hope that helps!
Read the picture carefully...there can be more than ONE ANSWER
Answer:
D
Step-by-step explanation:
Darlene's cat had a litter of southern kittens Three of the kittens were black what fraction of the kittens were not black also right this fraction into a division problem
Answer:
1/4
Step-by-step explanation:
A college statistics class conducted a survey of how students spend their money. They asked 25 students to estimate how much money they typically spend each week on fast food. They determined that the mean amount spent on fast food each week is $31.52 and the median is $32. Later they realized that a value entered as $2 should have been $20. They recalculate the mean and the median. Which of the following is true? Group of answer choices
a. The mean and median will increase.
b. The mean will increase, but the median will remain the same.
c. The mean will stay the same, but the median will increase.
d. Both the mean and median will remain the same.
Answer:
Option B, The mean will increase, but the median will remain the same.
Step-by-step explanation:
Given
Mean value is [tex]31.52[/tex] dollars
Median Value is [tex]32[/tex] dollar.
Mean is the average of all the units in a given set of data. Change in any of the number will change the mean.
Here the mean is 31.25
Total money would be [tex]31.25 * 25 = 781.25\\[/tex]
A number is changed from 2 to 20 , i.e addition of 18 dollars
the new mean would be 781.25 + 18/25 = 31.97
However, the median value is the value of the unit at the center of the arrangement. Hence, it will not change.
Option B is correct
a Toyota Yaris goes 15 km on one litre of petrol how much petrol will it need to get to paga from bawku,120km
Answer:
8 litre
Step-by-step explanation:
very simple 120÷15=8
hope it helps you
please mark me as brainlist
234.2 in expanded form
Answer:
Expanded Notation Form:
234.2
=
200
+
30
+
4
+
0.2
Expanded Factors Form:
234.2
=
2 ×
100
+
3 ×
10
+
4 ×
1
+
2 ×
0.1
Expanded Exponential Form:
234.2 =
2 × 102
+
3 × 101
+
4 × 100
+
2 × 10-1
Word Form:
234.2 =
two hundred thirty-four and two tenths
Find dy/dx using logarithmic differentiation.
y = (3 + x)^4/x , x>0
Find the equation of a line perpendicular to -3x + 5y = -1 that contains the point (0, -5)
Answer:
y = -5/3x - 5
Step-by-step explanation:
convert -3x + 5y = -1 to slope-intercept form:
5y = 3x - 1
y = 3/5x - 1/5
slope of a line perpendicular to the above equation would be -5/3
y = mx + b
-5 = -5/3(0) + b
b = -5
y = -5/3x - 5
Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured, and the scientists realize that the gas is leaking over time in a linear way. Its mass is leaking by 9.7 grams per minute. Eight minutes since the experiment started, the remaining gas had a mass of 339.5 grams. Let x be the number of minutes that have passed since the experiment started, and let y be the mass of the gas in grams at that moment. Use a linear equation to model the weight of the gas over time.
a. This line's slope-intercept equation is ___________
b. 31 minutes after the experiment started, there would be ____________ grams of gas left.
c. If a linear model continues to be accurate,______________ minutes since the experiment started, all gas in the container will be gone.
Answer: a. This line's slope-intercept equation: y=-9.7x+417.1
b. 31 minutes after the experiment started, there would be 116.4 grams of gas left.
c. If a linear model continues to be accurate,43 minutes since the experiment started, all gas in the container will be gone.
Step-by-step explanation:
Linear equation: y=mx+c (slope-intercept equation)
, where m= rate of change in y with respect to change in x , c= Initial value.
Let y= Mass of remaining gas after x minutes.
m= -9.7 (given)
At x= 8, y=339.5
Thus,
[tex]339.5=(-9.7)(8)+c\\\\\Rightarrow\ 339.5=-77.6+c\\\\\Rightarrow\ c= 339.5+77.6=417.1[/tex]
a. This line's slope-intercept equation: y=-9.7x+417.1
b. At x= 31 minutes
y=-9.7(31)+417.1
⇒ y=-300.7+417.1
⇒ y=116.4
31 minutes after the experiment started, there would be 116.4 grams of gas left.
c. Put y=0, we get
[tex]0=-9.7x+417.1\\\\ x=\dfrac{417.1}{9.7}\\\\ x=43[/tex]
If a linear model continues to be accurate,43 minutes since the experiment started, all gas in the container will be gone.
simplify the expression 4x+2-1/2x
answer 41x
Step-by-step
Milo has 5 rocks in his rock collection. He finds 40 rocks outside that he wants to put in his collection. If he places the rocks into boxes of 9, how many boxes of rocks will he have in his collection?
Answer:
puto el que lo lea
Step-by-step explanation:
jajajaja lol no
Answer:
5
Step-by-step explanation:
40+5=45. 45/9=5
Can somebody please help me and how do you do this step by step and I need the formula for this please.
radius of ½ circle = d : 2
= 6in : 2 = 3in
Total area = Rectangle area + ½Circle area + Triangle area
= (l×w) + ½(π×r²) + (½×b×h)
= (10×6) + ½(π×3²) + (½ × (14-10) × 6)
= 60 + 14.14 + 12 = 86.14in
Answer : 86.14inSee the bold one in line 2 of total area, thats the formula of all shape.