A scientist has a 120 mg sample of an unstable isotope. The amount of the substance remaining in the sample decreases at a rate of 16% each day. At the end of t days, there is less than 30 mg of the substance remaining. Which inequality represents this situation, and after how many days will the sample size remaining be less than 30 mg?
Answers
The inequality is 120*0.84^t < 30
120*0.84^t < 30
0.84^t < 30/120 < 0.25
t * ln 0.84 < ln 0.25
t < ln 0.25 / ln 0.84
t < 7.95
Answer = 8 days
Answer:
Step-by-step explanation:
Got it correct on Edmentum
Related Questions
The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. How many roots of f(x) are rational numbers
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The root of the function is such point [tex]x_0,[/tex] for which [tex]f(x_0)=0.[/tex]
The attached graph of the function [tex]f(x) = 2x^3 - 19x^2 + 57x - 54[/tex] shows, that the graph of the function intersects the x-axis in three points (2,0), (3,0) and (4.5,0).
This means that for
x=2, f(2)=0;x=3, f(3)=0;x=4.5, f(4.5).Thus, x=2, x=3 and x=4.5 are rational roots of the polynomial function f(x).
Answer: three rational roots.
The polynomial function f(x) = 2x^3 - 19x^2 + 57x - 54 has three rational roots at x=2, x=3, and x=4.5, as confirmed by the graph intersecting the x-axis at these points.
The graph of the function f(x) = 2x^3 - 19x^2 + 57x - 54 intersects the x-axis at three points: (2,0), (3,0), and (4.5,0). This implies that x=2, x=3, and x=4.5 are the roots of the polynomial function.
Since these values are rational, the function has three rational roots. Rational roots occur when the function evaluates to zero for specific rational input values.
In this case, f(2) = 0, f(3) = 0, and f(4.5) = 0. The graph crossing the x-axis at these points confirms their status as roots. The polynomial f(x) has three rational roots, which are x = 2, x = 3, and x = 4.5.
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What is an angle that is complementary to angle dge
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You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest?
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To earn $500 in interest at a 4% annual rate, you need to leave $2000 in the account for approximately 6.25 years.
The formula for simple interest is given by:
[tex]\[ I = P \times r \times t \][/tex]
Where:
- I is the interest earned,
- P is the principal amount (initial deposit),
- r is the annual interest rate (expressed as a decimal), and
- t is the time the money is invested or borrowed in years.
In this case, you want to find t, so rearrange the formula to solve for t:
[tex]\[ t = \frac{I}{P \times r} \][/tex]
Given that P = $2000, r = 0.04 (4% as a decimal), and I = $500, plug these values into the formula:
[tex]\[ t = \frac{500}{2000 \times 0.04} \][/tex]
Calculate the result to find out how long you must leave the money in the account to earn $500 in interest.
[tex]\[ t = \frac{500}{2000 \times 0.04} \]\[ t = \frac{500}{80} \]\[ t = 6.25 \][/tex]
Therefore, you must leave the money in the account for approximately 6.25 years to earn $500 in interest at a simple annual rate of 4%.
If the standard deviation of a population increases, what else must necessarily increase? (1 point)
the population's mean
the population's median
the population's mode
the population's variance
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Consider the function f(x) = (x − 3)2(x + 2)2(x − 1).
The zero ______? has a multiplicity of 1.
The zero −2 has a multiplicity of________? .
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we have
[tex]f(x)=(x-3)^{2}(x+2)^{2}(x-1)[/tex]
we know that
The zero of the function is the value of x when the value of the function is equal to zero
[tex]f(x)=(x-3)^{2}(x+2)^{2}(x-1)[/tex]
rewrite the function
[tex]f(x)=(x-3)(x-3)(x+2)(x+2)(x-1)[/tex]
The zero's of the function are
[tex]x=3\ x=3\ x=-2\ x=-2\ x=1[/tex]
so
[tex]x=3[/tex] ------> has a multiplicity of [tex]2[/tex]
[tex]x=-2[/tex] ------> has a multiplicity of [tex]2[/tex]
[tex]x=1[/tex] ------> has a multiplicity of [tex]1[/tex]
therefore
the answer is
The zero [tex]1[/tex] has a multiplicity of [tex]1[/tex]
The zero [tex]-2[/tex] has a multiplicity of [tex]2[/tex]
From the given function, f(x) = (x − 3)2(x + 2)2(x − 1);
The zero 1 has a multiplicity of 1.The zero −2 has a multiplicity of 2Zeros of a functionThe function f(x) = (x − 3)²(x + 2)²(x − 1) given can be expanded so that we have;
f(x) = (x − 3)(x-3)(x + 2)(x+2)(x − 1)Hence, the zeros of the function f(x) are;
x = 3, 3, -2, -2, 1We can conclude that the zero 1 has a multiplicity of 1 and the zero -2 has a multiplicity of 2.
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If 1 card is drawn at random from a standard 52-card deck, what is the probability that the card drawn is a face card?
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BRIANLIEST ~
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.
Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answers
x = number of hours the scooter is rented
y = total rent (in dollars)
"Amir rented a scooter at $43 for 3 hours" means x = 3 and y = 43 giving the point (3,43)
"he rents the same scooter for 8 hours, he has to pay a total rent of $113" means x = 8 pairs up with y = 113. The second point is (8,113)
The two points (3,43) and (8,113) can be used to find the slope
m = (y2 - y1)/(x2 - x1)
m = (113 - 43)/(8 - 3)
m = (70)/(5)
m = 14
The slope of 14 tells us that it costs $14 per hour to rent the scooter
If we simply consider the hourly cost of $14 per hour (and no additional fees), then the cost break down would look like this:
1 hour costs Amir $14
2 hours costs Amir $28 (2*14 = 28)
3 hours costs Amir $42 (3*14 = 42)
If we don't have any fixed costs, then it would cost Amir $42 total to rent the scooter for 3 hours. But it says the cost is actually 43 dollars. So the fixed cost, the y intercept, must be 1 dollar. Think of the $1 as the fee that Amir pays to get into the park or maybe as some kind of insurance. This fixed fee is not dependent on the number of hours Amir rents the scooter.
In other words, if m = 14, x = 3 and y = 43, then
y = mx+b
43 = 14*3+b
43 = 42+b
b = 1
Making the equation to be y = 14x+1
Answer: y = 14x+1
---------------------------------------------------------------
Part B
All we do here is go from y = 14x+1 to f(x) = 14x+1. We simply replace y with f(x) to get it into function notation.
---------------------------------------------------------------
Part C
The y intercept is 1 as this is the value of b in y = mx+b. Compare this to y = 14x+1.
Another way to look at this is that if we plug in x = 0 into y = 14x+1, we get y = 1. So the point (0,1) is on the function. This is where the graph crosses the y axis.
Starting at (0,1) go up 14 units and then to the right 1 unit. You'll arrive at (1,15) as the next point on this graph. Draw a straight line through (0,1) and (1,15) to complete the graph of y = 14x+1
You should have "number of hours" along the x axis and "cost (in dollars)" along the y axis for your proper labels. As for intervals, I would increment x by 1 each time (0, 1, 2, 3, ...) and increment y by 2 at the smallest or 5 at the largest. It will depend on your preference really.
X+y+z=1
2x+4y+6z=2
-x+3y-5z=11
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The question revolves around solving a system of three linear equations with three variables, using algebraic techniques such as substitution or elimination.
Explanation:The system of equations provided can be solved using methods such as substitution, elimination, or matrix operations. The equations given are:
x + y + z = 1 2x + 4y + 6z = 2 -x + 3y - 5z = 11
To solve this system, we can perform operations such as eliminating one variable at a time or using matrices to find the values of x, y, and z that satisfy all three equations simultaneously.
truck was caught in a haistorm that left his truck body damaged and his paint ob ruined Ned is fully insured through hi insurance company Which of the following components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm? a, bodily injury b. property damage c. collision d. comprehensive damage
Answers
It was damage not caused by another vehicle, but by weather.
Since Ned's truck suffered body damage due to a hailstorm, the components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm is comprehensive damage.
What is comprehensive car insurance coverage?A comprehensive coverage is an insurance policy which covers the cost of damages to a vehicle which has been involved in an accident that is not caused by a collision.
Comprehensive insurance covers losses such as:
theft,vandalism,hail, etc.Therefore, the components of Ned's insurance policy will take care of the damage done to Ned's truck during the hailstorm is comprehensive damage.
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Find the remainder when f(x) is divided by (x - k).
f(x) = 4x3 - 5x2 + 2x + 11; k= 3
Answers
12 21 69
----------------------
4 7 23 80
80 would be the remainder
Another method would be to plug 3 into the equation for x
[tex]4(3)^{3}-5(3)^{2}+2(3)+11[/tex] = 4(27) - 5(9) + 6 + 11 = 108 - 45 + 6 + 11 = 63 + 6 + 11 = 80
Answer:
The remainder is 80
Step-by-step explanation:
Given the polynomial
[tex]f(x)=4x^3-5x^2+2x+11[/tex]
we have to find the remainder when the above polynomial f(x) is divided by x-3
By remainder theorem when we put x=3 in f(x) we get the remainder i.e f(3)
[tex]f(3)=4(3)^3-5(3)^2+2(3)+11[/tex]
[tex]=108-45+6+11[/tex]
[tex]=80[/tex]
which is required remainder.
Hence, the remainder is 80
Find the exact value of the following. Do NOT use labels in your answer and do NOT round your answer. -3(1.2)^2 =
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Why does a horizontal line have a slope of 0, but a vertical line has anundened slope?
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Find the slope of the line passing through the two points.
(–7, 8), (–4, 3)
(12, 1), (36, 42)
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Plug in values.
3-8/-4-(-7)= -5/3 = slope
42-1/36-12=41/24=slope
If two angles are complementary, then they total 90o. converse: inverse: contrapositive:
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Converse:If two angles equal 90, then they are complementary
contrapositive: If two angles do not equal 90, then they are not complementary
Find the range of the logarithmic function f(x) = log4 x.
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Which is true about the functional relationship shown below?
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-hope this helps
Describe which of the two points lies on the graph of the line
-4x+y=-11
A.3,1
B.1,3
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-4(3) + (1) = -11
-12 + 1 = -11
-11 = -11 True
A) 3,1
hope this helps
Identify the property that justifies the following statement: if 16m=160,then m=10
Answers
Division Property of Equality
16m = 160
divide both sides by 16 to find m
m = 160/16 = 10
Answer:
Property of equality for division.Step-by-step explanation:
The given expression is
[tex]16m=160[/tex]
So, we use one of the properties of equalities for division, which states that if we divide one side of the equation, we also must divide the other side by the same number, to not mess up the balance of the equation. Applying this property, we have
[tex]\frac{16m}{16}=\frac{160}{16}\\ m=10[/tex]
A cube has a surface area of 900 cm what is the number of cubic cm in the volume of the cube
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SA = 6×(s^2), where "s" is one side or edge of each square surface face
900 = 6s^2
150 = s^2
[tex] \sqrt{150} = \sqrt{ {s}^{2} } [/tex]
[tex] \sqrt{25} \times \sqrt{6} = s[/tex]
[tex]5 \sqrt{6} = s[/tex]
So each side is
[tex]5 \sqrt{6} \: cm \: long[/tex]
The volume (V) of a cube is:
[tex]v = {s}^{3} = (5\sqrt{6})^{3} = {12.247}^{3} \\ = 1837 \: {cm}^{2} [/tex]
The measure of an angle is 9°. what is the measure of a complementary angle?
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so the complement of 9° = 81°
Write and equation of the line that passes through the point (2,4) and is perpendicular tothe line hows equation is 3y-6x+3
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It is perpendicular to the given line, which means the slope of this line is the negative reciprocal of this given line, so we need to find out the slope of the equation 3y=6x+3
divide each side by 3, you'll get y=2x+1, so we know the slope is 2, which is 2/1
the slope for the new line should be -1/2, the negative reciprocal of 1/2
Next, use point-slope format to write your equation. Your point is (2,4) and your slope is -1/2, so you have
(y-4)=-1/2(x-2)
If you want to simplify it: y-4=-1/2x+1 => y=(-1/2)x+5
The sum of two numbers is 35. Three times the larger number is the same as 4 times the smaller number. Find the smaller number
(HINT. Let x= larger number; 35- x= smaller number
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Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. What is her acceleration during this time?
Answers
a=(vf-vi)÷t
a=(25-10)÷(8-3)
a=15/5
a=3m/s^-2
Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. Her acceleration during this time will be 5 m/s².
What is acceleration?Acceleration is the rate of change in both speed and direction of velocity over time. When anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is always shifting, motion on a circle accelerates even while the speed is constant.
It is given that, Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s.
Acceleration is found as the ratio of the change in speed to the change in a time interval.
Acceleration = change in speed/ change in a time interval
Acceleration = (25-10) / (8-5)
Acceleration = (15)/(3)
Acceleration = 5 m/s²
Thus, Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. Her acceleration during this time will be 5 m/s².
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Daniel mows lawns on the weekend. He graphed his earnings below. What is the rate he charges to mow? A. $15.00 per lawn B. $7.50 per lawn C. $60.00 per lawn D. $1.50 per lawn
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To determine Daniel's rate per lawn mowing, we would need to divide his total earnings by the total number of lawns mowed. The answer can also be found by evaluating the slope of a graph with earnings on the y-axis and lawns mowed on the x-axis as the slope would represent his earnings per mow.
Explanation:Without the graph provided, we can't determine the exact answer to this problem. However, conceptually, Daniel's rate per lawn would be calculated by dividing the total amount he earned by the total number of lawns he mowed. For example, if he earned $60 from mowing 4 lawns, his rate would be $15 per lawn.
To find the answer using a graph, you would need to evaluate the slope of the line if the y-axis represents earnings and the x-axis represents lawns mowed. The slope of the line provides the rate, which is Daniel's earnings per mow.
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Find mCE
A. 40 DEGREES
B. 50 DEGREES
C. 75 DEGREES
D. 80 DEGREES
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Melanie made 72 peanut butter cookies and oatmeal cookies. She wants to make identical groups of cookies for her friends. Each group will be as large as possible, and she will use all of the cookies. How many cookies will each friend receive? Explain. Please help me
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PLEASE ANSWER! BRAINLIESTTTT
Why is it important to collaborate?
Discuss a project [either at home or at school] in which you have collaborated. Explain the benefits and drawbacks of working with someone else on collaboration projects.
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how to solve bh+hr=25 when solving for h
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Given the functions f(x) = 2x −1 and g(x) = 2x + 4, which operation results in the largest coefficient on the x term? addition subtraction multiplication two operations result in the same coefficient
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f(x) + g(x)
2x-1 + 2x + 4
4x -1 + 4
4x + 3
Largest coefficient on x = 4
Second lets do the subtraction. f(x) - g(x)
f(x) - g(x)
(2x-1) - (2x+4)
2x - 2x - 1 - 4
-5
Largest coefficient on x = 0
Third lets do the multiplication. f(x) *g(x)
(2x-1) * (2x+4)
[tex]4x^2 + 8x - 2x - 4[/tex]
[tex]4x^2 + 6x - 4[/tex]
Largest coefficient on x = 6
Answer: Multiplication will result in the largest coefficient on the x term.
One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?
A) y=2x-3 and y=x+39
B) y=2x-3 and x+y=39
C) y=2(x-3) and x+y=39
Answers
Let "one number" be y
Let the other number be x
This would mean y=2x-3
2x="two times the other number"
-3= "three less"
The correct answer:
B) y=2x-3 and x+y=39
B.y=2x-3 and x+y=39