1. Contaminated water is subjected to a cleaning process. The concentration of the pollutants is initially 5 mg per liter of water. If the cleaning process can reduce the pollutant by 10% each hour, define a function that can represent the concentration of pollutants in the water in terms of the number of hours that the cleaning process has taken place.
Answers
Answer:
\(C(t)=5\cdot(0.9)^t\)
Step-by-step explanation:
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
\(C(t)=C_o\cdot(1-r)^t\)
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The concentration of the pollutants starts at Co=5 mg/lt. We also know the pollutant reduces its concentration by 10% each hour. This gives us a value of r = 10% / 100 = 0.1
Substituting into the general equation:
\(C(t)=5\cdot(1-0.1)^t\)
Operating:
\(\boxed{C(t)=5\cdot(0.9)^t}\)
y(n) = 5(0.9)ⁿ
To answer this, we will make use of the exponential decaying function which is given by;y(n) = a(1 - b)ⁿ
where;
y is the final amount at time n,
a is the original amount
b is the decay factor
x is the amount of time that has passed.
We are told that the initial concentration of the pollutants is 5 mg/LThus;
a = 5 mg/L.
We are told that the pollutant reduces its concentration by 10% each hour. Thus; b= 10%
b = 0.1
Therefore Plugging in the relevant values into y(n) = a(1 - b)ⁿ, we have;y(n) = 5(1 - 0.1)ⁿ
y(n) = 5(0.9)ⁿ
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Related Questions
Simon goes into a cafe and buys 2 cups of coffee and a piece of cake.
Each
cup
of coffee costs £2.78.
The cake costs £2.85
If Simon pays with a £10 note, how much change will he get?
Answers
Answer:
1.59 change
Step-by-step explanation:
2.78*2=5.56
5.56+2.85=8.41
10.00-8.41=1.59
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Answer:
£1.59
Step-by-step explanation:
Cup of Coffee:
=>2 cups of coffee = 2(£2.78)
=> 2 cups of coffee = £5.56
Piece of cake = £2.85
Total cost = 5.56 + 2.85
=> £8.41
Now, the change:
=> £10-£8.41
=> £1.59
3x^2 - 24 = 0 ......... Solve equation by taking square roots
Answers
Answer:
x = 2 √ 2 , − 2 √ 2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
\(\displaystyle x=\±2\sqrt{2}\)
Step-by-step explanation:
\(3x^2-24=0\)
\(3x^2-24+24=0+24\)
\(3x^2=24\)
\(\displaystyle \frac{3x^2}{3}=\frac{24}{3}\)
\(x^2=8\)
\(x=\±\sqrt{8}\)
\(x=\±2\sqrt{2}\)
The flow of water from a faucet can fill a 4 -gallon container in 32 seconds. Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction.
Answers
Answer:
1 gallon=8 sec.
Step-by-step explanation:
you just divide.
write the equation for the circle graphed below.
Answers
Answer:
\((x -1)^2 + (y+1)^2 = 0.25\)
Step-by-step explanation:
Given
The attached graph
Required
The equation of the circle
The equation of a circle is:
\((x - h)^2 + (y - k)^2 = r^2\)
Where
\((h,k) \to center\)
\(r \to radius\)
From the attached graph,
\((h,k) = (1,-1)\)
\(r = 0.5\)
So, we have:
\((x - h)^2 + (y - k)^2 = r^2\)
\((x -1)^2 + (y--1)^2 = 0.5^2\)
\((x -1)^2 + (y+1)^2 = 0.5^2\)
\((x -1)^2 + (y+1)^2 = 0.25\)
Finnley has a tin of orange paint which will cover 46,400 cm². How many cuboids like the one shown below could Finnley completely cover with the paint? 20 cm 3 cm 10 cm
Answers
The total surface area of the cuboid can be calculated by adding the area of all six sides.
2(lw + lh + wh)
2(20x3 + 20x10 + 3x10)
2(60 + 200 + 30)
2(290)
580
Therefore, the surface area of one cuboid is 580 cm².
To find how many cuboids Finnley can completely cover with 46,400 cm² of paint, we need to divide the total surface area of the cuboid by the surface area of one cuboid.
46,400 / 580 = 80
Therefore, Finnley could completely cover 80 cuboids like the one shown with the tin of orange paint.
~~~Harsha~~~
Answer:
80 cuboids
Step-by-step explanation:
To find out the answer we must find the surface area of the cuboids;
2lw+2lh+2wh;
2*20*3+2*20*10+2*3*10;
580
46400/580 is the number of cuboids she can paint;
80
-24 + 36 / -3 = ?
What is the answer?
Answers
Answer:
-36
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
Simplify the '-24+36' to 12.
This leave you with 12/-3.
You then divide, leaving you with -4.
Find the value of x that will make kllm.
Answers
Answer:
hi
Step-by-step explanation:
\((4x + 11) + (6x - 13) = 180 \\ 10x + ( - 2) = 180 \\ 10x = 180 + 2 \
what is inequalities
Answers
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.
The most common symbols used in inequalities are:
">" (greater than): indicates that the value on the left side is larger than the value on the right side.
"<" (less than): indicates that the value on the left side is smaller than the value on the right side.
"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.
"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.
"≠" (not equal to): indicates that the values on both sides are not equal.
Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
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4x+5(7x-3)=9(x-5)
x????
Answers
Answer:
x=-1
Step-by-step explanation:
4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1
Answer:
\( \sf \: x = - 1\)
Step-by-step explanation:
Given equation,
→ 4x + 5(7x - 3) = 9(x - 5)
Now the value of x will be,
→ 4x + 5(7x - 3) = 9(x - 5)
→ 4x + 35x - 15 = 9x - 45
→ 39x - 15 = 9x - 45
→ 39x - 9x = -45 + 15
→ 30x = -30
→ x = -30 ÷ 30
→ [ x = -1 ]
Hence, the value of x is -1.
given a circle with center (-5,3) and radius sqrt 17 what is the slope of the tangent line to the circle that passes through the point (-1,2)
Answers
The slope of the tangent line that passes through the point (-1, 2) is 4, and the equation of the line is: y - 2 = 4(x + 1) or y = 4x + 6
To find the slope of the tangent line to a circle, we first need to find the equation of the circle.
Given the center and radius, the equation of a circle can be written as:
(x + 5)^2 + (y - 3)^2 = 17
Next, we find the equation of the line that passes through the point (-1, 2) and is tangent to the circle.
We can use the slope-point form of the equation of a line:
y - 2 = m(x + 1)
where m is the slope of the line.
To find the value of m, we need to find the slope of the line that is tangent to the circle at the point (-1, 2).
The slope of a tangent line to a circle at a point is equal to the derivative of the equation of the circle at that point.
Taking the partial derivatives of x and y in the equation of the circle, we get:
2(x + 5)dx + 2(y - 3)dy = 0
Rearranging and solving for the slope:
dy/dx = -(x + 5)/(y - 3)
Evaluating the slope at the point (-1, 2), we get:
dy/dx = -(−1 + 5)/(2 − 3) = 4
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Question 1:
S = {0,1}
Is Set S closed under addition?
Why or why not?
Answers
9514 1404 393
Answer:
no; 1+1=2, a number not in the set
Step-by-step explanation:
A set is closed under addition if the addition of any two members of the set results in a member of the set.
0 + 0 = 0 . . . in the set
0 + 1 = 1 . . . in the set
1 + 0 = 1 . . . in the set
1 + 1 = 2 . . . not in the set. The set is not closed under addition.
Annmarie spends1of her paycheck on rent,2on food, andon utilities. What fractional part of her paycheck does she have left for other expenses?Annmarie has of her paycheck left for other expenses.(Simplify your answer. Type an integer or a fraction.)
Answers
Annmarie spends= 1/2 rent
Annmarie spends= 1/5 food
Annmarie spends= 1/8 utilities
\(\frac{1}{2}+\frac{1}{5}+\frac{1}{8}=\frac{33}{40}\)she spends 33/40 in those 3 expenses
\(\frac{40}{40}-\frac{33}{40}=\frac{7}{40}\)she have have left for other expenses 7/40
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answers
Answer:
B
Step-by-step explanation:
For example let's set up a quadratic equation.
Let's use
f(x) = (x + 10)^2 + 7
The seven is the y intercept so let's ignore that and focus on the ten.
When we graph this we end up getting the picture below. Now, why is the vertex at -10? The reason is the equation starts off with a negative sign.
f(n) = (h - x) + k
So, if x is positive then it will remain negative but still go in positive just because the equation has a subtraction sign in it.
As a result when the equation has + 10, it shows that the x is negative because x = -10 and when you do
h- (-10) it becomes h + 10.
Hoped this helps
Slope for (5,-5) (3,5)
Answers
Answer:
-5
Step-by-step explanation:
5-(-5)/3-5=10/-2=-5
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Assume that by contributing your education you increase your yearly earning potential from 21,484 to 39,746 if the additional education cost $36,000 in about many years, will a it pay for itself
Answers
Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.
To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.
The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.
To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).
Payback Period = Cost of Education / Annual Increase in Earning Potential
Payback Period = $36,000 / $18,262
The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.
If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.
In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.
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Hello Can Someone Please Answer This Math Question
Answers
Answer:
180 cm2
Step-by-step explanation:
if you add all the sides together (10, 10, 4, 5, 5, 5) you'll get the sum of 36. if you divide the answer choices by the number of sides you'll get 36.
Janet needs to paint the walls of a room shaped like a
rectangular prism. The room
has a length of 10 ft., a width of 15 ft, and a height of 8 ft. How much paint does she need to cover the
Answers
To solve this problem, we will use the formula of rectangular prism surface area.
The formula is:
A=2(wl+hl+hw)
A is the area, w is the width, l is the length, and h is the height.
So we will put in all the numbers.
A=2((15)(10)+(8)(10)+(8)(15))
Multiple all the numbers inside:
A=2(150+80+120)
Add all the numbers inside:
A=2(350)
Multiply:
A=700ft^2
Hope this helped!
HELPPP ASAPPPP PLEASEEE
Answers
Answer:
with the years labeled on the horizontal axis and the number of hours labeled on the vertical axis. The graph shows that the number of hours spent watching TV declined steadily over the 5-year period, starting at around 1750 hours in Year 1 and falling to around 1300 hours in Year 5. The graph also shows a clear, downward-sloping trend from Year 1 to Year 5.
Step-by-step explanation:
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 13 of the 62 boxes on the shelf have the secret decoder ring. The other 49 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answers
Answer:
I'm pretty sure it is 7.4% or 0.074.
Step-by-step explanation:
Answer:
0.041 = 4.1%
Step-by-step explanation:
The probability the first box has a secret decoder ring is 13/62.
The probability the second box has a secret decoder ring is 12/61.
The probability of both is:
P = (13/62) (12/61)
P ≈ 0.041
Find the product. 65.25 x 9.45
Answers
start by making the multiplication as if they were whole numbers
\(\begin{gathered} 6525\cdot5=32625 \\ 6525\cdot4=26100 \\ 6525\cdot9=58725 \end{gathered}\)arrange the multiplication
count how many decimal places are there in total on both factors and add them together.
there are 2 in 65.25 and 2 in 9.45 meaning 4 decimal places in total
move the decimal point as many places you obtained
\((65.25)\cdot(9.45)=616.6125\)
i multiplied 65.25 x 9.45
A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answers
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
Suppose the number of business majors at liberal arts colleges are normally distributed and have a known population standard deviation of 21 students and an unknown population mean. A random sample of 35 liberal arts colleges is taken and gives a sample mean of 420 business majors. Find the margin of errorfor the confidence interval for the population mean with a 90% confidence level. Round the final answer to two decimal places.
Answers
Answer:
The margin of error for the confidence interval for the population mean with a 90% confidence level is of 5.84 business majors.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1-0.9}{2} = 0.05\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).
So it is z with a pvalue of \(1-0.05 = 0.95\), so \(z = 1.645\)
Now, find the margin of error M as such
\(M = z*\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
In this question:
\(\sigma = 21, n = 35\)
So
\(M = z*\frac{\sigma}{\sqrt{n}} = 1.645*\frac{21}{\sqrt{35}} = 5.84\)
The margin of error for the confidence interval for the population mean with a 90% confidence level is of 5.84 business majors.
Answer:
5.838
Step-by-step explanation:
To find the margin of error we need to identify three things: the z-score, σ, and n.
1.Find zα2 using invNorm. The invNormfunction has one input: probability.
Here, α=1−0.90=0.10. Probability is then 1−0.102=0.95. To find our z-score, we select invNorm after pressing 2nd then VARS. Type invNorm(0.95). The output Is 1.6448. This is the z-score.
2. σ=21.
3. n=35.
4. We type 1.6448×2135√ on the calculator. The output is 5.838, when rounded to three decimal places. This is the margin of error.
Based on the graph, which set shows the solution to log(2x+7)>-2/3x+2?
Answers
Answer:
D or [1.5, ∞)
Step-by-step explanation:
Got it right on edgenuity
A water tower that is 132 feet tall casts a 48-foot long shadow. If Shannon is 1 point
5'6" inches tall and standing near the tower, find the length of her shadow.
Answers
Answer:
2.03 ft
Step-by-step explanation:
132 divided by 48 is 2.75 and 5.6 divided by 2.75 is 2.03
the level of temperature of liquid in a thermometer is 26.52'c lower than the boiling poin. of water. what is the thermometer reading
Answers
The thermometer reading would be 73.48°C.
The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.
100 - 26.52 = 73.48
Hence, the thermometer reading would be 73.48°C.
In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.
By subtracting 26.52 from 100, we obtain a reading of 73.48°C.
Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.
In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.
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The students are trying to raise 3.000 but they only have 1200 how much would they need to get to 3000
Answers
help me please please please
Answers
The angle measures for this problem are given as follows:
a = 62º.b = 118º.c = 62º.d = 62º.How to obtain the angle measures?The sum of the measures of the internal angles of a triangle is of 180º.
The triangle in this problem is ABC, hence the measure of a is obtained as follows:
a + 68 + 50 = 180
a = 180 - (68 + 50)
a = 62º.
c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:
c = 62º.d = 62º.Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:
a + b = 180
62 + b = 180
b = 118º.
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what is the formula of finding sqare rood?
Answers
Answer:
Hi there your question was a little confusing
well I'm using a formula this \(X=\sqrt{Y}\)
Hope this helps :)
Step-by-step explanation:
Answer:
\( \huge\green{ \mid{ \underline{ \overline{ \tt ♡ ANSWER ♡ }} \mid}}\)
There's no specific formula to find the square root of a number, however we can find the square root of a number by the following methods:
i) By Prime Factorisation
ii) By Long Division
iii) By Repeated subtraction method
✏ By Prime Factorisation:Step I: Obtain the given number.
Step II: Reduce the given number into prime factors by successive division.
Step III: Now make pairs of prime factors in such a way that both the factors in each pair are equal.
Step IV: Take one factor from each pair and find the product of these factors.
Step V: The product obtained by multiplying the factors is the required square root.
✏ Long Division:Step 1: Firstly, we place a bar on every pair of digits starting from the unit digit. If the number of digits in it is odd, we put a bar on the single-digit too.
Step 2: Now we find the largest number whose square is less than or equal to the 1st number.
Step 3: Now we bring down the next bar number.
Step 4: For new divisor, we add the divisor & quotient.
Step 5: Number taken is the product of a new divisor and this digit is equal to or less than the new dividend.
✏ Repeated subtraction method:In this method, the given number is subtracted by 1, 3, 5, 7,… at every step till you get zero at the end. The number of steps in the solution is the required square root.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
what is 4 1/5+1 2/5 add and subtract mixed numbers no regrouping
Answers
Answer:
5 3/5 or 5.6
Step-by-step explanation:
Answer:
5 & 3/5
Step-by-step explanation:
4 plus 1 = 5
Since the fractions have the same denominator, this is easy. 1/5 + 2/5 = 3/5.
5 + 3/5 = 5 & 3/5
The HCF of three numbers is 8 and the sum of these numbers is 80. List the possible set of such three numbers.
Answers
Let's denote the three numbers A, B, and C.
Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.
Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.
Let's list the possible combinations:
(8, 16, 56): In this case, A = 8, B = 16, and C = 56. All three numbers are divisible by 8, and their sum is 8 + 16 + 56 = 80.(16, 8, 56): Here, A = 16, B = 8, and C = 56. Again, all three numbers are divisible by 8, and their sum is 16 + 8 + 56 = 80.(24, 8, 48): In this combination, A = 24, B = 8, and C = 48. All three numbers are divisible by 8, and their sum is 24 + 8 + 48 = 80.(8, 24, 48): Similarly, A = 8, B = 24, and C = 48. All three numbers are divisible by 8, and their sum is 8 + 24 + 48 = 80.These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).