(i) N(t) = No e^(-0.088t) (ii) approximately 323.3 g of the substance(iii) the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.(iv) approximately 7.88 days.
Describe Rate of change?The rate of change can be positive, indicating an increase in the value of the variable, or negative, indicating a decrease. It can also be constant, indicating a steady increase or decrease, or it can vary over time, indicating a more complex pattern of change. Understanding the rate of change of a variable is important in many fields, including engineering, economics, and finance, among others.
(i) Since the decay rate is given by -0.088 per day, the exponential function that models the decay is:
N(t) = No e^(-0.088t)
where No is the initial amount of the substance present at t=0.
(ii) If 400g of the substance is present at t=0, then we have No = 400. Substituting this value into the exponential function, we get:
N(t) = 400 e^(-0.088t)
To find how much will remain after 3 days, we need to evaluate N(3):
N(3) = 400 e^(-0.088*3) ≈ 323.3 g
Therefore, approximately 323.3 g of the substance will remain after 3 days.
(iii) The rate of change of the amount of the substance after t days is given by:
dN/dt = -0.088N
To find the rate of change after 3 days, we need to evaluate dN/dt at t=3:
dN/dt | t=3 = -0.088N(3) = -0.088(323.3) ≈ -28.4 g/day
Therefore, the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.
(iv) We want to find the value of t such that half of the original 400 g of the substance remains. In other words, we want to solve the equation:
N(t) = 200
Substituting No = 400 into the exponential function, we get:
400 e^(-0.088t) = 200
Dividing both sides by 400, we get:
e^(-0.088t) = 0.5
Taking the natural logarithm of both sides, we get:
ln(e^(-0.088t)) = ln(0.5)
Simplifying, we get:
-0.088t = ln(0.5)
Solving for t, we get:
t ≈ 7.88 days
Therefore, after approximately 7.88 days, half of the original 400 g of the substance will remain.
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The mean of the following data values is 36.
19, 23, 35, 41, 42
Answer:
To find the mean of a set of data, we need to sum up all the values in the set and divide by the number of values.
Sum of the data values = 19 + 23 + 35 + 41 + 42 = 160
Number of data values = 5
Mean = Sum of data values / Number of data values = 160 / 5 = 32
However, we are given that the mean is 36. Since the calculated mean is lower than the given mean, it means that we are missing a value that is higher than the other values in the set.
Let's call this missing value x. Then, we have:
(19 + 23 + 35 + 41 + 42 + x) / 6 = 36
Multiplying both sides by 6, we get:
19 + 23 + 35 + 41 + 42 + x = 216
Simplifying the left-hand side, we get:
160 + x = 216
Subtracting 160 from both sides, we get:
x = 56
Therefore, the missing value is 56, and the complete data set is:
19, 23, 35, 41, 42, 56
Now, we can calculate the mean as:
Mean = (19 + 23 + 35 + 41 + 42 + 56) / 6 = 216 / 6 = 36
So, the mean of the data values is indeed 36.
Answer:
32
Step-by-step explanation:
To find the mean of a set of numbers, we add up all the numbers and then divide by the total number of values.
Adding up the values:
19 + 23 + 35 + 41 + 42 = 160
We have a total of 5 values, so we divide the sum by 5:
160 / 5 = 32
Therefore, the mean of the given data values is 32, not 36.
You are trying to get back in shape. In the first week, you swim 15 laps every day.
Then, each week, you increase your distance by 5 laps. Which recursive formula
models this situation?
The recursive formula model to represent this situation is L(n) = L(n-1) + 5 where you can swim 15 laps every day.
What is recursive formula?A recursive formula is a formula that defines a sequence in terms of one or more of its preceding terms. In other words, it is a way to generate the terms of a sequence using the previous terms of the same sequence.
According to question:The given situation describes a sequence of numbers where each term is obtained by adding a fixed constant to the previous term. This is called an arithmetic sequence.In this case, we start with 15 laps swum in the first week, and then increase the distance by 5 laps each subsequent week. Let L(n) denote the number of laps swum in week n.To find the number of laps swum in week n, we can add 5 laps to the number of laps swum in week n-1, since the distance increases by 5 laps every week. This can be represented mathematically as:L(n) = L(n-1) + 5
where
L(n-1) represents the number of laps swum in the previous week.
The recursive formula above defines the arithmetic sequence that models the situation described in the problem. We know that L(1) = 15, since in the first week, 15 laps were swum, and we can use the formula recursively to find the number of laps swum in any subsequent week.To know more about recursive visit:
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1. Hiro has 18 highlighters, which is 4 fewer than Martin has. How many markers
does Martin have?
what are the steps???
Answer:
Let's use algebra to solve this problem:
Let's use the variable "m" to represent the number of markers that Martin has.
We know that Hiro has 4 fewer highlighters than Martin, so we can set up an equation:
18 = m - 4
This equation says that the number of markers Martin has (m) minus 4 is equal to the number of highlighters that Hiro has (18).
To solve for "m", we can add 4 to both sides of the equation:
18 + 4 = m
Simplifying this gives us:
22 = m
So Martin has 22 markers.
A lab technician draws a sample of blood. A cubic millimeter of the blood contains 22^5 red blood cells and 22^3 white blood cells. How many times more red blood cells are there than white blood cells?
There are 484 times more red blood cells than white blood cells in a cubic millimeter of blood.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, A lab technician draws a sample of blood.
A cubic millimeter of blood contains 22⁵ red blood cells and 22³ white blood cells.
The number of red blood cells in a cubic millimeter of blood is 22⁵,
and the number of white blood cells in the same volume is 22³.
To find out how many times more red blood cells there are than white blood cells, we need to divide the number of red blood cells by the number of white blood cells:
22⁵ / 22³ = 22⁵⁻³ = 22² = 484
Therefore, there are 484 times more red blood cells than white blood cells in a cubic millimeter of blood.
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Follow the directions to solve the system of equations by elimination.
8x + 7y = 39
4x – 14y = –68
Multiply the first equation to enable the elimination of the y-term.
Add the equations to eliminate the y-terms.
Solve the new equation for the x-value.
Substitute the x-value back into either original equation to find the y-value.
Check the solution.
The solution to the system of equations is (
,
).
The solution to the system of equations is (1/2, 5).
Describe Elimination Method?The elimination method involves manipulating these equations to eliminate one of the variables. This is done by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations, but with opposite signs. The equations are then added or subtracted, depending on the signs, to eliminate one of the variables.
To solve the system of equations by elimination, we can follow these steps:
Multiply the first equation by 2 to get rid of the y-term:
16x + 14y = 78
Add the second equation to the new equation to eliminate the y-terms:
16x + 14y + 4x - 14y = 78 - 68
20x = 10
Solve for x:
x = 1/2
Substitute x = 1/2 into the first equation to solve for y:
8(1/2) + 7y = 39
4 + 7y = 39
7y = 35
y = 5
Check the solution by substituting both x = 1/2 and y = 5 into both original equations:
8(1/2) + 7(5) = 39 (true)
4(1/2) - 14(5) = -68 (true)
Therefore, the solution to the system of equations is (1/2, 5).
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HELP!!!! LIMITED TIME PLEASE!!!!!
What is the domain of the function shown on the graph below?
(Photo of graph is added)
Select one,
(-3, -2,-1,0}
(-3,-2,2,3}
(-3,-2,-1,-0]
(-3, -2,-2,-3)
Answer:
(-3,-2,2,3}
that is the answer
graph system of equations to determine solution
y=1/2x+3
2y=x+6
The system of linear equation has infinitely number of solutions
What is the graph of system of linear equationThe collection of all ordered pairs that concurrently fulfill both equations makes up the graph of a system of linear equations. It is the collection of all points that are the solutions to both equations, in other words.
The system of linear equations in this issue is stated as
y = 1/2x + 3...eq(i)
2y = x + 6...eq (ii)
The graph demonstrates that the system has an infinite number of solutions and that both lines cross one another. This demonstrates that the system is intractable.
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Given the formula y=12/x where y is mi/hr and x is hours find the speed (y) when x is 10 hours
Answer:
1.2 mi/hr
Step-by-step explanation:
y=12/x
y=12/10
y=1.2 mi/hr
Answer:
[tex]\huge\boxed{\sf y = 1.2 \ mph}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle y=\frac{12}{x}[/tex]
Given that, x = 10
So,
[tex]\displaystyle y=\frac{12}{10} \\\\y = 1.2 \ mph\\\\\rule[225]{225}{2}[/tex]
What is the value 3/8 x - 4.5 when x = 0.4
x, y, z – natural numbers.
[tex] {3}^{x} + {5}^{y} + {7}^{z} [/tex] is divisible by 105.
Find the smallest possible value of x+y+z
The smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.
What are Natural Numbers?Natural numbers are a set of positive integers that are used for counting and ordering. In other words, natural numbers are the set of numbers that are used to represent the quantity of objects, such as 1, 2, 3, 4, 5, 6, and so on. Some definitions include zero as a natural number, while others define natural numbers to start from 1. In mathematics, natural numbers are denoted by the symbol "N" or "N+", and are sometimes referred to as counting numbers.
What are whole numbers?Whole numbers are a set of non-negative integers that include all natural numbers (positive integers) and zero. Whole numbers are used to represent quantities that cannot be divided into smaller parts, such as the number of people in a room, the number of apples in a basket, or the number of books on a shelf.
In the given question,
We know that 105 is a multiple of 3, 5, and 7. Therefore, if 3^x+5^y+7^z is divisible by 105, it must also be divisible by 3, 5, and 7.
If 3^x+5^y+7^z is divisible by 3, then 3^x ≡ 0 (mod 3), which means x ≥ 1.
If 3^x+5^y+7^z is divisible by 5, then 5^y ≡ 0 (mod 5), which means y ≥ 1.
If 3^x+5^y+7^z is divisible by 7, then 7^z ≡ 0 (mod 7), which means z ≥ 1.
Therefore, we have x+y+z ≥ 3.
We also know that 105 is the smallest multiple of 3, 5, and 7. Therefore, we want to find the smallest values of x, y, and z that will make 3^x+5^y+7^z divisible by 105.
If we want 3^x+5^y+7^z to be divisible by 105, we need x, y, and z to be multiples of 4, 4, and 3, respectively.
The smallest such values are x=4, y=4, and z=3. Therefore, the smallest possible value of x+y+z is 4+4+3=11.
So, the smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.
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Numbers multiply to seven and add to -8
Answer:
-7 and -1
Step-by-step explanation:
Remember, a negative times a negative equals a positive
The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate.
Principal $6500
Rate. 2%
Compounded. quarterly
Time. 3 years
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
Answer:
A. After 3 years, the amount in the account will be $6730.40.
B. The interest earned will be $230.40.
Step-by-step explanation:
Parallelogram ABCD has vertices A(0,0), B(2,4), C(x, y) and D(5,0).
What are the coordinates of point C?
Tge coordinates of point c is - 3 and 1
Answer: The fourth vertex is D(8, 0)
I’ll give more points!! A
C
Find the mAB
1040
1260
B
D
Answer:I’ll give more points!! A
Step-by-step explanation:I’ll give more points!! A
C
Find the mAB
[tex]\int\limits^3_2 2{x} \, dx* \frac{3x}{2}[/tex]
Answer:
We can solve this integral using the u-substitution method.
Let u = 3x, then du/dx = 3 and dx = du/3.
Substituting these values, we get:
∫2x * 2/3x dx = ∫4/3 du
Integrating, we get:
= (4/3)u + C
Substituting back u = 3x, we get:
= (4/3)(3x) + C
= 4x + C
Therefore, the solution to the integral ∫2x * 2/3x dx is 4x + C.
is 5x=7y linear equation
Yes, 5x=7y is a linear equatiοn.
What is linear equatiοn?First οrder equatiοns include linear equatiοns. In the cοοrdinate system, the linear equatiοns are defined fοr lines. A linear equatiοn in οne variable is οne in which there is a hοmοgeneοus variable οf degree 1 (i.e., οnly οne variable). Multiple variables may be present in a linear equatiοn. Linear equatiοns in twο variables, fοr example, are used when a linear equatiοn cοntains twο variables.
Linear equatiοn is an algebraic equatiοn in οne οr mοre variables where the pοwer οf each variable is less than οr equal tο 1.
Fοr example,
y = mx + c , an equatiοn in this fοrm can be called as linear equatiοn.
Sο in equatiοn 5x = 7y
We can write this equatiοn as 7y = 5x + 0.
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2.2.2 Give two pairs of equal angles?
A parallelogram has two pairs of equal angle.
What is parallelogram ?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.
The properties of a parallelogram are as follows: The opposite sides are parallel and equal. The opposite angles are equal.
A parallelogram has two pairs of equal sides.
It has two pairs of equal angles.
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I need help with this please
Answer:
b
Step-by-step explanation:
A headphone set that normally sells for $84 is marked down by 27%. What is the sale price?
Answer:
The answer is $61.32
A bin of soccer balls, basketballs, and volleyballs contains 112 balls. For every 3 soccer balls there are 5 basketballs and 6 volleyballs. How many more basketballs are there than soccer balls?
[tex]112 : ( 3 + 5 + 6)= 112 : 14 = 8[/tex]
basketballs = 8(5) = 40
soccer balls = 8(3) = 24
→ basketballs - soccer balls = 40 - 24 = 16
Use the unit circle to find the value of tan 315°.
let's recall, the x,y pairs are just the cosine,sine pairs.
[tex]\stackrel{ \cos(315^o) ~~ \sin(315^o) }{\left( \cfrac{\sqrt{2}}{2}~~,~-\cfrac{\sqrt{2}}{2} \right)}\hspace{4.5em}\tan(315^o)\implies \cfrac{\sin(315^o)}{\cos(315^o)} \implies \cfrac{ ~~ -\cfrac{\sqrt{2}}{2} ~~ }{\cfrac{\sqrt{2}}{2}}\implies \text{\LARGE -1}[/tex]
Fill in the sentence below with the description that most specifically applies to the quadrilateral below.
The answer to the given problem can be stated as, "The quadrilateral is most specifically a square because all of its sides are equal and angles are right angle."
What is a square?A square is type of rectangle of which all sides are equal.
The diagonals of a square are perpendicular bisector of each other.
The given diagram of the quadrilateral clearly shows the following information,
All the angles of the quadrilateral are equal to right angle,
And, all of its sides are equal.
The given information matches with the property of a square which implies that the given quadrilateral is a square.
Hence, the given quadrilateral is a square.
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Answer:
Rhombus.All sides are congruent.Step-by-step explanation:
We need to identify the quadrilaterals given in the question.
For first image , we can see that;
All sides are equal .Opposite angles are equal.These are the properties of rhombus in which all sides and opposite angles are equal.
Hence in the first image quadrilateral is a " Rhombus" .
[tex]\rule{200}2[/tex]
In the second image , the most appropriate option is all sides are equal , as in rhombus all sides are congruent.
QUESTION 13
Consider the following argument: If virtual reality video games are perfected in the 21st century, video games will become
the dominant entertainment industry. If video games become the dominant entertainment industry, Hollywood will go
bankrupt and California will lose much of its annual revenue. So, if virtual reality video games are perfected in the 21st
century, Hollywood will go bankrupt and California will lose much of its annual revenue. What is the logical form of this
argument?
O a. Disjunctive Syllogism
O b. Affirming a disjunct
O c. Affirming the consequent
O d. Denying the antecedent
O e. Hypothetical Syllogism
Disjunctive Syllogism is the logical form of the given argument. Therefore, the correct option is option A.
What is argument?An argument seems to be a statement or set of claims, known as premises, that seeks to assess the plausibility or acceptance of a conclusion. The logical, dialectical, and rhetorical perspectives are the three basic areas of study for arguments.
An argument in logic can be defined as a collection of propositions whereby a single one is tried to claim to follow the rest through deductively obtain reasonable that maintain truth from either the premises towards the conclusion. Disjunctive Syllogism is the logical form of the given argument.
Therefore, the correct option is option A.
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349 visitors purchased no costume. 71 visitors purchased exactly one costume. 12 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
The probability that the next person will purchase no costume is 80%.
What is the difference between a probability and an odds?
The possibility of an event occurring can be expressed using odds and probability, but they are computed and understood in different ways.
Probability, which is stated as a number between 0 and 1 (or between 0% and 100%), is the possibility that an event will occur. By dividing the number of positive possibilities by the total number of potential outcomes, the probability of an event happening is determined.
The possibility of an event happening is expressed differently by odds, which are expressed as a ratio of the number of favourable events to the number of negative outcomes. It is possible to state odds as "odds for" or "odds against."
Now,
The total number of visitors who purchased costumes is:
71 (exactly one) + 12 (more than one) = 83
The total number of visitors who did not purchase a costume is: 349
The probability that the next person will purchase no costume is:
349 / (349 + 83) = 349 / 432 ≈ 0.8079
Hence, the probability that the next person will purchase no costume is 80%.
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A city has 14200 people in a random sample of 80 people from the city 43 people say that have visited the city’s community garden which expression can you use to estimate the number of people in the city who have visited the city’s community garden
Answer:
we can estimate that about 7632 people in the city have visited the city's community garden.
Step-by-step explanation:
You can use a proportion to estimate the number of people in the city who have visited the city's community garden. The proportion is:
(Number of people in the city who have visited the community garden) / (Total number of people in the city) = (Number of people in the sample who have visited the community garden) / (Total number of people in the sample)
We can plug in the values given in the problem to get:
(x) / (14200) = (43) / (80)
To solve for x, we can cross-multiply and simplify:
80x = 14200 * 43
x = (14200 * 43) / 80
x ≈ 7632
Therefore, we can estimate that about 7632 people in the city have visited the city's community garden.
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= -4.9t^2+29.4t +1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?
In response to the given question, we have that The baseball takes 3 function seconds to reach its highest point as a result.
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The formula for the height of the baseball is [tex]h(t) = -4.9t2 + 29.4t + 1.[/tex]
A = -4.9 and B = 29.4 in this instance. The vertex's x-coordinate is as follows:
[tex]x = -b/2a = -29.4/(2*(-4.9)) = 3[/tex]
We need to assess h(3) in order to determine the maximum height:
[tex]h(3) = -4.9(3)^2 + 29.4(3) + 1 = 44.1[/tex]
Hence, the baseball may reach a height of up to 44.1 metres.
The x-coordinate of the vertex, which we discovered to be 3, may be used to determine how long it takes the baseball to reach its maximum height. The baseball takes 3 seconds to reach its highest point as a result.
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3. What is the solution of the equation −4(n+5)=−32 - 4 ( n + 5 ) = - 32 ? −13 - 13 −12 - 12 3 3 13
The solution of the given equation -4(n+5)=-32 is n=3.
What is equations ?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) between two expressions. The expressions on both sides of the equals sign have the same value. Equations are used to solve problems in mathematics and science.
To solve the equation, we need to isolate the variable n.
-4(n+5) = -32
Distribute -4 on the left side of the equation:
-4n - 20 = -32
Add 20 to both sides of the equation:
-4n = -12
Divide both sides by -4:
n = 3
Therefore, the solution of the given equation -4(n+5)=-32 is n=3.
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Given the following table with selected values of f (x) and g(x), evaluate f (g(2)).
x –5 –4 –1 2 4 7
f (x) 0 2 7 –1 –6 –4
g(x) –8 –1 2 4 7 1
–4
2
4
–6
The value of f(g(2)) from the given table is -6.
What are functions?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. Expressions of well-known functions can be found in many frequently used mathematical formulas. For instance, the calculation for a circle's area
Given that,
x –5 –4 –1 2 4 7
f (x) 0 2 7 –1 –6 –4
g(x) –8 –1 2 4 7 1
The value of g(2) = 4
The value of f(g(2)) = f(4) = -6
Hence, the value of f(g(2)) from the given table is -6.
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Find the area of a trapezoid that is 12in. and 5in. in length and 4in. in width.
Three girls share R12000 in the ratio 2:3:7 calculate how much each girl will get show calculations
According to the ratio , the three girls shares are R2000,R3000 and R7000.
What is ratio?
When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.
Here the given total share amount is R12000.
Now the ratio for three girls is 2:3:7.
Total = 2+3+7=12
Now the share amounts are,
=> [tex]\frac{2}{12}\times 12000[/tex] = [tex]2\times1000=R2000.\\[/tex]
=> [tex]\frac{3}{12}\times=3\times1000=R3000[/tex]
=> [tex]\frac{7}{12}\times12000=7\times1000=R7000[/tex]
Hence the three girls shares are R2000,R3000 and R7000.
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