You accidentally inhale some mildly poisonous fumes. From a blood sample poison concentration exponentially
Answers
The exponential function giving the concentration after t hours is given as follows:
[tex]C(t) = 0.00372(0.9359)^t[/tex]
What is an exponential function?The standard modelling of an exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
The meaning of the variables of the equation are given as follows:
a is the initial value of the exponential function, that is, the numeric value of y when x = 0.b is the rate of change of the exponential function, giving by how much y is multiplied when x increases by one.The initial value of the exponential function is given as follows:
a = 0.00372.
After eight hours, the concentration is given as follows:
C(8) = 0.00219.
Hence the rate of change is obtained as follows:
[tex]C(t) = 0.00372b^t[/tex]
[tex]0.00219 = 0.00372b^8[/tex]
[tex]b^8 = \frac{0.00219}{0.00372}[/tex]
[tex]b = \sqrt[8]{\frac{0.00219}{0.00372}}[/tex]
[tex]b = \left(\frac{0.00219}{0.00372}\right)^{\frac{1}{8}}[/tex]
b = 0.9359.
Hence the equation is:
[tex]C(t) = 0.00372(0.9359)^t[/tex]
Missing InformationThe problem is given by the image at the end of the answer, and it asks for the exponential function modelling the situation.
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Related Questions
5. On a cattle farm, the ratio of beef cattle to dairy cattle is 4:3.
3
(a) Interpret the ratio: For every
beef cattle, there are
cattle.
dairy
(b) If there are 24 dairy cattle, how many
beef cattle would there be? Show your
work.
Answers
For every 4 beef cattle there is 3 dairy cattle. For 24 dairy cattle there will be 32 beef cattle as per the given ratio of 3:4.
What is ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.
Here,
a. No for every 4 beef cattle there is 3 dairy cattle.
b. 4/3=x/24
x=4*24/3
x=32 beef cattle
There are 3 dairy cattle for every 4 beef cattle. According to the stated ratio of 3:4, there will be 32 beef cattle for every 24 dairy cattle.
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HELP PLEASE ILL DO ANYTHING ONE MCRIB BURGER
Answers
The solutions for the graphed linear inequality are (-4, 0), (-1, 4), (0, 0), and (-2, 0). The correct options are A. (-4, 0), B. (-1, 4), C. (0, 0), and E. (-2, 0)
Determining the solutions of a linear inequality from a graphFrom the question, we are to determine all of the solutions for the linear inequality whose graph is given
To do this, we will find the points that fall in the solution region (shaded portion of the graph)
A. (-4, 0)The point (-4, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
B. (-1, 4)The point (-1, 4) falls in the solution region. Thus, it is a solution for the linear inequality.
C. (0, 0)The poi0nt (0, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
D. (4, -1)The point (4, -1) does not fall in the solution region. Thus, it is not a solution for the linear inequality.
E. (-2, 0)The poi0nt (-2, 0) falls in the solution region. Thus, it is a solution for the linear inequality.
F. (0, -2)The point (0, -2) does not fall in the solution region. Thus, it is not a solution for the linear inequality.
Hence, the solutions are (-4, 0), (-1, 4), (0, 0), and (-2, 0).
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SOMEONE HELP ASAP PLEASE!!!!! Allie deposited $5,000.00 into a new savings account that earns 11% interest compounded
monthly. How long will it take for the balance to grow to $6,407.00?
Round your answer to the nearest month.
Answers
The time taken for the balance to grow is 2.3 years.
What is compound interest?
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
"Interest on interest,
Given, compound interest =6.407
principal = 5,000
rate = 11%
to find the time
we know compound interest = principle(1+rate)^t
6407= 5000(1+11/100)^t
6407/5000= (1.11)^t
1.28 = (1.11)^t
taking log
log (1.28)= log(1.11)^t
0.24/0.104 =t
t = 2.3
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A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1600 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answers
If the fuel efficiencies of each of the cars that week is 20 gallons of gas and 25 gallons of gas.
How to find the efficiencies?Let x represent the gallons consumed by car 1
Let y represent gallons consumed by car 2
Formulate an equation:
30x+40y = 1600 equation 1
x+y = 45 equation 2
Substituting equation 2 into equation 1,
30x+40(45-x) = 1600
30x+ 1800-40x = 1600
-10x+1800 = 1600
-10x = -200
Divide both side by -10x
x = -200/-10
x = 20
Substitute value of x into equation 2
x+y = 45
20+y = 45
y = 25
Hence,
Car 1 consumes 20 gallons of gas and Car 2 consumes 25 gallons of gas.
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Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100
Answers
Answer: C
she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.
30 points for this one man like that is a lot of points
Answers
Answer:
it is a subset where you are going to make sets from that one set
The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Answers
Number of camels are there at the safari park are 6 unit.
The animals at a safari park include camels, kangaroos and meerkats.
Let kangaroos are represented as K and Camels are represented as C and Meerkats are represented as M.
There are 12 more kangaroos than there are camels which means
K = C + 12.
There are 3 times as many meerkats as there are camels which means
M = 3C.
There are the same number of kangaroos as there are meerkats which means
K = M
If K = M
therefore,
3C = C + 12
2C = 12 ,
C = 6 unit.
So, K = 6 + 12 = 18
Or M = 18
Therefore number of camels, kangaroos and meerkats at the safari park are 6 , 18 and 18 respectively.
Number of camels are there at the safari park are 6 unit.
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A tennis ball has a volume of approximately
10.31 in ³
What is the radius of the tennis ball? Use 3.14 to
approximate 7.
Answers
By using the concept of volume of a sphere, the result obtained is
Radius of the tennis ball = 1.35 inch
What is Volume of a sphere?
Volume of the sphere is the total space taken by the sphere.
If r is the radius of the sphere, then the volume of the sphere is given by the formula
V = [tex]\frac{4}{3}\pi r^3[/tex]
Let the radius of the ball be r inch
Volume of the ball = [tex]\frac{4}{3}\pi r^3[/tex]
= [tex]\frac{4}{3} \times 3.14 \times r^3[/tex]
By the problem,
[tex]\frac{4}{3} \times 3.14 \times r^3 = 10.31\\r^3 = \frac{10.31 \times 3}{4 \times 3.14}\\r^3 = 2.46\\r = \sqrt[3]{2.46}\\ r = 1.35\ in[/tex]
Radius of the tennis ball = 1.35 inch
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Fwam is preheating his oven before using it to bake. Fwam wants to predict the final
temperature after a minutes. He wrote the equation y = 40x+79, where y represents the final temperature in degrees Fahrenheit. What is the meaning of the y- value when x = 1?
Answers
The solving linear equation states that the temperature of the oven is 119 after an minute.
What is a linear equation?A linear equation is just an algebraic equation of something like the form y=mx+b that only contains a constant and a first-order (linear) component, where m represents the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are now the variables.
According to the given data:Given:
y = 40x+79
X = number of minutes using it to bare:
When X = 1
y = 40(1)+79
y = 119
It means that the temperature of the oven is 119 after an minute.
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(A) find the perimeter of triangle BCF, to the nearest hundredth
(B) find the area of triangle BCF
Answers
Perimeter of triangle BCF is 19.24 units. Area of triangle BCF is 15 [tex]units^{2}[/tex].
Distance formula = [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2} }[/tex]
Perimeter = a + b + c
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
s = [tex]\frac{a+b+c}{2}[/tex]
Given, B(3,2), C(1,-2), F(-3,5).
BC = a = [tex]\sqrt{(3-1)^{2} +(2+2)^{2} }[/tex]
= [tex]\sqrt{2^{2} +4^{2} }[/tex]
= [tex]\sqrt{4+16}[/tex]
= [tex]\sqrt{20}[/tex]
= 4.47 units
CF = b = [tex]\sqrt{(1+3)^{2} +(-2-5)^{2} }[/tex]
= [tex]\sqrt{4^{2} +7^{2} }[/tex]
= [tex]\sqrt{16+49}[/tex]
= [tex]\sqrt{65}[/tex]
= 8.06 units
BF = c = [tex]\sqrt{(3+3)^{2} +(2-5)^{2} }[/tex]
= [tex]\sqrt{6^{2} +3^{2} }[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex]
= 6.71 units
Perimeter = a + b + c
= 4.47 + 8.06 + 6.71
= 19.24 units
s = [tex]\frac{a+b+c}{2}[/tex]
= [tex]\frac{19.24}{2}[/tex]
= 9.62
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]\sqrt{9.62(9.62-4.47)(9.62-8.06)(9.62-6.71)}[/tex]
= [tex]\sqrt{9.62*5.15*1.56*2.91}[/tex]
= [tex]\sqrt{224.91}[/tex]
= 14.99
≈ 15 [tex]units^{2}[/tex]
Hence, perimeter is 19.24 units and area is 15 [tex]units^{2}[/tex].
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Help asap 30 points!!!!
A company manufactures square floor tiles of area 625cm ^ 2 If the manufacturing error tolerance in the area of a tile is +/- 5cm ^ 2 , how close to the ideal length should each tile be controlled?
Answers
Considering the area of a square, the measure of how close to the ideal length should each tile be controlled is of:
A. 0.098 cm.
How to calculate the area of a square?The area of a square of side length s is given by the square of the side length, hence the equation is:
A = s².
For a floor with area of 625 cm², the side length is:
s² = 625
s = square root of 625
s = 25 cm.
Considering the error tolerance, the possible areas are given as follows:
Smallest area: 620 cm².Largest area: 630 cm².The side length for the smallest area would be of:
s² = 620
s = square root of 620
s = 24.90 cm.
The side length for the largest area would be of:
s² = 630
s = square root of 630
s = 25.098 cm.
The smallest difference, from the side lengths with tolerance to the standard side length, is of:
25.098 - 25 = 0.098 cm.
Meaning that option A is the correct option.
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Construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2. Explain how you determined your answer.
WILL GIVE BRAINLYIST
Answers
The rational function is (x + 2)/(x - 3)(x + 2) which has a vertical asymptote at X = 3, and a removable discontinuity at x = -2.
Function
The function is referred as a mathematical expression that defines a relationship between one variable and another variable.
Given,
Here we need to construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2.
Through the given question, we have been given that the rational function that has a vertical asymptote at x = 3, and a removable discontinuity at x = -2.
Here the x = 3 is a vertical asymptote.
So the one factor in the denominator is (x - 3),
And the discontinuity at x = - 2 can be removed, so the another common factor in the numerator and denominator is x+2.
Therefore, the rational function would be :
f(x) = (x + 2)/(x - 3)(x + 2)
So, the rational function would be (x + 2)/(x - 3)(x + 2).
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If you throw exactly two heads in three tosses of a coin you win $41. If not, you pay me $29. If you played this game 713 times how much would you expect to win or lose?
Answers
Two heads in three tosses is 3/8, 3/8x713=267.375. 267.375×41=10,962.375.
5/8x713=445.62, 445.62×29=12,923.125
So 10,962.375-12,923.125=-1960.75
Therefore if you played this game, you would statistically lose $1960.75
rewrite each expression (2+g)8
Answers
Answer:
8×2+8×g
Step-by-step explanation:
Identify the domain and range of the relation, and determine whether the relation is a function.
{(0, 3),(-1/3,0),(-5, 2),(1/3,4)}
Answers
range: {3,0,2,4}
it is a function
A basketball player in a game makes x free throws worth 1 point and y 2-point baskets. The player needs to score at least 28 points to win the scoring title. What inequality represents the number and type of shots the player needs to win the title?
Answers
The inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have A basketball player in a game who makes [x] free throws worth 1 point and [y] free throws worth 2 point baskets. The player needs to score at least 28 points to win the scoring title.
The inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
Therefore, the inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
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Rewrite as a simplified fraction.
Answers
Answer: 23/100
Step-by-step explanation: You would automatically just round it to .23. With any fraction you put it over 100. 23/100 then divide by a factor but for this one there is no simplified fraction so 23/100
Susie is visiting the U.S. from Mexico. One day she stopped by a market and found a stall selling tomatoes for 0.83 dollars per pound. If 1 peso was worth 0.053 dollars that day, how much did the tomatoes cost in pesos per kilogram?
First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side of the equation.
Answers
The value of given ratio is 34.45 peso/kg as the given ratio are : 1 peso/0.053 dollar, 0.053 dollar/1 peso, 1 kg/2.2 lbs, 2.2 lbs/1 kg, 0.83 dollar/1lbs.
What is ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.
Given ratio,
1 peso/0.053 dollar
0.053 dollar/1 peso
1 kg/2.2 lbs
2.2 lbs/1 kg
0.83 dollar/1lbs * 2.2 lbs/1 kg* 1 peso/ 0.053 dollar = 34.45 peso/kg
The value of the given ratio is 34.45 pesos per kilogram because the ratios are 1 peso/0.053 dollar, 0.053 dollar/1 peso, 1 kg/2.2 lbs, 2.2 lbs/1 kg, 0.83 dollar/1lbs.
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In order to start a small business, a student takes out a simple interest loan for $4000.00 for 6 months at a rate of
9.75%.
a. How much interest must the student pay?
b. Find the future value of the loan.
Answers
Answer:
a. $195
b. $4,195
Step-by-step explanation:
Use the equation A = P(1 + rt)convert rate into decimal (0.0975)convert time into years to make things easier (0.5 years)Solve: A = 4000(1 + (0.0975 × 0.5)) = 4195A = $4,195.00Interest: $4,195 - $4,000 = $195
The sum of two odd consecutive integers is 88. Find the integers.
Answers
Answer:
43, 45 are the numbers
Step-by-step explanation:
A rectangular wall measures 15 ft along the floor. The area of
the wall is 180 ft². What is the height of the wall?
Answers
Answer:
The height is 12ft
Step-by-step explanation:
In order to find the height, you have to divide the area by the width which is 180ft divided by 15ft, you get 12ft, and if you double-check 15 x 12 gets you 180, which is the area.
A man is paid N12,000 for 4 days. Find his pay for: (i) 2 days
Answers
Answer:
N6000
Step-by-step explanation:
4 days 12000
2 days. ?
12000*(2/4) = 6000
What is the sum of the first eight terms in this series?
2 + 10 + 50 + 250 + …
Answers
Answer:
195312
Step-by-step explanation:
Using the formula for the sum of a geometric sequence,
[tex]\frac{2(1-(5)^8)}{1-5}=195312[/tex]
y = 3x + 6
What is the gradient?
What is the y-intercept?
Answers
Answer: Gradient: 3. y-intercept: 6
Step-by-step explanation:
An online electronic store's sales are currently increasing at a rate of 2.7% monthly. If they had $65,000 in sales for this month, what will their sales be in 1 year?
Answers
The Sales of the electronic store in 1 year is 66,776.88
Applications of Compound interest:
Compound interest is an interest that is calculated on the principal and the interest accumulated over the previous period. The concept of compound interest can be used in different types of situations like an Increase in population or a decrease in population, Depreciation, or increasing the value of an item, etc.
The formula for compound interest is given by
Total amount, A = P(1 + r/n)^nt
where P = initial amount
r = rate of increase
n = number of compounds in year
t = time period in years
Here we have,
The rate of increase in sales r = 2.7% (per monthly)
=> r = 2.7/100 = 0.027
Here sales are increased monthly
then the number of compounds per year = 12
Sales in this month, P = 65000
From above formula
Sales in 1 year, A = 65000(1 + 0.027/12)¹²
= 65,000(1 + 0.00225)¹²
= 66,776.88
Therefore,
Sales of the electronic store in 1 year = 66,776.88
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A cube has an edge measuring 7 inches.
What is the volume of the cube, in inches?
Answers
What is the slope of a line that is perpendicular to y = 6/7x + 2 and passes through point (−2, 3)?
Answers
The slope of the line that is perpendicular to y is m=6/7.
What do you mean by slope?
A number used to define a line's direction and steepness in mathematics is called the slope or gradient of the line.
The slope is denoted by m,
m = slope
According to the data in the given question:
We have to determine the slope of line that is perpendicular to y,
y=6/7x+2
For the slope, we need follow this equation, where m is slope,
y=mx+b............(1)
In the given question,
m=6/7
Therefore, the slope of the line is m=6/7.
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I need help with this question anyone?
Answers
Answer:
B; 14 cents/1 ounce
Step-by-step explanation:
So you were given the information that there is 140 cents per 10 ounces. Now, we have to get that into a unit rate, which is a number over 1. It would have to be B because the info. was cents/ounces and typically money is over amount.
So you do 140/10
That equals out to 14/1
So it is 14 cents/1 ounce.
Hope this helps!!! :)
A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling a number greater than 3.
If there is more than one element in the set, separate them with commas
Answers
The Sample space for number greater than 3= {4, 5, 6}
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
A number cube with faces labeled from 1 to 6 will be rolled once.
so, Sample Space = { 1, 2, 3, 4, 5, 6}
sample space for number greater than 3= {4, 5, 6}
Thus, the probability is 3/6 or 1/2.
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calculate the arithmetic mean of the numbers 7 and 17, 1/3 and-2/5, -12 and 7, -121 and 49, -16, -9, and 4
47 POINTSSSSSSSSSSSS
Answers
The arithmetic mean of the numbers is -6 11/15
What is arithmetic mean?Arithmetic mean is often referred to as the mean or arithmetic average. It is calculated by adding all the numbers in a given data set and then dividing it by the total number of items in that set.
therefore, arithmetic mean= sum of items/ no of items
The average of numbers,7, 17, 1/3 ,-2/5, -12 ,7, - 121, 49,-16,-9and 4 is obtained by adding the numbers to together and dividing the result by the total frequency.
The sum of the numbers is 7 +17 +1/3-2/5 -12+7 - 121+ 49-16-9+ 4= -1111/15
the total number of items in the set is 11
therefore arithmetic mean = -1111/15÷ 11
= -1111/15×1/11
=-101/15
= -6 11/15
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