A virus takes 13 days to double its original population (A=2A_0). How long will it take to triple its population? Round to the nearest tenth.
Answer:
20.6
Step-by-step explanation:
A virus takes approximately 20.6 days to triple its original population.
What is the formula of exponential growth?"[tex]f(x)=ab^x[/tex],
where a is the initial value
b is the growth rate
x is time. "
For given question,
Suppose the function for the population growth is,
[tex]A(t)=A_0\times b^t[/tex] .........(1)
For t = 13, the population growth of virus would be,
[tex]\Rightarrow A(13)=A_0\times b^{13}[/tex] ..........(2)
But we have been given that a virus takes 13 days to double its original population.
[tex]\Rightarrow A(13)=2\times A_0[/tex] .........(3)
From (2) and (3),
[tex]\Rightarrow A_0\times b^{13}=2\times A_0\\\\\Rightarrow b^{13}=2\\\\\Rightarrow b=1.0548[/tex]
We need to find the number of days to triple its original population
[tex]\Rightarrow A(t)=3\times A_0[/tex] ...........(4)
From (1) and (4),
[tex]\Rightarrow A_0\times b^t=A_0 \times 3\\\\\Rightarrow (1.0548)^t=3\\\\\Rightarrow t=20.6[/tex]
Therefore, a virus takes approximately 20.6 days to triple its original population
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Solve the distance, rate, time problem using a system of two linear equations in two variables.
A plane can travel 960 miles in 2 hours (120 minutes) with a tailwind. The return trip against the wind takes 2 hours and 40 minutes (160 minutes). Find the speed of the plane in still air and the speed of the wind.
Define two variables (state what each variable represents).
Set up a system of two linear equations using the two variables defined in part (A).
Solve the system of equations by addition or substitution.
State your answer as a sentence and include units.
Answer:
960 would be correct becasue it says it in the problem.
This question is designed to be answered without a calculator.
Use this graph of function f.
For how many values of x is f not differentiable over the interval (–4, 4)?
Answer:
4
Step-by-step explanation:
In the graph of the function, between the interval (-4, 4), there are 4 values of x for which the given function is not differentiable.
The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.
here,
The function from observation seems to be a discontinuous function,
And the function is not differentiable at x = -1, 0, 1, and 3.
So there are 4 points in the interval (-4, 4) where the function is not differentiable.
Thus, In the graph of the function, between the interval (-4, 4), there are 4 values of x for which the given function is not differentiable.
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What is the absolute value of -27 1/3
The absolute value of -27 1/3 is 27 1/3. The meaning of absolute value is the distance from the number and zero. -27 1/3 is 27 1/3 away from zero.
Answer: 27 1/3
Reason: The absolute value is the distance from that number to zero, and that's why it's that answer.
I hope this helps, and Happy Holidays! :)
What is the measure of angle c? Pls hurry
Answer:
I think the answer is 43
Step-by-step explanation:
Because b=83
The total value of triangle angles =180
So 54+83=137
180-137=43
A small garden has an area of 25 square yards. How long is each side of the garden? *
Answer:
5
Step-by-step explanation:
the ratio of boys and girls in class is 3:2 Tthere are 15 boys how many total of boys and girls are in class
Answer: 15 boys and 10 girls
Step-by-step explanation:
15/3=5, so the you have to multiply 2 by 5 to get the number of girls. 2x5=10, so to get the total number of students you add 15+10 which gets you 25 students, but if it’s just asking for girls, then it’s 10.
Answer:
25
Step-by-step explanation:
3:2 = 15:10 ( 3x5 = 15 boys; 2x5 = 10 girls)
15+10=25 total boys and girls
Solve For y:
-1/2=3/8y
y=
Answer:
y = -4/3
Step-by-step explanation:
multiply each side with a reciprocal of 3/8 which is 8/3.
8/3 * -1/2 = -4/3
Answer:
-4/3
Step-by-step explanation:
What is an equation of the line that passes through the point ( 6 , − 2 ) (6,−2) and is perpendicular to the line 6 x + y = 2 6x+y=2?
Answer:
An equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:
[tex]y=\frac{1}{6}x-3[/tex]Step-by-step explanation:
We know that the slope-intercept form of the line equation is
y=mx+b
where m is the slope and b is the y-intercept.
Given the line
6x+y=2
Simplifying the equation to write into the slope-intercept form
y = -6x+2
So, the slope = -6
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.
Thus, the slope of the perpendicular line will be: -1/-6 = 1/6
Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 1/6 and the point (6, -2)
[tex]y-\left(-2\right)=\frac{1}{6}\left(x-6\right)[/tex]
[tex]y+2=\frac{1}{6}\left(x-6\right)[/tex]
subtract 2 from both sides
[tex]y+2-2=\frac{1}{6}\left(x-6\right)-2[/tex]
[tex]y=\frac{1}{6}x-3[/tex]
Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:
[tex]y=\frac{1}{6}x-3[/tex]Jerome wants to rent a car for 8 days, and he's interested in the collision damage waiver but not the loss damage waiver. If the daily rate is $60 and CDW is $66, what is his total rental cost?
A$588
B$480
C$546
D$1008
Answer:
c?
Step-by-step explanation:
Answer:
C.546
Step-by-step explanation:
60×8=480+ 66=546
A hot air balloon can hold up to 300 pounds of weight. The balloon's pilot weighs 140 pounds. How many 20-pound bags of sand (b) can also be carried by the hot air balloon? Select three options.
A -2
B 0
C 5
D 8
E 10
Answer:
8
Step-by-step explanation:
300 - 140 = 160 so 160 divided by 20 is 8
Answer:
8, 0, 10
Step-by-step explanation:
I need help plss
Hola
Graham decided to play football this year instead of getting a part-time job. Last year he made about $1,100 during football season. He also spends about $9 on eating out after each game. His team plays a 10-game season. What is his opportunity cost of playing football?
10,091 because it's a 10 season football season and he spends 9 dollars every game
Step-by-step explanation:
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The opportunity cost of playing football for Graham is $1,190.
What is the Opportunity cost?The opportunity cost of certain activity in microeconomic theory is the value or gain given up by engaging in that activity in comparison to engaging in an alternative activity. Simply put, if you do a bone activity, you forfeit the potential to choose another.
Given that Graham made $1,100 during football season. Also, Graham spends about $9 on eating out after each game and his team plays a total of 10 games in a season.
Therefore, the opportunity cost of playing football for Graham is,
Opportunity cost
= Amount that Graham would have made in a part-time job + Total cost of playing football season
= $1,100 + (Number of games × Amount spend in a single game)
= $1,100 + (10×$9)
= $1,100 + $90
= $1,190
Hence, the opportunity cost of playing football for Graham is $1,190.
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The class can contain at most 28 students.
Answer:
s < 28
Step-by-step explanation:
I can write linear equations
1. Through: (-1,3), Slope=2
2.Through: (3,3), slope= -2
2= f/8 f= solve the equation
You deposit $500 into an account that is compounded quarterly at a rate of 7.2%. In how many years will it take for your account to have over $1000?
Answer:
4560 is right answer
Step-by-step explanation:
4560 is right answer
Is TA congruent to GO? Proof?
Answer:
Yeah
Step-by-step explanation:
Which equation represents a proportional relationship?
Answer:
y = 3x
Step-by-step explanation:
A proportional relationship should be represented by an equation in this format:
y = kx
An experiment involving learning in animals requires placing white mice and rabbits
into separate, controlled environments, the environment I and environment II.
The maximum amount of time available in the environment I is 500 minutes, and the maximum
amount of time available in environment II is 600 minutes.
The white mice must spend 10 minutes in environment I and 25 minutes in environment II, and
the rabbits must spend 15 minutes in environment I and 15 minutes in environment II. Identify which set of constraints and objective function is correct? x=white mice and y=rabbits
Answer:
Kk Kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Following are the calculation to the given question:
Suppose x represents a number of white mice while y denotes the number of bunnies.10 minutes is the time needed by mice in habitat 1.15 minutes is indeed the time required by the rabbit in habitat 1.Overall time needed [tex]= 10x + 15y[/tex]In environment 1, the maximum allowed time is 500 minutes.[tex]\bold{10 x +15y \leq 500}[/tex]
Likewise,
Mice need 25 minutes in environment 2 to complete their tasks.15 minutes is indeed the time taken by a rabbit in environment 2.Overall time needed [tex]= 25x + 15y[/tex]In environment 2, the maximum amount of time accessible is 600 minutes.Hence, the answer is " [tex]\bold{25x +15y \leq 600}[/tex]".
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Which situation has a net result of zero?
The temperature was -9'F and fell 9°F.
Janet had $4 and gave $3 to her friend.
High tide was 5.5 ft and now low tide is -0.5 ft.
The hot-air balloon rose 539 feet. It then lost 539 feet of altitude.
Answer:
D. The hot-air balloon... results in a net of zero
Step-by-step explanation:
Thanks for the points my guy :)
have a great day
Answer:
canberry
Step-by-step explanation:
Question 1 Imaginary & Complex Numbers-Addition & Subtraction Solve the following: (7 – 21) – (2+61) = O 9 +82 O 5 - 42 0 5 - 82 0 5+ 8i
Answer:this did not work for me
Step-by-step explanation:
LOOK A PICTURE HURRY PLS LIKE RIGHT NOW
Answeri think it’s 96 or 84 I’m. It sure I had this like 3 years ago
Step-by-step explanation:
How many works can be formed for rearranging the letters of the word PROBLEMS such that P and S the first and last position respectively
Find the distance between a and b
Answer:I believe it is 2.4
Step-by-step explanation:
Paula knows the total cost for 100 students will be $750, and the cost total cost for 150 students is $1050. What is the caterer’s fixed cost and the rate per student served?
Step-by-step explanation:
the price charged for 100 students reflects the cost per student that applies to the order as a whole.
100 * 6 = $600, so the fixed cost is 750-600 = 150.
...
We can check this by substituting in the other equation.
Does 150*6 + 150 = 1050?
150*6=900
900+150 = 1050.
Yes, it does
...
We can express this relationship by the equation:
y = mx + b
where
y = total cost
m = $6 per student
x = number of students
b = fixed costs = 150
y = 6x + 150
The caterer’s fixed cost and the rate per student served is $6 and $150
How to choose what quantity to multiply the first equation?This method is actually called method of elimination to solve a system of linear equations.
We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).
If we have equations:
[tex]a_1x + b_1y = c_1\\a_2x + b_2y = c_2[/tex]
then, if we want to eliminate variable x, then we have to multiply equation 1 with
[tex]-\dfrac{a_2}{a_1}[/tex]
which will make coefficient of x in first equation as
[tex]a_1 \times - \dfrac{a_2}{a_1} = -a_1[/tex]
Then adding both equation will eliminate the variable x.
Given;
Cost of 100 students= $750
Cost of 150 students= %1050
Let the fixed cost of caterer be x
and the cost per student be y
x+100y=750...(1)
x+150y=1050...(2)
solving the above equations;
50y=300
y=6
x=750-600=150
The fixed cost is $150, while the per-student cost is $6.
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Does this graph represent a function? Why or why not? 10 22 -10B2 10 8 A. No, because it fails the vertical line test. B. No, because it is not a straight line. C. Yes, because it passes the vertical line test. O D. Yes, because it has two straight lines.
Answer: I need to see the graph
Step-by-step explanation:
At 3 P.M., the temperature was 9 degrees fahrenheit. By 11 P.M., it had
dropped 31 degrees fahrenheit. What was the temperature at 11 P.M.?*
Answer: -22 degrees
Step-by-step explanation:
Which equation calculates the number of 1/8 foot pieces you can cut from 5 feet of ribbon
Answer:
40
Step-by-step explanation:
The number ribbons cut from the 5 feet long one is 40 ribbons, the equation is n = 5÷1/8
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x - 5 = 16 is an equation.
Given that, a ribbon of 5 feet long ribbon is cut into n 1/8-foot-long ribbons, we need to determine the equation calculates the number of 1/8 foot pieces,
So, the equation =
n = 5÷1/8
n = 40
Hence the number ribbons cut from the 5 feet long one is 40 ribbons, the equation is n = 5÷1/8
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“How mathematics is involved in Merchandising?”
Answer:
You have to have the number of items you paid for and know what numbers you're calculated at checkout.