3. Exponential Function:
Bacteria grows on food by doubling every hour.
If the bacteria initially covers 10% of the food, it will
cover the entire food source in 3.3 hours.
Answers
Answer:
[tex]y=0.1(2)^x[/tex]
where x is time in hours, and y is the number of bacteria in percent in decimal form.
Step-by-step explanation:
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function. x is the independent variable.y is the dependent variable.
Define the variables:
Let x = time (in hours)Let y = number of bacteria (in percent in decimal form)If the bacteria grows on food by doubling every hour then the growth rate b = 2.
If the bacteria initially covers 10% of the food then y = 10% when x = 0.
Therefore, a = 10% = 0.1.
Therefore, the equation is:
[tex]y=0.1(2)^x[/tex]
Substitute x = 3.3 into the found equation:
[tex]\begin{aligned}x=3.3 \implies y & =0.1(2)^{3.3}\\& =0.9849155307...\\& =1.0\:\sf (nearest\:tenth)\end{aligned}[/tex]
As 1.0 = 100%, this justifies the claim.
[tex]\begin{array}{|c|c|c|}\cline{1-3} x & y & y \\\cline{1-3} 0 & 10\% & 0.1\\\cline{1-3} 1 & 20\% & 0.2\\\cline{1-3} 2 & 40\% & 0.4\\\cline{1-3} 3 & 80\%\ & 0.8\\\cline{1-3} 4 & 160\% & 1.6\\\cline{1-3}\end{array}[/tex]
Related Questions
theo needs 1 1/2 cups of flour for one recipe and 2 3/4 cups of flour for a second recipe. Theo only has a 1/4 cup measuring cup. How many times will theo need to fill the 1/4 cup measuring cup to measure the flour he needs for the two recipes?
Answers
17 times theo will need to measure the flour for both the recipes.
WHAT IS BODMAS ?Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems. B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as BODMAS.
The order of operations (or operator precedence) in mathematics and computer programming refers to a set of rules that represent standards for which operations to carry out first in order to evaluate a specific mathematical expression. For instance, since the advent of contemporary algebraic notation, multiplication has been given a higher priority than addition in mathematics and most computer languages.
As a result, 1 + (2 3) = 7 rather than 1 + (2 3) = 9 is the value assigned to the expression 1 + 2 3. Exponents were first used in the 16th and 17th centuries, when addition and multiplication were given priority. Exponents could only be used as a superscript to the right of their base. Consequently, 3 + 52 = 28 and 3 52 = 75.
CALCULATIONfirst add the total amount of flour =
= [tex]1\frac{1}{2} + 2\frac{3}{4}[/tex]
= 1.5 + 2.75
= 4.25
no. of times = 4.25 * 4/1 = 17 times
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While shopping kyla found a dress that she would like to purchase but it cost $52.25 mor3 than she has
Answers
Kyla should babysit for 9.5 hours to buy the dress.
Double number line represents the comparison of numbers by representing them in equal ratio. The required double number line for the question is attached as figure.
The row I indicates the amount earned and row II indicates the number of hours Kyla should babysit. As is evident from the double number line, the average of last two amounts is the amount required by Kyla. Calculations are as follows -
Required amount = (49.5 + 55)/2
Required amount = 52.25
Now, the time between last two columns of row II will also be taken as average for calculation. So, time required to earn 52.25 after earning 49.5: (9 + 10)/2
Time = 0.5
Total time required to babysit = 9 + 0.5
Total time = 9.5 hours
Thus, Kyla should babysit for 9.5 hours to buy the dress.
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The complete question is -
While shopping, Kyla found a dress that she would really like, but it cost $52.25 more than she has. Kyla charges $5.50 an hour for babysitting. She wants to figure out how many hours she must babysit $52.25 to buy the dress. Use a double number line to support your answer.
in class, we proved that the number of ways of tiling a $1 \times n$ rectangle with $1 \times 1$ and $1 \times 2$ tiles is $f {n 1}.$ (a) use a tiling argument to give a combinatorial proof that \[f 1 f 2 f 3 \dots f n
Answers
Here is a straightforward recursion you may employ to calculate the value.
let's use rectangles with integer aspects to represent the quantity of tilings of a $2 instances n$ rectangle as $T(n)$. There are $22n-2$ techniques to accomplish this if no rectangles of height $2$ are hired, wherein case we lessen to two wonderful times of the $1 times n$ state of affairs. If no longer, we set a situation based at the top-proper rectangle's $2 height. With the preliminary conditions $T(0)=1$ and $T(1)=2$, this results in $$T(n)=22n-2+sum k=0n-1 T(okay)+sum 0leq k ell leq n-1T(ok)22(n-ell-1)$. The center term inside the recursion corresponds to the case where the rightmost rectangle of top $2$ is absolutely the rightmost rectangle inside the tiling.It should be noted that the formula $2n-1$ for the $1 times n$ case is incorrect if $n=0$.
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What should I do when I finish High school and college
Answers
Answer: You should try to figure out the job you want and do that and maybe make a bucket list. Also, live your future out and your hapiness is what counts.
Step-by-step explanation:
Jenna can't wait to play in her new sandbox! Her mom fills the sandbox with seven 50-pound bags of sand. Then, Jenna uses her bucket to dump out sand 10 times. If she dumps out 8 ounces of sand each time, how many pounds of sand are left in the sandbox?
Answers
Answer:
345 pounds
Step-by-step explanation:
Each bucket dumps out 8 ounces of sand
8 ounces = 1/2 pound
So total sand dumped 10 times = 1/2 x 10 = 5 pounds
Originally sandbox had 7 x 50 = 350 pounds of sand
Sand left in box = 350 - 5 = 345 pounds
What value of "x" makes the equation -4x+7=2x+13 true?
OA. -4
OB. -1
OC. 2
OD. O
Answers
Answer:
B. -1
Step-by-step explanation:
Let's solve your equation step-by-step.
−4x+7=2x+13
Step 1: Subtract 2x from both sides.
−4x+7−2x=2x+13−2x
−6x+7=13
Step 2: Subtract 7 from both sides.
−6x+7−7=13−7
−6x=6
Step 3: Divide both sides by -6.
−6x/−6 = 6/−6
x=−1
10. Sam earns a salary of $25,000 while Charlie earns a salary of $30,000. They each receive
a $2000 raise. Which of the following is true?
(a) Sam's raise is larger than Charlie's in both absolute and relative terms.
(b) The raises are the same in absolute terms, but Sam's is larger in relative terms.
(c) The raises are the same in relative terms, but Sam's is larger in absolute terms.
(d) The raises are the same in absolute terms, but Charlie's is larger in relative terms.
Answers
If the salary of Sam is $25000 and Charlie earns $30000 and each get a raise of $2000 then the statement "The raises are the same in absolute terms, but Charlie's is larger in relative terms" is true.
Salary of Sam = $25000
Raise in Sam's Salary = $2000
New Total Salary = $25000 + $2000 = $27000
Salary of Charlie = $30000
Raise in Charlie's Salary = $2000
New Total Salary = $30000 + $2000 = $32000
Hence the absolute value of their salaries are same but Charlie will get more in relative terms.
Hence, option d is correct.
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You start at (6,4) and move 4 units left and 2 units down what point will you end up on?
Answers
Answer:(2,2)
Step-by-step explanation:
because if you follow the steps you will end up there
A sum of £350 is invested at simple interest and amounts to £476 after 3 years. Calculate
(a) the total interest
(b) the rate per cent per annum.
Answers
Answer:
(a) $126
(b) .453333%
Step-by-step explanation:
(a) 476 - 350 = $126
(b)
[tex]si = p \times r\times t \\ 476 = 350 \times r\times 3 \\ 476 = 1050r \\ \frac{476}{1050} = r \\ r = 0.453333\%[/tex]
HELP PLEASEEE
If g (x) = x² + 6 and ƒ (x) = 2x − 4, find g (ƒ (x))
Answers
Step-by-step explanation:
Plug in 2x-4 in the function g(x)
[tex]g(f(x)) = {(2x - 4)}^{2} + 6 \\ \\ g(f(x)) = (2x - 4)(2x - 4) + 6 \\ = 4 {x}^{2} - 8x - 8x + 16 + 6 \\ g(f(x)) = 4 {x}^{2} - 16x + 22[/tex]
HOPE THIS HELPS
are there any points with integer coordinates on a line if a line passes through (5,-8.5) and (13.8, 6.9)?
please provide a yes or no and examples.
Answers
There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
Does a line contain coordinates with only integers?
In this problem we have a line that passes through two points on a Cartesian plane and herein we must check if that line contains at least one point with integer coordinates. First, determine the equation of the line:
Slope
m = [6.9 - (- 8.5)] / (13.8 - 5)
m = 7 / 4
Intercept
b = - 8.5 - (7 / 4) · 5
b = - 69 / 4
The equation of the line is y = (7 / 4) · x - 69 / 4.
Second, evaluate the equation of the line at different integers:
x= 6
y = (7 / 4) · 6 - 69 / 4
y = - 27 / 4
x = 7
y = (7 / 4) · 7 - 69 / 4
y = - 5
x = 8
y = (7 / 4) · 8 - 69 / 4
y = - 13 / 4
x = 9
y = (7 / 4) · 9 - 69 / 4
y = - 3 / 2
x = 10
y = (7 / 4) · 10 - 69 / 4
y = 1 / 4
x = 11
y = (7 / 4) · 11 - 69 / 4
y = 2
x = 12
y = (7 / 4) · 12 - 69 / 4
y = 15 / 4
x = 13
y = (7 / 4) · 13 - 69 / 4
y = 11 / 2
There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
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solve the function please
for f(x) = x^2 - 2x + 1 , find f(x+h)-f(x) / h , h ≠ 0
Answers
For the given function f(x) = x^2 - 2x + 1, the difference quotient is {2x + h - 2]
How to find the difference quotient for the function f(x)?
Here we have the function f(x) = x^2 - 2x + 1
And we want to find the difference quotient, which is:
( f(x + h) - f(x))/h
Replacing the actual function there we get:
[ (x + h)^2 - 2*(x + h) + 1 - x^2 + 2x - 1]/h
Now we can simplify the numerator, we will get:
[ x^2 + 2xh + h^2 - 2x - 2h + 1 - x^2 + 2x -1]/h
[2xh + h^2 - 2h]/h
Taking the quotient we get:
{2x + h - 2]
That is the difference quotient for the function f(x).
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Write a linear function f(x)=mx+b for the table
Answers
The standard form the linear function is f(x)= -3x-3.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+3. Where:
m= the slope. It can be calculated for Δy/Δx .
b= the constant term that represents the y-intercept.
For the given example: m=5 and b=3.
You should replace in the minimum two given values for x and y in the standard form for a linear equation mx+b . Thus, you will write a system linear where from it, you can find the coefficients m and b. See below.
For x=0 and y=-3y=mx+b
-3=0*m+b
-3=b
For x=-2 and y=3y=mx+b
3= -2*m+b
Now, you find b=-3, then
3= -2*m-3
3+3= -2m
6=-2m
m= -3
Thus, you can write f(x)= -3x-3.
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What is the answer to
|x+8|=|2x+1| ?
Answers
Answer:
[tex] \sf \large \: x=7 or x=−3[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
|x+8|=|2x+1|
Solve Absolute Value.
|x+8|=|2x+1|
We know eitherx+8=2x+1orx+8=−(2x+1)
x+8=2x+1(Possibility 1)
x+8−2x=2x+1−2x(Subtract 2x from both sides)
−x+8=1
−x+8−8=1−8(Subtract 8 from both sides)
−x=−7
−x/−1 = −7/−1
(Divide both sides by -1)
x=7
x+8=−(2x+1)(Possibility 2)
x+8=−2x−1(Simplify both sides of the equation)
x+8+2x=−2x−1+2x(Add 2x to both sides)
3x+8=−1
3x+8−8=−1−8(Subtract 8 from both sides)
3x=−9
3x/3 = −9/3
(Divide both sides by 3)
x=−3
Check answers. (Plug them in to make sure they work.)
x=7(Works in original equation)
x=−3(Works in original equation)
Answer:
7
Step-by-step explanation:
x+8=2x+1
Subtract x on both sides. Subtract 1 on both sides
x=7
b. Parallel lines are lines that will never intersect. Do parallel lines exist in spherical geometry? Explain your answer.
Answers
Yes parallel line exist in spherical geometry. The radius or diameter and the tangent can be a pair of parallel line in spherical geometry
How parallel can exist in spherical geometryThe tangent of the sphere refers to a line that make contact with only a point in the sphere. The tangent is perpendicular to the center and the radius can be drawn to be parallel to the tangent.
The radius refers to a line running from the center to an end of the circle. Two radius can be drawn say radius A and radius B. Radius A will be drawn perpendicular to the tangent and radius B drawn perpendicular to radius A.
The pair of lines tangent and radius B will be parallel to each other.
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Multiply and simplify completely
√6 x 3√54
Answers
Answer:
54
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] and [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then
[tex]\sqrt{6}[/tex] × 3[tex]\sqrt{54}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9(6)}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{6}[/tex] × [tex]\sqrt{6}[/tex] × 3 × 3
= 6 × 9
= 54
[tex]{ \qquad\qquad\huge\underline{\boxed{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{6} \times 3 \sqrt{54} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{2 \times 3} \times \sqrt{2 \times {3}^{3} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {2}^{2} \times {3}^{4} } [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times 9[/tex]
[tex]\qquad \sf \dashrightarrow \:18[/tex]
alysha is at a local library with her best friend. they've noticed a lot of cute boys in the library, and alysha bets that of the next twenty people to enter the library, exactly 12 will be cute boys. assuming there is a 50% chance that the next person to walk into the library is a cute boy, what is the probability that alysha will win the bet?
Answers
The probability that Alysha will win the bet is 0.12013
Let ‘x’ be the number of cute boys from next 20 persons that enter the library
And assume x be the integral values from 0 to 20
Given, the probability is 50% that the next person that enters the library is a cute boy,
total number of trials n=20 and probability of success p=50% = 0.5 = 1/2.
Hence, the p.m.f of X is given by
fX(x) = 20Cx(1/2)x(1−1/2)20−x
=20Cx(1/2)x(1/2)20−x
=20Cx(1/2)20
=20!(20−x)!x!⋅ 1220
=0,1,2,…,19,20
and the probability that X=x,
thus
P(X=x)=20!(20−x)!x!⋅1220
x=0,1,2,…,19,20
P(X=x)=20!(20−x)!x!⋅1220
x=0,1,2,…,19,20.
In particular, for X=x=12
P(X=12)=20!(20−12)!12!⋅1220
=20!8!12!⋅1220
≈0.12013
Hence, the probability that exactly 12 persons of the next 20 persons that walk into the library are cute boys is only approximately 0.12013.
Therefore, 0.1203 is less than 0.5, then it is more probable that Alysha will lose the bet than win it.
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find the value of x:
Answers
110+2x=180 degree ( angle sum property of triangle)
2x=180-110
2x=70
X=70/2
X=35 degree
B = 35 degree
C=B alternate interior angles
C=35 degree
Answer:
The answer to the question is 35 degrees
Please help me with this geometry question. Answer should be entered like this (answer, answer) thank you
Answers
Answer:
Q is the point (3, 4).
Step-by-step explanation:
The formulae for the coordinates of a point (h, k) which divides a line joining the points (x1, y1) and (x2, y2) in the ratio m : n is:
h = (mx2 + nx1) / (m + n), k = (my2 + my1)/(m+n)
Now we have S = (x1, y1) = (-2, -6) and T = (x2, y2) = (5, 8) and
m = 5 and n = 2.
So here, for point Q:
h = (5*5) + 2*-2)/(2+5)
= 21/7
= 3.
k = (5*8 + (-6*2) / 7
= 28/7
= 4.
a11
for -4, 8, -16, 32, …
Answers
Step by step:
Every other number will be negative then positive etc
What is the answer rounded to the
hundredths
place?
9.3478 m
+2.73 m
12.0778 m
➜>>
→ [?] m
Answers
Answer:12.8
Step-by-step explanation: u just round it
Solve 6-2x=3x
What would the answer be and step by step guide to completing it
Answers
Answer:
x=6/5
Step-by-step explanation:
6=2x+3x
5x=6
x=6/5
Show how 2/5 + 4/10 is the same as 4/5
Answers
Answer:
Explained through Step-by-step (Showed Work)
Step-by-step explanation:
Question: Show how 2/5 + 4/10 is the same as 4/5
Step-by-step:
2/5 and 4/10 are fractions. (So is 4/5)
To add fractions together, we need the denominators to be the same. This means that the bottom number of 2/5, which is 5 and the bottom number of 4/10 which is 10 have to be the same.
The easiest way to do this is to simplify 4/10. To simplify 4/10, we divide both the numerator (top number) and the denominator (bottom number) by the Greatest Common Factor.
In this case, 2 is the Greatest Common Factor because 4 divided by 2 is 2 and 10 divided by 2 is 5.
so, 4/10 can be simplified to 2/5.
Now, we can add 2/5 and 2/5 together by only adding the numerators. 2 + 2 = 4
so, 2/5 + 2/5 = 4/5
4/5 = 4/5
Therefore, 2/5 + 4/10 is the same as 4/5.
Hope this helps
Sarah had a balance of $162 in her bank account at the start of the week. She withdrew $63.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday, she deposited $87.30.At the end of the week, Sarah had ___(less or more) money in her savings account than she had at the beginning of the week.
How much more or less? $_______
Answers
Answer:
Less; $25.90 less than at the beginning of the week
Step-by-step explanation:
162-(63.50+23.25+26.45)=162-113.20=48.80
48.80+87.30=136.10; 162>136.10
162-136.10=Δ$25.90
$25.90 less
: two six-sided dice are thrown. the numbers on the dice determine which player gets a point. player 1 gets a point if the product of the numbers on the dice is even. player 2 gets a point if the product is odd.
Answers
Both games A as well as B are unfair.
For the game to be fair, both players have to have equal possibilities of prevailing the sport.For sport A.player 1 gets a factor if the made from the numbers at the cube is even. player 2 receives a factor if the product is extraordinary.The fabricated from the numbers at the dice is even if:(i) both the numbers are even.(ii) one of the numbers is extraordinary and the other is even.The product of the numbers within the dice is ordinary simplest when each the numbers are unusual.hence, game A favours player 1.For game B.player 1 receives a point if the sum of the numbers on the cube is even. participant 2 receives a factor if the sum is bizarre.The sum of the numbers at the cube is even when:(i) each the numbers are even.(ii) both the numbers are bizarre.The sum of the numbers in the dice is odd only when one of the numbers is even and the alternative is unusual.subsequently, sport B favours player 1.accordingly, both games favour player 1 and are unfair.To learn more about probability, visit :
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Describe a real-world situation that can be modeled by the equation y = 1/20x be sure to describe which each variable represents
Answers
The equation can be modelled to a real scenario where every purchase can be use to calculate sales tax.
How to find a real world situation that models an equation?The equation to be modelled is as follows:
y = 1 / 20x
let
x = The total price of purchases
y = The amount of sales tax
This simply means a person pays 1 / 20 or 5% of every purchase he/she makes.
The total price of the purchase(including tax) is x while the actual amount of tax paid is y.
Let's say you buy a goods worth 400 dollars. Let's calculated the tax as follows:
x = $400
Therefore,
y = 1 / 20 × 400
y = 1 / 20 × 400
y = $20
Hence, the tax for a purchase of 400 dollars is 20 dollars.
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Nineteen marbles are shared between some children.
Each child receives six marbles and there is one marble left over.
How many children share the marbles
Answers
please help im about to fail math solve for x: 5/2x+1/2x=7+7/2x
Answers
Answer:
yall smart
Step-by-step explanation:
HELP ME QUICK!!
Joe wants to wallpaper the back wall of his bedroom. The wall is in the shape of a rectangle its length of 17 feet and its width is 13 feet suppose wallpaper cost five dollars for each square foot how much will paper cost for the wall
Answers
Based on the shape of the back wall of Joe's bedroom and the dimensions of the rectangle, and the cost per square foot, the paper cost of the wall would be $1,105
What is the paper cost of the wall?First, find the area of the back wall of Joe's bedroom because this is the area that would need to be covered by the wall paper:
Area of rectangle = Length x Width
Solving gives:
= 17 x 13
= 221 square foot
The cost to cover the wall based on the cost in dollars of each square foot is:
= Number of square feet x Cost per square foot
= 221 x 5
= $1,105
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Which table has a constant of proportionality between y and az of 0.6?
Choose 1 answer:
(G
z
Y
47
6
8
-8
4
9
14
H
10
13
y
2.4
5.4
8.4
y
3
2
9 6
15 10
Answers
Answer:
C
Step-by-step explanation:
if you divide the y by x, the answer it will give you will be 2/3 or .6