Answer:
Every 1.71 seconds, the bacteria loses [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]B(t) = 8500 * (\frac{8}{27})^\frac{t}{3}\\[/tex]
Required [Missing from the question]
Every __ seconds, the bacteria loses [tex]\frac{1}{2}[/tex]
First, we model the function from t/3 to t.
[tex]B(t) = 8500 * (\frac{8}{27})^\frac{t}{3}\\[/tex]
Apply law of indices
[tex]B(t) = 8500 * (\frac{8^\frac{1}{3}}{27^\frac{1}{3}})^t[/tex]
Evaluate each exponent
[tex]B(t) = 8500 * (\frac{2}{3})^t[/tex] --- This gives the number of bacteria at time t
At time 0, we have:
[tex]B(0) = 8500 * (\frac{2}{3})^0[/tex]
[tex]B(0) = 8500 * 1[/tex]
[tex]B(0) = 8500[/tex]
Let r be the time 1/2 disappears.
When 1/2 disappears, we have:
[tex]B(r) = \frac{B(0)}{2}[/tex]
[tex]B(r) = \frac{8500}{2}[/tex]
[tex]B(r) = 4250[/tex]
So, we have:
[tex]B(t) = 8500 * (\frac{2}{3})^t[/tex]
Substitute r for t
[tex]B(r) = 8500 * (\frac{2}{3})^r[/tex]
Substitute [tex]B(r) = 4250[/tex]
[tex]4250 = 8500 * (\frac{2}{3})^r[/tex]
Divide both sides by 8500
[tex]\frac{4250}{8500} = (\frac{2}{3})^r[/tex]
[tex]\frac{1}{2} = (\frac{2}{3})^r[/tex]
Take log of both sides
[tex]log(\frac{1}{2}) = log (\frac{2}{3})^r[/tex]
Apply law of logarithm
[tex]log(\frac{1}{2}) = r\ log (\frac{2}{3})[/tex]
Make r the subject
[tex]r = log(\frac{1}{2}) / log (\frac{2}{3})[/tex]
[tex]r = \frac{-0.3010}{-0.1761}[/tex]
[tex]r = 1.71[/tex]
Hence, it reduces by 1/2 after every 1.71 seconds
Answer:
Every second, the number of bacteria is multiplied by a factor of 0.67
Step-by-step explanation:
Let's rewrite the base so that the exponent is just t.
(8/27)^t/3=((8/27)^1/3)t=(2/3)^t
Therefore, we can rewrite the modeling function as follows.
B(t)=8500⋅(2/3)t
According to this model, the number of bacteria is multiplied by 2/3 every second. Rounding this to two decimal places, we get 2/3 ≈0.67
Jeremiah's pet lizard ate 46 pounds of food during April. There are 30 days in the month April . At that rate how many days would a 100 pound bag of lizard food
O About 19 days
O About 18 days
O About 15 days
O About 65 days
Answer:
about 65 days
Step-by-step explanation:
46/30 = 1.53 pounds per day
100/1.53 = about 65
P(Jack or Queen or 2)
The area of sandbox in park is represented by 2X^2-5x-3 find the dimensions of the sandbox in terms of
Answer:
The dimension of the sandbox is (2x+1) by (x - 3)
Step-by-step explanation:
It seems the complete question will be:
The area of sandbox in park is represented by 2X^2-5x-3 find the dimensions of the sandbox in terms of x.
Step-by-step explanation:
From the question, the given expression is 2X^2-5x-3. This can be rewritten as
[tex]2x^{2} -5x-3[/tex]
If the area of the sandbox in park is represented by this expression, then the dimensions of the sandbox will be the product of the factors. To determine the factors, we will factorize the given quadratic expression.
Factorizing the expression [tex]2x^{2} -5x-3[/tex], we get
[tex]2x^{2} -6x+x-3[/tex]
[tex]2x(x-3)+1(x-3)[/tex]
[tex](2x+1)(x-3)[/tex]
Hence, the dimension of the sandbox is (2x+1) by (x - 3)
I need help is for today!!!!
Answer:
angle b = 25°
for angle A = 180 - 50 (ie 25 + 25)
angle a =130°
Critique the reasoning of others. Sally states that the equation g(x) = x2 + 3x − 10 represents a quadratic function that is the product of the expressions that define the two linear functions a(x) = x + 2 and b(x) = x − 5. Is Sally correct? Explain.
Answer:
Step-by-step explanation:
No, not quite. She's close.
The middle term (often called the linear term) is + which means that the absolute value of the factors must be plus.
(x + 5)(x - 3) is what should should think.
x + 5 = 0
x = - 5
x + 2 = 0
x = - 2
(x + 5)(x - 2)
x^2 - 2x + 5x - 10
x^2 + 3x - 10
a) If the blue squares
weigh 3 pounds each,
how much does each
green triangle weigh?
Answer:
they weigh 2 pounds each
C.
The high temperature this Sunday is expected to be 5 degrees warmer than the
high temperature this Saturday. Using the line c = 2t - 89, how many more
cups of lemonade should Lin expect to sell on Sunday than Saturday? Explain or
show your reasoning.
Answer: 10 more
Step-by-step explanation:
Because 2 x 79 -89 =69
69-59=10
Please help with this?
When solving the equation 3n2−15n=3 by completing the square, what is your first step?
Subtract 3 from each side of the equation.
Divide each side of the equation by 3.
Add 15n from each side.
Divide −15by 2 and square the result.
Answer: Subtract 3 from each side of the equation(A)
Step-by-step explanation:
3n2−15n=3
1:Subtract 3n2 from both sides.
-15n=3-3n2
2:Divide both sides by -15.
-15n/-15=3-3n2/-15
3:Dividing by −15 undoes the multiplication by −15.
n=3-3n2/-15
4:Divide 3−3n 2 by −15
n=n2-1/5
An equation is formed of two equal expressions. The first step in solving the given equation is to Subtract 3 from each side of the equation.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation 3n²-15n=3 can be done as,
3n²-15n=3
3n²-15n-3=3-3
3n²-15n-3=0
(3n²-15n-3)/3=0/3
n²-5n-1=0
Therefore, the first step in solving the given equation is to Subtract 3 from each side of the equation.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ2
there is no answer for this on brainly, if you answer this, you're making history.
Answer:
103.62
Step-by-step explanation:
Formula: v = πr²[tex]\frac{h}{3}[/tex], v = πr²h
Given: π = 3.14, r = 3, h = 5
Sub: 3.14(3)²[tex]\frac{5}{3}[/tex]
Simplify: 3.14(9)[tex]\frac{5}{3}[/tex]
Simplify: (28.26)[tex]\frac{5}{3}[/tex]
Solve: 47.1
Given: π = 3.14, r = 3, h = 6
Sub: 3.14(3)6
Simplify: (9.42)6
Solve: 56.52
V = v1 + v2
V = 47.1 + 56.52
V = 103.62
The total volume of the figure is 103.62
Which greater than 4^3
Answer:
3^4
Step-by-step explanation:
4^3=64
3^4=81
Attachment below, please answer. (No fakes or reported)
Answer:
she is smart.
Step-by-step explanation:
she
used
her
brain.
I need help with this assignment
Answer and Step-by-step explanation:
This is negative slope (or a downwards negative slope).
When the slope is negative, the line goes from right to left from top to bottom.
#teamtrees #PAW (Plant And Water)
Which polyhedra (regular or irregular) have perfect symmetry (plane of symmetry and rotation of symmetry) and why ?
Answer:
regular
Step-by-step explanation:
because an irregular polyhedron is formed by polygons of different shapes where all the components are not the same.
Find the surface area of the following figure below. Use 3.14 for pi
Question:
Find the surface area of the following figure below. Use 3.14 for pi
Answer:
9
Step-by-step explanation:
The circle has the same value of the side which is 3 so the length and width is 3 too. So the formal is L x W = Area. So this means 3 x 3 = 9
By solving the inequality 10a < 50, the answer will be
a < 5
a < 8
a < 10
a < 50
Answer:
a < 5
Step-by-step explanation:
Given
10a < 50 ( divide both sides by 10 )
a < 5
Nick is going to the skating ring once in 12 days. Victoria
Answer:
idek there is only half a question
Step-by-step explanation:
A freight train and a passenger train leave a rail yard at the same time and travel on parallel tracks,
The passenger train travels 5 mph faster than the freight train. The combined distance traveled
after 3 hours is 135 miles. What is the average speed of the freight train?
A 70 mph
B 20 mph
C 22 mph
D 19 mph
Answer:
C. 22 mph
Step-by-step explanation
Assign the speed of the freight train as; x mph
Since the passenger train travels 6 mph faster than the freight train, its speed will be; (x + 6) mph
In 2 hours, the freight and passenger trains will have traveled (distance = speed * time);
2x and 2(x + 6) miles respectively
Both add up to 100 miles. Therefore;
2x + 2(x +6) = 100
4x + 12 = 100
4x = 88
x = 22
x + 6 = 28
Pls pls pls pls help do not get giving branlist
Answer:
0.512 = 51.2%
1.94 = 194%
0.9 = 90%
1.33 = 133%
1.14 = 114%
1.42 = 142%
Step-by-step explanation:
To convert a decimal to a percent, move the decimal point two spaces to the right.
Converting a percent to a decimal works the same way, except you move the decimal two spaces to the left.
[Note: If there aren't enough numbers to go over two spaces, place a zero at the end. For example, if you have 0.9, and you need to convert it into a percent, you'd place a zero after the 9, making it 0.90.]
Daisy purchased a food processor
for $23,000 in the year 2009. It loses its value by 7% per year. What is
the price of the food processor in 2012?
Answer:
$18500.21
Step-by-step explanation:
Good god, that is a really expensive food processor
If using the method of completing the square to solve the quadratic equation x^2+11x+30=0x 2 +11x+30=0, which number would have to be added to "complete the square"?
Answer:
(11/2)² or 121/4 would be added to the equation x ² +11x+30=0, to "complete the square".
Step-by-step explanation:
x 2 +11x+30=0
Write the equation in the form of the square
(x)^2 + 2(x) (11/2) + (11/2)^2 + 30 - 121/4= 0
Square of the first element + 2 into first element into 2nd element + square of 2nd element gives the complete square formula.
How we obtained the second element?
The mid term broken must always be equal to the mid term given.
Hence
2(x) can only be equal to 11x if we multiply it by 11 and divide it with 2.
So the second term must be 11/2 .
To complete the square this second term ( 11/2)² is added and then subtracted to keep the equation equal to the original equation.
(x)^2 + 2(x) (11/2) + (11/2)^2 + 30 - 121/4= 0
Putting it in the form of square
(x+ 11/2)^2 + 120-121/4= 0
Taking LCM and solving
(x+ 11/2)^2 - 1/4= 0
(x+ 11/2)^2 = 1/4
Taking square root on both sides
(x+ 11/2) = ± 1/2
x= - 11/2 ± 1/2
x= -10/2= -5
x= -12/2= -6
7 + n = -5 what does n equal to.
Answer: n=-12
Step-by-step explanation: Hope this help :D
Answer:
hola
Step-by-step explanation:
pouta
GUYS THIS IS THE HARDEST QUESTION EVER PLEASE ANSWER CAREFULLY YOU HAVE BEEN WARNED! 1 + 2 + 3 + 4 + 5 = ?
6
Step-by-step explanation:
because 1 + 2 =3 3+4 = 5 5 +6 = 6 please mark brainlist
the shopkeeper received an interest of $6159 from an investment that offers compound interest at 3.5% p.a. after 10 years. What is the initial investment amount? correct your answer to the nearest dollar.
Answer:
Amount invested = $15,000 (Approx.)
Step-by-step explanation:
Given:
Amount of interest received = $6,159
Rate of interest = 3.5%
Number of year = 10 year
Find;
Amount invested
Computation:
Using compound interest formula
I = P[(1+r)ⁿ - 1]
6,159 = Amount invested[(1+3.5%)¹⁰ - 1]
6,159 = Amount invested[(1+0.035)¹⁰ - 1]
6,159 = Amount invested[(1.035)¹⁰ - 1]
Amount invested = $15,000 (Approx.)
A regular pentagon has an apothem of 4 centimeters.
What is the area of the regular pentagon in square centimeters? Round your answer to
the nearest tenth.
Answer:
[tex] \boxed{A ≈ 58.1 \: cm^{2}} [/tex]
Step-by-step explanation:
When given a regular polygon.
s = a × 2 tan (π / n [radians]).
s = a × 2 tan (180 / n [degrees])
A = (n × s × a) / 2
Where s is the side length, n is the number of sides, a is the apothem length, and A is the area.
You may also see A = p × a.
Where p is the perimeter, the perimeter is the same as n × s.
The apothem is also known as the inradius.
______________________________________
Given a regular pentagon which has 5 sides, and an apothem of 4 cm.
s = 4 × 2 tan (180 / 5) = 4 × 2 × (0.726542528) = 8 × (0.726542528) = 5.81234022404.. ≈ 5.8 cm.
Now that we have sufficient information, we can now solve for the area.
A = (n × s × a) / 2
A = (5 × 5.81234022404.. cm × 4) / 2
A = (20 × 5.81234022404.. cm) / 2
A = (116.236804481.. cm²) / 2
A = 58.1234022404.. cm²
A ≈ 58.1 cm²
The area of the regular polygon is the amount of space it covers
The area of the regular polygon is 58.1 square centimeter
The given parameter is:
[tex]\mathbf{a=4}[/tex]
Start by calculating the side lengths using
[tex]\mathbf{s = 2a\ tan (\frac{180}{ n} )}[/tex]
Where n represents the number of sides.
In this case
[tex]\mathbf{n =5}[/tex]
So, we have:
[tex]\mathbf{s = 2a\ tan (\frac{180}{ 5} )}[/tex]
[tex]\mathbf{s = 2a\ tan (36)}[/tex]
Substitute 4 for (a)
[tex]\mathbf{s = 2 \times 4\ tan (36)}[/tex]
[tex]\mathbf{s = 8\ tan (36)}[/tex]
[tex]\mathbf{s = 5.8123}[/tex]
The surface area is then calculated as:
[tex]\mathbf{A = \frac{n \times s \times a}{ 2}}[/tex]
So, we have:
[tex]\mathbf{A = \frac{5 \times 5.8123 \times 4}{2}}[/tex]
[tex]\mathbf{A = 58.123}[/tex]
Approximate
[tex]\mathbf{A = 58.1}[/tex]
Hence, the area of the regular polygon is 58.1 square centimeter
Read more about areas at:
https://brainly.com/question/12000718
Pls help
Pls help
Pls help
Answer:
600ft²
Step-by-step explanation:
Oh boy, this is gonna be a long one, so proceed with caution:
So we're gonna start with the one to the very left, we can split this into three different rectangles:
So we got the length of the bottom minus the length we don't want there because we're doing the big rectangle:
35 - 10 = 25
25 x 20 = 500
So we're just gonna keep that on a back burner, cause now we gotta do the two smaller ones:
So we got the measure from the one side, but we gotta subtract the 10 from the other side:
20 - 10 = 10
10 x 10 = 100
Now we gotta add that all up:
500 + 100 = 600
So the area of the first shape is 600ft²
I gotta go, but hope this helps a little bit
WILL MARK BRAINLIEST.
Answer:
1. Proportional
2. Not proportional
3. Proportional
Step-by-step explanation:
You can tell because the line is straight, which shows how the graph is proportional. Hope this helps!
No LINKS PLEASE!!
2x+5→△ ← 4x−3
Answer:
x equals 4
Step-by-step explanation:
2 times 4 is 8 plus 5 is 13 and them 4 times 4 is 16 and 16 minus 3 is 13
A manufacturer is interested in creating a new item. His research team starts with a model consisting of the functions =−3(+2)2+3 , y = - 3 and y = 0. What is the height of the shape?
Answer:
[tex]x = -2[/tex]
Step-by-step explanation:
Given
[tex]y=\frac{-3}{(x+2)^2}+3[/tex]
[tex]y = - 3[/tex]
[tex]y = 0[/tex]
The question has confusing details because the height of a shape do not relate to the given parameters.
A more complete question found on the brainly shows that the complete question asks for the asymptote of the function.
To do this, we have:
[tex]y=\frac{-3}{(x+2)^2}+3[/tex]
Take LCM
[tex]y = \frac{-3 + 3(x+2)^2}{(x+2)^2}[/tex]
Equate the denominator to 0
[tex](x + 2)^2 = 0[/tex]
Take square roots of both sides
[tex]x + 2 = 0[/tex]
Solve for x
[tex]x = -2[/tex]
Hence, the asymptote is at [tex]x = -2[/tex]
The distance from the Earth to the Moon is 384 000 km. Work out the time it would take a car travelling at 100 km/h to travel 384 000 km. Give your answer in days
(Show your working out)
Answer:
3840
Step-by-step explanation:
thbyrtjnbyj
whats is the value of 4+4
Answer:
8 is the answer \(-ㅂ-)/ ♥ ♥ ♥(╯°□°）╯︵ ┻━┻
Answer: 8
Step-by-step explanation: