The rate of the increase would be 18.56% to the nearest percent.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Seema obtained a score of 57% on her exam, that corresponds to 67 out of 100.
We have been given 120 bacteria to start, which increases to 200 bacteria in 3 hours.
The population-increasing formula is given by
⇒ P(n) = P₀(1+ r)ⁿ
Here P(n) = 200, P₀ = 120, and n = 3
Substitute the values in the above equation,
⇒ 200 = 120(1+ r)³
⇒ 200 / 120 = (1+ r)³
⇒ 5/3 = (1+ r)³
⇒ ∛5/3 = 1+ r
⇒ ∛5/3 - 1 = r
⇒ r = 0.18563
⇒ % r = 18.56%
Therefore, the rate of the increase would be 18.56% to the nearest percent.
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The rate of increase for a bacteria culture that starts with 120 bacteria and grows to 200 after 3 hours is calculated by dividing the increase in population (80) by the initial population (120) and then multiplying by 100 to get the percentage. The rate of increase is 66.67%, which rounds to 67% to the nearest percent.
To find the rate of increase to the nearest percent for a bacteria culture that starts with 120 bacteria and grows to 200 bacteria after 3 hours, we must calculate the percentage growth over the time period given.
First, we need to find the absolute increase in the number of bacteria:
Final population - Initial population = Increase in population
200 - 120 = 80
Next, we calculate the rate of increase based on the initial population:
(Increase in population / Initial population)
(80 / 120)
Multiplying by 100 to get the percentage: (80 / 120) ×100
Rate of increase = 66.67%
Rounded to the nearest percent, the rate of increase is 67%
Find the area of the larger regular pentagon if the smaller pentagon has an area of 43.01 inches^2. The side length of the small pentagon is 5 and the side length of the large pentagon is 8.
True or false the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle
Answer:
True
Step-by-step explanation:
Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.
Then
EB=EC;FC=FA;GA=GB.Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then
m∠OBE=m∠OCE=90°;m∠OCF=m∠OAF=90°;m∠OBG=m∠OAG=90°.You get three pairs of congruent triangles:
ΔOBE≅ΔOCE;ΔOCF≅ΔOAF;ΔOBG≅ΔOAG.This gives you that
[tex]OB=OC=OA.[/tex]
Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.
A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the slant height is 5 cm. Find the VOLUME of the tea bag.
At a sandwich shop they offer 3 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. Each type of sandwich has a combination of exactly 3 ingredients: 1 bread, 1 meat, and 1 cheese. How many types of sandwiches are possible?
The sandwich shop could yield a total of 45 types of sandwiches based on the three categories provided; namely, bread, meat, and cheese. According to the counting principle in mathematics, you multiply the amount of options available from each category to get the total combinations possible.
Explanation:In the scenario described, to determine the possible number of sandwiches, we need to analyze the provided combinations. We have 3 types of bread, 5 kinds of meat, and 3 kinds of cheese. Each sandwich exactly contains one item from each category.
To find out all possible sandwich combinations, we multiply the number of choices in each category. This is known as the counting principle.
So, the formula would be:
Number of sandwich combinations = Types of Bread * Types of Meat * Types of Cheese
Plugging the given numbers into this formula, we get:
Number of sandwich combinations = 3 * 5 * 3 = 45
So, there are 45 possible sandwich combinations available in this sandwich shop.
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Julio checked the temperature of a bag of frozen peas and found it was at −13°C. After he left the bag out of the freezer for an hour, its temperature rose to 8°C. What was the change in temperature in an hour?
a)−21°C
b)21°C
c)5°C
d)−5°C
In 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg
Answer: it’s 1:1
Step-by-step explanation:
Write an equation for the translation of the function. y = cos x; translated 6 units up
Answer:
[tex]y=cos(x)+6[/tex].
Step-by-step explanation:
We are asked to write an equation for the translation of the function [tex]y=cos(x)[/tex] to 6 units upwards.
Let us recall transformation rules.
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:
[tex]y=cos(x)+6[/tex]
Therefore, our required equation would be [tex]y=cos(x)+6[/tex].
If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?
Answer:
If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?
Step-by-step explanation:
If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.
If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.
The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(4)=64
Driving on the North West Express-way, Debbie averaged 62 miles per hour for 3 & one fourth hours. How far did she drive?
1/4 = 0.25
s0 3 1/4 = 3.25
62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form
What is -11-8-13(-10)? And how did you get you're answer
The sum of two numbers is 54 . the smaller number is 12 less than the larger number. what are the numbers?
What is the precise definition of an angle? question 1 options:?
Which is heavier 9 5/8 pounds or 9 3/4 pounds
A quiz has 4 multiple-choice questions with 4 possible answer choices each. for each question, there is only 1 correct answer.a student guesses each answer at random. what is the probability of getting exactly 3 questions correct, to the nearest percent?(3 correct and 1 incorrect)
Answer: (quartered spinner) (4) (1/256)
Find the area of a sector that has a central angle of 40 and a radius of 2 cm. Round your answer to the nearest 100th. Use 3.14=
HELP QUICK!!!
An ellipse has foci F1(9, 0) and F2(11, 6), and the point (1, 6) is on the ellipse. Identify the constant sum for the ellipse.
a 20
b 10
c 0
d 100
Answer: 20
Step-by-step explanation:
Evaluate 9 - b when b = 8
Equations are expressions separated by an equal sign. The value of the expression 9-b is b is 8 is given as 1
Equations and expressionsEquations are expressions separated by an equal sign
Given the expression 9 - b
If b = 8, we will have to substitute the value of 8 into the expression to have:
f(b) = 9 - b
f(8) = 9 - 8
f(8) = 1
Hence the value of the expression 9-b is b is 8 is given as 1
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20 POINTS, PLEASE HELP ASAP!!!!
Solve 2x + 5y = −13
3x − 4y = −8
Webassign find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (6, 36), and the x-axis.
Someone help me please !!!
Answer:
1. 10
2. 12
3. Sqrt 130
4. Sqrt 45
Step-by-step explanation:
To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.
1. a=6, b=8, c=?
[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]
2. a=5, b=?, c=13
[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]
3. a=7, b=9, c=?
[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]
4. a=2, b=?, c=7
[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]
Twenty times the square of a non-zero number is equal to 15 times the number
Which algebraic expression represents “the difference of 54 and a number”?
For this case, the first thing we should do is define a variable.
We have then:
x: unknown number
Then, we write the algebraic expression that models the following problem:
the difference of 54 and a number.
We have then:
[tex]54-x[/tex]
Answer:
An algebraic expression that represents "the difference of 54 and a number" is:
[tex]54-x[/tex]
Answer:
A
Step-by-step explanation:
Rectangular prisms A and B are similar.
The edge of prism B is 3 times that of prism A. How many times the volume of prism A is the volume of prism B?
The sum of two numbers is 33. Twice the first number minus the second number equals 18. Find both numbers.
The both numbers are = 17 and 16
Solving for the unknown numbersThe sum of two numbers = 33
Let the two numbers be X and y.
therefore X + y = 33 ----> equation 1
Twice the first number minus the second number= 18.
That is,
2x - y = 18 -----> equation 2
From equation 1 make X the subject of formula;
X = 33 – y
substitute X into equation 2,
2(33 – y) - y = 18
66 – 2y – y = 18
66 – 3y = 18
66 – 18 = 3y
48 = 3y
y = 48/3
y = 16
Substitute y = 16 into equation 1
Therefore, X +16 = 33
X = 33 –16
X = 17
Therefore, he both numbers are = 17 and 16
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The cells of a certain culture of bacteria double every 6 minutes. If the culture contains 100 cells in the beginning, then the total number of cells P in this culture after t minutes is given by the exponential equation P = 100(2)t/6. Identify the number of minutes it will take for the number of cells to exceed 50,000.
A) 53 min
B) 49 min
C) 48 min
D) 54 min
Since the growth is exponential, therefore I believe the correct form of the equation is:
P = 100 (2)^(t / 6)
Where t / 6 is the exponent of 2
So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:
P = 100 (2)^(t / 6)
50000 = 100 (2)^(t / 6)
500 = 2^(t / 6)
log 500 = (t / 6) log 2
t / 6 = log 500 / log 2
t = 6 * 8.96578
t = 53.8 mins = 54 mins
Answer:
D. 54 min
Applying the distributive property, the expression becomes (3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4). What is the simplified product in standard form?
From 75 campsites to 120 campsites
subtract 75 from 120
120-75 =45 more campsites
Please help me !!!!!!!!