If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?
The function that describes a cell population of 100 cells tripling every hour is stated by the formula p(t) = 100(3)^t, which represents exponential growth.
Explanation:This problem describes a phenomenon where the initial population experiences exponential growth in a way that it triples every hour. Exponential growth is typically represented by the function p(t) = p⁰×r^t, where:
- p(t) represents the final amount of entities (in this case, population) after time t,
- p0 is the initial amount of entities (in this case, initial population),
- r is the growth factor,
- and t is time.
In these types of problems, the base number of the exponent (in this case 3) represents the growth factor. This is based on the fact that every time period (in this case, every hour), the population triples, or in other words, gets multiplied by 3.
The initial population given is 100 cells. This is represented by p0 in our formula and is also the coefficient in our function.
By considering both the initial population and the rate at which it triples, we can construct the function as p(t) = 100 × 3^t.
Therefore, according to our built function, the correct choice is b. p(t) = 100 × 3^t.
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Question:If a population of 100 cells triples every hour, which function represents p(t), the population after t hours?
a. p(t)=3(100)^t
b. p(t)=100(3)^t
c. p(t)=3t+100
d. p(t)=100t+3
The graph of a function in the form f(x) a(x - h)2 +k is shown. Use the graph to find an equation for f(x).
Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(7.5, 4.5) , B′(4.5, 10.5) , and C′(1.5, 6) . The center of dilation is the origin.
What is the scale factor of the dilation?
Answer:
3/2
Step-by-step explanation
I need help with question 7, don't really get it?
The volume of a cone is 471.24 cubic inches and the height is 8 inches. What is the diameter
Without calculating, explain how many decimal places are in the product 0.6 X0.4 X 1.9. Rewrite the expression as the product of two decimals to support your answer.
The product 0.6 x 0.4 x 1.9 has three decimal places.
Explanation:To determine the number of decimal places in the product 0.6 x 0.4 x 1.9, we can rewrite each decimal as the product of two decimals and count the total number of decimal places.
0.6 can be written as 0.6 x 1.0, which has one decimal place.
0.4 can be written as 0.4 x 1.0, which also has one decimal place.
1.9 can be written as 1.9 x 1.0, which has one decimal place.
Since each decimal has one decimal place, the product 0.6 x 0.4 x 1.9 has a total of three decimal places.
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Which is NOT a Correct name for the line shown
nR is not a correct name for the line shown.
What is Line?A line is a straight geometrical figure in one dimension. It is extended to both sides to infinity.
A line only has length and has no width, thus it is a one dimensional figure.
Given is a line where both sides extended to infinity.
The line is given a name n.
So we can denote the given line as n.
There are points marked on the line like R, S and T.
So we can denote the line also has the lines RT, ST and RS.
But we cannot denote the line with names like n R, n S and n T, all of which are incorrect notation.
Hence the incorrect notation for the given line is the second option n R.
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wo equations are given below: a − 3b = 9 a = b − 3 What is the solution to the set of equations in the form (a, b)? (−9, −6) (−4, −3) (−6, −3) (−9, −7)
Carter has 60 balloons. 4/12 of the balloons are black, and 3/12 of the balloons are white. The rest of the balloons are red. Which series of calculations shows how many red balloons Carter has?
To find the number of red balloons Carter has, subtract the number of black and white balloons from the total number, using fractions to represent the proportion of black and white balloons. Multiply the total number of balloons by the fraction representing red balloons to find the number of red balloons.
Explanation:To find the number of red balloons Carter has, we need to subtract the number of black and white balloons from the total number of balloons. Since 4/12 are black and 3/12 are white, we can add these fractions together to find the total fraction of balloons that are either black or white: 4/12 + 3/12 = 7/12.
To find the fraction of balloons that are red, we can subtract the fraction of black and white balloons from 1 (since the sum of all fractions should equal 1): 1 - 7/12 = 5/12.
To find the actual number of red balloons, we can multiply the total number of balloons (60) by the fraction of red balloons: 60 x 5/12 = 25 red balloons.
5% sales tax on a $81.08 bookcase
Choose a number from 101 to 110 write it draw a picture to show it as 10 tens and more.
Choose a number from 101 to 110, we selected 106. To represent it with tens and ones, draw ten groups of ten for 'ten tens' which equals 100, and then draw 6 individual objects depicting 'and more' to visually show that 106 is 100 plus 6.
To choose a number from 101 to 110 and represent it as ten tens and more, let's select the number 106. The number 106 can be broken down into ten tens (which is 100) and an additional 6 to make up the full number.
A visual representation of this could be:
For the ten tens, you can draw ten groups of ten sticks or circles together, which would represent 100.
For the additional 6, draw six more sticks or circles away from the groups of tens.
So the drawing will show ten sets of ten objects, such as sticks or dots for the tens, and then six individual objects for the ones, clearly indicating that 106 consists of 100 (ten tens) plus 6 more.
At the malt shop a large chocolate shake takes 0.2 of a pint of milk. If a medium shake takes 0.7 the amount of a large, how much does the medium shake take?
Find x and y, given that line KL and line MN are parallel. Please show how you got your answer.
Leta is making strawberry-almond salad for a party. For every head of lettuce that she uses, she adds 5 ounces of almonds and 10 strawberries. If she uses 75 ounces of almonds, how many heads of lettuce, how many strawberries does Leta use?
sum of 5 z and 4 divided by two is 7
An 8-foot piece of pipe is cut into 1/3 foot sections. How many sections of pipe are there?
A) 20
B) 24
C) 30
D) 36
To join a fitness club there is a $30 joiner fee and a $12 monthly fee. Write an equation in slope intercept form that models this situation.
Tymere says that 7/10 × 7/10 equals 49/10. Which of the statements below is true?
Taxicabs downtown charge a flat fee of $2.50, plus a state tax of $0.50, plus $0.50 for each 1/5 mile they travel with a passenger.
Explain how you would write 1/5 mile as a fraction with 10 in the denominator, a fraction with 100 in the denominator, and as a decimal.
Final answer:
To convert 1/5 mile to other forms, it can be represented as 2/10 when the denominator is 10, 20/100 when the denominator is 100, and 0.2 as a decimal.
Explanation:
To convert 1/5 mile into a fraction with 10 in the denominator, multiply both the numerator and the denominator by 2 to get 2/10. To get a fraction with 100 in the denominator, multiply both the numerator and the denominator of 1/5 by 20 to get 20/100. As a decimal, 1/5 is equivalent to 0.2 because 1 divided by 5 equals 0.2.
Dennis is thinking of two number. The only common factors of the number are 1 and 3.Thier first common multiple is 18.One of the number is 9. What is the other number?
Final answer:
Dennis's other number, considering the conditions of only having 1 and 3 as common factors and 18 as the least common multiple with 9, is 6.
Explanation:
To solve the problem regarding Dennis's numbers, it's crucial to understand the conditions provided: the numbers only share common factors of 1 and 3, one of the numbers is 9, and their first common multiple is 18. To find the other number, knowing one of the numbers allows us to apply the rule of least common multiples (LCM). Since 9's factors are 1, 3, and 9, and the LCM with the other number is 18, this other number must be divisible by itself and 3 but not be a multiple of 9 to maintain the unique common factors condition. The only number that satisfies the condition in which 18 is the LCM and shares only 1 and 3 as common factors with 9, would be 6, since 18 is the smallest number that both 9 and 6 can divide into without other common multiples.
60 out of 300 is what percent?
60 is 20% of 300.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Let x% be a number such that
x% of 300 is 60
This forms an equation in one variable which can be solved by transposition.
[tex]x/100\times 300=60[/tex]
Simplifying it to calculate value of x.
On multiplying 100 both sides,
[tex]300x=6000[/tex]
On dividing 300 both sides,
x=20%
Thus, 20% of 300 is 60.
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How does the volume of the cylinder compare to the volume of the cone
the jacksons went camping in a state park.One of the tents they took is shown . What is the volume of the tent.
The volume of the Jacksons' camping tent is 94.5 cubic feet. To calculate the volume, you multiply the dimensions: height (3.5 ft) by length (6 ft) by width (4.5 ft).
Explanation:The formula for calculating the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
The length (l) of the tent is 6 feet, the width (w) is 4.5 feet, and the height (h) is 3.5 feet.Substitute these values into the formula: V = 6 ft * 4.5 ft * 3.5 ft.Multiply the values together: V = 94.5 cubic feet.The volume of the tent is determined by multiplying its length, width, and height. In this instance, the Jacksons' tent has a volume of 94.5 cubic feet, providing ample space for their camping needs. Understanding the volume of a three-dimensional object is essential for assessing its capacity and ensuring it meets the requirements of its intended use.
Complete Question:
The Jacksons went camping in a state park. One of the tents they took is shown, tent size in the attached picture 3.5 ft high, 6 ft long and 4.5 ft wide. What is the volume of the tent?
Wolfgang wants to enlarge a picture he developed. Which factor listed below would scale up (enlarge) his picture the most if he used it to multiply its current dimensions? 7/8 14/14 1 4/9 3/2
Final answer:
The factor that would scale up Wolfgang's picture the most is 1 4/9.
Explanation:
The factor that would scale up Wolfgang's picture the most is 1 4/9.
To find the scale factor, we compare the given factors: 7/8, 14/14, 1 4/9, and 3/2.
Out of these options, 1 4/9 would enlarge the picture the most when used to multiply its current dimensions.
Chick fil a prints out a free sandwich coupon receipt every 7 receipts. What is the probability of not getting a coupon receipt
jackie says that if a solid figure cannot roll,then it has faces.is jackie correct?
Answer:
Yes, Jackie's answer would be correct
which numbers are rational? select all that apply. A. pi B. √50 C. 2.3 D. √144
Answer:
C and D
Step-by-step explanation:
2.3 (repeating) repeats itself over and over again into infinity.
pi goes on into infinity.
Juan has a box that is filled with toys. The box is 3 1/2 feet long,6 feet wide ,and 3 feet high. What is the volume and surface area of a box.
You are having a discussion about sequences with your classmate. She insists the the sequence 2,3,5,8,12 must be either arithmatic or geometric. Is she correct or incorrect? Explain.
Kevin is making a picture frame. He has. Piece of trim that is 4 feet long. How many 14-inch-long pieces can Kevin cut from the trim? How much of a foot will he have left over ————
Pls explain how u got the answer