There are 72 mice in Mouse Town. The population of mice in mouse town doubles every 8 months. How long ago was the population of mice less than ten?
Make brainlest ( don't remember what's it called)
Answers
aka 24 months
============================================================
Explanation:
The population follows this function
y = 72*(2)^x
where x is the number of eight-month periods and y is the population.
So if for instance we had x = 2, then it represents two periods of 8 months each, giving 2*8 = 16 months total.
Normally with timescale problems like this, negative time values do not make sense. However, having x be negative will allow us to look back in time to figure out when y < 10.
Let's see what x is when y = 10.
y = 72*(2)^x
10 = 72*(2)^x
10/72 = 2^x
0.1389 = 2^x approximately
log(0.1389) = log(2^x)
log(0.1389) = x*log(2)
x = log(0.1389)/log(2)
x = -2.8479 also approximate
-----------
If x = -2, then,
y = 72*(2)^x
y = 72*(2)^(-2)
y = 18
and if x = -3, then,
y = 72*(2)^x
y = 72*(2)^(-3)
y = 9
This means that 3 eight-month periods ago, the population was less than 10 mice.
So this is 3*8 = 24 months = 2 years.
-----------
Checking the answer:
If we were to start at 9 mice and double the population, then it goes to 18 mice. Then that doubles to 36, and so on.
Here's a table showing this process
\(\begin{array}{|c|c|} \cline{1-2} \text{Time In Months} & \text{Population}\\ \cline{1-2} \text{0} & \text{9}\\ \cline{1-2} \text{8} & \text{18}\\ \cline{1-2} \text{16} & \text{36}\\ \cline{1-2} \text{24} & \text{72}\\ \cline{1-2} \end{array} \)
The table confirms the answer of 24 months = 2 years.
The process of using logs is almost like reversing this process shown in the table.
The population of mice in Mouse Town was less than ten about 24 months ago or 2 years ago.
Given that there are 72 mice, the population of mice in mouse town doubles every 8 months.
We need to determine the when was the population of mice less than ten.
Let's assume that "t" represents the number of 8-month periods that have passed since the population of mice in Mouse Town was less than ten. We know that the population of mice doubles every 8 months.
So, if "x" is the initial population of mice when it was less than ten, then the population at "t" periods would be "\(\mathrm{x \times 2^t}\)"
Given that the current population is 72 mice, we have the equation:
\(\mathrm{72 = x \times 2^t}\)
Since we are looking for the time when the population was less than ten, we can set up the inequality:
\(\mathrm{x \cdot 2^t < 10}\)
Now, we can solve for "t":
\(\mathrm{72 = x \cdot 2^t} \\\\\mathrm{x = \frac{72} {2^t}}\)
Substitute the value of "x" into the inequality:
\(\mathrm{\frac{72}{2^t} < 10}\)
Simplifying the inequality we get,
\(\mathrm{2^t > 7.2}\)
Now, take the logarithm (base 2) of both sides to solve for "t":
t > ㏒₂(7.2)
Using a calculator, the approximate value of log2(7.2) is around 2.85.
Therefore, "t" must be greater than 2.85, but since "t" represents the number of 8-month periods, it cannot be a fraction. We round it up to 3.
So, at least 3 eight-month periods have passed since the population of mice in Mouse Town was less than ten.
To find out the number of years ago, multiply 3 by 8 months (the length of each period):
3 × 8 = 24 months
Therefore, the population of mice in Mouse Town was less than ten about 24 months ago or 2 years ago.
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Related Questions
A lighthouse is 7 miles off a straight shoreline. Fourteen miles down the coast is a restaurant where the lighthouse keeper is planning to meet his friends. If he can row at 2.7mph and walk at 4mph, where should he land, as measured from the point on the shore nearest to the lighthouse, in order to make the fastest possible time to the restaurant? Round your answer to the nearest whole number.
Answers
The lighthouse keeper should land approximately 3 miles from the point on the shore nearest to the lighthouse in order to make the fastest possible time to the restaurant.
To determine the fastest possible time for the lighthouse keeper to reach the restaurant, we need to calculate the time it takes for him to row to the shore and then walk to the restaurant. The key is to minimize the total time taken.
Let's denote the distance from the landing point to the restaurant as x miles. The time taken to row to the shore can be calculated as 7 miles divided by the rowing speed of 2.7 mph, which is approximately 2.59 hours.
The time taken to walk from the landing point to the restaurant can be calculated as (14 + x) miles divided by the walking speed of 4 mph.
To minimize the total time, we need to find the value of x that minimizes the sum of the rowing time and the walking time. So, we can set up the equation:
Total time = 2.59 hours + (14 + x) miles / 4 mph
To find the value of x that minimizes the total time, we can take the derivative of the equation with respect to x, set it equal to zero, and solve for x.
However, given that we are asked to round the answer to the nearest whole number, we can simplify the problem by considering the value of x that yields the smallest whole number total time.
By trying different values of x, we can find the value that minimizes the total time.
When x = 0, the total time is 2.59 + 14 / 4 = 6.59 hours.
When x = 1, the total time is 2.59 + 15 / 4 = 6.84 hours.
When x = 2, the total time is 2.59 + 16 / 4 = 7.09 hours.
Continuing this process, we find that the smallest whole number total time occurs when x = 3.
Therefore, the lighthouse keeper should land approximately 3 miles from the point on the shore nearest to the lighthouse in order to make the fastest possible time to the restaurant.
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ou spend 242 minutes in chemistry class each week. How many minutes will you spend in
Chemistry at the end of the school year (36 weeks)?
Answers
8712 minutes
Explanation:
242x36
how to solve −9x + 5 < 17
Answers
Answer:
x > -1 1/3
Step-by-step explanation:
-9x + 5 < 17
Subtract 5 on each side
-9x < 17
divide by -9 on each side, which causes for the greater than sign to flip because we are dividing by a negative
x > -1 1/3
1. Lukas deposited $3000 into a
savings account that earns
3.7% interest compounded
annually. What is the total
value of the account after 5
years?
Answers
slope= -3/2; passes through (-4,7)
Answers
Answer:
your very welcome!
Step-by-step explanation:
2
passes through (4,7) slope is 2
Which of the following is most likely the next step in the series?
Answers
Answer:
A) Triangle
Step-by-step explanation:
Each shape in this series has one less side than its predecessor, therefore, the triangle is next because it has one less side than the square.
The triangle is isosceles find the length h of side x in simplest radical form with a rational denominator
Answers
Answer:
x = √3
Step-by-step explanation:
Find the diagram attached
Given
Opposite = √3
Adjacent = x
Acute angle theta = 45degrees
According to SOH CAH TOA;
tan theta = opp/adj
tan 45 = √3/x
x = √3/tan45
x = 1
x = √3
Hence the value of x in its simplest radical form is √3
decide whether enough information is given to prove that $\triangle abc\cong\triangle dbe$ using the sss congruence theorem. explain. two triangles, triangle a c b and triangle d e b that share a common vertex b. point b is on the segment a d. in triangle a c b, side a c is marked with single tick, side b c is marked with double ticks and side a b is marked with three ticks. in triangle d e b, side d e is marked with single tick, side b e is marked with double ticks and side b d is marked with three ticks.put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse.you are given that $\overline{ab}\cong$ response area, $\overline{bc}\cong$ response area, and $\overline{ac}\cong$ response area. so, the triangles response area be proven congruent using the sss congruence theorem.
Answers
No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.
The SSS congruence theorem expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.
Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.
From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.
Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.
So, given triangle is proved to congruent by SAS congruency not by SSS congruency.
Hence, enough information is not given.
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HELP FAST!! What is another way to write x 7/3?
Answers
The way that the exponent illustrated as x ^7/3 can be written is 3✓x^7
How to explain the exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Expressing large numbers in terms of powers is known as an exponent. Therefore, the exponent describes the number of times a number has been multiplied by itself.
Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is written as bn. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to base multiplication when n is a positive integer; therefore, bn is the result of multiplying n bases:
In this case, it should be noted that x ^7/3 will simply be the cube root of x raised to power 7. This is illustrated as x ^7/3.
Therefore, the correct option is C.
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pls help. pls pls pls im begging youIn the sequence below, we add any two consecutive entries to get the very next entry. the last two entries are 37 and 60 in that order.the first entry is 4. how many numbers are in this sequence in all
Answers
Answer:
hi its 7
Step-by-step explanation:
There are 7 numbers in the given sequence.
Here,
The last two entries are 37 and 60 in the order.
The first entry is 4.
What is Sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Now,
First term is 4.
Last two terms are 37 and 60.
Condition is given as, we add any two consecutive entries to get the very next entry.
For find the third number from the last is as;
x + 37 = 60
x = 60 -37
x = 23
Continuing this pattern we get the sequence;
4, 5, 9, 14, 23, 37, 60
Clearly, There are 7 entries in the given sequence.
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PLSSS HELP!!!!
NEED HELP ASAP.....
I HAVE TIME LIMIT
READY TO GIVE 25 POINTS
AND BRAINLIEST
Suhana walks 30 minutes to her school everyday. Her father who is a farmer decides to buy her a bicycle.
He has a cow and a buffalo on his farm. The two animals had cost him Rs 1800 and Rs 2400 respectively. Selling the cow will fetch him a profit of 10% whereas on the buffalo he will suffer a loss of 5%
He decides to sell his buffalo. The next day, he goes to the market and completes the deal.
The bicycle which costs Rs 900 is sold by the shopkeeper for Rs 1008.
Suhana’s father deposits Rs 1200 of the remaining amount in the bank at 9% p.a. for 3yrs.
Suhana is grateful to her father and works very hard as she realizes the
sacrifices her parents make for her.
What is the amount the farmer will receive at the end of 3 years??
Answers
Answer:
i think you need apply the compound interest
What is the area in square millimeters of the yellow triangle outlined on the origami figure at the right (b = 3cm h= 1.76)
Answers
Answer:
2.64
Step-by-step explanation:
b*h=5.28
5.28/2=2.64
5
Select the correct answer from each drop-down menu.
What is the distance and midpoint between points D and E on the number line?
D
E
+++
-4-3-2 -1 0 1 2 3
distance =
midpoint =
|||||||
4
5
Reset
Next
Answers
Answer:
4.20
Step-by-step explanation:
hope this helps
Can, you help me thanks. <3
Answers
Answer:
I think the 1st one is the answer
Step-by-step explanation:
if it helpful to you give me a brainliest
Which of the following represents 3,280 written in scientific notation?
a
3.82 x 10²
b
32.8 x 10²
c
3.28 x 10³
d
328.0 x 10³
Answers
Answer:
3.28 *10^3 represents 3,280 written in scientific notation.
Town A and Town B are located at the points shown in the diagram. Mr. Peterson
wants to drive from Town A to Town B. He can choose between the route that takes
him through Towns P and Q, or the route that takes him through Town R. Each unit on
the grid equals 1 kilometer.
Answers
Answer:
To find the shorter route, we need to calculate the distances for both routes and compare them.
Route through Towns P and Q:
The distance between Town A and Town P is 3 units to the right and 5 units up, so it is √(3² + 5²) = √34 km.
The distance between Town P and Town Q is 2 units to the right, so it is 2 km.
The distance between Town Q and Town B is 4 units to the right and 4 units down, so it is √(4² + 4²) = 4√2 km.
Therefore, the total distance for this route is √34 + 2 + 4√2 km.
Route through Town R:
The distance between Town A and Town R is 5 units to the right and 3 units up, so it is √(5² + 3²) = √34 km.
The distance between Town R and Town B is 5 units to the right and 7 units down, so it is √(5² + 7²) = √74 km.
Therefore, the total distance for this route is √34 + √74 km.
Comparing the distances, we can see that:
√34 + 2 + 4√2 km ≈ 10.2 km
√34 + √74 km ≈ 12.6 km
Therefore, the shorter route is the one that goes through Towns P and Q, which is approximately 10.2 km long.
Describe two ways to find the answer. Select all that apply.
A.
Rewrite the fraction with a denominator of 100 so the numerator gives the percent. Then, divide to write the fraction as a decimal.
B.
Rewrite the fraction with a denominator of 100 so the numerator gives the decimal. Then, divide to write the fraction as a percent.
C.
Divide to find the decimal, and then divide by 100 to find the percent.
D.
Divide to find the decimal, and then write the decimal as a percent.
Answers
Answer:
A and D
Step-by-step explanation:
Which of the following is the correct graph of the compound inequality 4p + 1 >-11 or 6p +3 <39
Answers
Answer:
Option C
only there is p > -3
p < 6
Answer:
c
Step-by-step explanation:
Solve for the unknown value.
Answers
may u show me the unknown value ? Im not sure I undertsand
Answer:
where is the unknow value
Step-by-step explanation:
Use the position equation given below, where s represents the height of the object (in feet), v0 represents the initial velocity of the object (in feet per second), s0 represents the initial height of the object (in feet), and t represents the time (in seconds), as the model for the problem. s = −16t2 + v0t + s0 An aircraft flying at 900 feet over level terrain drops a supply package.
(a) How long does it take until the supply package to strike the ground? (Round your answer to three decimal places.) t = sec
(b) The aircraft is flying at 158 miles per hour. How far does the supply package travel horizontally during its descent? (Round your answer to one decimal place.) ft
Answers
Answer:
(a) 7.5 seconds
(b) The horizontal distance the package travel during its descent is 1737.8 ft
Step-by-step explanation:
(a) The given function for the height of the object is s = -16·t² + v₀·t + s₀
The initial height of the object s₀ = 900 feet
The initial vertical velocity of the object v₀\(_y\) = 0 m/s
The time it takes the package to strike the ground is found as follows;
0 = -16·t² + 0×t + 900
900 = 16·t²
t² = 900/16 = 62.25
t = √62.25 = 7.5 seconds
(b) Given that the horizontal velocity of the package is given as 158 miles/hour, we have
158 miles/hour = 231.7126 ft/s
The horizontal distance the package covers in the 7.5 second of vertical flight = 231.7126 ft/s × 7.5 s = 1737.8445 feet = 1737.8 ft to one decimal place
The horizontal distance the package travel during its descent = 1737.8 ft.
Number 5 reason +++++++
Answers
Answer:
it's reason is : given BAD =CAD
In which triangle is the value of x equal to tan−1(StartFraction 3.1 Over 5.2 EndFraction)?
(Images may not be drawn to scale.)
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle opposite to side with length 3.1 is x.
A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 5.2 is x.
Answers
The right triangle that shows the length of the two sides is 5.2 and 3.1.
It is required to find the triangle.
What is trigonometry?The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.
Given:
In trigonometry function, in a right triangle, a tangent of an angle x is equal to the ratio of the opposite side to angle x to the adjacent side to angle x.
According to given question we have:
Given that angle x will be:
\(x=tan^{-} \frac{3.1}{5.2}\)
The opposite to angle x or perpendicular = 3.1 units
The adjacent side to angle x or base angle = 5.2 units
Therefore, the right triangle that shows the length of the two sides is 5.2 and 3.1.
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Answer:
b
Step-by-step explanation:
David is a nurse, he wants to buy an apartment near his sister. Apartments in her neighborhood cost around $120,000. The bank has approved him for a loan with an interest rate of 3.95%. David is a recent graduate and needs his monthly payment to be low, he can afford to pay about $550 a month. David plans to sell the apartment or refinance the loan within five years when he knows he will be earning more money. PLEASE HELP
Answers
Answer:
Describe how anthropology challenges more commonly held notions of progress
Step-by-step explanation:
A method for determining whether a critical point is a relative minimum or maximum using concavity.
Answers
To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.
If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.
On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.
If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.
Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.
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Complete question is:
What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.
Later on in this module, you will learn how to model events by writing trigonometric functions. for now, do some research on events that are cyclical or periodic. write a discussion post about one of those events. be sure to describe the event and the period.
Answers
The events that are cyclical are:
The change of seasons each yearEarth Rotation.Moon Phases.Tides.The events that are periodic are:
Pendulum OscillationSimple harmonic motionstuning fork,, etc.What are Cyclical events?Cyclical events are known to be event that occurs in a specific order e.g. Changes in the economy.
The Events that take place only after a regular interval of time are known to be periodic event.
Therefore, the events that are cyclical are:
The change of seasons each yearEarth Rotation.Moon Phases.Tides.The events that are periodic are:
Pendulum OscillationSimple harmonic motionstuning fork,, etc.Learn more about Cyclical events from
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Which of the following numbers is a whole number? A −2 C 4.1 B 3 D \pi
Answers
Answer: B
Step-by-step explanation: A whole number is a number that is not a decimal or a fraction and is over 0.
The circumference of a circle is 5π cm. what is the area of the circle? responses 25π cm² , 25 pi, cm² 10π cm² , 10 pi, cm² 6.25π cm² , 6.25 pi, cm² 2.5π cm²
Answers
The area of circle calculated form the circumference of circle is 6.25π cm².
The circumference of circle is represented by the formula -
Circumference = 2πr, where r is the radius of the circle.
Keep the value of circumference to find the radius of circle.
5π = 2πr
Cancelling π on each side of the equation
2r = 5
r = 5/2 cm
Now, we know the area of circle is given by the formula -
Area = πr²
Keep the values of radius in the formula -
Area = π× (5/2)²
Taking square on Right Hand Side of the equation
Area = 25π/4
Performing division on Right Hand Side of the equation
Area = 6.25π cm²
Thus, the area is 6.25π cm².
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The Bem Sex Role Inventory (BSRI) provides independent assessments of masculinity and femininity in terms of the respondent's self-reported possession of socially desirable, stereotypically masculine and feminine personality characteristics Alison Konrad and Claudia Harris sought to compare northern U.S. and southern U.S. women on their judgments of the desirability of 40 masculine, feminine, or androgynous traits. Suppose that the following are the scores from a hypothetical sample of northern U.S. women for the attribute Sensitive 3 1 1 23 Calculate the mean, degrees of freedom, variance, and standard deviation for this sample
Answers
The mean for the sample is calculated by adding up all the scores and dividing by the number of scores in the sample. In this case, the sum of the scores is 28 (3+1+1+23) and there are 4 scores, so the mean is 7 (28/4).
The degrees of freedom for this sample is 3, which is the number of scores minus 1 (4-1).
The variance is calculated by taking the difference between each score and the mean, squaring those differences, adding up all the squared differences, and dividing by the degrees of freedom. In this case, the differences from the mean are -4, -6, -6, and 16. Squaring these differences gives 16, 36, 36, and 256. Adding up these squared differences gives 344. Dividing by the degrees of freedom (3) gives a variance of 114.67.
The standard deviation is the square root of the variance. In this case, the standard deviation is approximately 10.71.
the mean score for the northern U.S. women on the attribute Sensitive is 7, with a variance of 114.67 and a standard deviation of approximately 10.71. These statistics provide information about the distribution of scores for this sample.
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Therefore, the mean is 7, the degrees of freedom is 3, the variance is 187.33, and the standard deviation is 13.68 for this sample of northern U.S. women on the attribute Sensitive.
To calculate the mean, we add up all the scores and divide by the number of scores:
Mean = (3 + 1 + 1 + 23) / 4 = 7
To calculate the degrees of freedom (df), we subtract 1 from the number of scores:
df = 4 - 1 = 3
To calculate the variance, we first find the difference between each score and the mean, square each difference, and add up all the squared differences. We then divide the sum of squared differences by the degrees of freedom:
Variance = ((3-7)² + (1-7)² + (1-7)² + (23-7)²) / 3
= 187.33
To calculate the standard deviation, we take the square root of the variance:
Standard deviation = √(187.33)
= 13.68
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Find an equation for the line in the form ax+by=c, where a,b, and c are integers with no factor common to all three and a≥0 Through (1,−3), perpendicular to x+y=5 The equation of the line is (Type an equation. )
Answers
The equation of the line, in the form ax+by=c where a,b, and c are integers, with no common factor, and a≥0, is -x + y = -4.
To find the equation of a line perpendicular to x+y=5 and passing through the point (1, -3), we need to determine the slope of the given line and then find the negative reciprocal of that slope to obtain the slope of the perpendicular line. The equation x+y=5 can be rewritten as y=-x+5. Comparing this equation to the standard form y=mx+b, we see that the slope of the line is -1. The negative reciprocal of -1 is 1, so the perpendicular line will have a slope of 1. Now, we can use the point-slope form of a line to find the equation. Using the point (1, -3) and the slope 1:
y - y₁ = m(x - x₁)
y - (-3) = 1(x - 1)
y + 3 = x - 1
Rearranging the equation:
x - y = 4
Now, we can multiply the equation by -1 to have the coefficient of x as a positive integer:
-(x - y) = -4
-x + y = -4
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a survey was given to a random sample of 1900 voters in the united states to ask about their preference for a presidential candidate. of those surveyed, 1520 respondents said that they preferred candidate a. at the 95% confidence level, what is the margin of error for this survey expressed as a proportion to the nearest thousandth? (do not write
Answers
Rounding to the nearest thousandth, the margin of error for this survey, expressed as a proportion, is approximately 0.020.
To calculate the margin of error for a survey, we can use the formula:
Margin of Error = Z × √((p × (1-p)) / n)
Where:
Z represents the z-score corresponding to the desired confidence level,
p represents the proportion of respondents who preferred candidate A,
n represents the sample size.
The sample size (n) is 1900, and the proportion of respondents who preferred candidate A is 1520/1900.
p = 1520/1900
≈ 0.8
We need to find the z-score corresponding to a 95% confidence level. For a 95% confidence level, the z-score is approximately 1.96.
Substituting the values into the formula:
Margin of Error = 1.96 × √((0.8 × (1-0.8)) / 1900)
Calculating the expression inside the square root:
(0.8 × (1-0.8)) ≈ 0.16
Margin of Error = 1.96 × √(0.16 / 1900)
Calculating the square root:
√(0.16 / 1900) ≈ 0.01016
Margin of Error = 1.96 × 0.01016
≈ 0.0199
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