Part a: Time taken to double the population of chipmunks is 5/2 months.
Part b: Population at population size; P = 200 is 50.
Explain the term average rate of population change?the country, region, or geographic area's average yearly rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and indeed the overall population for that year.Part a: Time taken to double the population of chipmunks;
P(t) = 100[1 + (0.3)t + (0.04)t²].
P(0) = 100[1 + 0 + 0] = 100
P(t) = 200 = 100 + 30t + 4t²
4t² + 30t − 100 = 0
2t² + 15t − 50 = 0
(2t − 5)(t + 10) = 0
t = 5/2
It will take 5/2 months population to double its initial size P(0).
Part b: Population at population size; P=200
P'(t) = 0 + 30 + 8t
P = 200 when t = 5/2
P'(200) = 30 + 8(5/2)
P'(200) = 30 + 20
P'(200) = 50
Thus, the instantaneous rate of growth of the population when the population size is P=200 is 50.
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The heights of seedlings are normally distributed. Given that 10% of the seedlings are taller than 15 cm and 5% are shorter than 4 cm, find the mean and standard deviation of the heights.
Answer:
Step-by-step explanation:
The normal distribution is defined by its mean and standard deviation, so if we know that the heights of the seedlings are normally distributed and we know certain percentiles of the distribution, we can find the mean and standard deviation.
We are given that 10% of the seedlings are taller than 15 cm, which means that 90% of the seedlings are shorter than or equal to 15 cm. This tells us that the 90th percentile of the distribution is 15 cm.
Similarly, we are given that 5% of the seedlings are shorter than 4 cm, which means that 95% of the seedlings are taller than or equal to 4 cm. This tells us that the 95th percentile of the distribution is 4 cm.
Since the normal distribution is symmetrical, the mean of the distribution is the value that separates the upper and lower halves of the distribution. In this case, the mean is the value that separates the lower 95% from the upper 5%, which means it is the value that is exactly halfway between the 95th and 90th percentiles.
To find the mean, we can add the 95th percentile (4 cm) and the 90th percentile (15 cm) and divide by 2:
mean = (4 + 15) / 2
= 19 / 2
= 9.5 cm
To find the standard deviation, we can use the fact that the normal distribution has the property that approximately 68% of the values fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations.
Since we know that the 95th percentile (4 cm) is 2 standard deviations below the mean and the 90th percentile (15 cm) is 2 standard deviations above the mean, we can set up the equation:
4 cm = mean - 2 * standard deviation
15 cm = mean + 2 * standard deviation
Solving for standard deviation, we get:
standard deviation = (15 cm - 4 cm) / (2 * 2)
= 11 cm / 4
= 2.75 cm
So, the mean height of the seedlings is 9.5 cm and the standard deviation is 2.75 cm.
Answer:
There are many possible ranges, including (−∞,15.051464)
and (15.051464,18.6844845)
as well as 31.5±0.6270678
(centered on the mean). Observe, in R:
> pnorm(15.051464, 31.5, 10) - pnorm(-Inf, 31.5, 10)
[1] 0.05
> pnorm(18.6844845, 31.5, 10) - pnorm(15.051464, 31.5, 10)
[1] 0.05
> pnorm(32.1270678, 31.5, 10) - pnorm(30.8729322, 31.5, 10)
[1] 0.05
In general, if you are given a small enough but otherwise arbitrary number a∈R
you can find a unique b
such that b>a
and
∫baϕ(x,31.5,10)dx=0.05,
where ϕ
is the normal density. For example, if a=10
, then b≈16.42
. Again in R:
> qnorm(pnorm(10, 31.5, 10) + 0.05, 31.5, 10)
[1] 16.42003
So your question doesn’t determine the answer uniquely: I’m free to choose the upper or lower bound of the interval or any particular point relative to those (e.g. the midpoint) arbitrarily.
If you had asked for a 95% interval, it would have been a reasonable assumption (but an assumption nonetheless) that you want an interval centered on the mode, median, or mean. But for a 5% interval, it’s not obvious that you want that — in practice it’s more likely that you want the upper tail or the lower tail.
That said, at a fundamental level, the answer is the same: use the cumulative distribution function and/or its inverse, as appropriate.
Write the equation
of the line in
Slope-Intercept
Form.
Answer: y= -2/3x + 0
Explanation: y= mx +b
Y-intercept at (o,o), so b is 0
Let's pick 2 points (-3,2) ( 0,0), so the slope is -2/3
So the equation is y=-2/3x + 0
A roller coater i at a peed of 4m/. It accelerate at a rate of 6m/. What i it velocity after 3 econd?
Therefore the solution of this question is the velocity of roller coaster after 3 second is 22 m/s
What is velocity?The rate at which an object's position is changing as perceived from a given point of view and as described by a certain unit of time is known as its velocity.
Here,
The speed of roller coaster is 4m/s
The acceleration of roller coaster is 6m/s2
So,
we have to find the velocity after 3 second
thus we use the formula v=u + at
Putting values
=> v = 4 +6*3
=> v = 4 + 18
=> v = 22 m/s
Therefore the velocity of roller coaster after 3 second is 22 m/s
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h(x) = (gof)(x) =1/(x+3) ²
Let
Which of the following could be a possible decomposition of h(x)?
Answer:
One possible decomposition of h(x) is:
h(x) = (1/x²) * (1/(1 + 3/x))
This decomposition can be obtained by applying the identity (a/b) * (1/c) = a/(b*c).
Another possible decomposition of h(x) is:
h(x) = 1/((x+3)*(x+3))
This decomposition can be obtained by applying the identity (a/b) * (c/d) = (ac)/(bd).
Note that these are just two possible decompositions of h(x) and there may be other ways to decompose the function as well. The choice of decomposition will depend on the specific context and the intended use of the function.
Step-by-step explanation:
!!PLEASE HELP!!
A bag holds 25 potatoes. If the
potatoes in the bag are split among 5
people, how many potatoes does each
person get?
Hello,
I hope you and your family are doing well!
If the potatoes in the bag are split equally among 5 people, each person will get 25 potatoes / 5 people
= 25/5
=5 potatoes.
Therefore, each person will receive 5 potatoes.
----
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Happy Holidays!
yolanda has $84 to purchase x pairs of mittens and y scarves as gifts for her relatives. a pair of mittens costs $6 and a scarf costs $4 could yolanda buy 5 pairs of mittens and scarves?
Answer:
Yes
Step-by-step explanation:
[tex]6[/tex] × [tex]5 = 30[/tex]
[tex]4[/tex] × [tex]5 = 20[/tex]
[tex]30 + 20 = 50[/tex]
[tex]84-50=34[/tex]
Yolanda can purchase 5 pairs of mittens and 5 scarves and still have $34 leftover.
Michelle pays $185.76 for a table and chair. If the actual price is $172, what is the sales tax rate?
Answer:
The sales tax is 13.72
Step-by-step explanation:
The average person uses approximately gallons of water outdoors per day
Anserw:
Say the averge water a person uses a day is 90 gallons 30% of the water is used outside a day. So that would mean around 27 gallons.
hope that helps :)
Step-by-step explanation:
Which statement best describes the relationship between changes in air pressure and wind speeds? Responses
When a high- and a low-pressure air mass are far apart, air moves quickly from high to low pressure.
When a high- and a low-pressure air mass are far apart, air moves quickly from low to high pressure.
When a high- and a low-pressure air mass are far apart, air moves quickly from low to high pressure.
When a high- and a low-pressure air mass are close together, air moves slowly from high to low pressure.
The statement that best describes the changes in air pressure and wind speed is C. When a high- and a low-pressure air mass are far apart, air moves slowly from high to low pressure.
What is the relationship between pressure and wind?The weight of air molecules pressing down on the Earth is referred to as air pressure. As you ascend from sea level into the atmosphere, the pressure of the air molecules changes. The greatest pressure exists at sea level, where the density of air molecules is greatest.
Atmospheric pressure, also known as barometric pressure, is the pressure that exists within Earth's atmosphere. The region with low pressure will always get winds from the high pressure. This means that the region of low will attract winds from the high pressure and vice versa.
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Every month, noah takes home around $2,000. He uses $1,000 to cover his share of rent, utilities, transportation, and groceries. He uses around $650 on entertainment, eating out with friends, and other incidentals. The other $350, he divides between saving for emergencies and paying his student loans. What money management strategy is noah using?.
Noah is using the 50/30/20 budgeting strategy because he is using 50% of his income for his basic needs, 30% for entertainment, and 20% for savings and debt repayment.
What is money management?Money management in mathematics is the application of mathematical principles and techniques to the management of personal or corporate money. It entails the use of mathematical tools like equations, graphs, and statistics to analyse financial data and make educated decisions about budgeting, saving, investing, and spending. Mathematicians also use probability and risk analysis to manage money by estimating the likelihood of different financial events and making decisions based on the benefits and dangers of various financial options. Overall, mathematicians' understanding of money management enables people and organisations to better manage their financial resources and reach their financial objectives.
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F(x)=1/4(0+4)(0+4)+3
The evaluation of the function would be f(x) = 7.
Step-by-step explanation:I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
What is the value of x?
Answer:
x = 3
Step-by-step explanation:
CD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is
[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BC}{AC}[/tex] ( substitute values )
[tex]\frac{x}{2.25}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )
3x = 4 × 2.25 = 9 ( divide both sides by 3 )
x = 3
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $2.05 and the cost of a large greeting card is $3.70. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get x small greeting cards and y large greeting cards?
It would cost $25.05 to buy 5 small and 4 large cards.
What is Total cost?
The total cost is the sum total of costs of individual items.
Given,
Cost of small card = $2.05
Cost of large card = $3.70
Therefore,
Total cost = total cost of small card + total cost of large cards
= 5*(2.05) + 4*(3.70)
= 10.25 + 14.8
= 25.05
Hence, It would cost $25.05 to buy 5 small and 4 large cards.
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PLEASE HELP ASAPP!!
In the figure below, isosceles triangle STU is congruent to triangle SRU.
Answer:
36
Step-by-step explanation:
[tex]m\angle TSU=36^{\circ}[/tex] using the definition of an isosceles triangle. By CPCTC, [tex]m\angle USR=36^{\circ}[/tex].
Evaluate the expression for x = 3, y=1/3 , and z = 5.
12x−3y
_______
4x−z
Answer:
5
Step-by-step explanation:
12x - 3y
------------
4x - z
Input the values provided:
12(3) - 3(1/3)
------------------
4(3) - 5
Start by simplifying the numerator and denominator expressions:
-numerator;
12(3) = 36
3(1/3) = 1
36 - 1 = 35
-denominator:
4(3) = 12
12 - 5 = 7
Then divide:
35
----
7
This will equal to 5, which is your final answer.
Hope this helps! :D
a tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. at the start of a weekend, her win ratio is exactly $\dfrac{1}{2}$. during the weekend, she plays four matches, winning three and losing one. at the end of the weekend, her win ratio is greater than $\dfrac{503}{1000}$. what's the largest number of matches she could've won before the weekend began?
The largest number of matches she could have won before are 164 matches.
What is a ratio?A ratio shows the relation between two amounts. For example, the ratio of apples to pears in a basket or the ratio of women to men in a town.
How to calculate the number of matches this player had?First represent the matches she had won, using n as a reference. This means:
[tex]\frac{n}{2n} = \frac{1}{2}[/tex]
Then, based on this let's add the current ratio:
[tex]\frac{n+3}{2n+4} = \frac{503}{1000}[/tex]
Based on this, let's solve this inequality to find out the number of matches the player won before. Follow these steps:
Cross multiply = 1000n + 3000 > 1006 n + 2012Solve this operation = 1000 - 1006 = 6 and 3000 - 2012 = 988Divide = 988 / 6 = 164.66 which can be rounded as 164Based on the previous process, the number of matches the player could have won before the weekend began was 164 matches.
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Rewrite in simplest terms 5(-9q+7)-3(5q+5)
Answer:
-60q+20
Step-by-step explanation:
With 2.4 million digital subscribers, Game Informer Magazine (ranked first) has 1150% more digital subscribers than National Geographic (ranked third). How many digital subscribers does National Geographic have?
The number of subscribers of the third-ranked Magazine is 1116,279.
What is algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Here, we have
Given
Number of digital subscribers = 2.4 million
Percentage increment = 1150%
Let x represent the number of subscribers the third-ranked magazine
The relationship between the number of subscribers of the top-ranked and third-ranked magazines is defined as follows;
2.4 million = x + 1150% of x
Convert to digits only
2,400,000 = x + 1150% * x ------- By reordering
x + 1150% * x = 2,400,000
x + 1150/100 * x = 2,400,000
x + 1.15 * x = 2,400,000
Now we Factorize
x(1 + 1.15) = 2,400,000
x (2.15) = 2,400,000
Now we Divide through by 2.15
x = 2,400,000/2.15
x = 1116,279.07
x = 1116,279
Hence, the number of subscribers of the third-ranked Magazine is 1116,279.
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Add
-1/2 + 2/7
SIMPLEST FORM!
Answer:
-3/14
Step-by-step explanation:
Step 1) Convert into -7/14 + 4/14
Step 2) -7/14 + 4/14= -3/14
(04.01 MC)
The graph of a linear function is shown.
graph of a line going through 0 comma 1 and 3 comma 3
Based on the graph, which of the following represents a solution to the equation?
a
(−3, −1)
b
(−1, −3)
c
(1, 3)
d
(3, 1)
The solution set of the function based on the graph is (3, 1). Option D
What is the solution set?We know that the solution set of a function would be obtained as the points where the graph cut the axes of the graph. The graph has to do with a system in which information is presented in the x, y coordinate system.
In this kind of system, the vertical axis is the y axis while the horizontal axis is the x axis, as such we would need to plot the data points of the graph and then try to obtain the points that would correspond to the solutions of the points on the graph.
We would now need to observe the graphs so as to be able to obtain the correct presentation of the data points that would serve as the solutions of the graph as we can see the function plotted completely here.
The line cut the y axis at y =1. If we trace this point to the point that it corresponds to in the x axis we have x = 3 and we have the required points as (3, 1).
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word problem for 3x + 5=20
Answer: A gym membership cost 3 dollars a month. There is an initial fee of $5. How many months would you need to be paying for the membership to have spent 20 dollars?
Step-by-step explanation:
3x+5=20
3x=15
x=5
5 Months
Find the perimeter of stu
Answer:
32
Step-by-step explanation:
we have to find the side of the bigger triangle by making a ratio
5/8=7/x
cross multiply
5x=7(8)
5x=56
/5. /5
x=11.2
now for the other side
5/8=8/x
5x=8(8)
5x=64
/5. /5
x=12.8
we know all three sides 11.2, 12.8 and 8 so we add them
11.2+12.8+8
24+8
32
hopes this helps
A town’s population of children increased from 376 to 421 during the past year.Which equation shows how to find the percent increase?
A. p=(421−376)/376
B. p=(421−376)/421
C. p=376/(421−376)
D. p=(376+421)/376
The percentage increase in the population of the chilrden since past year is 11.96%.
What is Percentage ?
A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
According to the question, the town's population of children increased from 376 to 421 during the past year.
So, the increase in the population of the children is-
Increase =421-376
Increase =45
Now, the percentage increase in population of the children per year is calculated as-
Percentage Increase [tex]$=\frac{\text { Increase }}{376} \times 100 \%$[/tex]
Percentage Increase [tex]$=\frac{45}{376} \times 100 \%$[/tex]
Percentage Increase [tex]$=0.1196 \times 100 \%$[/tex]
Percentage Increase [tex]$=11.96 \%$[/tex]
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ABCD is a paralleogram if m
If ABCD is a parallelogram and ∠D=57° then ∠BCD =123°
What is a parallelogram ?
A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.
Using corresponding angle property int he parallelogram we can se that the ∠D is equal to exterior ∠C (57° ) because side AD and BC are parallel
and we know ∠C + exterior ∠C will be 180°
∠BCD=180° - 57°
∠BCD =123°
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Joey is considering two bowling membership plans. The plans are detailed here. Plan 1: $35 for monthly pass and $2 fee for each bowling visit Plan 2: $10 for each bowling visit. Select the equation for plan 2.
a. y=35x+2
b. y=2x+35
c. y=10x
d. y=-10x
The equation for plan (2) is y = 10x.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the second plan costs $10 for each bowling visit.
Therefore, the total cost, y, for x bowling visit is:
y = 10x
Hence, the equation for the plan (2) is y = 10x.
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suppose you pick a point uniformly at random from the interval [0, 1]. given your point, your friend picks a point uniformly at random between 0 and your point. (a) find the joint probability distribution of the two points. (b) find the expectation of the product of the two points. (c) find the marginal distribution of the point your friend picks. (d) check that the pdf from (c) satisfies all conditions for being a pdf. (e) find the conditional distribution of your point given your friend point.
(a) The joint probability distribution of the two points will be 1/x, 0<x<1, 0<y<1
(b) The expectation of the product of the two points will be 1/6
(c) The marginal distribution of the point your friend picks will be (-1/2) lny^2
We have, X=(0,1)
Y | X=X=(0, X)
a) Let f(x,y) be the joint probability distribution of the two points will be:
f(X)=1
f(Y|X)=1/x
[tex]$$\begin{aligned}& f(x, y)=f(X) f(Y \mid X=x)=1 / x, 0 < x < 1,0 < y < x\end{aligned}$$[/tex]
b) Let E(XY) be the expectation of the product of the two points.
[tex]$$\begin{aligned}E(XY)=& \int_0^1 \int_0^x \frac{x y}{x} d y d x=\frac{1}{6} \quad \text { (Decimal : } 0.16667 \ldots \text { ) }\end{aligned}$$[/tex]
c) Let f(y) be the marginal distribution of the point your friend picks.
So, the value of f(y) will be:
[tex]$$\begin{aligned}& \mathrm{f}(\mathrm{y})= \\& \int_y^1 \frac{1}{x} d x=-\frac{1}{2} \ln \left(y^2\right)\end{aligned}$$[/tex]
d)for 0<y<1
[tex]$$\begin{aligned}& f(y) > =0 \\& \int_0^1-\frac{1}{2} \ln \left(y^2\right) d y=1\end{aligned}$$[/tex]
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which of the following is not a polynomial? a -4x+3y b p^2q-3pq^2 c 4-x d 2/y
The option that is not a polynomial is d 2/y
How to determine the option that is not a polynomialAn equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.
Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.
a. -4x + 3y this is a polynomial
k = -4 and 3
n = 1
b. p^2q - 3pq^2 this is a polynomial
k = 1 and 3
n = 2
c. 4 - x this is a polynomial
k = -1
n = 1
d 2/y this is not a polynomial
= 2y^-1
A polynomial does not have a variable in the denominator or have a negative exponents. Hence this is not a polynomial
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At a local college, only 60% of students live off campus. Of those who live off campus, 58% of those students get a part-time job. Of those who live on campus, 67% work part-time. The tree diagram shows how the college students are divided into subgroups.
What is the percentage of students who live off campus and do not have a part-time job?
42.6%
34.8%
25.2%
24.3%
The percentage of students who live off campus and do not have a part-time job is 25.2%
The correct answer option is option C
What percentage of students who live off campus and do not have a part-time job?Percentage of students who live off campus = 60%Percentage of students who live off campus and gets a part-time job = 58%Percentage of students who live on campus = 40%Percentage of students who live on campus and gets a part-time job = 67%Students who live off campus and gets a part-time job = Percentage of students who live off campus and gets a part-time job × Percentage of students who live off campus × 100
= 58% of 60% × 100
= 0.58 × 0.60 × 100
= 0.348 × 100
= 34.8%
percentage of students who live off campus and do not have a part-time job = Percentage of students who live off campus - Students who live off campus and gets a part-time job
= 60% - 34.8%
= 25.2%
Consequently, 25.2% of students live off campus and do not have a part-time job.
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two people are scuba diving. one diver is 36 feet below the surface. the other river is 44 feet below the surface. what integers represent where the divers are with respect to the surface? which diver is deeper?
The correct integers are;
For first diver, the elevation = - 36 feet
For second diver , the elevation = - 44 feet
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
One diver is 36 feet below the surface.
And, The other diver is 44 feet below the surface.
Now,
Since, One diver is 36 feet below the surface.
And, The other diver is 44 feet below the surface.
Hence, The correct integers to represent the surface are;
For first diver, the elevation = - 36 feet
For second diver , the elevation = - 44 feet
Thus, The correct integers are;
For first diver, the elevation = - 36 feet
For second diver , the elevation = - 44 feet
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A line k passes through the points (−5,−5) and (1,37). A second line h passes through the points (−3,−33) and (3,9). Is line k parallel to line h? Why or why not?
line k and second line h are not parallel lines because the have different slopes.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Where x₁ - x coordinate
y₁ - y coordinate
m - slope
A line k passes through the points (−5,−5) and (1,37).
Then Slope m = 37 + 5/ 1 + 5
m = 7
Now Write the equation as;
y + 5 = 7(x + 5)
y = 7x + 30
A second line h passes through the points (−3,−33) and (3,9).
Then Slope m = 9 + 3/ 3 + 33
m = 0.33
Now Write the equation as;
y + 33 = 0.33(x + 3)
Hence, line k and second line h are not parallel lines because the have different slopes.
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