Answer:
The estimated size of the population in 10 days is of 1372 mosquitos.
Step-by-step explanation:
Population after t days:
The population after t days is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
P(0)=574.
So
[tex]P(t) = 574e^{rt}[/tex]
P'(0)=50
[tex]P^{\prime}(t) = 574re^{rt}[/tex]
Since P'(0)=50
[tex]574r = 50[/tex]
[tex]r = \frac{50}{574}[/tex]
[tex]r = 0.0871[/tex]
So
[tex]P(t) = 574e^{0.0871t}[/tex]
Estimate the size of the population in 10 days
This is P(10).
[tex]P(10) = 574e^{0.0871*10} = 1372[/tex]
The estimated size of the population in 10 days is of 1372 mosquitos.
The size of the population of mosquito follows an exponential model.
The size of the population in 10 days is 1370
The given parameters are:
[tex]\mathbf{P(0) = 574}[/tex]
[tex]\mathbf{P'(0) = 50}[/tex]
An exponential function is represented as:
[tex]\mathbf{P(t) = P(0) \times e^r^t}[/tex]
So, we have:
[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]
Differentiate
[tex]\mathbf{P'(t) = 574r}[/tex]
Substitute 0 for t
[tex]\mathbf{P'(0) = 574r}[/tex]
Substitute [tex]\mathbf{P'(0) = 50}[/tex]
[tex]\mathbf{50 = 574r}[/tex]
Divide both sides by 574
[tex]\mathbf{0.087 = r}[/tex]
So, we have:
[tex]\mathbf{r = 0.087 }[/tex]
The function becomes
[tex]\mathbf{P(t) = 574 \times e^r^t}[/tex]
[tex]\mathbf{P(t) = 574 \times e^{0.087t}}[/tex]
In 10 days, t = 10.
So, we have:
[tex]\mathbf{P(10) = 574 \times e^{0.087 \times 10}}[/tex]
[tex]\mathbf{P(10) = 574 \times e^{0.87}}[/tex]
Solve
[tex]\mathbf{P(10) = 1370}[/tex]
Hence, the size of the population in 10 days is 1370
Read more about exponential functions at:
https://brainly.com/question/11487261
what are the powers of 3 through 1000? AND DONT JUST SAY A FEW I NEED ALL OF THEM
Answer:
1, 3, 9, 27, 81, 243, 729
Step-by-step explanation:
The powers of 3 are:
[tex]3^0 = 1[/tex]
[tex]3^1 = 3[/tex]
[tex]3^2 = 9[/tex]
[tex]3^3 = 27[/tex]
[tex]3^4 = 81[/tex]
[tex]3^5 = 243[/tex]
[tex]3^6 = 729[/tex]
[tex]3^7 = 2187[/tex]
And so on...
So through 1000: 1, 3, 9, 27, 81, 243, 729
Find the median of 19, 29, 36, 15, and 20. Show all the steps that you took to find your answer.
Answer:
20
Step-by-step explanation:
What is 1 divided by 1/6
Answer:
6
Step-by-step explanation:
help teacher graph only
9514 1404 393
Answer:
see attached
Step-by-step explanation:
A graphing calculator or spreadsheet program can plot these points for you. It's probably no more work to actually plot the points yourself on the given graphs than it is to type them into a program.
As you know, the x-coordinate is the horizontal distance from the y-axis. Positive is to the right.
The y-coordinate is the vertical distance from the x-axis. Positive is up.
Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both, in case one of them does not show up. From past experience, Christine knows that there is a 55% chance that Dave will not show up and a 45% chance that Mike will not show up. Dave and Mike do not know each other and their decisions can be assumed to be independent. a. What is the probability that both Dave and Mike will show up
Answer:
a) 26.79%, b) 50.42% and c) 22.79%
Step-by-step explanation:
a. What is the probability that both Dave and Mike will show up?
As decisions of showing up can be assumed to be independent, the probability will be given by
(1-0.53)(1-0.43)=(0.47)(0.57)=0.2679=26.79%
b. What is the probability that at least one of them will show up?
There are two possibilities for this to happen:
Dave shows up but Mike does not. The probability of Dave to show up is (1-0.53)=0.47 and the probability that Mike does not is 0.43. Then, as these events are independent, the probability for both of them to happen is (0.47)(0.43)=0.2021=20.21%
Mike shows up but Dave does not. The probability of Mike to show up is (1-0.43)=0.57 and the probability that Mike does not is 0.53. Then, as these events are independent, the probability for both of them to happen is (0.57)(0.53)=0.3021=30.21%
Therefore, the probability that at least one of them will show up? is 20.21%+30.21%=50.42%.
c. What is the probability that neither Dave nor Mike will show up?
As decisions of showing up can be assumed to be independent, the probability will be given by
(0.53)(0.43)=0.2279=22.79%
Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 27% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance.
(a) Find the probability distribution of X. [Hint: Let S denote a homeowner that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.27)(0.73)(0.27)(0.27) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.)
x 0 1 2 3 4
p(x) ___ __ __ __ __
(c) What is the most likely value for X?
(d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)
Answer:
a)
P(X = 0) = 0.2840
P(X = 1) = 0.4201
P(X = 2) = 0.2331
P(X = 3) = 0.0575
P(X = 4) = 0.0053
c) The most likely value for X is 1.
d) 0.2959 = 29.59% probability that at least two of the four selected have earthquake insurance.
Step-by-step explanation:
For each homeowner, there are only two possible outcomes. Either they are insured against earthquake damage, or they are not. Homeowners are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
27% of all homeowners are insured against earthquake damage.
This means that [tex]p = 0.27[/tex]
Four homeowners are to be selected at random.
This means that [tex]n = 4[/tex]
(a) Find the probability distribution of X.
This is the probability of each outcome. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.27)^{0}.(0.73)^{4} = 0.2840[/tex]
[tex]P(X = 1) = C_{4,1}.(0.27)^{1}.(0.73)^{3} = 0.4201[/tex]
[tex]P(X = 2) = C_{4,2}.(0.27)^{2}.(0.73)^{2} = 0.2331[/tex]
[tex]P(X = 3) = C_{4,3}.(0.27)^{3}.(0.73)^{1} = 0.0575[/tex]
[tex]P(X = 4) = C_{4,4}.(0.27)^{4}.(0.73)^{0} = 0.0053[/tex]
So the probability distribution is
P(X = 0) = 0.2840
P(X = 1) = 0.4201
P(X = 2) = 0.2331
P(X = 3) = 0.0575
P(X = 4) = 0.0053
(c) What is the most likely value for X?
P(X = 1) has the highest probability, so X = 1 is the most likely value.
(d) What is the probability that at least two of the four selected have earthquake insurance?
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.2331 + 0.0575 + 0.0053 = 0.2959[/tex]
0.2959 = 29.59% probability that at least two of the four selected have earthquake insurance.
find the inequality represented by the graph please helpp
Answer:
y=3/4x
Step-by-step explanation:
Consider the graph below:
What is the equation of the line in slope-intercept form?
The equation of the line is
Answer:
y=-5/4x+5
Step-by-step explanation:
The line goes down 5 for every 4 to the right, and it crosses the y-axis at (0,5).
If the Pixie Sticks cost 4.50 per pound and Nicholas spends 8.10, How many pounds did he purchase?
Answer:
Step-by-step explanation:
Nicholas has purchased 1.8 pounds of pixie sticks.
Jane has purchased 3.0 pounds of Jolly ranchers.
Step-by-step explanation:
Cost of 1 pounds of pixie sticks = $4.50
Let the number of pixie sticks = x
Total money spend on x pounds of pixie sticks = $8.10
Nicholas has purchased 1.8 pounds of pixie sticks.
Cost of 1 pounds of Jolly ranchers = $3.25
Let the number of Jolly ranchers = y
Total money spend on y pounds of Jolly ranchers = $9.75
Jane has purchased 3.0 pounds of Jolly ranchers.
Over a 10-year period, Snow City had a snowfall of 478 inches. The snowfall during the past year was 56 inches. If the variable s stands for the total amount of snow for the other 9 years, which would be a reasonable value for s? A. 0.6 inches B. 420 inches C. 730 inches O D. 11 inches
Answer:
b.
Step-by-step explanation:only reasonable answer if you are subtracting 56 and attempting to estimate to the closest value. my guess, not TOTAL aswer,
Need help finding the slope and the equation
Answer:
y=2x
Step-by-step explanation:
Slope is 2 because its increasing by 2 each time
starts at 0, 0
7a-4b - [5a-3 {b-2 (a-b) }]
Answer: -4a+5b
Hope this helps!
At Wilson High School 34 girls participate in soccer, 39 girls participate in basketball, and 13 girls participate in both soccer and basketball. How many girls participate in either soccer or basketball?
Answer:
Hello ppcarrerasx3 I am going to be your personal instructor on brainly ty for choosing us for 5 star awnsers
The correct answer is will play
It is modified to show future aspect, but is still simple.
Step-by-step explanation:
Answer:
47 in soccer and 52 in basketball
Step-by-step explanation:
2. You have a bag containing 5 red markers, 6 green markers, and 4 blue markers. You reach Into the bag, select 1 marker, replace it, and then select another marker. What is the probability
that you selected a blue marker and then a green marker?
14.3%
10.7%
73.3%
83.3%
Answer:
10.7%
Step-by-step explanation:
possibility to get a blue marker : 4/15
possibility to get a green marker: 6/15
possibility to get a blue then a green: 24/225
= 10.666666%
= 10.7%
How many degrees would an angle that
is cut from 1o/3 a circle measure
Which of the following statements explains why using a credit card is similar
to taking out a loan?
Sorry this answer has taken this long to reach you, but the correct answer is the bottom right one: "When using loans and credit cards, the amount of money paid back is usually more than the amount borrowed."
Answer:
D
Step-by-step explanation:
PLEASE HELP
Jada designed a school basement . She made 8 computer labs that were 75 square feet each. The hallway was 81 square feet . How many square feet is the basement ?
Without graphing, compare the slopes and the intercepts of the
graphs of the functions f(x) = x + 1 and g(x) = f(2x).
Answer:
graph f(x) passes through the y-axis at 1:00 whereas g(x) passes through the origin.
Acellus
Find the standard deviation of
the given data rounded to the
nearest hundredth.
3,4,5,7,10,12,15
Answer:
17.4
Step-by-step explanation:
3 + 4 + 5 + 7 + 10 + 12 + 15)/7 = 8
(3^2 + 4^2 + 5^2 + 7^2 + 10^2 + 12^2 + 15^2)/7 - 8^2 = 17.14285714
17.14285714 = 17.4
Solve by using trial and error method. 3x = 16
Answer:
here the value of x is 8
Step-by-step explanation:
16/3 = 8
A cereal box says that it now contains 25% more cereal. If it originally had 12 ounces of cereal, how much does it have now?
Answer:
15
Step-by-step explanation:
Answer:
21 ounces.Step-by-step explanation:
This is percentage increase.In order to find that, we simply do:
(100+25)% = 125%
100% = 12 ounces
125% = ?
12*125/100 = 9 ounces
Add it up to the original amount:
12+9 = 21 ounces
PLEASE HELP WITH MY MATH
Carl is attempting to find the value of x by using the side spotter therom. Carl set up the proportion 6/3 = 12/x. if carl is correct what should his answer be ? if carl is incorrect what is the correct proportion and answer
they more answers than a and b I couldn't fit them
Answer:
[tex]x = 6[/tex]
Carl is correct
Step-by-step explanation:
Given
[tex]\frac{6}{3} = \frac{12}{x}[/tex]
See attachment
Required
Is Carl correct?
Using the side spotter theorem, the proportion is:
[tex]\frac{AB}{BC} = \frac{AE}{ED}[/tex]
This gives:
[tex]\frac{6}{3} = \frac{12}{x}[/tex]
This proportion is equivalent to Carl's.
Hence, Carl is correct.
Solving further: Cross Multiply
[tex]6 * x = 12 * 3[/tex]
[tex]6 * x = 36[/tex]
Make x the subject
[tex]x = \frac{36}{6}[/tex]
[tex]x = 6[/tex]
2) The perimeter of a rectangle is 74 cm. The length of the rectangle is 5 cm less
than twice the width. Find the length and width of the rectangle.
69 is the width 133 is the length
Step-by-step explanation:
im not that sure though lol
A company has 118 employees of whom x are members of a union. How many employees are not union members?
Looking for the answer to this
Given system of linear equations are ,
x + y = 2 -3x + y = 2And we need to find the Solution of the linear equation . So let's Firstly number the equations .
[tex]\large{\red{\frak{ Given}}}\begin{cases} \sf x + y = 2\qquad ..........(i) \\\\\sf -3x + y = 2 \qquad ..........(ii) \\\end{cases}[/tex]
→ Multiplying equⁿ (i) by 3 ,
=> 3 ( x + y ) = 2*3
=> 3x + 3y = 6
→ Adding the two equations ,
=> 3x + 3y -3y + y = 6 + 2
=> 4y = 8
=> y = 8/4
=> y = 2
→ Put y = 2 in (i) ,
=> x + y = 2
=> x + 2 = 2
=> x = 2- 2
=> x = 0
★ Hence the required solution is ( 0 , 2 ) .Margo can purchase tile at a store for $0.99 per tile and rent a tile saw for $24. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores?
PLEASE HELP ME HOMEWORK DUE TONIGHT!!!
Answer:
60 tiles
Step-by-step explanation:
Make equations equal,
.99x + 24 = 1.39x
Move all terms containing x to the left side of the equation & subtact 24
-.4x = -24
Divide
x = 60
Double check:
.99(60) + 24 = 83.4
1.39(60) = 83.4
i hope this helps :)
The number of days in a month is measured in the ones.
A. True
B. False
Answer:
False
Step-by-step explanation:
It is pretty simple
Answer:
That statement is false I think
help me figure this out
Answer:
Each number matches up below. The left side is x, and the right is y.
1 ⇒ 192
2 ⇒ 384
4 ⇒ 768
6 ⇒ 1152
10 ⇒ 1920
Step-by-step explanation:
We know in 1 serving, there is 192 calories. Following this, to find the calories for 2 servings, we multiply 192 by 2.
192*2 = 384
When we know the calories but not the serving, you divide the calories by 192
768/192 = 4
royal lawncare company produces and sells two packaged products
What is 56x92.2÷3?
Answer this fast for brainliest
Plz help
Answer:
1721.06666667
Step-by-step explanation:
Answer:
1795.73333333
Step-by-step explanation:
hope this helps