Answer:
c. dP/dt = (1/5)P
Step-by-step explanation:
Given that the rate of change of population with respect to time dP/dt is directly proportional to the population, P, we have
dP/dt ∝ P
dP/dt = kP
Given that dP/dt = 2 million insects per day and P = 10 million insects after 5 days, So,
2 = k × 10
k = 2/10
k = 1/5
So, dP/dt = kP
dP/dt = (1/5)P
The option C is correct
DifferentiationThe rate of change of a function with respect to the given variable.
How to get the option?The rate of change of population with respect to time is directly proportional to the population P. We have
[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} \propto P\\\\\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP[/tex]
[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t}[/tex] is 2 million insects per day and P = 10 million insects after 5 days. So
[tex]\begin{aligned} \dfrac{\mathrm{d} P}{\mathrm{d} t} &= kP\\2 &= 10k\\k &= \dfrac{1}{5} \\\end{aligned}[/tex]
Then
[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP\\\\ \dfrac{\mathrm{d} P}{\mathrm{d} t} = \dfrac{1}{5} P[/tex]
Thus, option C is correct.
More about the Differentiation link is given below.
https://brainly.com/question/24062595
Evaluate the expression x + 8/27. Evaluate the expression for x=8/9
Answer: 32/27
Step-by-step explanation:
x = 8/9
x + 8 /27
[tex]\frac{8}{9} + \frac{8}{27} \\\\\frac{8}{9} * 3 = \frac{24}{27}\\\\\frac{24}{27} + \frac{8}{27}\\\\\frac{24 + 8}{27} \\\\\frac{32}{27}[/tex]
Answer:
Substitute the value of the variable into the equation and simplify.
Exact Form:
32 /27
Step-by-step explanation:
ANSWER FAST!
The table shows the linear relationship between the number of right tickets purchased and the total cost of admission plus ride tickets at a carnival. which function can be used to find y, The total cost of attending the carnival in purchasing x ride tickets?
A. Y= 25x +8
B. Y= 8x + 25
C. Y= 8x+ 0.25
D. Y= 0.25x + 8
Answer:
c
Step-by-step explanation:
Find the length of x.
a. 33.8
b. 48.3
c. 84.3
d. 72.0
Find the slope, I don't know how though.
Answer:
slope is -2
Step-by-step explanation:
An airline claims that its average taxi time is 15 minutes, and the standard deviation is 1.4 minutes. The taxi time has a bell/mound shape distribution. On a flight with this airline, you observe that the taxi time is 18 minutes. Calculate the z score for your flight's taxi time. Round the final answer to 2 decimal places.
Answer:
The z score for your flight's taxi time is of 2.14.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
An airline claims that its average taxi time is 15 minutes, and the standard deviation is 1.4 minutes.
This means that [tex]\mu = 15, \sigma = 1.4[/tex]
On a flight with this airline, you observe that the taxi time is 18 minutes. Calculate the z score for your flight's taxi time.
This is Z when [tex]X = 18[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 15}{1.4}[/tex]
[tex]Z = 2.14[/tex]
The z score for your flight's taxi time is of 2.14.
You can convert the variate which tracks heights of trees to standard normal variate. That value of standard normal variate is called the z score and shows the area of the considered area in the plot of the standard normal distribution.
The z score for our flight's taxi time is approx 2.14286
How to convert a normal distribution variate to standard normal distribution variate?Suppose you have got a normal distribution variate with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] (let the variate is denoted by X), then we have
[tex]X \sim N(\mu, \sigma)[/tex]
To convert it to standard normal distribution with mean 0 and the standard deviation as 1 ( [tex]Z \sim N(0,1)[/tex] ), we have:
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
For the given case we have:
Let the average taxi time be tracked by random variable X, then, as the mean time is 15 minutes, and the standard deviation 1.4 minutes , thus,
[tex]X \sim N(15, 1.4)[/tex]
Converting it to standard variate:
[tex]Z = \dfrac{X - 15}{1.4}[/tex]
Since the observed taxi time was 18 minutes, thus, we have X = 18,
Getting the z score:
[tex]Z = \dfrac{18 - 15}{1.4} = \dfrac{3}{1.4} \approx 2.14286[/tex]
Thus,
The z score for our flight's taxi time is approx 2.14286
Learn more here about normal distribution here:
brainly.com/question/14989264
how much would 11 trillion divided equally amongst 300 million people be? Time sensitive question
Answer:
36666.6666667
Step-by-step explanation:
Cant really be equal
2x-1=7
Not sure how to start to solve this equation
Answer:
x equals 4. 2x4 is 8-1equals 7
Answer: x=4
Step-by-step explanation: 2x−1=7
2x−1+1=7+1
2x/2=8/2
x=4
Gabrielle's age is three times Mikhail's age. The sum of their ages is 84. What is Mikhail's age?
Answer: 21
Step-by-step explanation:
84 divided by 4 = 21 since grabielle is 21, and then mikhail is gonna be 3 times more so it’s gonna be 63
Answer:
Mikhail=21
Gabrielle=63
Step-by-step explanation:
G=3M
G+M=84
G=84-M
3M=84-M
4M=84
M=21
G=63
Simplify (0.24) × (-0.15)
Answer:
0.036
Step-by-step explanation:
Answer:
0.24 x 0.15 = 0.036
Step-by-step explanation:
First ignore the decimal points so you have 24*15 = 360.
You have to start at the right, and move the decimal point 4 places. So, you get 0.036. Pls give brainliest.
Find Principal when Time = 5 years, Interest - $ 500; Rate = 5%
Answer:
P = $2,000
Step-by-step explanation:
Interest = Principal x Rate x Time
500 = P(.05)(5)
500 = .25P
P = 500/.25
P = 2000
Find the slope and y-intercept of equation y= 10x + 18
Answer:
slope is 10
y-intercept is 18
Step-by-step explanation:
The slope and y-intercept in y = 10x + 18 are 10 and 18 respectively.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given a line in slope-intercept form which is y = 10x + 18.
We know in y = mx + b, slope = m, and y-intercept = b.
∴ In y = 10x + 18.
Slope = 10 and y-intercept = 18.
learn more about lines and slopes here :
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Which property is used in the first step to solve this equation
4(x-6)=5
4x-24 = 5
4x= 29
x=29/4
Answer:
Distributive property
Step-by-step explanation:
4/5×5/6 can you help me
Answer:
2/3
Step-by-step explanation:
4/5*5/6 =2/3
please mark
Answer:
2/3
(Decimal Form : 0.6)
Step-by-step explanation:
There are 450 student at a school if each classroom codes 30 students How many classrooms are Needed at the school
Answer:
15 rooms are needed at the school
Step-by-step explanation:
Solve:
Divide 450 (the number of students) by 30 (the number of students per classroom)
450/30= 15
Check your work:
30*15= 450
Hope this helps!
Lavilla is a famous resort in Italy. All of its rooms are always booked in the winter season. On average, 2800 skiers come to the resort every week (7 days). On average, skiers stay in Lavilla for 4 days. Each skier spends $40 daily in local restaurants. Question 1 (1 point) The average number of skiers in Lavilla is: _____________ [skiers].
Answer:
The average number of skiers in Lavilla are 1,600 skiers
Step-by-step explanation:
The number of skiers that come to Lavilla on average each week = 2,800 skiers
The number of days each skier stays in Lavilla = 4 days
The amount each skier spends in local restaurants daily = $40
According to Little's Law, we have;
L = λ·W
Where;
L = The average number of skiers in Lavilla
λ = The effective arrival rate of the skiers = 2,800 skiers per week arrive
W = The number of days each skier stays at Lavilla = 4 days = 4/7 week
The average number of skiers in Lavilla, 'L', is therefore, given as follows;
L = 2,800 skiers/weel × (4/7) week = 1,600 skiers
The average number of skiers in Lavilla, L = 1,600 skiers
who wants a slushie ?
Answer:
i want a slushie what's your favorite slushie flavor
What is the leading coefficient of the polynomial f(c) defined below? need help asap!
Answer: 7
Step-by-step explanation:
The leading coefficient is the number before the term with the highest power in your polynomial. The coefficient is just a number or constant that is before a variable in your expression.
In this case, the highest degree in this polynomial is five. If we look at the coefficient of that term, we see that it is seven.
put a digit in the gap, such that the answer is a whole number 10x + 11 = 144
Answer:
13.3 or 13
Step-by-step explanation:
10x+11=144
10x=144-11
10x=133
x=133/10
x=13.3
SOMEONE HELP I'LL MARK CORRECT ANSWER BRAINLY
Answer:
B
Step-by-step explanation:
5r+r= what dose this equal
Answer:
Step-by-step explanation:
5
How do you determine if a function is even, odd, or neither
Answer:
You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.
Step-by-step explanation:
The next day the gas tank in dad’s car holds 24 gallons. The gas tank in mom’s truck holds 50% less than that. How much gas does the truck’s tank hold?
24 gallons * 50%
24 gallons * .5
=12
24-12
= 12
thy answer is 12 .
Answer:
Mom's truck would hold 12 gallons.
Step-by-step explanation:
If you take 24 and divide it into 2 parts you would get your answer because 50% would be half of the whole number of that makes any sense
SOLVE: 3x+4y = 18 and -2x+4y = 8
Answer:
1, if solved for x = 6 - 4y/3 & y = 9/2 - 3x/4
2, x = -4 + 2y & y = 2 + x/2
Step-by-step explanation:
convert the following equation into standard form Y equals negative 7X over 8 +4
9514 1404 393
Answer:
7x +8y = 32
Step-by-step explanation:
Clear fractions and add the opposite of the x-term.
y = -7x/8 +4
8y = -7x +32 . . . . . multiply by 8
7x +8y = 32 . . . . . .add 7x
WORTH 20 POINTS!! HELP PLEASEE
The function g(t) = - 16t2 + vt + h represents the height of an object, g, in feet, above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet.
A model rocket is launched off the ground at an initial velocity of 80 feet per second.
Part B: What domain makes sense for the function in this context?
1. all positive numbers
2. 0 ≤ t ≤ 100
3. 0 ≤ t ≤ 5
4. all real numbers
Answer:
Step-by-step explanation:
g(t) = -16t² + vt + h
"rocket is launched off the ground at an initial velocity of 80 feet per second"
v = 80
h = 0
g(t) = -16t² + 80t
:::::
The roots of -16t² + 80t are t=0 and t=5. In other words, the rocket hits the ground after 5 seconds.
Domain: 0 ≤ t ≥ 5
Expand this expression
.-(-5+ +12)
Answer:
-(-5+12)
opening bracket
-1×-5=5
-1×+12=-12
5+12=17
Answer: = -7
Step-by-step explanation:
you have to remove the + sign and the period and your answer will be -7
Marks car get 32 mpg. He is planning a road trip from Miami to Atlanta. he plans to drive 200 miles. the first day and 480 the next. How many more gallons will he use the second day compared to the first.
Answer:8.75 gallons
Step-by-step explanation:
well first his car drives 32 mpg, so with this info you divide 200 by 32.Which is 6.25 gallons.Then do the same with 480,480 divided by 32 which is 15 gallons.subtract it 15-6.25 which is 8.75.8.75 more gallons is the answer.
What is the value of x in the equation -2 = 5x + 3
Answer:
-1
Step-by-step explanation:
someone help whats the work for what is 107% of 150
Answer:
If it's 107% of 50 the answer would be 53.5
If it's 107% more than 50 it would be 103.5
Step-by-step explanation:
107% of 50 is 53.5
50 × 107% = 53.5
50 × 107% = 53.5
+50
--------
103.5
Answer:
160.5
Step-by-step explanation:
you but 107% 150 = what it well give you the answer
Solve for a 4/a+4= -1/a+9
Answer:
a = -8
Step-by-step explanation:
4/a + 4 = -1/a + 9
-1(a + 4) = 4(a + 9)
-1a - 4 = 4a + 36
-5a - 4 = 36
-5a = 40
a = -8