The approximate population 3 years after the population started being recorded is 2584 people option (C) is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
It is given that:
The population of a community is modeled by this exponential function, where x represents the number of years since the population started being recorded:
p(x) = 2,400(1.025)×
Plug x = 3 years in the above function.
P(3) = 2400(1.025)³
P(3) = 2400x1.0768
P(3) = 2584.53 ≈ 2584 people
Thus, the approximate population 3 years after the population started being recorded is 2584 people option (C) is correct.
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2/3 + y^2/3 = 4
(-3√3, 1)
(astroid)
Differentiate both sides of
[tex]x^{2/3} + y^{2/3} = 4[/tex]
implicite with respect to x :
[tex]\dfrac23 x^{-1/3} + \dfrac23 y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]
Solve for the derivative dy/dx :
[tex]x^{-1/3} + y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = - x^{-1/3} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\dfrac{x^{-1/3}}{y^{-1/3}} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\left(\dfrac yx\right)^{1/3}[/tex]
Get the slope at the given point (-3√3, 1) :
[tex]\dfrac{\mathrm dy}{\mathrm dx}(-3\sqrt3,1) = -\left(\dfrac{1}{-3\sqrt3}\right)^{1/3} = \dfrac1{(3\sqrt3)^{1/3}} = \dfrac1{\sqrt3}[/tex]
Then the equation of the tangent line to the curve through (-3√3, 1) is
[tex]y - 1 = \dfrac1{\sqrt3}(x+3\sqrt3) \\\\ \boxed{y = \dfrac1{\sqrt3}x + 4}[/tex]
what expression is equivalent to (f + g)(4)
Answer:
Answer: The Expression (f + g)(4) is equal to f(4) + g(4).
Step-by-step explanation:
A pool is being filled with a hose. The equation y=12x represents the relationship between
the number of gallons of water in the pool (V) and the number of minutes the water runs (X). If
this relationship is represented on a graph, which ordered pair would not lie on the line?
50 POINTS NEED HELP ASAP PLS AND THANK YOU
It is observed that point (18, 206) does not lie on the line. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation is given below.
y = 12x
Where 'y' represents the number of gallons of water in the pool and 'x' represents the number of minutes the water runs.
The equation is drawn below.
From the chart, it is seen that point (18, 206) doesn't lie on the line. Then the right choice is D.
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I need some help with y = tan(x − π/4 ) + 1
thats the graph for it hope it helps
I NEED HELP WITH THIS MATH PROBLEM!!!!!
WHICH EXPRESSION IS EQUIVALENT TO -8M-8+3M-6?
-11m-2 -5m-2
-5m-14 or -16m-3
Answer:
-5m-14
Step-by-step explanation:
-8M-8+3M-6
Add -8m and 3m, -8 + 3m = -5m
Next add negative 8 and 6, -6 + -8 = -14
Lastly, put it together, -5m -14.
Hope that helps!
Anyone know this!? Plz heppl
Answer:
-2+I nhgjkhgggggcdffdssssdddddfffyhjbnj
Share ur negativity…
Answer:
I'm almost 30,000 dollars in debt
Step-by-step explanation:
It makes me cry
A grocery store offers a cheese and fruit sampler that combines cheddar cheese that costs $8 per kilogram with kiwis that cost $3 per kilogram. How many kilograms of each were used to make a 5 kg mixture that costs $4.50 per kilogram?
Answer:
I have 1000$ i wanna buy it
Step-by-step explanation:
Answer is 2.1 kg and 2.9 kg.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=".
Given that,
Amount of cheese = $8 per kg
Amount of kiwis = $ 3 per kg
Assume
X = quantity of chees
Y = quantity of kiwi
According to the given information,
X + Y = 5 ...(i)
8X + 3Y = (5)4.50 ....(ii)
From (ii) = 3x(i),
5x = 10.5
x = 2.1 kg
Now put the value of x into (i),
y = 2.9 kg
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Find the measure of the third angle in each of the following triangles. The triangles are not drawn to scale.
a.
A triangle has two of its angles labeled 60 degrees and 60 degrees.
b.
A right triangle has the angle between the hypotenuse and one of the legs labeled 30 degrees.
a. The measure of the missing angle is
nothing. (Simplify your answer.)
b. The measure of the missing angle is
nothing. (Simplify your answer.)
Answer:
A. 60 degrees
B. 60 degrees
Step-by-step explanation:
(a)
60 degrees +60 degrees + missing angle = 180 degrees
(angle sum property of triangle)
missing angle = 180 - 120 = 60 degrees
(b)
90 degrees + 30 degrees =120 degrees +missing angle = 180 degrees
missing angle = 60 degrees
what is the inverse of g?
g(x) = 3/x+7
Given function :-
[tex]\bf \implies g(x) = \dfrac{3}{x}+7[/tex]
To find its reverse , substitute y = g(x) .[tex]\bf \implies y = \dfrac{3}{x}+7[/tex]
Interchange x and y .[tex]\bf \implies x = \dfrac{3}{y}+7[/tex]
Solve for y .[tex]\bf\implies \dfrac{3}{y}= x -7 \\\\\bf\implies y =\dfrac{3}{x-7} [/tex]
Replace y with f-¹(x) .[tex]\implies\boxed{\red{\bf f^{-1}(x) = \dfrac{3}{x-7} }}[/tex]
how do you prove that vertical angles are ⩭
Answer:
congruent
Step-by-step explanation:
If two angles are vertical angles, then they're congruent
hope it helps
mark me brainliest
What is the solution to the system -3×+4y+2z=-3 2×-4y-z=0 y=3x-13
Answer:
x=5, y=2, z=2
Step-by-step explanation:
y=3x-13
-3x+4y+2z = -3x + 4(3x-13) + 2z = 9x+2z-52 = -3
9x + 2z = 49 ... (1)
2x-4y-z = 2x-4(3x-13)-z = -10x-z+52 = 0
10x + z = 52 ... (2)
(2)*2-(1): 11x = 55 x = 5
y = 3x-13 = 15-13 = 2 y=2
z = (49-9x) / 2 = 2 z = 2
Bill is 30 years old. He has just started a new job, and he cycles to work. The
probability of having a serious accident on any given day is 10E−4
(and the days are independent of each other as far as cycling accidents are concerned). He works 250 days per year, and will work for 35 years before retiring to North Hatley–unless a cycling accident catches up with him first.
a) What is the probability that he gets through his career without a serious
cycling accident?
b) Thirty years pass. Bill continues to cycle, and has never had a serious
accident. However, the probability of accident on any given day remains 10E−4
Is the probability that he will get through his entire career without an accident the
same? If so, explain why. If not, calculate it and interpret.
Using the binomial distribution, we have that:
a) 0.4168 = 41.68% probability that he gets through his career without a serious cycling accident.
b) Considering that the probability of an accident on a given day is independent of any other day, now just the last five years are considered, thus, the probability changes and there is a 0.8825 = 88.25% probability that he will get through his entire career without an accident the same.
For each day, there are only two possible outcomes. Either there is an accident, or there is not. The probability of there being an accident on a day is independent of any other day, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
0.0001 probability of an accident on a given day, thus [tex]p = 0.0001[/tex]250 days, for 35 years, thus the number of days is [tex]n = 250(35) = 8750[/tex].Item a:
The probability is P(X = 0), thus:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8750,0}.(0.0001)^{0}.(0.9999)^{8750} = 0.4168[/tex]
0.4168 = 41.68% probability that he gets through his career without a serious cycling accident.
Item b:
The probability changes, as we consider now just five years.The number of days is now [tex]n = 250(5) = 1250[/tex].Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8750,0}.(0.0001)^{0}.(0.9999)^{1250} = 0.8825[/tex]
Considering that the probability of an accident on a given day is independent of any other day, now just the last five years are considered, thus, the probability changes and there is a 0.8825 = 88.25% probability that he will get through his entire career without an accident the same.
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Anything will help plss
Answer:
2, not rational 4,not rational 3,yes rational 5,yes rational
Step-by-step explanation:
hopefully thats correct
Anyone know the common ratio and zero term for this ?
4, 12, 36, ...
Answer:
36/12=3
12/4=3
Therefore, common ratio is 3
Tn = ar^(n-1)
T0=4*3^(0-1)
4*1/4
4/3
11(d-c)+3(c+d),when c=6,d=9
The value of 11(d-c)+3(c+d) by using the values c=6 and d=9 is 69.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 11(d-c)+3(c+d)
Now, put the values of c= 6 and d= 9 we get
11(d-c)+3(c+d)
= 11 (9- 6) + 3( 9+3)
= 11 (3) + 3 (12)
= 33+ 36
= 69
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need help 15.3+7.2 it is adding
Answer: below
Step-by-step explanation: 22.5
What is the result of 96-8? Use the model to find the answer.
00
12
32
helpp meeeee plsssss
Answer true or false
Answer:
true
Step-by-step explanation:
please mark brainiest
Your boss sends you to the hardware store to buy tie down rope. He tells you to buy the best deal. What is the savings per unit between the best deal and worst deal?
Answer:
Explain more
Step-by-step explanation:
You need to explain more like add an image or tell us how much much money is a rope.
Marcia needs to wrap a gift box that's 16 in x 18 in x 44 in.
How much wrapping paper will she need to cover the surface area of the box?
A) 1,784 in^2
B) 12,672 in^2
C) 6,336 in^2
D) 3,568 in^2
Answer:
B. 12,672 in^2
16 x 18 x 44 = 12672
Answer:
D.
Step-by-step explanation:
Factorise 3a2 (squared) - 7a
What’s the answer?
Don’t use the calculator.
Step-by-step explanation:
[tex] {3a}^{2} - 7a \\ a(3a - 7) \\ \\ \\ \\ \\ \\ hope \: it \: helps \\ stay \: safe \: healthy \: and \: happy[/tex]
whats is 2+2?
im confused pls explain
The curved surfaces area of a right circular cylinder is 264 sq. metres and its volume is 924 cu.metres. The diameter and height of the cylinder is
In a random sample of 175 community college students, the mean number of hours spent studying per week is 13.7 hours and the standard deviation is 4 hours.
Assuming the distribution of the number of hours community college students study per week is normally distributed, approximately how many of the students in the sample study between 9.7 and 17.7 hours per week?
Answer:
Approximately there are 119.47 students per week
Step-by-step explanation:
The # of students in the sample study between 9.7 and 17.7 hrs per week;
P (9.7 < x < 17.7) = P ((9.7 - 13.7)/4 < 7 < (17.7-13.7)/4)
P (-4/4 < 7 < 4/4)
P (-1 < 7 < 1)
0.8413 - 0.1587
0.6827
Therefore the # of student = n P
175 * 0.6827
119.47
Natalie is a real estate agent and earns a 3% commission on all homes she sells. She estimates that she will earn $8,250 on the next house she sells. She actually earns $9,210. What was Natalie’s estimate for the selling price of the home? What was the actual selling price of the home?
Using the percentage principle, the estimated and actual sale price of the Home are $275, 000 and $307,000 respectively.
Commission on sale = 3%Estimated commison = $8250
Let Estimated sale price = P
3% × P = 8250
0.03p = 8250
p = 8250 / 3
p = $275000
Actual commission earned = $9210
Let Actual sale price = P
3% × P = 9210
0.03p = 9210
p = 9210 / 3
p = $307,000
Therefore, the estimated and actual sale price are $275,000 and $307,000 respectively.
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Find the perimeter of the figure below. Notice that one side length is not given.
Step-by-step explanation:
Perimeter of the quadrilateral = sum of the length of all the four sides. Note: Missing side of the quadrilateral = Perimeter of the quadrilateral - Sum of the length of three sides.
7+2n=8n-5
n=?
whatsl does n equal
8n -2n=7+5
6n =12
n =2
this is the answer
PLEASE HELP ITS MATH THANK YOUUUU