Sydney placed 10 guppies in a fish tank she recorded the number of guppies in the tank
Answers
Answer:
[tex]g(n) = 10 * 3^{n}[/tex]
Step-by-step explanation:
Given
See attachment for table
Required
Determine the explicit formula for the table
First, we need to check if the guppies increases at arithmetic progression or geometry progression.
For arithmetic progression:
We calculate the common difference (d)
[tex]d = g(n) - g(n-1)[/tex]
Take n as 1
[tex]d = g(1) - g(1-1)[/tex]
[tex]d = g(1) - g(0)[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(0) = 10[/tex]
[tex]d = 30 - 10[/tex]
[tex]d = 20[/tex]
Take n as 2
[tex]d = g(2) - g(1)[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(2) = 90[/tex]
[tex]d = 90 - 30[/tex]
[tex]d = 60[/tex]
The two differences are not equal. So, this
For geometry progression:
We calculate the common ratio (r)
[tex]r = \frac{g(n)}{g(n-1)}[/tex]
Take n as 1
[tex]r = \frac{g(1)}{g(1-1)}[/tex]
[tex]r = \frac{g(1)}{g(0)}[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(0) = 10[/tex]
[tex]r = \frac{30}{10}[/tex]
[tex]r = 3[/tex]
Take n as 2
[tex]r = \frac{g(2)}{g(1)}[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(2) = 90[/tex]
[tex]r = \frac{90}{30}[/tex]
[tex]r = 3[/tex]
The two ratios are equal.
So, the next step is to calculate the explicit formula using n term of a geometric progression.
Because the progression starts from 0, we make use of the following formula
[tex]g(n) = g(0) * r^{n}[/tex]
Substitute values for g(0) and r
[tex]g(n) = 10 * 3^{n}[/tex]
Hence:
The explicit formula is: [tex]g(n) = 10 * 3^{n}[/tex]
Related Questions
What is the constant of proportionality in this relationship ???? Help fast !!!
Answers
Answer:
3.28
Step-by-step
(3,18.85)
(2,12.57)
18.85-12.57/3-2=3.28
PLEASE HELP :( WILL GIVE bRAINLIEST
Answers
Answer: im gonna say D srry if it wrong
Step-by-step explanation:
Answer:
answer is b because water evaporates
Which graph best represents the solution for this inequality?
Answers
Step-by-step explanation:
6|4w + 2| - 2 > 10
6|4w + 2| > 12
|4w + 2| > 2
4w + 2 > 2 or 4w + 2 < -2
4w > 0 or 4w < -4
w > 0 or w < -1.
The correct graph is the 2nd option.
41.628 divid by 1,000
Answers
Answer:
41.628
Step-by-step explanation:
i dont know how but that is what the calculator said
WILL GIVE BRIANLESST
Answers
Answer:
I would say number 2
Step-by-step explanation:
hope this helped
Answer:
B.(-1,3)
you just have to count up 6 points above from where the first car is parked,once you count up 6 thats where the second car parked.
hope that helped you out:)
please mark me brainiest
pls help asap no trolls!!
Answers
Answer:
w= 1
x = 6
Step-by-step explanation:
Congruent Triangles
When two triangles are determined to be congruent, their side lengths and angles have the same measure.
We are given the condition that triangles FGH and ABC are congruent. This implies that sides FH and AC have the same measure, or, equivalently:
x + 12 = 18
Solving:
x = 18 - 12 = 6
x = 6
Similarly, sides HG and CB have the same length, thus:
w + 45 = 46
Solving:
w = 46 - 45 = 1
w= 1
Ricardo has r minutes left on his cell-phone card. He wants to call his friend and still have 8 minutes left over to make calls later. Which expression describes the length of time he can talk to his friend?
A. 8 – r
B. 8r
C. r + 8
D. r – 8
Answers
Answer:
I would go with r - 8
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
if you subtract r by 8 then you will get the remaining minutes left on ricardo's cellphone card. Lets say r=20 so, 20-8=12. therefore, Ricardo would be able to call his friend for 12 minutes. hope this helped
find the area of the unshaded reason for these two problems
Answers
9514 1404 393
Answer:
a) 96 m²
b) 26,000 ft²
Step-by-step explanation:
The area of the unshaded region is the difference between the overall area of the rectangle and the area of the shaded region. It can also be found directly using the dimensions of the unshaded region.
a) We have the height of the right triangle, but need to know its base. The Pythagorean theorem can help with that. Let the base of the triangle be represented by x. Then ...
x² +16² = 20²
x² = 400 -256 = 144
x = √144 = 12
The area of the unshaded triangle is given by the formula ...
A = (1/2)bh
A = (1/2)(12)(16) = 96 . . . . square meters
__
b) The shaded area at upper left is a square 100 ft on a side. Its area is ...
A = s² = (100 ft)² = 10,000 ft²
The shaded area at upper right is a triangle with base and height 120 ft and 150 ft. Its area is ...
A = (1/2)bh = (1/2)(120 ft)(150 ft) = 9,000 ft²
The area of the overall rectangle is ...
A = LW = (300 ft)(150 ft) = 45,000 ft²
So, the unshaded area is ...
unshaded area = overall area - left shaded area - right shaded area
unshaded area = 45,000 ft² -10,000 ft² -9,000 ft² = 26,000 ft²
Compute the surface area of the portion of the sphere with center the origin and radius 4 that lies inside the cylinder x^2+y^2=12
Answers
Answer:
16π
Step-by-step explanation:
Given that:
The sphere of the radius = [tex]x^2 + y^2 +z^2 = 4^2[/tex]
[tex]z^2 = 16 -x^2 -y^2[/tex]
[tex]z = \sqrt{16-x^2-y^2}[/tex]
The partial derivatives of [tex]Z_x = \dfrac{-2x}{2 \sqrt{16-x^2 -y^2}}[/tex]
[tex]Z_x = \dfrac{-x}{\sqrt{16-x^2 -y^2}}[/tex]
Similarly;
[tex]Z_y = \dfrac{-y}{\sqrt{16-x^2 -y^2}}[/tex]
∴
[tex]dS = \sqrt{1 + Z_x^2 +Z_y^2} \ \ . dA[/tex]
[tex]=\sqrt{1 + \dfrac{x^2}{16-x^2-y^2} + \dfrac{y^2}{16-x^2-y^2} }\ \ .dA[/tex]
[tex]=\sqrt{ \dfrac{16}{16-x^2-y^2} }\ \ .dA[/tex]
[tex]=\dfrac{4}{\sqrt{ 16-x^2-y^2} }\ \ .dA[/tex]
Now; the region R = x² + y² = 12
Let;
x = rcosθ = x; x varies from 0 to 2π
y = rsinθ = y; y varies from 0 to [tex]\sqrt{12}[/tex]
dA = rdrdθ
∴
The surface area [tex]S = \int \limits _R \int \ dS[/tex]
[tex]= \int \limits _R\int \ \dfrac{4}{\sqrt{ 16-x^2 -y^2} } \ dA[/tex]
[tex]= \int \limits^{2 \pi}_{0} } \int^{\sqrt{12}}_{0} \dfrac{4}{\sqrt{16-r^2}} \ \ rdrd \theta[/tex]
[tex]= 2 \pi \int^{\sqrt{12}}_{0} \ \dfrac{4r}{\sqrt{16-r^2}}\ dr[/tex]
[tex]= 2 \pi \times 4 \Bigg [ \dfrac{\sqrt{16-r^2}}{\dfrac{1}{2}(-2)} \Bigg]^{\sqrt{12}}_{0}[/tex]
[tex]= 8\pi ( - \sqrt{4} + \sqrt{16})[/tex]
= 8π ( -2 + 4)
= 8π(2)
= 16π
Alex has a collection of cards: 4 are black, 2 are blue, 3 are white, and 1 is brown. What is the probability that he will pick a black card twice without replacement?
Answers
what is 9/10 ÷ 3/5 will give brainlist
Answers
Answer:1.5
Step-by-step explanation:
4x + 2y = 4
Is y a function of x?
Answers
Rewrite the function using algebra to get this:
y = -x + 2
That forms an equation of a line whose slope is -2 and whose y-intercept is 2
Help please with number 11
Answers
Answer:
No
Step-by-step explanation:
The triangles are not similar since triangle B has an angle (18 cm) that does not correspond to 10, unlike the other angles which you can get by multiplying 3/2.
The answer Is A. 6cm,8cm,10cm
19. Which property of equality is illustrated below?
If 7+9= 11 +5 and 11 + 5 = 16, then 7+9 = 16
A. Transitive
B. Substitution
C. Reflexive
D. Symmetric
Answers
abraham has 16 blue marbles and 18 rwd marbles. if he wamts to place them in identical groups without any marbles left over
Answers
Answer:
If Abraham divides them into 2 separate groups, he should have 17 marbles on each group.
Step-by-step explanation:
4. Kiran's uncle is 54 years old. He is 8 years older than three times Kiran's age. Find Kiran's age,
Answers
Kiran's age = x
Uncle's age = 54
Also,
Uncle's age = 8 + 3x
Now,
8 + 3x = 54
3x = 54 - 8
3x = 46
x = 46/3
x = 15.33
x = 15 (rounded)
Wang Yan drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed. What is the approximate average fuel consumption rate, between the 100^\text{th}100
th
100, start superscript, start text, t, h, end text, end superscript kilometer and the 400^\text{th}400
th
400, start superscript, start text, t, h, end text, end superscript kilometer?
Answers
Answer:
Step-by-step explanation:
5/6 liters
Answer:
5/6
Step-by-step explanation:
khan
inverse laplace of L^-1 {5s/s^2 + 3s - 4}
Answers
Answer:
[tex]e^t+e^{-4t}[/tex]
Step-by-step explanation:
We have to simplify the original function using partial fraction, hence:
[tex]\frac{5s}{s^2+3s-4} =\frac{5s}{(s-1)(s+4)}\\\\=\frac{A}{s-1}+\frac{B}{s+4}\\\\Therefore:\\\\\frac{A(s+4)+B(s-1)}{(s-1)(s+4)}=\frac{5s}{(s-1)(s+4)}\\\\Eliminating\ the \ denominator:\\\\A(s+4)+B(s-1)=5s\\\\substitute\ s=1:\\\\A(1+4)+B(1-1)=5(1)\\\\5A=5\\\\A=1\\\\tsubstitute\ s=-4:\\\\A(-4+4)+B(-4-1)=5(-4)\\\\-5B=-20\\\\B=4\\\\Therefore\ substituting\ A\ and\ B\ gives:\\\\\frac{5s}{s^2+3s-4}=\frac{1}{s-1}+ \frac{4}{s+4}\\\\[/tex]
[tex]From\ Laplace\ inverse:\\\\But\ L^{-1}[\frac{1}{s-a} ]=e^{at}\\\\Hence:\\\\L^{-1} [\frac{5s}{s^2+3s-4}]=L^{-1}[\frac{1}{s-1} ]+L^{-1}[\frac{4}{s+4} ]=e^{t}+4e^{-4t}\\\\L^{-1} [\frac{5s}{s^2+3s-4}]=e^{t}+4e^{-4t}[/tex]
x reduced by 13 is atleast 15
Answers
Answer:
If you need an inequality here it is, can't really tell what you're trying to ask.
x-13≤15
Step-by-step explanation:
When we are talking about AT LEAST we are talking about the minimum.
For example, if I start a party and the age requirements for the party is at least 15, that means anyone who is 15 or older can enter the party.
So in your question, it says x reduced by 13 is at least 15, so reduced basically means to minus. So we are going to have x-13.
Then you have the "is at least 15". The at least is your sign for your inequality.
For example,
At least=≤
At most=≥
So the "is at least 15" is ≤15
Plug the numbers in: x-13≤15
Factor the trinomial
x^2+12x+6^2
Answers
Answer:
(x+6)(x+6) or (x+6)^2
Step-by-step explanation:
factors of 36 that add up to 12 = 6
so (x+6)(x+6)
(can I get brainliest please)
Evaluate the following function for (3, -1):
f(x, y) = 2x – 3y + xy^2
Answers
Answer:
f(3, -1) = 12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x, y) = 2x - 3y + xy²
(3, -1) is x =3 and y = -1
Step 2: Evaluate
Substitute: f(3, -1) = 2(3) - 3(-1) + 3(-1)²Exponents: f(3, -1) = 2(3) - 3(-1) + 3(1)Multiply: f(3, -1) = 6 + 3 + 3Add: f(3, -1) = 9 + 3Add: f(3, -1) = 12In (3,-1) the first number is x and the second number is y.
Replace x and y in the equation and solve:
2x - 3y + xy^2 = 2(3) -3(-1) + (3)(-1)^2
Simplify:
6 + 3 +3 = 12
The answer is 12
A triangle has side lengths of 6, 8 and 10. Which side lengths could be possible in a similar triangle
A) 3,4, and 7
B) 13.2, 17.6, and 22
C)9,15, and 16
D) 1.2, 1.6, and 2.5
Answers
Hope this helps!!
what is 8% of 24?
im just putting this here bc it too short
Answers
Ming took a cab across town. His fare was $22, and he leaves an 18% tip. What is the total amount Ming pays the cab driver?
Answers
Answer:
$25.96
Step-by-step explanation:
Multiply the original price by the decimal value of the percentage then add that number to the original price
22*.18=3.96
3.96+22=25.96
Expand and simplify (x - 5)(x - 4)
Answers
Answer:
(x - 5) (x - 4)
x(x - 4) - 5(x -4)
x^2 - 4x - 5x - 20
x^2 - 9x - 20
Expand: x (x - 4) - 5 (x - 4)
Simplify: x^2 - 9x - 20
SOMEONE PLZ GELP WITH NUMBER ONE.
Answers
Answer:
900
Step-by-step explanation:
Each group of 3 starred angles plus the 4th angle which is an interior angle of the triangle has a total measure of 360 degrees. The sum of the measures of the three angles of the triangle is 180 degrees.
total measure of the starred angles = 4 * 360 - 180
total measure = 900 degrees
Will likes two brands of healthy breakfast cereal. In Superfiber cereal, there are 5 grams of fiber in one cup. In Fiber Oats cereal, there are 4 grams of fiber in one cup. Let x represent the number of cups of Superfiber Will ate this week and let y represent the number cups of Fiber Oats he ate this week. Which inequality represents the situation if the cereal Will ate this week contained at least 30 grams of fiber?
a)5x + 4y ≥ 30
b)4x + 5y ≥ 30
c)4x + 5y ≤ 30
Answers
Answer:
A.
Step-by-step explanation:
Answer:
a. 5x + 4y ≥ 30
Step-by-step explanation:
for edge 2020:)
Please help me answer
Answers
Answer:
No
Step-by-step explanation:
what is the answer to -6x²-x+3+5x+7
Answers
Hello!
Let's simplify step-by-step.
−6x2−x+3+5x+7
=−6x2+−x+3+5x+7
Combine Like Terms:
=−6x2+−x+3+5x+7
=(−6x2)+(−x+5x)+(3+7)
=−6x2+4x+10
Answer:=−6x2+4x+10Thank you for asking this question!
It would be greatly appreciated if you thanked me and marked me as the brainliest!
Have an amazing day.
What is the value of the expression when x=4?*
4x3 + 4x
Answers
Answer:
38
38 38 38 38 38 38 38 38okay so all you're going to do 4 * 3 + 4 * 4 what is going to give you 12 +16