In the given Fibonacci sequence , 8th number is 13 mad 11th number is 55 .
What is a Fibonacci Sequence?
The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
The next number is found by adding up the two numbers before it:
the 2 is found by adding the two numbers before it (1+1),the 3 is found by adding the two numbers before it (1+2),the 5 is (2+3),and so on!In a Fibonacci sequence, the number is equal to the sum of the two preceding numbers.
so the seventh number is 3+5 = 8
8th number is 5+ 8 = 13
11th number is 21+34 = 55
now the sequence becomes 0,1,1,2,3,5,8,13,21,34,55
Hence , the 8th number is 13 mad 11th number is 55.
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to the nearest cent, calculate the total cost of the recipe by finding the total cost of each of the ingredients and adding them all together. ingredients amount amount in converted units ep unit cost ($/unit) total ($) leeks 4 oz 3.00/lb yellow squash 10 oz 2.85/lb butter 1 oz 3.00/lb spinach 8 oz 2.25/lb eggs 6 ea 2.75/dozen
The total cost of the recipe is 521.875 cents
In this question, we need to calculate the total cost of the recipe by finding the total cost of each of the ingredients and adding them all together.
The ingredients amount in converted units
ep amount conversion unit cost ($/unit)
leeks 4 oz 0.25 lb 3.00/lb
yellow squash 10 oz 0.625 lb 2.85/lb
butter 1 oz 0.0625 lb 3.00/lb
spinach 8 oz 0.5 lb 2.25/lb
eggs 6 ea 0.5 dozen 2.75/dozen
First, we have to determine to total cost per ingredient.
1. 0.25 x 3.00 = $0.75 (leeks)
2. 0.625 x 2.85 = $1.78125 (yellow squash)
3. 0.0625 x 3.00 = $0.1875 (butter)
4. 0.5 x 2.25 = $1.125 (spinach)
5. 0.5 x 2.75 = $1.375 (eggs)
Now, we can add the cost per ingredient to know the total cost.
$0.75 + $1.78125 + $0.1875 + $1.125 + $1.375
= $5.21875
= 521.875 cents
Therefore, the total cost is 521.875 cents
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If two quantities are equal to the same quantity, then they are __equal__ to each other: if a = b and b = c, then __a=c
___is it either transitive or symmetrical ?
Show that the solution of the Neumann problem vều = 0 if r < R, un(R, ) = f(0) (where UN du/aN is the directional derivative in the direction of the outer normal) is u(r, 6) = Ao + r™(An cos nd + Bn sin në) B) n=1 with arbitrary Ao and 1 An focos no do, TORN-1 -TT 1 Bn = fe sin no do. TTnR7 -1 -TT
The solution of Neumann problem, ∇²u= 0 if r < R , Uₙ (R,θ) = f(θ) is u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ) with boundary conditions uᵣ (r,θ) = ∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ) and
Aₙ=∫(f(θ)cosnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]
Bₙ=∫(f(θ)sinnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]
Given that
The solution of Numann problem
∇²u= 0 if r < R , Uₙ (R,θ) = f(θ)
Use polar co-ordinates (r,θ)
uᵣᵣ + 1/r uᵣ+ 1/uᵣ (uθθ) = 0 ,0 < r< R,
0 <θ <2π and ∂u/∂r(R,θ) = f(θ) is directional derivative
r²d²u/dr² + rdu/dr + d²u/dθ² = 0
Let , r = ε⁻ᵗ , u(r(t),θ)
uₜ = uᵣ(rₜ) = - e⁻ᵗ uᵣ
uₜₜ =( - e⁻ᵗ uᵣ )ₜ = ε⁻ᵗuᵣ + e⁻²ᵗ uᵣᵣ
= r uᵣ+ r²uᵣᵣ
Thus we have, uₜₜ + uθθ = 0
Let u(t,θ) = X(t)Y(θ)
Which gives X''(t)Y(θ) + X(t)Y"(θ) = 0
X"(t)/X(t) = - Y"(θ)/Y(θ) = λ
From Y"(θ) + λ Y(θ) = 0
We get, Yₙ(θ) = aₙ cosnθ + bₙ sinnθ
λ= n² , n =0, 1, ...
With these values of λn we solve,
X"(t) - n² X(t) = 0
If n = 0 , X₀(t) = c₀t + d₀
X₀(r) = -c₀log (r) + d₀
If n not equal to 0 then
Xₙ (t) = cₙeⁿᵗ + dₙ e⁻ⁿᵗ
Xₙ(r) = cₙ(r)⁻ⁿ + dₙ (r)ⁿ
We have u₀(r, θ) = X₀(r)Y₀(θ)
= a₀ ( - c₀(log r) + d₀)
uₙ(r,θ) = Xₙ(r) Yₙ(θ)
= (cₙ r⁻ⁿ+ dₙrⁿ)(aₙ cosnθ + bₙ sinnθ)
But u must be positive at t =0
So, cₙ = 0 ; n = 0,1,2....
u₀ (r,θ) = a₀ d₀
uₙ(r,θ) = dₙ rⁿ( aₙ connθ + bₙ sinnθ)
By superposition , we can write as
u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ)
Boundary conditions gives
uᵣ (r,θ)=∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ)
the coefficients aₙ , bₙ for n ≥ 1 are determined are Fourier series for f(θ)
but a₀ is not determined from f(θ) therefore , it may take arbitrary value. By using Fourier series,
Aₙ= Integration of(f(θ)cosnθ dθ/π n R⁽ⁿ⁻¹⁾) where θ∈[-π, π]
Bₙ= Integration of (f(θ) sinnθ dθ/π nR⁽ⁿ⁻¹⁾) where θ∈[-π, π]
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Graph the composite function g(f(x))
Answer: f
Step-by-step explanation:
The domain of a composite function f(g(x)) is the set of those inputs x in the domain of g for which g(x) is in the domain of .
Math- i need help with this please help
On solving the provide question, based on the congruent triangles properties, we got to know that x= 76° and 90°.
what are congruent triangles?Congruent triangles are two triangles that are identical in terms of their size and form. The two congruent triangles remain congruent whether you rotate, flip, or flip one of them. If two triangles have the same number of sides, then their angles and congruence must match.
How can you tell whether two triangles are congruent?As a result, we can determine that two triangles are congruent if all three of their sides are equal. We also understand that if there is a side, an angle between the sides, and a third side that is congruent, the three sides are congruent. which means sides, corners, and sides.
For green -
=> x = 76° ( both side are same)
For orange -
=> x = 90°
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Joe Jan wants to receive $22,000 each year for the next 22 years. Assume a 6% interest rate compounded annually. How much must Joe invest today? (Round your answer to the nearest cent.)
If Joe deposits $264,954.31 today then he will reach his goal
Define Present Value
Finding the appropriate quantity of money to deposit today in order to ensure a specific amount of future payments is one objective of financial analysis. The target payment amount, the quantity and frequency of payments, and the interest rate all influence the present value, which is the value in today's dollars.
Given,
Joe want to receive each month = $22,000
Interest rate = 6%
number of payment = 22 years
We know, the formula of present value is
Present value = pmt * (1 - (1/ (1+r)ⁿ) ) / r
pmt = $22,000
r = 0.06
n = 22 years
Now, plug in the values
Present value = $22,000( 1 - (1/(1+0.06)²² ) / 0.06
=$22,000( 1 - (1/(1+0.06)²² ) / 0.06
≈ $264,954.311
Hence, If Joe deposits $264,954.31 today then he will reach his goal.
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Jimena purchased $24 worth of crafting supplies. The tax rate in her city is 6.25%. What is the total cost of the crafting supplies?
The total cost of the crafting supplies is $25.5. This can be find using percentage and rate concepts.
What is tax rate and percentage?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent , half of it is 50 percent , none of something is 0 percent.
Tax is the money that govt collects based on income, sales and other activities.
A tax rate is the percentage at which an individual or corporation is taxed.
In the given que,
Purchased amount = $24.
Tax rate = 6.25%
Tax paid = 24*(6.25/100)
= $1.5
So, total amount paid = $1.5 + $24
= $25.5
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Roberta took two tests. She scored 10 points more on the second test. Her average score for the two tests was 75 points. If x= her score on the first test, and y= her score on the second test, then the average is given by the formula x+y2. What did she score on the second test? She scored points on the second test. The solution is
If Roberta took two tests. She scored 10 points more on the second test. she score 70 on the second test.
How to find the number of score?Average score = (x+y)/2
he scored 10 points less on the second test than he did on the first.
y = x - 10
Replace y with x-10
(x + x - 10) / 2
(2x-10)/2
Average score on both tests is 75
(2x-10)/2 = 75
Multiply both sides of this equation by 2
2x-10 = 150
Add 10 to both sides
2x = 160
Divide both sides by 2x
x = 160/2
x = 80 (She got 80 on the first test)
He got 80 - 10 = 70 (She got 70 on the second test)
(80+ 70) / 2 = 150/2 = 75 (She got average of 75 on both tests)
Therefore she scored 70 on the second test is your solution.
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Can someone check if I did this one right? I’m not sure if I graphed it right or not.
Answer:
All Correct! The corinates on the graph are all graphed in the correct position.
Answer:
Yes, you are correct.
Step-by-step explanation:
the orthogonal projection y of y onto a subspace w can sometimes depend on the orthogonal basis for w used to compute y. True/False ?
False. The orthogonal projection of y onto a subspace W is never reliant on any particular basis and always depends simply on W.
The term "orthogonality" can be used when the vector space contains an inner product and is complete (i.e., wh
en it's a Hilbert space). When the range and the null space are orthogonal subspaces, the projection is said to be orthogonal.
In order to portray three-dimensional objects in two dimensions, orthographic projection (also known as orthogonal projection and analemma) is used. Every plane of the picture appears in an affine transformation on the viewing surface thanks to orthographic projection, a type of parallel projection in which all of the projection lines are orthogonal to the projection plane. An oblique projection, also known as a parallel projection in which the projection lines are not orthogonal to the projection plane, is the reverse of an orthographic projection.
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Here are the first four terms of a sequence. -1 4 9 14 Write an expression for the n th term of this sequence.
Answer:
The nth term is aₙ = 5n - 6-------------------------------------
Given sequence:
-1, 4, 9, 14, ...We observe that it has a linear increase and common difference of terms is 5:
4 - (-1) = 9 - 4 = 14 - 9 = 5So d = 5, a₁ = - 1, find the nth term:
aₙ = a₁ + (n - 1)daₙ = - 1 + (n - 1)*5 = - 1 + 5n - 5 = 5n - 6hooke's law describes an ideal spring. many real springs are better described by the restoring force (fsp)s
The mathematical expression for the work performed by the spring and the cubic term is W=3.3488J C=%3.4
The spring's and the cubic term's labor Question Parameters:
How much effort is required to compress this spring 15 cm
Take into account a spring with k = 250 N/m and q = 900 N/m3.
In general, the mathematical formula for the force is given as
(FSp)s=−kΔs−q(Δs)^3
Location of Work done
W = int dxF.
Hence
W=3.3488J
b)Where a cubic term is mathematically given as
C={0.1139}/{3.3488}
C=%3.4
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please help me!!! this is due tomorrow
Answer:
Below
Step-by-step explanation:
Multiply L number and Bottom number ...then add the R number to get the top number
? = 100 - (3*24) = 28
Select ALL expressions that are equivalent to -40x+100
4(10x+96)
20(-2x+5)
2
10(4x-10)
10(-4x+10)
Answer:
20(-2x+5)
10(-4x+10)
Step-by-step explanation:
20(-2x+5) = -40x+100
10(-4x+10) = -40x+100
You just need to expand the brackets
Determine whether the sequence is arithmetic or not .if it is,find the common difference and the next three terms given
2,5,8,11,...
2,-4,6,8,10,...
-6,-10,-14,-18,...
40,42,44,46,...
1.2,1.8,2.4,...
1,5,9,13,.
Therefore the common difference in this AP series is 4 and the next 3 terms are 1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.
Arithmetic sequences are what?Rows with a defined pattern, in which the difference between two consecutive terms is equal and fixed, are referred to as arithmetic sequences and series, also known as rows and counting series. In other words, by adding a fixed integer to the previous term, each term in the arithmetic arrangement is obtained from the previous term. To put it another way, every term in the arithmetic series (except from the first term) is obtained by adding a specific integer to the term that comes before it.
Here,
This mathematical sequence can be written as follows:
A, A+D, A+2D, A+3D, A+4D, etc. , a+(n-1)d or
where:
First term: a
d stands for common variation.
It is stated that the arithmetic sequence formula is
a = a + (n-1)d
where
First term: a
n = the number of terms
d stands for common variation.
Common Difference
In mathematical terminology, the common difference is the difference between two words.
2, 5, 8, 11, and more problems
Answer: To determine if a row is an arithmetic sequence or not, first identify the similarities between the rows.
d = 5 - 2 d = 8 - 5 d = 11-8
d = 3.
Each of them differs by 3 points.
The following three words are then 2, 5, 8, 11, 11+3, 11+6, 11+9 or 2, 5, 8, 11, 14, 17, and 20.
Issues 2, 4, 6, 8, and 10 exist.
Answer:
d = -4 - 2 = -6
d = 6 - (-4) = 10
It does not contain arithmetic sequences because there is no common difference.
Challenge: -6, -10, -14, -18,...
Answer:
d = -10 - (-6) = -4
d= -14 - (-10) = -4
d= -18 - (-14) = -4
There is a -4 difference between them all.
The following three terms are then 6, 10, 14, 18, -18, -18 + (-4), -18 + (-8), -18 + (-12), or 6, 10, 14, 18, -18, -22, -26, -30.
Issues 40, 42, 44, 46,...
Answer:
d = 42 - 40 = 2
d = 44 - 42 = 2
d = 46 - 44 = 2
All of them differ by 2 points.
The subsequent three words are either 40, 42, 44, 46, 48, 50, 52 or 40, 42, 44, 46, 46 + 2, 46 + 4, 46 + 6.
Issues: 1.2, 1.8, 2.4,...
Answer:
d = 1.8 - 1.2 = 0.6
d = 2.4 - 1.8 = 0.6
They are all separated by 0.6.
1.2, 1.8, 2.4, 2.4 + 0.6, 2.4 + 1.2, 2.4 + 1.8 or 1.2, 1.8, 2.4, 3.0, 3.6, 4.2 are the following three words.
Issues 1, 5, and 9,13
Answer:
d = 5 - 1 = 4
d = 9 - 5 = 4
d = 13 - 9 = 4
They are all divided by 4 in common.
The subsequent three terms are either 1, 5, 9, 13, 17, 21, or 25. These are 1, 5, 9, 13, 13 + 4, 13, 8, 13, and 12.
Therefore the common difference in this AP series is 4 and the next 3 terms are 1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.
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Find the average value of f(x)=−2sin(x)+5cos(x) over the interval [π,2π] .
The average value of the trigonometric equation f(x) = - 2 · sin x + 5 · cos x over the interval [π, 2π] is equal to 2 / π.
How to determine the average value of a function on a given intervalIn this question we find the definition of a trigonometric equation consisting in the sum of two trigonometric functions on a given interval [a, b], of which we must determine its average value by means of the following integral equation:
[tex]m = \frac{1}{b - a} \cdot \int\limits^b_a {f(x)} \, dx[/tex]
Where:
a - Lower boundb - Upper boundFirst, write the entire trigonometric equation and the bounds of the interval:
f(x) = - 2 · sin x + 5 · cos x, a = π, b = 2π
Second, obtain the result of the integral equation:
[tex]m = -\frac{2}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\sin x} \, dx + \frac{5}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\cos x} \, dx[/tex]
[tex]m = \frac{2}{\pi}\cdot \cos x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex] + [tex]\frac{5}{\pi}\cdot \sin x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex]
m = (2 / π) · (cos 2π - cos π) + (5 / π) · (sin 2π - sin π)
m = (2 / π) · (1 - (- 1)) + (5 / π) · (0 - 0)
m = 2 / π
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Erica wants to get in better shape so she decides to go to a gym that advertises 4 training sessions for $330. How much will it cost Erica for 24 training sessions.
Answer: 1980
Step-by-step explanation:
1. If 4 sessions is 330 dollars, and how much is 24 sessions you have to multiply 4 times 6 and the answer is 24.
2. If 4 times 6 is 24 you have to multiply 330 by 6
3. We break down 330 dollars, so 300 times 6 is 1800, i like to take away the zeros so 3 times 6 is 18 and we add 2 zeros becuase 300 has 2 zeros. And we do the same think with 30, but this time add 1 zero because 30 has 1 one zero.
4. the answer is 1800 dollars, you're welcome!
A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Al steps onto the start of the walkway and stands. Bob steps onto the start of the walkway two seconds later and strolls forward along the walkway at a constant rate of 4 feet per second. Two seconds after that, Cy reaches the start of the walkway and walks briskly forward beside the walkway at a constant rate of 8 feet per second. At a certain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle person.
The distance between the start of the walkway and the middle person is 52 feet.
It is given that a 100 foot long moving walkway moves at a constant rate 6 feet per second.
AI steps into the start of the walkway and stands this means speed of AI is 6 feet per second.
Bob steps onto the start of he walkway two second later and stolls forward along walkway 4 feet per second that means 10 feet [per seconds.
And CY reaches the starts of the walkway and walks briskly forward beside the walkway at a rate of 8 feet per second.
At the time s we gave that,
[tex]\frac{8(s-4)+10(s-2)}{2}[/tex] = 6s
[tex]\frac{8s -32 + 10s - 20}{2}[/tex] = 6s
18s - 52 = 12s
6s = 52
s = [tex]\frac{26}{3}[/tex]
At the time AI has travels,
6* [tex]\frac{26}{3}[/tex] = 52 feet.
Therefore distance between the start of the walkway and the middle person is 52 feet.
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Solve the system of two linear equations by the method of elimination (also called addition method). For a dependent system, give the answer in the form of an ordered pair in terms of x. (If there is no solution, enter NO SOLUTION.) x - y = -15 -3x + 3y = 45 (x, y) =?
x - y = -15 -3x + 3y = 45 (x, y) = the system of two linear equations using the method of elimination ( 5, 45).
x - y = -15
-3x + 3y = 45
written as
3x - 3y = -15
+3x + 3y = 45
6x = 30
x = 5
Substitute x = 5 into either of the linear equations to find y.
x - y = -15
5 - y = -15
y = 45
Therefore, the solution is (5, 45).
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HELP ME PLEAESEASE!! I need this done
A group of teenagers were asked whether they like the flavor of coconut and whether they watched basketball games.
The table shows the probabilities of results.
Watching basketball games and liking the flavor of coconut
(choose: "are" or "are not") independent events because the probability of a teenager from the group watching basketball games (choose: "is equal to" or "is not equal to") the probability of a teenager from the group watching basketball games given that they like the flavor of coconut.
Watching basketball games and liking the flavor of coconut "are" independent events because the probability of a teenager from the group watching basketball games "is not equal to" the probability of a teenager from the group watching basketball games given that they like the flavor of coconut.
What are independent events in probabilityIndependent events is the events which occur freely of each other. An event A is said to be independent of another event B if the probability of occurrence of one of them is not affected by the occurrence of the other.
We observe that the event of watching basketball games does not affect liking the flavour of coconut, hence they are independent events their probabilities are most likely not the same.
Therefore, we use "are" for the first statement to show the two events are independent and "is not equal to" for the probability statement.
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Edmund is designing his garden. For every yellow tulip, he plans to plant two whites lilies. Using only these two types of flower, he plans to plant 12 flowers in his garden. How many of each type of flower will Edmund plant in his garden?
Solving a system of equations we will see that Edmund will plant 4 yellow tulips and 8 white lilies.
How many of each type of flower will Edmund plant in his garden?Let's define our variables as:
x = number of yellow tulips.y = number of white lilies.We know that for each yellow tulip he will plant two white lilies, then:
y = 2x
And we also know that he wants to plant 12 flowers, so:
x + y = 12
Then we have a system of equations:
x + y = 12
y = 2x
Substituting the second equation into the first one, we will get:
x + 2x = 12
3x = 12
x = 12/3
x = 4
Then the value of y is:
y = 2x
y = 2*4 = 8
Then he will plant 4 yellow tulips and 8 white lilies.
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A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. Find P(A and B)
A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. then P(A and B) = 0.18
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
If A and B are events defined on the sample space with P(A) = 0.6 and P(BIA) = 0.3.
To find P(A and B),
we use the formula of conditional probability,
P( A and B ) = P (BIA) P(A)
P( A and B ) = 0.6 × 0.3
P( A and B ) = 0.18
Therefore, P ( A and B ) is 0.18.
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a nonprofit organization sells chances for a $50,000 classic mustang at $100 per ticket. it sells 1500 tickets and offers four prizes, summarized in the table. what are the expected winnings (or loss) for each ticket? (round your answer to the nearest cent.)
The nonprofit company charges $100 each ticket for the opportunity to win a $50,000 vintage Mustang. With four prizes and 1500 tickets sold, he expects to lose $54.53 on each one.
The chance of winning is multiplied by the bet multiplier to determine the mathematical anticipated value. Typically, expected value is estimated for a bet of one unit. To determine the predicted profit, multiply the win chance by the stake amount.
Chances of getting first prize = 1/1500
Chances of getting second prize = 1/1500
Chances of getting third prize = 1/1500
Chances of getting Fourth prize = 1/1500
Cost of one ticket = $100
Expected winning = -100 +1/1500 (56000 + 6600 + 4300 + 1300)
= -100 + 68200/1500
= - 54.53 dollars
There is an expected loss of $54.53.
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Here is a picture of the Mostar Bridge in Bosnia.The diagram shows one side of the bridge find the area of the bridge (yellow part). show your work.
The area of the bridge(yellow part) is 297.9 m².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
From the given diagram the area of the bridge is the total area of the larger rectangle - the area of a semicircle - the area of the smaller rectangle.
We know the area of a rectangle is (length×width) and the area of a semicircle is (1/2)πr².
∴ The area of the bridge is = {(34×20) - (24×6.5) - (1/2)π(12)²} m².
= {680 - 156 - 226.1} m².
= 297.9 m².
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Thomas Calculus Chapter 14 Exercise 14.5 Q15:
Find the derivative of the function at Po in the direction of u.
f(x, y, z) = xy + yz + zx , Po = (1, -1, 2), u = 3i + 6j - 2k
The answer given in the solution of this website stated 21 using the concept of limits.
However, I tried another method using partial derivatives and get the answer of 3 instead. Could anyone help check which method and answer is correct. Thanks!
Need answers quick!
P/8 is larger or equal to -5
P>=40
P>=40
P>=-13
P>=-40
Answer:
(d) P ≥ -40
Step-by-step explanation:
You want the solution to P/8 ≥ -5.
SolutionMultiply both sides of the inequality by 8.
8(P/8) ≥ 8(-5)
P ≥ -40
5. Look at the two grids below How many squares can you count in each one?
You did not copy the image with the question. Sometimes you have to screenshot or use the Snip-it app to get the image.
Amy got a part-time job working 15 hours a week $12 per hour. How much will she make each week?How many weeks per month will she need to work to cover her monthly expenses?
hmmm let's recall from https://brainly.com/question/30111897 that's she needs 625 bucks to make it monthly.
so her part-time at 15h at $12 per hour, well, that's just 15*12 = 180 bucks weekly, how many weeks she needs to work? well, 625 ÷ 180 ≈ 3.47, so pretty much 3 weeks and about 7 hours more, not quite kinda, 3 weeks and 7 hours is really 624, well if she saves a buck somewheres and get a buck that'll do it =), hmmm so one can say 3 weeks and 8 hours I guess, that's 636 bucks, to cover the 625 expenses.
As the X value of y=2x+80 the y value increases or decreases
Answer:
y value also increases
Step-by-step explanation:
As the X value (also known as the independent variable) of the equation y = 2x + 80 increases, the Y value (also known as the dependent variable) will also increase. This is because the coefficient of the X term (2) is positive, which means that for every increase in the X value, the Y value will also increase by an amount equal to twice the increase in the X value.
For example, if the X value increases from 2 to 3, the Y value will increase from 84 (which is calculated as 22 + 80) to 86 (which is calculated as 23 + 80). Similarly, if the X value increases from 3 to 4, the Y value will increase from 86 to 88, and so on.
A conical-shaped reservoir has a depth of 20 feet and a radius of 10 feet. Water is leaking out so that the surface is falling at the rate of 1/2ft/hr. Find the rate, in cubic feet per hour at which water is draining when the water is 8 feet deep. V=1/3πr2h
The rate at which water is draining when the water is 8 feet deep is calculated to be 2.54 ft³/ h
The vertex angle of the conical-shaped reservoir can be given as follows;
tan θ = R/H
Here R represents the radius and H illustrates the depth
so here we can say that the vertex angle will remain constant; therefore;
r/y = R/H
r/8 = 10/20
r = (10/20) × 8
r = 4
now for the volume, we can say;
V=1/3πr^2h
also, we can say;
r = y/2
Therefore here we will have;
V = 1/3π(y/2)^2y = 1/12 πy³
now for volume flow rate, we can determine as follows;
Q = dV/dt = 3/12πy²(dy/dt)
Q = 1/4 πy²v
Substituting the values as follows;
Q = 1/4 π(8)²(1/2)ft³/h
Q = 2.54 ft³/ h
To learn more about radius; click here:
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