Answer:
B. $580
Step-by-step explanation:
Value of the retirement fund after x years:
The value of the retirement fund after x years is given by the following function:
[tex]y(x) = 307.6(1.11)^x[/tex]
Which is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made?
This is y(6). So
[tex]y(6) = 307.6(1.11)^6 = 575.34[/tex]
Close to $580, and thus, the correct answer is given by option B.
Answer:
B. $580 is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made.
Thus it is little close to answer because actual answer is $575.34.
Determine which value best approximates the length of the arc represented by the integral ∫_0^1 √1 + [d/dx(4/x+1)]² dx.
(Make your selection on the basis of a sketch of the arc and not
by performing any calculations.)
(a) 10
(b) -5
(c) 2
(d) 4
(e) 1
Answer:
Option C
Step-by-step explanation:
From the question we are told that:
Length of arc integral
[tex]l=\int_0^1 \sqrt{1 + [\frac{d}{dx}(\frac{4}{x+1})]^2 dx}[/tex]
The Sketch is attached below
From the Graph
Approximation gives length of arc as
[tex]l=\sqrt{5}[/tex]
[tex]l=2[/tex]
Option C
Lance is selling T-shirts for $10 each and hats for $12.50 each. He wants to earn at least $400 per week to cover his expenses. Which graph best represents the number of T-shirts and hats Lance should sell to meet his goal?
Answer:
Step-by-step explanation:
A tank contains 1000L of pure water. Brine that contains 0.04kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.06kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min.
1. How much salt is in the tank after t minutes?
2. How much salt is in the tank after 60 minutes?
Answer:
1) x = [ - (12/1000)* e∧ ( - 15/1000)*t + 12/1000 ] /e∧ - (15/1000)*t
2) x = - 0,012 * ( e ∧ 0.18 + 0,012 ) / e∧-0,18
Step-by-step explanation:
1.-Quantity of salt in the tank after t minutes
The rate of change of the quantity of salt in the tank is:
dx(t) /dt = original quantity (0) + input quantity - output quantity (1)
quantity = concentration* rate Then
input quantity = 0.04 Kg/lt * 5 Lt/min + 0.06 Kg/lt * 10Lt/min = 0.2 Kg/min
+ 0.6 Kg/min = 0,8 Kg/lt
output quantity = Output concentration * rate of draining
rate of draining = 15 Lt/min
The input quantity and the output quantity occur at the same rate therefore the volume in the tank is constant 1000Lt.
output quantity = (x/1000 )*15
Plugging these values in equation (1) we get.
dx/dt = 0,8 - ( x/1000)* 15
The last one is a differential first-order equation like
x´ + P(t)*x = q(t)
and the solution is:
x*μ = ∫ q(t)*μ*dt + C
where μ is the integration factor e ∧ ∫p(t)*dt
let´s call b = -15/1000
μ = e ∧ ∫p(t)*dt = e∧∫ b*dt = e∧ b*t = e∧ ( -15/1000)*t
μ = e∧ - (15/1000)*t
Then x*μ = x * e∧ - (15/1000)*t
∫ q(t)*μ*dt = ∫ 0.8 * e∧ - (15/1000)*t*dt = 0.8 * ∫ e∧bt * dt
∫ q(t)*μ*dt = 0.8 * ( 1/b ) e∧bt = - 0,8 *( 15/1000) * e∧ ( - 15/1000)*t
∫ q(t)*μ*dt = - (12/1000)* e∧ ( - 15/1000)*t
x * e∧ - (15/1000)*t = - (12/1000)* e∧ ( - 15/1000)*t + C
Initial condition t = 0 x = 0
0 = - (12 / 1000 )* e⁰ = C
C = 12/1000
x * e∧ - (15/1000)*t = - (12/1000)* e∧ ( - 15/1000)*t + 12/1000
x = [ - (12/1000)* e∧ ( - 15/1000)*t + 12/1000 ] /e∧ - (15/1000)*t
When t = 60 min
x = [ - (12/1000)* e∧ ( - 15/1000)*12 + 12/1000 ] / e∧ - (15/1000) * 12
x = - 0,012 * ( e ∧ 0.18 + 0,012 ) / e∧-0,18
4 7/8 - 2 3/8 simplest form
Answer:
2 1/2
Step-by-step explanation:
4 7/8= 39/8
2 2/8= 19/8
39/8 - 19/8 = 20/8 = 2 4/8 = 2 1/2
Let r be the binomial random variable corresponding to the number of people that will live beyond their 90th birthday,
r ≥ 15.
We want to find
P(r ≥ 15)
using the normal approximation given 625 trials and a probability of a 4.4% success on a single trial.
Answer:
P(r ≥ 15) = 0.9943.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
625 trials and a probability of a 4.4% success on a single trial.
This means that [tex]n = 625, p = 0.044[/tex]
Mean and standard deviation:
[tex]mu = E(X) = np = 625*0.044 = 27.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{625*0.044*0.956} = 5.13[/tex]
P(r ≥ 15)
Using continuity correction, this is [tex]P(r \geq 15 - 0.5) = P(r \geq 14.5)[/tex], which is 1 subtracted by the p-value of Z when X = 14.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14.5 - 27.5}{5.13}[/tex]
[tex]Z = -2.53[/tex]
[tex]Z = -2.53[/tex] has a p-value of 0.0057
1 - 0.0057 = 0.9943
So
P(r ≥ 15) = 0.9943.
A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowing in at 4 liters per minute. The solution is mixed well and drained at 4 liters per minute. Let xx be the amount of salt, in grams, in the fish tank after tt minutes have elapsed. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution xx and the unknown concentration of incoming brine cc. dxdt
Answer:
dx/dt = 4c - 4x/15
Step-by-step explanation:
a. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution
Let c be the concentration of the incoming brine in grams per liter. Since it flows in at a rate of 4 liters per minute, the mass flow in is thus 4m.
Let x be the mass of salt present at time, t. The concentration of salt present at time, t is thus mass of salt/volume of tank = x/15. Since the well mixed solution is drained at 4 liters per minute, the mass flow out is thus 4x/15.
The net rate of change of amount of salt dx/dt = mass flow in - mass flow out
dx/dt = 4c - 4x/15
Mass of a proton: 1.007825 units
Mass of a neutron: 1.008665 units
Calculate the mass Defect of 214 N has actual mass of 14.0031 u.
Given:-
mass of proton = 1.007825 umass of neuron = 2.008625 u .Actual mass = 14.0031 uTo find:-
The mass defect.Answer:-
Mass defect arises when the mass of the atom differs from the sum of masses of nucleons . As we know that the nucleus of an atom is made up of neutrons(n) and protons (p) , and the total mass of a atom is the mass of nucleons ( protons and neutrons ) as electrons have mass very low as compared to that of n or p .
If we denote mass number by [tex]\green{A}[/tex] , then ;
[tex]\implies A = n_{\rm neutrons} + n_{\rm protons} [/tex]
Let [tex] Z[/tex] be the atomic number, then ;
[tex]\implies n_p = Z [/tex]
So, the number of neutrons will be;
[tex]\implies n_n = (A-Z) [/tex]
Therefore total mass would be ;
[tex]\implies M = m_pZ +m_n (A-Z) [/tex]
Then the mass defect would be ,
[tex]\implies\underline{\underline{\green{ \Delta M = [Zm_p + (A-Z)m_n - M ] }}} [/tex]
where ,
[tex]Z [/tex] = atomic number[tex] A[/tex] = mass number[tex] m_p [/tex] = mass of a proton[tex] m_n [/tex] = mass of a neutron_______________________________________
Now we know that the Atomic number of Nitrogen is 7(Z) and its mass number is 14(A) .
Now substitute the respective values,
[tex]\implies \Delta M = 7(1.007825) + (14-7)1.008665 - 14.0031 \\ [/tex]
[tex]\implies \Delta M = 7.054775 + 7(1.008665) - 14.00 31 [/tex]
[tex]\implies \Delta M = 7.054775 + 7.060655 - 14.0031 [/tex]
[tex]\implies \Delta M = 14.11543 - 14.0031 [/tex]
[tex]\implies \underline{\underline{\green{ \Delta M = 0.11233 \ u }}}[/tex]
Hence the mass defect is 0.11233 u .
Also this mass defect appears as energy which is responsible for the binding of nucleons together.
and we are done!
Need help finding the factor of 2y^2-2y-4
Answer:
hope it helps you............
Answer:
2(y - 2)(y + 1)
Step-by-step explanation:
Given
2y² - 2y - 4 ← factor out 2 from each term
= 2(y² - y - 2) ← factor the quadratic
Consider the factors of the constant term (- 2) which sum to give the coefficient of the y- term (- 1)
The factors are - 2 and + 1, since
- 2 × 1 = - 2 and - 2 + 1 = - 1 , then
y² - y - 2 = (y - 2)(y + 1)
Then
2y² - 2y - 4 = 2(y - 2)(y + 1) ← in factored form
Which of the following coordinates exists on the line y = 2x + 4?
A. (2, 4)
B. (1, 5)
C. (-3, -2)
D. (-1, 3)
What is the value of angle v?
Answer:
x = 5
Step-by-step explanation:
a) The third interior angle of this triangle is 180 - 20 x.
The three interior angles must sum up to 180 degrees.
Therefore, 60 + 7x + 5 + 180 - 20x = 180, or
65 + 180 - 13x = 180, or
65 - 13x = 0
Finally, 13x = 65, and so x = 5
Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'?
Answer:
The length of BC is 14 units.Step-by-step explanation:
[tex]hope \: \: it \: \: helps} \beta \alpha \infty [/tex]
The length of B'C' is 0 units.
What is translation?It is the movement of the shape in left, right, up, and down direction.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The length of AD = 5 units.
Since the rectangle translates down by 4 units,
The length of A'D' =5 units.
The width of the original rectangle is AB, which is 3 units.
Since the rectangle translates to the right by 2 units,
The width of the new rectangle = 3 units.
Now,
The length of B'C' is the same as the length of AD', which is 5 units.
Subtracting 5 units from 5 units gives us a length of 0 units.
Thus,
The length of B'C' is 0 units.
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Find the value of x° in rhombus ABCD.
Find the missing length indicated
x = 65
Step-by-step explanation:
cos theta = 25/x
cos theta = x/169
25/x = x/169
x² = 169 x 25
x = 65
The missing length x = 65, using the Pythagoras Theorem.
What is the Pythagoras Theorem?
According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
How to solve the question?In the question, we are asked to find the value of x.
In the right triangle ABC, by Pythagoras' Theorem,
AC² + BC² = AB²,
or, x² + BC² = (144 + 25)²,
or, BC² = 169² - x² ... (i).
In the right triangle ACD, by Pythagoras Theorem,
AD² + DC² = AC²,
or, 25² + DC² = x²,
or, DC² = x² - 25² ... (ii).
In the right triangle BCD, by Pythagoras Theorem,
BD² + DC² = BC²,
or, 144² + x² - 25² = 169² - x² {Substituting BC² = 169² - x² from (i) and DC² = x² - 25² from (ii)},
or, x² + x² = 169² + 25² - 144² {Rearranging},
or, 2x² = 28561 + 625 - 20736,
or, 2x² = 8450,
or, x² = 4225,
or, x = √4225 = 65.
Thus, the missing length x = 65, using the Pythagoras Theorem.
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PLEASE HELP WILL MARK BRANIEST
Answer:
1.14male studying biology
Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image ABCD.
The slope of 'D'is
Reset
Next
Il rights reserved.
Properties of Dilati...
DELL
Answer:
(D) is equal to 8 so that means that u have to divide and multiply all in one
Answer:
Reflection
Step-by-step explanation:
f(x)=3x-3
g(x) 3x^3+5
Find F(-3) and g(-2)
Answer:
f(-3) = -12
g(-2) = -19
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 3x - 3
g(x) = 3x³ + 5
f(-3) is x = -3 for function f(x)
g(-2) is x = -2 for function g(x)
Step 2: Evaluate
f(-3)
Substitute in x [Function f(x)]: f(-3) = 3(-3) - 3Multiply: f(-3) = -9 - 3Subtract: f(-3) = -12g(-2)
Substitute in x [Function g(x)]: g(-2) = 3(-2)³ + 5Exponents: g(-2) = 3(-8) + 5Multiply: g(-2) = -24 + 5Add: g(-2) = -19Answer:
f(-3) = -12
g(-2) = -19
Step-by-step explanation:
1.
f(x) = 3x - 3
One is asked to find (f(-3)), substitute (-3) into the given function (f) in place of (-3), and solve to evaluate,
f(-3) = 3(-3) - 3
Simplify,
= -9 - 3
= -12
2.
g(x) = [tex]3x^3+5[/tex]
The problem asks one to find (g(-2)), subtitute (-2) into the function in place of (x) and solve to find tis value,
g(-2) = [tex]3(-2)^3+5\\[/tex]
Remember any number raised to an exponent is equal to the base (the number that is being raised to the exponent) times itself the number of times that the exponent indicates,
[tex]=3(-8)+5\\=-24+5\\=-19[/tex]
How much would $100 invested at 8% interest compounded continuously be
worth after 15 years? Round your answer to the nearest cent.
A(t)=Poet
O A. $332.01
O B. $220.00
O C. $317.22
D. $285.67
Answer:
Step-by-step explanation:
A = [tex]pe^{rt}[/tex]
A = 100[tex]e^{.08 *15}[/tex]
A=. $332.01
The value of the investment after 15 years is $332.01.
Option A is the correct answer.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
The continuous compounding formula is given by:
[tex]A = Pe^{rt}[/tex]
Where:
A = the ending amount
P = the principal (initial investment)
e = the mathematical constant (approximately equal to 2.71828)
r = the interest rate (as a decimal)
t = the time period (in years)
Using this formula, we can find the value of the investment after 15 years:
A = 100 \times e^{0.08 \times 15} ≈ $332.01
Therefore,
The value of the investment after 15 years is $332.01.
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simplify into one fraction 8x/x-8 - 2/x-8
Answer:
- 2+8x/x
Step-by-step explanation:
See image below:)
FYI you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free
Answer:
(8x-2) / (x-8)
Step-by-step explanation:
8x/x-8 - 2/x-8
Since the denominator is the same, we can add the numerators
(8x-2) / (x-8)
1. Find the equation of variation where a varies jointly as b and c, and a = 36 when b = 3 and c = 4.
1. Find the equation of variation where a varies jointly as b and c, and a = 36 when b = 3 and c = 4.
Solution:-[tex]\sf{a = kbc}[/tex]
[tex]\sf\rightarrow{36= k(3)(4)}[/tex]
[tex]\sf\rightarrow{K= \frac{36}{12}}[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{3}}}[/tex]
Answer:-Therefore, the required equation of variations is a = 3bc.[tex]{\large{——————————————————}}[/tex]
#CarryOnMath⸙
to train for a race, you plan to run 1 mile the first week and double the number of miles each week for five weeks. How many miles will you run for the 5th week. math problem
Answer:
16 Miles
Step-by-step explanation:
For every week you simply multiply the number of miles from the previous week by 2, therefore
Week 1: 1
Week 2: 2
Week 3: 4
Week 4: 8
Week 5: 16
please help meeeeeeee
pt 4
Answer:
The answer is
[tex]2 {x}^{2} + 3x - 1 = 0[/tex]
Why? Below I explain
Step-by-step explanation:
That formula has three variables a, b and c.
So, a = 2, b = 3 and c = -1
Because the formula is written like
[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4 \times a \times c} }{2 \times a} [/tex]
Please help will mark BRAINLIEST!!!
Answer:
b, c, a
Step-by-step explanation:
In a triangle, the largest angle is opposite the longest side. The smallest angle is opposite the shortest side.
This triangle has 2 given angles, 50° and 60°.
We can find the measure of the third angle, x.
50 + 60 + x = 180
x + 110 = 180
x = 70
The three angles have measures 50°, 60°, and 70°.
The shortest side is opposite the smallest angle. That is side a.
The longest side is opposite the largest angle. That is side b.
The order from longest to shortest is
b, c, a
What is the tens digit in the sum 7! + 8! + 9! + … + 2006!
You can get the tens digit of any number n by computing the quotient
(n (mod 100)) / 10
and ignoring the remainder.
Taking the given sum (mod 100) gives
7! + 8! + … + 2006! ≡ 7! + 8! + 9! (mod 100)
since the last 1997 terms (i.e. 10! up to 2006!) in the sum are multiples of 100. That is,
• every term beyond 100! is obviously a multiple of 100
• every term beyond 25! contains a factor of both 4 and 25
• every term beyond 10! contains two factors each of both 2 and 5 (i.e. every factorial term contains 4, 5, and 10)
The remaining sum is easy to compute by hand:
7! + 8! + 9! = 7! (1 + 8 + 8 × 9) = 5040 × 81 = 408,240
so the tens digit is 4.
How do you find the surface area
Answer:
It depends on what shape you have. Here are some formulas for different shapes.
Step-by-step explanation:
Rectangular prism: 2lw + 2lh + 2wh
Cylinder: 2 pi r² + 2 pi rh
Sphere: 4 pi r²
Cone: pi r² + pi rl
Square-based pyrimid: 1/2lp +B
I hope this helps!
Fran swims at a speed of 2.1 km/h in still water. The Lazy River flows at a speed of 0.7 km/h. How long will it take Fran to swim 10 km upstream?
What is Fran's speed while swimming upstream?
Answer: Fran's speed while swimming upstream = 1.4 km/h
Step-by-step explanation:
Given: Fran's swimming speed = 2.1 km/h
Speed of river = 0.7 km/h
The direction against the stream is called upstream.
Speed in Upstream = Fran's swimming speed - Speed of river
= 2.1-0.7 km/h
= 1.4 km/h
hence, Fran's speed while swimming upstream = 1.4 km/h
Alec bakes spherical rolls of bread. Each roll is about 8cm
wide. What is the approximate volume of each roll? Use
3.14 to approximate a.
Answer:
Step-by-step explanation:
2143.57
-5x=25 how to solve this problem
which symmetry does y= -x^2-2x have? x-axis symmetry, y-axis symmetry, origin symmetry, or no symmetry?
Answer:
Step-by-step explanation:
The curve is symmetric about x = 1
so does not qualify for y-axis symmetry, nor the others.
Kin travels 440 miles by train at an average speed of 110 mph.
Ayaan flies the same distance at an average speed of 880 mph.
Find the difference between their travel times.
Give your answer in hours.
Answer:
3 1/2 hours
Step-by-step explanation:
time = distance/speed
440/110 = 4 hours
440/880 = 1/2 hours
4 minus 1/2 is 3 1/2
Answer:
hi
Step-by-step explanation:
i just need some points sorry not sorry
Reflect (-3, 4) across the y-axis. Then reflect the result across the x-axis.
