Lucas invests $2000 per year in his retirement account for 40 years in an investment with an average annual return of 10%. Approximately how much will he have after 40 years?
A.$88,000
B.$176,000
C.$312,000
D.$975,000
The amount Lucas would have in his account is $885,000.
The formula that would be used to determine the amount of money Lucas would be in 40 years is:
The formula for calculating future value = A x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
A = amount invested each year = $2000r = interest rate = 10%n = number of years = 40 years$2000 x [(1.1^40 - 1) / 0.1] = $885,000
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A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained the wishes the estimate to be within three percentage points
with 90% confidence, assuming that
(a) he uses the estimates of 21.3% male and 19.5% female from a previous year?
(b) he does not use any prior estimates?
(a)n (Round up to the nearest whole number)
(b) (Round up to the nearest whole number.)
Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
Item a:
The estimate is [tex]\pi = 0.213 - 0.195 = 0.018[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2[/tex]
[tex]n = 53.1[/tex]
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.05[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
[tex]n = 751.7[/tex]
Rounding up, a sample of 752 should be taken.
A similar problem is given at https://brainly.com/question/25694087
If x = 36 and y = 40 and “x varies directly as y”, then find “x” when y = 80.
Answer:
x= it will be 76
Mr. Reyes baked 4 batches of muffins for his class each batch had 12 muffins. if Mr. Reyes Has 24 students, How many muffins will each student receive?
Answer:2 muffins
Step-by-step explanation: First you have to see how many muffins he baked. 12x4 = 48 thus giving us the amount of muffins he baked. 48 muffins. If each student gets the same amount of muffins 48/24 = 2.
So each person would get 2 muffins.
Hope this helps :)
A soccer goalpost is to be made of 40 feet of
Jumber. The school has 27 feet. How much
umber should be purchases?
Answer:
13 more should be purchased.
40-27=13
6/11 = q/3
Pls help me!
Hi, I got 8 points off on this problem, can you help me figure out what I did wrong?
Answer:
Possible errors: Triangle classification and definition.
Step-by-step explanation:
An isoceles triangle has at least two congruent sides of the same length.
Given the triangle that has two equal angles, and that you'll have to prove that the triangle also has two equal sides.
Using the Converse of Isoceles Triangle Theorem, where it states that if a triangle has two congruent angles < PQR ≅ < PRQ, for which opposite sides of those angles are congruent:
The opposite side of <PQR is line PR.The opposite side of <PRQ is line PQ.Additionally, connecting point P to point X along the line QR such that PX ⊥ QR, divides △PQR into two symmetrical sections, where points Q and R are equidistant from point X.
Answer:
Possible errors: Triangle classification and definition.
-3/5 > -4/5 in a number line
Answer:correct
Step-by-step explanation: >
Help me please ………..
Answer:
Step-by-step explanation:
Answer:
<QSR = 55°(180°-125°)
Step-by-step explanation:
therefore, p-8=55°
p=(55+8)° = 63°.
hope this helps you.
Are the following polynomial sets open or closed?
6. (x ^ 2 + x - 4) - (x ^ 2 + x + 8)
7. (2 - x)(1 + 3x)
8. (5b - 3c)(7b - 3c)
Answer:
All closed.
Addition, subtraction as well as multiplication of polynomials result into another polynomial. Therefore, the set of polynomials is closed under addition, subtraction and multiplication.
Open polynomial set is (x² + x - 4) - (x² + x + 8)
Closed polynomial sets are (2 - x)(1 + 3x) and (5b - 3c)(7b - 3c)
What is polynomial?A polynomial is an expression consisting of variables and their coefficients, operations of addition, subtraction, multiplication, and positive-integer powers of variables are involved in polynomial. If the result of a polynomial set applying different operations is polynomial then it is closed under that operation.
Given, polynomial sets
(x² + x - 4) - (x² + x + 8)
Applying subtraction operation
x² + x - 4 - x² - x - 8
Subtracting like terms
-12
The result is integer, it is open polynomial set
(2 - x)(1 + 3x)
Applying multiplication operation
2 - x - x - 3x²
= 2 - 2x - 3x²
The result is polynomial, it is closed polynomial set
(5b - 3c)(7b - 3c)
Applying multiplication operation
35b² - 15bc - 21bc + 9c²
= 35b² - 36bc + 9c²
The result is polynomial, it is closed polynomial set
Hence, (x² + x - 4) - (x² + x + 8) is an open polynomial set
(2 - x)(1 + 3x) and (5b - 3c)(7b - 3c) are closed polynomial sets.
Learn more about polynomials here:
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g A long-term study has revealed that a test for cancer in men is very effective. The study shows that 89% of the men for which the test is positive actually have cancer. If a man selected at random tests positive for cancer with this test, what is the probability that he does not have cancer
(PHOTO) Please help me need this done by tomorrow thank you.
Answer:
x = 13
Step-by-step explanation:
Corresponding angles equal one another.
[tex]8x-20=4x+32\\4x-20=32\\4x=52\\x=13[/tex]
Solve by elimination Solve by elimination or substitution: 4x + 2y = 6 and x - 3y = 5
Step-by-step explanation:
since we need to multiply only one equation with something, elimination might be a good method here. we bring both equations to 4x terms and then subtract the second from the first equation :
4x + 2y = 6
- 4x - 12y = 20
-----------------------
0 14y = -14
y = -1
=> e.g. in the second original equation
x - 3×-1 = 5
x + 3 = 5
x = 2
PICK 5 RELEVANT VOCABULARY TERMS AND SUMMARIZE THEM .
yooo, i need help with this...
1.3.2 checkup - lessons learned
2. What is the slope of the line represented by the table of values below? How do you know?
Answer:
y=2/3x-4
Step-by-step explanation:
we can see that x goes up 1 for every 1.5y and if we start y at 0 x starts at -4 so if y is one than x has to be 2/3-4 becuase it is -4 + 2/3 for every 1 y goes up or one for every 1.5 y goes up. hope this answer was helpful.
Help help help help hell
Answer:
m = N - f
Step-by-step explanation:
The original equation:
N = m + f
if we have to solve for m, then we have to isolate it, so subtract f from both the sides and that would be the answer.
Hope this helps!
A large grocery store needs to decide how many bottles of 2 liter
Dr. Pepper to stock each week in the store. The store must decide how many bottles to stock each week. The weekly demand for 2 liter Dr. Pepper follows a Normal Distribution with a mean of 550 bottles and a standard deviation of 26 bottles. The store desires that the probability that they do not run out of 2 liter bottles of Dr. Pepper in a week to be .995.
How many bottles should they stock at the beginning of the week to have a .995 probability of not running out during the week. Choose what you believe is the best answer from the following:
i) 601,
ii) 610
iii) 617
iv) 483
v) 490
vi) none of the above
Answer:
I Kinda Confused Man
Step-by-step explanation:
I Dont Even Know The Right Answer
solve the following stystem -4x + 2y = 0 and x + y = -1
2.
Which of the following describes the parabola with the equation y = x2 + 2x + 1?
A. The axis of symmetry is x = −1 and the vertex is (−1, 0).
B. The axis of symmetry is x = 0 and the vertex is (0, 1).
C. The axis of symmetry is x = 1 and the vertex is (1, 4).
D. The axis of symmetry is x = 1 and the vertex is (1, 2).
Answer:
The answer is A. The axis of symmetry is x= -1 and the vertex is (-1,0)
Step-by-step explanation:
Answer: x=1
A. The axis of symmetry is x = −1 and the vertex is (−1, 0).
Step-by-step explanation: graph{x^2+2x+1 [-10, 10, -5, 5]}
Explanation:
This is a quadratic equation so it makes a Parabola on a graph.
Information:
x-intercept: (1,0)
y-intercept: (0,1)
vertex: (1,0)
line of symmetry: x=1
...............................................................................................................................................
The answer is option a via completing the square
y= x^2+2x+1
y= (x+1)^2+1
so it will have an aos of -1 and a vertex of (-1,0)
...............................................................................................................................................
it will have an aos of -1 and a vertex of (-1,0)
Step-by-step explanation:
made a 100%
The table shows information about some children.
Age 11
Age 12
Total
Girls
7
a
b
Boys
с
5
8
Total
d
9
e
A pupil is selected at random.
What is the probability of selecting a boy?
Give your answer in its simplest form.
I wrote this on a document in my previous years in school.
Please help me with this problem
Hello this will be easy for you.
Look at the picture, you have the angle UTR which is of 90° degrees. Thus the angle UTS is also 90° .
But the sum of the angles of a triangle is by property equal to 180° so the angle UVT must be equal to 180-90-64 = 26°.
Now we are getting near to solve that x+8 degrees angle.
Recall that UVT is 26° ok ? So 180-26 = x+8
Thus
x+8 = 154
x = 154 - 8
x = 146
Finally the angle UVS = 154 and the value of x = 146
You can see all the angles in the image attached below
Good luck you will be the best
Help my first time learning this it’s an easy problem
Answer:
I don't know but I I would just say C maybe?
Answer:
I say do B
Step-by-step explanation:
B and C look approximately the same but B look smaller
If I’m wrong I’m srry :<
The initial population of a town is 3800, and it grows with a doubling time of 10 years. What will the population be in 8 years?
Please show step by step!
Answer:
The population was 3040 people in 8 years.
Step-by-step explanation:
find unit rate;
3800/10 = 380
380 x 8 = 3040
Given that m||n, find the value of x.
Answer:
x = 24°
Step-by-step explanation:
Using 180-degree formula, we can find x.
=> 84 + 4x = 180°
=> 4x = 180 - 84
=> 4x = 96
=> 24°
Therefore, x = 24°
Hoped this helped.
Answer:
[tex] {\boxed {\sf{x = 24 \degree}}}[/tex]
Step-by-step explanation:
In the given figure we have two consecutive interior angles.
We know that each pair of consecutive interior angles is supplementary.
So,
4x+84 = 1804x = 180 - 844x = 96x = 96/4x = 24Therefore, x = 24°
Please answer number 8
Answer:
d q knows
Step-by-step explanation:
sory need points
How much did i paint if i painted 3/4 of 3/4 of a wall
Answer:
(4) 1/4x = 3/4 (4)
1x=3
Step-by-step explanation:
3/4 x
÷ = ÷
1/4 1
(4) 1/4x = 3/4 (4)
1x=3
What is the slope of the line between the points ( 2 , 7 ) and ( 7 , 1 )?
Answer:
slope = - [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 7 ) and (x₂, y₂ ) = (7, 1 )
m = [tex]\frac{1-7}{7-2}[/tex] = [tex]\frac{-6}{5}[/tex] = - [tex]\frac{6}{5}[/tex]
Hello there! :)
To find the slope of the line when we are given 2 points, we use the following formula:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-7}{7-2} \\\frac{-6}{5}[/tex]
So the slope is -6/5. Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]MysteriousNature :)[/tex]
Can anyone answer this?
Answer:
∠AMB = 103°
Step-by-step explanation:
The sum of angles in ∆AMB is ...
(∠A)/2 +(∠B)/2 + ∠AMB = 180°
∠AMB = 180° -(∠A +∠B)/2 = 180° -(58° +96°)/2
∠AMB = 103°
Which line has a constant of proportionality between y and x of 4/3
Answer:
Line A: constant of proportionality is 4/3
Step-by-step explanation:
The equation in question is y = (4/3)x, where (4/3) is the constant of proportionality as well s the slope of the line. The only line here that has a slope greater than 1 is the blue line (A).
Solve for B -(12 x 2) x (-6) = -12 x (2 x b)
A. -6
B. 6
C. -12
D. 12
Answer:
Option A
Step-by-step explanation:
-(12 x 2) x (-6) = -12 x (2 x b)
=> -24 x -6 = -12 x 2b
=> 144 = -24b
=> b = -6
Hoped this helped.
