The difference in the account balances is approximately $266,275.76. (option a).
Here we know that the
Yearly contribution = $5,000
Retirement age = 65
Average annual rate of return = 6.5%
Account balance at retirement age = $431,874.32
Using these values, we can calculate the total number of contributions made from age 35 to 65:
Number of contributions = (Retirement age - Starting age) = (65 - 35) = 30 contributions.
Now, let's calculate the future value of the contributions made from age 35 to 65. We can use the formula for the future value of an ordinary annuity:
Future Value = $5,000 * [(1 + 0.065)³⁰ - 1] / 0.065
Calculating this expression gives us:
Future Value = $799,874.61 (approximately)
Using the same values as before, but changing the starting age to 20, we need to calculate the number of contributions made from age 20 to 65:
Number of contributions = (Retirement age - Starting age) = (65 - 20) = 45 contributions.
Applying the future value formula to this scenario, we have:
Future Value = $5,000 * [(1 + 0.065)⁴⁵ - 1] / 0.065
Calculating this expression gives us:
Future Value = $1,066,150.37 (approximately)
Finally, to determine the difference in the account balances, we subtract the future value from scenario 1 (starting at age 35) from the future value from scenario 2 (starting at age 20):
Difference in Account Balances = Future Value (Age 20) - Future Value (Age 35)
Difference in Account Balances = $1,066,150.37 - $799,874.61
Difference in Account Balances = $266,275.76
Hence the correct option is (a).
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Meena’s father’s present age is six times Meena’s age. Five years from now she will be one-third of her father’s present age. What are their present ages?
Answer:
Meena age = 5 yrs Meenas father = 30
Step-by-step explanation:
let,
meena's age = x
meena's father's age = 6x
Five years from now
meena's age will be 1/3(6x)
meena's father's age will be 6x+5
A/Q
x+5+6x+5=2x+6x+5
=x+6x-2x-6x=5-5-5
= -x =-5
= x =5
meena's age = 5
meena's father's age = 6x
= 6×5
= 30
Joel spends 272727 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of 606060 minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?
Joel spent 72.5% of his time exercising after playing soccer on Tuesda
How to determine the percentage?The given parameters are
Minutes spent on Tuesday = 27 more minutes than Monday
Total minutes spend = 60
This means that
Tuesday = Monday + 27
Monday + Tuesday = 60
Make Monday the subject in Tuesday = Monday + 27
Monday = Tuesday - 27
Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60
Tuesday - 27 + Tuesday = 60
Evaluate
2 * Tuesday = 87
Divide by 2
Tuesday = 43.5
The percentage of time spent exercising on Tuesday is then calculated as
Percentage = 43.5/60 * 100%
Evaluate the expression
Percentage = 72.5%
Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday
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The plane is tiled by congruent squares of side length $a$ and congruent pentagons of side lengths $a$ and $\frac{a\sqrt{2}}{2}$, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58
The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.
How to determine the percentage?Since the side of the small square is a, then the area of the tile is
given by:
Area of tiles = 9a²
Note: With an area of 9a², 4a² is covered by squares while 5a² by pentagons.
This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:
Percent = 5/9 × 100
Percent = 0.555 × 100
Percent = 55.5 ≈ 56%.
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Complete Question:
The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58
I need help cancelling units
Answer:
60:1
Step-by-step explanation:
60:1 = 366:x
60x = 366
x = 6.1
366 minutes is equivalent to 6.1 hours.
Convert 366 minutes to hours.
Knowing that in 60 minutes = 1 hour.[tex]\boldsymbol{\sf{Therefore \ \to \ 366 \not{m}*\dfrac{1 \ hr}{60\not{m}}=6.1 \ hr }}[/tex]
We conclude that a time of 366 minutes is equal to 6.1 hours
There are 60 minutes in 1 hour. To convert from minutes to hours, divide the number of minutes by 60. For example, 120 minutes equals 2 hours because 120/60=2.
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
the following 3 equations are equivalent :
• x + 1 = 4
• 2 + x = 5
• -5 + x = -2
Step-by-step explanation:
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
-5 + x = - 2
Let’s take this equation :
x + 1 = 4
=======
By Adding 1 to both sides of the equation we get :
x + 1 + 1 = 4 + 1
⇔ x + 2 = 5
⇔ 2 + x = 5
Then the equations x + 1 = 4 and 2 + x = 5 are equivalent.
…………………………………………………………………
On the other hand ,if we subtract 6 from both sides
of the equation x + 1 = 4 we get :
x + 1 - 6 = 4 - 6
⇔ x - 5 = -2
⇔ -5 + x = -2
Then the equations x + 1 = 4 and -5 + x = -2 are equivalent.
Answer:
A. 2 + x = 5
B. x + 1 = 4
E. -5 + x = -2
Step-by-step explanation:
right on edg, hope it helps ya'll.
Write two expressions that have a solution of x = 4.
ASAP!! Ty
Answer:
X multiplied by 2 is 8
X divided by 2 is 4
Step-by-step explanation:
This is the quickest thing i can give you
a) The cosine rule can be used to find the value of x in the triangle below.
What number completes the following calculation? x² = 12² +152 - 2 x 12 x 15 x cos(?)
b) What is the value of x? Give your answer to the nearest integer.
Answer:
see explanation
Step-by-step explanation:
(a)
(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )
x² = 12² + 15² - (2 × 12 × 15 × cos71°)
(b)
x² = 144 + 225 - 360cos71°
= 369 - 360cos71° ( take square root of both sides )
x = [tex]\sqrt{369-360cos71}[/tex]
≈ 16 cm ( to the nearest integer )
Find the 8th term of the geometric sequence 5, -15, 45
Answer:
a₈ = - 10935
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-15}{5}[/tex] = - 3 , then
a₈ = 5 × [tex](-3)^{7}[/tex] = 5 × - 2187 = - 10935
Alishia rides her bike 45.3 km in 143 minutes. what is her average speed in kilometers per hour?
Average speed of Alishia is 19 kilometers per hour
Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance. Speed is how fast something is going at a particular moment. Average speed measures the average rate of speed over the extent of a trip
Given :
Distance = 45.3 km
Time taken = 143 minutes = 143/60 =2.384 hours
∴ Average speed = 45.3/2.384 = 19 kilometers per hour
Thus the average speed of Alishia is 19 kilometers per hour.
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A bakery offers a sale price of $3.30 for 3 muffins. what is the price per dozen?
Answer:
$13.20
Step-by-step explanation:
A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.
3.30*4=13.20
The population mean is symbolized as ________________, whereas the sample mean is symbolized as __________________. Group of answer choices n; N N; n
The population mean is symbolized as μ. The sample mean is symbolized M.
What is a Population?
A population in statistics, is a the total number of people of a group that shares similar characteristics that are of interest to a researcher. Example of population a researcher can understudy include:
Sixth grade students taking mathApple watch usersPeople who patronize a shopping mall, etc.What is a Sample?A sample is a subset of a population, which is drawn using any sampling technique. An example of a sample is 100 randomly selected persons who patronize a shopping mall.
What is the Population Mean?The population mean can be defined as the average data value of a particular group characteristics that is measured by the researcher. The symbol for population mean is: μ.
What is the Sample Mean?
The sample mean can be defined as the average data value of the sub-group of an entire population that having characteristics that are of interest to a researcher. The symbol for sample mean is: M.
In summary, the population mean is symbolized as μ. The sample mean is symbolized M.
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A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. the interest rate applicable is j2 = 5.5% p.a. applicable for the rst ve years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
A mortgage payment is typically made up of four components: principal, interest, taxes, and insurance. The Principal portion is the amount that pays down your outstanding loan amount. Interest is the cost of borrowing money. The amount of interest you pay is determined by your interest rate and your loan balance.
The term “loan” can be used to describe any financial transaction where one party receives a lump sum and agrees to pay the money back. A mortgage is a type of loan that's used to finance a property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.
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Outside a home, there is a 4-key keypad numbered 1 through 4. The correct six-digit code will open the garage door. The numbers can be repeated in the code
(a) How many codes are possible?
(b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?
(a) The number of possible codes is
(Type an integer or fraction. Simplify your answer)
(b) The probability that the correct code is given on the first try, assuming that the owner doesn't remember it is
(Type an integer or fraction Simplify your answer.)
Using the Fundamental Counting Theorem, it is found that:
a) 256 codes are possible.
b) The probability is [tex]\frac{1}{256}[/tex].
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
There are 4 keys, each with 4 options, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex].
Then the number of codes is:
[tex]N = 4^4 = 256[/tex]
And the probability is:
[tex]p = \frac{1}{256}[/tex].
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(6x - 4)(3 - 2x)/4x - 6
[tex] \frac{(6x - 4)(3 - 2x)}{(4x - 6)} = \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} [/tex]
[tex] \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} = \frac{(3x - 2)(3 - 2x)}{(2x - 3)} [/tex]
[tex] \frac{(3x - 2)(3 - 2x)}{(2x - 3)} = \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} [/tex]
[tex] \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} = - (3x - 2)[/tex]
[tex] - (3x - 2) = 2 - 3x[/tex]
Solve the equation. Simplify your answer.
2 (3-x) = 16 (x+1)
pls help me on this one :((
Answer:
B
Step-by-step explanation:
Finding the area of the trapezoid using the lengths in the diagram, we get (c)(2d+a+b)/2.
This is equal to c(d+b), so:
(1/2)(c)(2d+a+b)=c(d+b)
(1/2)(2d+a+b)=d+b
d+0.5a+0.5b=d+b
0.5a+0.5b=b
0.5a=0.5b
a=b
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
The value of the constant of variation include 8, 3.2, and 1.25
How to find the constant?From the information given, when x = -0.5, y = -4.0. The constant will be:
y = kx
-4 = -0.5k
k = -4.0/-0.5
k. = 8
When x = 2.5, y = 8
y = kx
8 = 2.5k
k = 8/2.5
k = 3.2
When x = 4, y = 5
y = kx
5 = 4k
k = 5/4
k = 1.25
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the height of a can of coke is in 11 cm and the radius is 6 cm calculate the total surface area of the can in cm^3 assuming that the
can is a closed cylinde
Answer:
The total surface area of the the cylinder is 640.56cm², surface are is always give in cm² not in cm³ b/c cm³ indicates the volume of the cylinder not the surface area.
Step-by-step explanation:
Hello!
. SA=2πr(r+h) ,or 2πr²+h(2πr)
SA=2(3.14)(6cm)(6cm+11cm)SA=6.28(6cm)(17cm)SA=37.68cm(17cm)SA=640.56cm²Answer:
204π cm^2
which is 640.88 cm^2 to the nearest hundredth.
Step-by-step explanation:
Surface area = 2 * area of the base + area of the curved side.
= 2*π *r^2 + 2*π*r*h
= 2π(6)^2 + 2π(6)(11)
= 72π + 132π
= 204π cm^2.
The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.
Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
If we had increased the confidence level, the margin of error also would have increased.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.
The sample size and the estimate are given as follows:
[tex]n = 450, \pi = 0.47[/tex].
The lower and the upper bound of the interval are given, respectively, by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.4239[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.5161[/tex]
The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
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please help me solve this
Explanation:
The proof can be had by making use of the AAS congruence postulate (twice) and CPCTC.
We start by showing ΔPQY≅ΔPRX, then by showing ΔXQN≅ΔYRN. The proof is then a result of CPCTC.
Proof1. PQ≅PR, ∠Q≅∠R . . . . given
2. ∠P≅∠P . . . . reflexive property of congruence
3. ΔPQY≅ΔPRX . . . . AAS congruence postulate
4. PX≅PY . . . . CPCTC
5. PX+XQ=PQ, PY+YR=PR . . . . segment sum theorem
6. PX+XQ = PY +YR . . . . substitution property
7. PX +XQ = PX +YR . . . . substitution property
8. XQ = YR . . . . subtraction property of equality
9. ∠XNQ≅∠YNR . . . . vertical angles are congruent
10. ΔXNQ≅ΔYNR . . . . AAS congruence postulate
11. XN ≅ YN . . . . CPCTC
__
Additional comment
You probably did steps 1-3 in part (a) of the problem.
Solve each equation
Note:now you need to perform inverse operations to solve for the variables. For example in (2/3x -6) try adding 6 to both sides first then multiply the reciprocal of 2/3 (meaning the flipped version)
The factorise form of the two expression are as follows:
2 (x - 3) (x - 9)-3(x + 5)(x + 7) How to solve an expression?b. (x - 3)(2 / 3 x - 6) = 0
Therefore, let's open the brackets
2 / 3 x² - 6x -2x + 18 = 0
2 / 3 x² - 8x + 18 = 0
multiply through by 3
2x² - 24x + 54 = 0
Hence,
2 (x - 3) (x - 9)
c.
(-3x - 15)(x + 7) = 0
Therefore,
-3x² - 21x - 15x - 105 = 0
-3x² - 36x - 105 = 0
-3(x + 5)(x + 7)
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What is the range of the function f(x) = |x – 3| + 4?
R: {f(x) ∈ ℝ | f(x) ≥ 4}
R: {f(x) ∈ ℝ | f(x) ≤ 4}
R: {f(x) ∈ ℝ | f(x) > 7}
R: {f(x) ∈ ℝ | f(x) < 7}
Answer: R: {f(x) ∈ ℝ | f(x) ≥ 4}
Step-by-step explanation:
[tex]|x-3| \geq 0[/tex] for all real x, so the range is [tex]f(x) \geq 4[/tex].
Please help me with this
Answer:A or C
Step-by-step explanation: i guessed plus 19 hours ago
Why cant the a value in the standard form of a quadratic function ax^2+bx+c=0 be equal to 0?
Answer:
the equation is no longer quadratic
Step-by-step explanation:
A quadratic equation is a polynomial equation in which the highest-degree term has degree 2.
What happens when a = 0?The value a=0 makes the squared term disappear. If 'a' is zero, the equation becomes a linear equation, not a quadratic equation:
bx +c = 0
Which relationship describes a function?
O (bedrooms, sale price)
(acres of land, appraised value)
(sale price, bedrooms)
(appraised value, property tax)
The relationship which best defines a function, for the houses on Katrina's street exists appraised value, property tax.
How to read the data from the table?Table exists a form to describe the data of the two or more variables.
To read the data from the table, examine for the value of one variable, and obtain the resultant value of other variables from the related block.
The table below details some of the characteristics of the houses on Katrina’s street. Let's estimate the most suitable choice whose relationship defines a function.
The function exists in the relationship between various variables. This relation or the expression provides the output, by accepting some input value of variables.The output for a function is related to the input and provides various outputs with various input values.Only appraised value and property tax, in the given table, supplies a unique value per time.The relationship which nicely illustrates the function, of the houses on Katrina's street exists between the appraised value and property tax.
Therefore, the correct answer is option d) (appraised value, property tax).
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Answer: D
Step-by-step explanation: Appraised Value , Property Tax
The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is symbolized by _____.
Considering that the value of 126.07 is valid for the population, it is a parameter.
What is the difference between a statistic and a parameter?If the measure is defined only for the sample, it is a statistic.If the measure can be defined for the population, it is a parameter.In this problem, the mean blood pressure is calculated for all employees, which means that it is valid for the population, hence it is a parameter.
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The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.
1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)
2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)
Answer:
460 gallons392 cmStep-by-step explanation:
The necessary units conversion can be accomplished by multiplying by appropriate conversion factors. Quantity can be found by multiplying rate by time.
1)The number of gallons of water produced by melting 1.9 m³ of ice is ...
[tex]1.9\text{ m$^3$ (ice)}\times\left(\dfrac{100\text{ cm}}{1\text{ m}}\right)^3\times\dfrac{0.92\text{ cm$^3$ (water)}}{1\text{ cm$^3$ (ice)}}\times\dfrac{1\text{ gal}}{3800\text{ cm$^3$}}\\\\=\dfrac{1.9\times10^6\times0.92}{3800}\text{ gal}=\boxed{460\text{ gal}}[/tex]
2)Multiplying the melting rate by time and converting to height, we have ...
[tex]\dfrac{179.4\text{ km$^3$}}{1\text{ yr}}\times\dfrac{364\text{ cm}}{1000\text{ km$^3$}}\times6\text{ yr}\approx\boxed{392\text{ cm}}[/tex]
__
Additional comment
The area of the world's oceans is about 361e6 km², so addition of 1000 km³ of water might be expected to increase the water level by (1000/361)e-6 ≈ 2.77e-6 km = 0.277 cm. Something seems a little off in this problem statement.
Mark this and retum
S
R
Which statements are true about triangle QRS? Select
three options.
The side opposite ZQ is RS.
The side opposite ZR is RQ.
The hypotenuse is QR.
The side adjacent to ZR is SQ.
The side adjacent to 4Q is QS.
Save and Exit
Next
Submit
The statements that are correct about right triangle QRS are:
Side opposite ∠Q is RS not RQHypotenuse of the right triangle is QRAdjacent side to ∠Q is QSWhat is a Right Triangle?A right triangle posses a right angle which is in opposite direction to the hypotenuse.
Considering the right angle triangle, it can be deduced that Side opposite ∠Q is RS not RQ, and Adjacent side to ∠Q is QS.
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Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats .
What is the probability that a kid who goes to the doctor has a sore throat given that he has a fever?
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 30%
How to determine the probability?The given parameters are:
P(Fever) = 70%
P(Fever and sore throat) = 21%
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is calculated as:
P = P(Fever and sore throat)/P(Fever)
So, we have:
P = 21%/70%
Evaluate
P = 30%
Hence, the probability is 30%
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What are the center and radius of the circle given by x^2 + y^2 - 16x + 8y + 4 = 0?
The center of the circle = (8, -4)
The radius of the circle = [tex]\sqrt{76}[/tex]
Finding the center and radius of a circle from the equationThe given equation of the circle is:
[tex]x^2+y^2-16x+8y+4=0[/tex]
The equation can be expressed and simplified as:
[tex]x^2-16x+y^2+8y=-4\\\\x^2-16y+8^2+y^2+8y+4^2=-4+8^2+4^2\\\\(x-8)^2+(y+4)^2=-4+64+16\\\\(x-8)^2+(y+4)^2=76[/tex]
The general equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Comparing the two equations:
The center, (a, b) = (8, -4)
The radius, r = [tex]\sqrt{76}[/tex]
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