At age 23, someone sets up an IRA (individual retirement account) with an APR of 7%. At the end of each month he deposits $75 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
Answers
Answer:
The ira will contain $228,278.05 when he retires at age 65. This is 6.04 times the amount of money he deposited.
Step-by-step explanation:
In order to solve this problem, we can make use of the following formula:
\(FV=PMT[\frac{(1+i)^{n}-1}{i}]\)
Where:
FV= Future value of the ira
PMT= the amount of money you deposit each month
i= is the interest rate per period
n=number of periods
in this case we will assume the interest will be compounded each month.
So:
FV this is what we need to know.
PMT= $75 the amount he will deposit each month
t = 42 years,
this is 65-23=42
n=42 years * 12 months/year = 504 months
i=0.07/12
So we can now use the given formula:
\(FV=PMT[\frac{(1+i)^{n}-1}{i}]\)
\(FV=75[\frac{(1+\frac{0.07}{12})^{504}-1}{\frac{0.07}{12}}]\)
So we get:
FV=$228,278.05
which is the amount of money he will have after 42 years.
In total, he deposited:
$75*504months = $37,800
so he will have:
\(\frac{228,278.05}{37,800}=6.04\) times the amount of money he deposited throughout this time.
Related Questions
usage patterns are a variable used in blank______ segmentation.
Answers
Answer:
usage patterns are a variable used in market segmentation.
Step-by-step explanation:
Usage patterns are a variable used in behavioral segmentation.
Behavioral segmentation is a marketing strategy that divides a market into different segments based on consumer behavior, specifically their patterns of product usage, buying habits, and decision-making processes. This segmentation approach recognizes that customers with similar behavioral characteristics are likely to exhibit similar preferences and respond in a similar manner to marketing initiatives.
Usage patterns, as a variable, help marketers understand and classify customers based on how they interact with a product or service. This can include factors such as the frequency of product usage, the amount of product used, the timing of purchases, brand loyalty, product benefits sought, and other behavioral indicators.
By analyzing usage patterns, marketers can identify distinct segments within their target market and tailor marketing strategies to meet the unique needs and preferences of each segment. This enables companies to develop more targeted marketing campaigns, optimize product offerings, improve customer satisfaction, and drive customer loyalty.
Overall, behavioral segmentation, including the consideration of usage patterns, allows companies to better understand and connect with their customers by aligning their marketing efforts with specific behaviors and motivations.
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In the triangles, XY = MP and YZ = PN. Triangles Y X Z and P M N are shown. The length of side X Z is 23 inches. The length of side M N is 19 inches. Sides X Y and M P are congruent. Sides Y Z and P N are congruent. If mAngleP = 85°, which is a possible measure for AngleY? mAngleY = 80° mAngleY = 85° mAngleY = 100° mAngleY = 180°
Answers
Answer:
\(m\angle Y = 85\°\)
Step-by-step explanation:
In Triangles YXZ and PMN
\(XY \cong MP\\YZ \cong PN\)
Since the third side of triangle subtended by two congruent sides will always be congruent, the two triangles are congruent by SSS congruence theorem.
Therefore:\(\triangle XYZ \cong \triangle MPN\\\)
If the measure of angle P = 85°
Since P and Y are in the same positions(as seen in the diagram) in the two triangles respectively, the measure of angle Y is also 85 degrees.
Answer:
I believe the correct answer would be m<Y= 100° which would be letter C.
Step-by-step explanation:
What is the standard form of a line?
Answers
50 pts PLZ HURRY AND HELP IM TIMED
How many faces does the solid made from the net below have?
5
6
10
15
Answers
Answer: 10 is your answer
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Just keep looking at the faces.
Hopefully im correct, this is my 1st one :)
There are 326 students in the sixth - grade class at Jefferson middle school . WENTY Percent of The sixth - grade students have a pet at home . About How many students have a pet at home
Answers
Answer:
26% = 0.26
0.26 x 326=84.76. so about 84
Step-by-step explanation:
A cylinder has radius 2.5 meters. its volume is 50pi meters. Find its height.
Answers
Answer :
8 meters .⠀
Explanation :
The volume of the cylinder is 50π cubic meters.The cylinder has radius 2.5 meters.⠀
To Find :
The height of the cylinder.⠀
Solution :
⠀
We know,
\({ \longrightarrow\qquad \bf\pi {r}^{2}h = \bf{Volume_{(cylinder) } }}\)
⠀
Where,
r is the radius of the cylinder.h is the height of the cylinder.⠀
Now, Substituting the values :
\({ \longrightarrow\qquad \sf\pi \times {(2.5)}^{2} \times h = {50 \pi } }\)
\({ \longrightarrow\qquad \sf\pi \times 6.25 \times h = {50 \pi } }\)
⠀
Cancelling π from both sides :
\({ \longrightarrow\qquad \sf \cancel\pi \times 6.25 \times h = {50 \: \cancel \pi } }\)
\({ \longrightarrow\qquad \sf 6.25 \times h = {50 } }\)
\({ \longrightarrow\qquad \sf h = { \dfrac{50}{6.25} } }\)
\({ \longrightarrow\qquad {\pmb {\bf{h = {8 } }}}}\)
⠀
Therefore,
The height of the cylinder is 8 meters .simplify.
\( \sqrt[4]{16 {x}^{4} {y}^{12} } \)
assume all variables are non negative
Answers
Answer: \(2xy^3\\\\\)
===============================================
Work Shown:
\(z = \sqrt[4]{16x^4y^{12}}\\\\z = \sqrt[4]{2^4*x^4*(y^3)^4}\\\\z = \sqrt[4]{(2xy^3)^4}\\\\z = 2xy^3\\\\\)
An alternative method is this
\(z = \sqrt[4]{16x^4y^{12}}\\\\z = \sqrt[4]{16}\sqrt[4]{x^4}\sqrt[4]{y^{12}}\\\\z = \sqrt[4]{2^4}\sqrt[4]{x^4}\sqrt[4]{y^{12}}\\\\z = 2^{4/4}x^{4/4}y^{12/4}\\\\z = 2^{1}x^{1}y^{3}\\\\z = 2xy^{3}\\\\\)
the function h(t) = −16t2 48t 36 models the height of a ball, in feet, at t seconds after being thrown into the air. what is a reasonable range for the function?
Answers
To determine a reasonable range for the function h(t) = -16t^2 + 48t + 36, we need to consider the physical context of the problem.
Since the function represents the height of a ball thrown into the air, the range of the function should be the set of all possible heights that the ball can reach. In this case, the ball is thrown upward and then falls back down due to gravity.
The vertex of the parabolic function can give us some insights. The vertex of the parabola h(t) = -16t^2 + 48t + 36 occurs at the value of t = -b/2a = -48 / (2 * -16) = 1.5 seconds. Plugging this value into the function, we find h(1.5) = 54 feet.
Therefore, a reasonable range for the function is all heights from 0 feet up to a maximum height of 54 feet. In interval notation, the range can be expressed as [0, 54].
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Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead?
Answers
Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.
Given statement;
Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.
→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.
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Based on Ben's work shown, how would he respond?
The point IS a solution to the system. Only one of the equations resulted in an
identity.
The point is NOT a solution to the system. Both equations resulted in identities.
The point is NOT a solution to the system. Only one of the equations resulted in
an identity.
The point IS a solution to the system. Both equations resulted in identities.
Answers
Correct option: (A) The point IS a solution to the system. Only one of the equations resulted in an identity.
What is an identity equation?An equality that is true regardless of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic formulas. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.
An identity is an equation that, regardless of the values used, is always true. Since 2x + 3x will always equal 5, regardless of the value of, this statement is an identity. The example might be written as 2x+ 3x = 5x since identities can be represented with the symbol "≡"
2x + y = 4
now, putting the values in the equation (6,-8)
2(6) + (-8) = 4
or, 12 - 8 = 4
or, 4 ≡ 4
This equation, point IS a solution to the system.
x + 3y = - 20
or, 6 + 3(-8) = -20
or, 6 - 24 = -20
or, - 18 ≠ - 20
So, for this equation the result is not identity.
Thus, option A is the correct answer.
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Arun is going to invest $7,700 and leave it in an account for 20 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Arun to end
end up with $13,100?
Answers
Arun is going to invest $7,700 and leave it in an account for 20 years. Assuming theinterest is compounded continuously, what interest rate, to the nearest hundredth ofa percent, would be required in order for Arun to endend up with $13,100?
So first you do 13,100 minus 7700 equals 5400. Now you have 5400 you want to divide it by 20 which equals 270. So over the course of 20 years it went up to 13100. Which means every year it had to go up by $270 but that’s not a percent so… we have to divide 13100 by 5400 which equals 2.43 (Hope this helps)
Can you solve all please
Answers
B) 3
C) 3
D) 3
I think those are the first four
Answer:
A) 3
B) 3
C) 3
D) 3
I think those are the first four
Step-by-step explanation:
there are 100 fifty fifty tickets for sale for $3 each. first prize is $150. determine the expected value when 1 ticket is purchased.
Answers
When purchasing one ticket for $3 from a pool of 100 fifty-fifty tickets, the expected value is approximately -$1.50.
The expected value of an event is calculated by multiplying the probability of each outcome by its corresponding value and summing them up. In this case, there are 100 fifty-fifty tickets for sale, each priced at $3. The first prize is $150. To determine the expected value when purchasing one ticket, we need to calculate the probability of winning and losing, as well as their respective values.
Since there are 100 tickets and the outcome is fifty-fifty, the probability of winning is 1/100 or 0.01 (1%). The value of winning is $150, while the value of losing is -$3 (the cost of the ticket). Therefore, we can calculate the expected value as follows:
Expected value = (Probability of winning * Value of winning) + (Probability of losing * Value of losing)
Expected value = (0.01 * $150) + (0.99 * -$3)
Expected value = $1.50 - $2.97
Expected value ≈ -$1.47
Thus, the expected value when purchasing one ticket is approximately -$1.47, indicating that, on average, the buyer can expect to lose $1.47 per ticket purchased.
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Suppose ∠A and ∠B are complements, while ∠B and ∠C are supplements. If m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1), then m∠A=44, m∠B=46, and m∠C=134. TRUE OR FALSE? Please show your work.
Answers
Answer:
TRUE
Step-by-step explanation:
Angle <A and angle <B are complementary, which means their sum must be = 90
Angle <B and angle <C are supplementary which means their sum must be = 180
Now let's see
m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)
first find the sum of A and B
3x + 17 + 55 - x = 90 add like terms
2x + 72 = 90 subtract 72 from both sides
2x = 18 divide both sides by 2
x = 9
TRUE OR FALSE is asked for
m∠A=44, m∠B=46, and m∠C=134
to find that we just replace c with 9 with every expression given for angles
m<A = 3x + 17
m<A = 3*9 + 17 = 44
m<B = 55 - x
m<B = 55 - 9 = 46
m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.
The answer is TRUE
The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have:
∠A and ∠B are complements, while ∠B and ∠C are supplements.
∠A + ∠B = 90 degree
3x + 17 + 55 - x = 90
2x = 18
x = 9
Angle ∠B and angle ∠C are supplementary:
∠B + ∠C = 180
55 -x + 67(x/3 - 1) = 180
x = 9
Put the value of x and find angles A, B, and C.
m∠A = 44
m∠B = 46
m∠C = 134
∠A + ∠B = 90
∠B + ∠C = 180
The above statement is true.
Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.
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A card is drawn from a standard deck, put aside, and then another card is drawn. What is the probability that the first card is a king and that the second card is a queen?
Answers
1/221 chance of getting that exact outcome, pretty sure uwu
i play poker so i gotta learn stuff like this
What is an algebraic expression for each word phrase? a. 11 more than twice a number x b. 2 less than the quotient of 5 and a number x c. The product of 4 and the sum of a number x and 8
Answers
Answer:
a.) 11>2x.
b.) 2<5÷x.
c.) 4(x+8).
The word phrases into an algebraic expression will be 2x + 11, 5/x - 2, and 4(x + 8).
How to convert the sentence into an expression?The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.
Convert all the word phrases into an algebraic expression. Then we have
a. 11 more than twice a number x. Then we have
⇒ 2x + 11
b. 2 less than the quotient of 5 and a number x. Then we have
⇒ 5/x - 2
c. The product of 4 and the sum of a number x and 8. Then we have
⇒ 4(x + 8)
The word phrases into an algebraic expression will be 2x + 11, 5/x - 2, and 4(x + 8).
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What is Arrhenius's definition of an acid?
O a substance that dissociates in water to produce hydroxide ions (OH)
O a substance that dissociates.in water to produce hydrogen ions (H+).
o
any substance that can donate hydrogen ions (H+)
Answers
\(\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}\)
Arrhenius theory of an acid: This theory was discovered by Sir Svante Arrhenius in 1887. According to this theory acids are hydrogen containing compounds, when dissolves in water it gives (H+) ions.
\(\large{\underline{\underline{\pmb{\sf{\color {red}{Question:}}}}}}\)
\( \sf \red{What \: is \: Arrhenius's \: definition \: of \: an \: acid?}\)
\( \implies\) (B) substance that dissociates.in water to produce hydrogen ions (H+).So, option (B) is correct.
\( \boxed{ \frak \red{happy \: learning}}\)
Please help me i dont understand this
Answers
Answer:
209.3
Step-by-step explanation:
V=πr^2h / 3
= 3.14 x 25 x 8 /3
= 209.3
. Describe how to get the mixed number answer to 19÷6 from the
whole-number-with-remainder
answer. By considering a simple word problem, explain why the
method you describe makes
sense."
Answers
To obtain the mixed number answer to 19 ÷ 6 from the whole-number-with-remainder answer, divide the numerator (19) by the denominator (6).
To find the mixed number answer to 19 ÷ 6, we divide 19 by 6. The whole-number quotient is obtained by dividing the numerator (19) by the denominator (6), which in this case is 3. This represents the whole number part of the mixed number answer, indicating how many complete groups of 6 are in 19. Next, we consider the remainder. The remainder is the difference between the dividend (19) and the product of the whole number quotient (3) and the divisor (6), which is 1. The remainder, 1, becomes the numerator of the fractional part of the mixed number.
This method makes sense because it aligns with the division process and provides a clear representation of the result. It shows the whole number part as the number of complete groups and the fractional part as the remaining portion. This representation is helpful in various real-world scenarios, such as dividing objects or quantities into equal groups or sharing items among a certain number of people.
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determine the null and alternative hypotheses. the null hypothesis is always that the mean difference is 0. the alternative hypothesis is either that. true or false
Answers
In hypothesis testing, the null hypothesis (H0) is a statement that there is no significant difference between two groups, or that a certain parameter is equal to a specified value. In this case, the null hypothesis is that the mean difference is 0, meaning there is no significant difference between the two groups being compared.
The alternative hypothesis (Ha), on the other hand, is a statement that contradicts the null hypothesis. It can be one-tailed (directional), indicating that the mean difference is greater than or less than 0, or two-tailed (non-directional), indicating that the mean difference is not equal to 0. So, to determine the null and alternative hypotheses in this case, we know that the null hypothesis is that the mean difference is 0. The alternative hypothesis can be either one of the following:
- Ha: The mean difference is not equal to 0 (two-tailed)
- Ha: The mean difference is greater than 0 (one-tailed)
- Ha: The mean difference is less than 0 (one-tailed)
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10) A circle has center at (-5, 3) and passes through the point (-1, 3).
a) Give the radius of the circle.
b) Give the equation of the circle described.
Answers
b) (x+5)^2+(y-3)^2=4^2
The distance between the x values in the center point and a point included in the graph will give you the radius.
The x values are 4 units apart (-5 to -1) so your radius is 4 units
Circle formula:
(x-h)^2+(y-k)^2=r^2
Where (h,k) is the center point and r is the radius
Replace h with -5, k with 3, and r with 4 to get equation listed in answer above
Hope this helps!!
A 14-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 12 feet from the base of the building. How high up the wall does the ladder reach?
Answers
The ladder reaches abοut 7.21 feet up the wall is 14-fοοt ladder is placed against a vertical wall οf a building, with the bοttοm οf the ladder standing οn level grοund 12 feet frοm the base οf the building.
What is traingle?A triangle is a geοmetrical shape that has three sides and three angles.
We can use the Pythagοrean theοrem tο sοlve this prοblem. The Pythagοrean theοrem states that in a right triangle, the square οf the length οf the hypοtenuse (the lοngest side) is equal tο the sum οf the squares οf the οther twο sides. In this case, the ladder is the hypοtenuse οf a right triangle, and the wall and the grοund are the οther twο sides.
Let's call the height up the wall that the ladder reaches "h". Then we have:
ladder² = wall² + grοund²
Substituting in the given values, we get:
14² = h² + 12²
Simplifying:
196 = h² + 144
Subtracting 144 frοm bοth sides:
52 = h²
Taking the square rοοt οf bοth sides:
h = √52
Simplifying:
h ≈ 7.21 feet
Therefοre, the ladder reaches abοut 7.21 feet up the wall.
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What is the formula for residential value
Answers
Residual Value = The percent of the cost you are able to recover from the sale of an item x The original cost of the item.
Answer:
i am not sure man
Step-by-step explanation:
Troy lives in California. He bought a pair of shoes made in China. Which statement describes the shoes?
Answers
Answer:
Step-by-step explanation:
His shoes were made in China. Certainly that describes the shoes at least partially.
15-7m=-5-2m solve the equation
Answers
Helpcppdpdppd nessxbshzj
Answers
Answer:
dear hope it helps you...
How can 2 fathers and 2 sons divide 3 automobiles among themselves with each receiving one?
Answers
Answer:
haha i know this riddle
Step-by-step explanation:
there is a guy and he has had a son, and his son has also had a son, so there are technically 3 guys, but 2 fathers and 2 sons
what is elasticity?
Answers
Answer:
the ability of an object or material to resume its normal shape after being stretched or compressed; stretchiness.
Step-by-step explanation:
Answer:
the ability of an object or material to resume its normal shape after being stretched or compressed
Which numbers are factors of 12? Check all that apply
2
5
6
12
24
Answers
Answer:
2 6 12
Step-by-step explanation:
there are the only factor of 12 there
please help and don't waste my time with inaccurate answers. will give brainliest if the answer is correct.:)))
Answers
Answer:
allie saw 68 near sighted patients
sam saw 59 near sighted patients
Step-by-step explanation:
40% of 170 = 68
0.4 × 170 = 68
25% of 236 = 59
0.25 × 236 = 59