The amount of IRA when he will retire at age 65 = $83448.27
And the total deposits made over the time period is less than the the amount of IRA
We have been given, at age 19, someone sets up an IRA (individual retirement account) with an APR of7 %. At the end of each month he deposits $20.00 in the account.
We need to find the IRA when he retires at age 65.
here, 65 - 19 = 46 years
So, the period would be,
46 × 12 = 552 months
Monthly deposit= $20
And the interest rate would be,
Interest = 0.07/12
= 0.0058
To calculate the future value, we need to use the following formula:
FV= {A × [(1 + i)^n-1]} / i
A= monthly deposit
i = interest rate
n = period
So, the Future Value of Annuity
= 20 × ([1 + 0.0058]^552 - 1 ) / (0.0058)
= 20 × 24.2 / 0.0058
= $83448.27
So, the amount of IRA when he will retire = $83448.27
Deposits made over the time period = 20 × 46 × 12 = $11040
Difference = 83448.27 - 11040
= $72408.27
This means, the total deposits made over the time period is less than the the amount of IRA he will get when he retires at age 65.
Therefore, the amount of IRA when he will retire at age 65 = $83448.27
And the total deposits made over the time period is less than the the amount of IRA
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K is the midpoint of JL. If JK = 6x and JL = 13x − 7, what is JK?
The length of JK is 42.
JL is a line and K is the mid-point of that line.
J____________.___________L
K
From this we get:
JK = KL
JL = JK + KL
JL= 2JK = 2KL
Here it is given that,
JK = 6x and JL = 13x - 7
JL = 2JK
13x - 7 = 2× 6x
13x - 7 = 12x
x = 7
We have to find the length of JK
JK = 6x
=6× 7
= 42
Therefore the length of JK is 42.
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Solve 3(x + 2) > x.
A. {x | x < -3}
B. {x | x > -3}
C. {x | x > -1}
D. {x | x < -1}
The solution for the inequality 3(x + 2) > x is given by:
B. {x | x > -3}.
How to solve an inequality?An inequality is solved similarly to an equality, in which we isolate the desired variable.
The biggest difference is the fact that the solution for the inequality won't be a single value like the solution for the equality, it will be a range containing infinity real values.
For this problem, the inequality is given as follows:
3(x + 2) > x.
Applying the distributive property, we have that:
3x + 6 > x.
Now we move x to the left side and 6 to the right side, both with inverse signals, hence:
3x - x > -6.
2x > -6
x > -6/2
x > -3.
Hence the correct option for the inequality in this problem is given by option B.
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which equation are correct select each other answers
Answer:
they all are correct asu know first expression is multiple by other one so u can check
What are the dimensions of a right triangle with an eight-inch hypotenuse and an area of 16 square inches?
The dimensions of the given right triangle would be 5.66 inches and 11.31 inches.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Let the legs of the triangle be x and y
Using the Pythagorean theorem:
c² = a²+b²
So the hypotenuse will be:
x² + y² = 8²
x² + y² = 64
x² = 64 - y²
So the area of the triangle is:
A = 1/2bh
A = 1/2xy
⇒16 = 1/2xy
32 = xy
x = 32/y
x² = 1024/y²
Substitute the above value in x² = 64 - y² and solving for y we get:
1024/y² = 64 - y²
1024 = 64y²- y⁴
This can be written as:
y⁴ - 64y² + 1024 = 0
Thus y = 4√2 = 5.66
x = 64/(4√2)= 16/√2 = 8√2 = 11.31
Therefore, the dimensions of the given right triangle would be 5.66 inches and 11.31 inches.
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The midpoint of AB is M (−6, 2). If the coordinates of A are (-5, -2), what are
the coordinates of B?
Answer:
(-7,6)
Step-by-step explanation:
Midpoints
x = (x1 + x2)/2
y = (y1 + y2)/2
-6 = (-5 + x2)/2
x2 - 5 = -12
x2 = -7
2 = (-2 + y2)/2
y2 - 2 = 4
y2 = 6
Evalúe the limit. Show steps
Answer: sqrt{3} over 2, this also equivalent to 0.866025
ƏR Ər Find for the following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x ADSER y, w = 2xy
The chain rule tells us how to find derivative of a composite function., The following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x-y, w = 2xy ƏR/Əx= 9/7 and ƏR/Əy = 9/7.
What is chain rule?The Chain Rule is a mathematical method to differentiate a composition of the functions. From this composition of the functions, we can discern the functions' derivatives and their relationships.
In other words, the derivative of composite function = derivative of the outside function × derivative of the inside function.
The Chain Rule gives:
ƏR/Əx= ƏR/Əu × Əu/Əx + ƏR/Əv × Əv/Əx + ƏR/Əw × Əw/Əx
= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *1 + \frac{2v}{u^{2}+v^{2}+w^{2} } *2+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2y[/tex]
When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so
ƏR/Əx = 6/14 × 1+ 2/14 ×2+ 4/14×2 = 18/17 = 9/7
ƏR/Əy= ƏR/Əu × Əu/Əy + ƏR/Əv × Əv/Əy + ƏR/Əw × Əw/Əy
= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *2 + \frac{2v}{u^{2}+v^{2}+w^{2} } *(-1)+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2x[/tex]
When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so
ƏR/Əy = 6/14 × 2 + 2/14 × (-1) + 1/14 × 2= 18/14 = 9/7
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The sun is shining on a house and fence. The roof of the house is 16 feet from the ground and makes a shadow 24 feet long. The fence is 4 feet tall. How long is the fence's shadow?
The length of the shadow of fence will be equal to 6 feet.
Proportionality may be defined as the term which can be used to describe or denote a relationship between two entities which are always in the same ratio. For example, the number of bananas is proportional to the number of trees with the proportionality being average number of bananas per number of trees. Here, we are given the height of house = 16 feet and length of its shadow = 24 feet and also the height of fence = 4 feet. Since, both house and fence lie in the same area they both are proportional. Let the length of shadow be x. Since, they are proportional
16/24 = 4/x
2/3 = 4/x
=> x = 12/2
=> x = 6 feet.
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6. A certificate of deposit (CD) is a savings instrument that many banks offer. It usually gives a
higher interest rate, but you cannot access your investment for a specified length of time.
Suppose you deposit $3000 in a CD paying 6% interest, compounded monthly. How much will
you have in the account after 20 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases} \\\\\\ A=3000\left(1+\frac{0.06}{12}\right)^{12\cdot 20} \implies A=3000(1.005)^{240}\implies A \approx 9930.61[/tex]
(02.01, 02.02 HC)Vanessa and William are stuck simplifying radical expressions. Vanessa has to simplifyx3William has to simplify 15xx.x4. Usingx6full sentences, describe how to fully simplify Vanessa and William's expressions. Describe if Vanessa and William started with equivalentexpressions or if they started with expressions that are not
ANSWER:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=x^{\frac{1}{2}} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the given expression is the following:
[tex]\frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}[/tex]The other expression is the following:
[tex]\sqrt[16]{x\cdot \:x^3\cdot \:x^4}[/tex]We simplify in each case:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{4}{3}-\frac{5}{6}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=\sqrt[16]{x^{1+3+4}}=\sqrt[16]{x^8}=x^{\frac{8}{16}}=x^{\frac{1}{2}} \end{gathered}[/tex]This means that the expressions are equal
Find the equation of the graph given below. Notice that the cosine function is used in the answer template, representing a
cosine function that is shifted and/or reflected.
When entering in your answer, use the letter a rather than the multiplication symbol.
Provide your answer below:
Answer:
y = 1/2cos(x/2 -5π/4) -1
Step-by-step explanation:
You want the equation of the shifted and scaled cosine function shown in the graph.
TranslationA point on a function f(x) will be translated (right, up) = (h, k) by the transformation ...
g(x) = f(x -h) +k
ScalingA function will be vertically expanded by a factor of p and horizontally expanded by a factor of q by the transformation ...
g(x) = p·f(x/q)
Graphed functionThe graph shows a cosine function with a peak-to-peak amplitude of 1, which is 1/2 the parent function's amplitude, so p=1/2.
The period is (9π/2 -π/2) = 4π, which is twice the period of the parent cosine function, so q=2.
The first peak of the graphed waveform is at x=5π/2, and the midline of the graphed waveform is y=-1, so we have (h, k) = (5π/2, -1).
Putting these transformations together, we find the equation of the graph to be ...
y = 1/2cos((x - 5π/2)/2) -1 . . . . . . scaling applied before translation
y = 1/2cos(x/2 -5π/4) -1
Find the product.
(b-na)(4b+9na)
Enter the correct answer.
The product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
How do you find the product of an expression?Algebraic expressions can be multiplied using the following procedures. You can start by calculating the algebraic sum of the like and unlike terms, multiplying the term coefficients, and adding the variable powers with the same base.
Given:
To find the product of (b-na)(4b+9na).
To determine the product, multiply each term of the first expression by each term of the second expression.
(b-na)(4b+9na)
= 4b² + 9abn - 4abn - 9a²n²
= 4b² + 5abn - 9a²n²
Therefore the product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
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In the box below, explain why this is an error. What should he have done?
He should have divided both sides by -10.
Maddox has $100 and plans to spend $20 each time he goes to the movies. At this rate,how many times can Maddox go to the movies?O $5O 5 timesО 4 timesO $120
ANSWER
EXPLANATION
addox has $100.
He plans to spend $20 each time he goes to the movies.
To find out how many times he can go to the movies,
Meghan has her own business. When she makes money, it is called income. When she spends money, it is called expenses. Choose the phrases below to explain how to use positive or negative integers to represent income and expenses.
You would use
Choose...
integers to represent income because it is a
Choose...
amount.
You would use
Choose...
integers to represent expenses because they are
Choose...
income.
The positive integer represents an addition to the income while.a negative integer represents a subtraction.
How to illustrate the information?Positive integers are used to represent income since they indicate an increase rather than a decrease in the financial value of the company. In other words, cash is coming in rather than leaving. A positive number 10 is used as an example to illustrate an increase in operating revenue when there is profit on items sold, say $10.
When you express an expense with a negative number, you're actually subtracting money value rather than adding it. In other words, money is leaving the company rather than being brought in. For instance, when a transportation expense is incurred to deliver items to the customer, it is recorded as an expense deducted from, let's say, the business' revenue sales. Since they are already identified and recognized as expenses and deducted nonetheless, they are typically shown in brackets in accounting to signify negative worth.
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Use the graph to write the factorization of x2 + 4x - 5.10+y = x2 + 4x-5-1010-10O A. (x + 1)(x - 5)B. (x + 5)(x-1)C. (x-3)(x-2)D. (X+6)(x-2)
Solution
From the given graph
The zeros of the given graph are
[tex]x=-5,1[/tex]Converting the zeros to roots gives
[tex]\begin{gathered} x=-5,1 \\ x=-5 \\ x+5=0 \\ x=1 \\ x-1=0 \end{gathered}[/tex]The factorized form of the equation of the given graph is
[tex](x+5)(x-1)[/tex]Hence, the answer is option B
i need help with this asap Consider the following equations.Approximate the solution to the equation f(x) = g(x) using three iterations of successive approximation. Use the graph below as a starting point.
we have the equations
[tex]\begin{gathered} f(x)=\frac{x+1}{x^2} \\ \\ g(x)=\frac{x-1}{x+1}+1 \end{gathered}[/tex]equate both equations
[tex]\frac{x+1}{x^2}=\frac{x-1}{x+1}+1[/tex]First iteration
For x=1
[tex]\begin{gathered} \frac{1+1}{1^2}=\frac{1-1}{1+1}+1 \\ \\ 2=1 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} \frac{2+1}{2^2}=\frac{2-1}{2+1}+1 \\ \\ \frac{3}{4}=\frac{1}{3}+1 \\ \\ \frac{3}{4}=\frac{4}{3} \\ 0.75=1.33 \end{gathered}[/tex]For x=1.5
[tex]\begin{gathered} \frac{1.5+1}{1.5^2}=\frac{1.5-1}{1.5+1}+1 \\ \\ \frac{\frac{5}{2}}{\frac{9}{4}}=\frac{\frac{1}{2}}{\frac{5}{2}}+1 \\ \\ \frac{20}{18}=\frac{1}{5}+1 \\ \frac{10}{9}=\frac{6}{5} \\ 1.11=1.2 \end{gathered}[/tex]the answer must be less than 1.5 and greater than 1
so
Verify each option
A ----> 13/8=1.625 -----> is not a solution
B ----> 23/16=1.4375 ---> could be an approximate solution
C ---> 25/16=1.5625 ----> is not a solution
D ---> 7/4=1.75 ----> is not a solution
therefore
The answer is option BSelect the three pairs of numbers that 403 is between.
Answer:
1 and 403 13 and 31 13 and 31
Step-by-step explanation:
If Alejandra estimates that one outfit welghs two pounds and one pair of shoes welghs three pounds, which graph represents the number of
outfits and shoes that Alejandra can pack while staying under the weight limit?
A graph which represents the number of outfits and shoes that Alejandra can pack while staying under the weight limit is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In this scenario, the x-axis represents the number of outfits while the y-axis represents the number of shoes. Additionally, since one pair of shoes weighs three (3) pounds and one outfit weighs two (2) pounds, the x and y coordinates would be given by this inequality:
2x + 3y < 30
Making y the subject of formula, we have:
3y < -2x + 30
Dividing all through by 3, we have:
3y/3 < -2x/3 + 30/3
y < -2x/3 + 10
Note: For 30 pounds, there would be 10 shoes (0, 10) while for 30 pounds, there would be 15 outfits (15, 0).
In conclusion, the boundary line is dashed or dotted to indicate that the boundary is not part of the solution because the inequality symbol is less than (<).
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HELP! ALgebra 2
A soccer ball is kicked into the air so that its height, h, in feet, after t seconds is given by the function:
h(t)= -16t^2+96
What is the maximum height the ball reaches?
How long is the ball in the air?
The maximum height reached by the ball in discuss as described is; 96 while the time spent by the ball in the air is; 0 seconds.
What is the maximum height the ball reaches and how long was the ball in the air?It follows from the task content that the maximum height of the ball in the air is to be determined and so.is the time spent by the ball in the air.
Therefore, since the correct form of the function given is;
h(t) = -16t² + 96
By expressing the function above in vertex form; it follows that we have;
h(t) = -16 (t - 0)² + 96.
This vertex form function above therefore translates to the fact that the point, (0, 96) represents the vertex of the balls motion curve.
Ultimately, the maximum height reached by the ball is; 96 and the time it takes to reach this height is; 0 seconds.
PS; The scenario above in real life situation would translate to dropping a ball from the top.
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Element X is a radioactive isotope such that every 70 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 610 grams, how much of
the element would remain after 17 years, to the nearest whole number?
The element would remain 515 grams after 17 years.
What is isotope?Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.
Given Data
the initial mass of a sample of Element X is 610 grams
Element X is a radioactive isotope such that every 70 years, its mass decreases by half.
Since the half-life, or the number of years after which an isotope decays to half its original level, is stated to be 70 years.
k = [tex]\frac{2}{70}[/tex]
k= 0.0099
Equation-
N = 610e⁻⁰°⁰⁰⁹⁹ˣ
x = time
time = 17
N = 610 e⁻⁰°⁰⁰⁹⁹⁽¹⁷⁾
N = 610(0.845)
N = 515.49
The element would remain 515 grams after 17 years.
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Can i get some help
Answer:
Explanation:
iven the function:
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 44% probability of winning the first contract. If they win the first contract, the probability of winning the second is 66%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 54%.
A. What is the probability that they win both contracts?
B. What is the probability that they lose both contracts?
C. What is the probability that they win only one contract?
A) The probability that the Aerospace Company wins both contracts is 29.04%.
B) The probability that the Aerospace Company loses both contracts is 70.96%.
C) The probability that the Aerospace Company wins only one contract is 23.76%.
What is the probability?Probability describes the chance or likelihood of an expected event occurring out of many outcomes.
Probability is a ratio of an outcome versus many possible events.
Probability is represented as a percentage, fraction, or decimal, like a ratio.
How the probabilities are calculated:The probability of winning the first contract = 44%
The probability of losing the first contract = 56% (1 - 44%)
The probability of winning the first and the second contract = 66%
The probability of losing the first and the second contract = 34% (1 - 66%)
The probability of losing the first contract and winning the second = 54%
A) The probability that they win both contracts = the probability of winning the first contract multiplied by the probability of winning the second contract.
= 29.04% (44% x 66%)
B) The probability that they lose both contracts = 1 minus the probability of winning both contracts.
= 70.96% (1 - 29.04%)
C) The probability that they win only one contract = the probability of winning the first contract multiplied by the probability of winning only the second contract.
= 23.76% (44% x 54%)
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Please help me I’m miserable because I was sick.It’s 2:00AM and this is due at 8 somebody please help me
Answer:
see explanation
Step-by-step explanation:
(a)
the angles shown are alternate interior angles and are congruent
(c)
since they are congruent , then
- 1 + 8x = 7x + 11 ( subtract 7x from both sides )
- 1 + x = 11 ( add 1 to both sides )
x = 12
(d)
then
7x + 11 = 7(12) + 11 = 84 + 11 = 95
- 1 + 8x = - 1 + 8(12) = - 1 + 96 = 95
Claudia is considering taking a vacation but she's not sure if she wants to drive or fly somewhere. She realized that it would take her the same amount of time to drive 150 miles as it would take a plane to fly 1350 miles. If the plane is flying 400 mph faster than the car, how fast is each traveling?
Solution
For this case we know that the distance covered by the plane is 1350 mi and the velocity 400 mph
We also know that the distance is given by:
D= vt
Let D= Distance travelled by the car and airplane
Vp= Vc+ 400 (Velocity of the plane)
1350 = (Vc +400)*t
150 = Vc * t
We can solve for t and we got:
t= 150/Vc
Replacing in the first equation we got:
1350= (Vc+400)* (150/Vc)
Solving for Vc we got:
1350= 150 + 60000/Vc
1200 = 60000/Vc
Vc= 60000/1200= 50 mph
Then the velocity of the car is Vc= 50mph and for the plane
Vp= 50+ 400= 450 mph
can someone help me with this
If each of the 4 sloping side ahs length 10 cm
This implies they have length 40 cm altogether
To find the base length, simply subract the 40 cm from the total length of 68cm
68 - 40 = 28
each base length = 28/4 = 7cm
Area of the square base is = l x l = 7 x 7 = 49 cm²
Write a quadratic function given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
y=(x+3)(x=2)
y=(x-3)(x+2)
y=3(x-3)(x-2)
y=3(x-3)(x+2)
Quadratic function is 3(x+3)(x-2) given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
What is quadratic function?In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
Standard form, vertex form, and intercept form are three alternative ways a quadratic function can be expressed. The basic forms of each of them are as follows:
f(x) = ax² + bx + c in standard form, where a 0.
Vertex form: (h, k) is the vertex of the parabola representing the quadratic function, and f(x) = a(x - h)² + k is the equation.
The quadratic function's x-intercepts are (p, 0) and (q, 0), and its intercept form is f(x) = a(x - p)(x - q), where a 0.
Given Data
Roots (-3,0) and (2,0)
Point (1,-12)
y = a(x-(-3) (x-2)
y = a(x+3)(x-2)
Equating points
-12 = a(1+3)(1-2)
-12 = a(4)(-1)
-12 = -4a
a = 3
f(x) = 3(x+3)(x-2)
Function is 3(x+3)(x-2).
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You are the diving officer on a submarine conducting diving operations. As you conduct your operations, you realize that you can relate the submarine’s changes in depth over time to some linear equations. The submarine descends at different rates over different time intervals.
1. The depth of the submarine is 50 ft below sea level when it starts to descend at a rate of 10.5 ft/s. It dives at that rate for 5 s.
Part A
Using a linear function, the constraints for the values of x and of y, respectively, are given as follows:
x: 0 ≤ x ≤ 5.y: -102.5 ≤ y ≤ -50.What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the constant rate of change.The coefficient b is the y-intercept of the function, which is the initial value of the function.In the context of this problem, we have that:
The initial depth is of 50 ft, hence the intercept is of -50.The submarine descends at a rate of 10.5 ft/s, hence the slope is of -10.5.Thus the linear function that models the depth of the submarine after x seconds is given by:
f(x) = -50 - 10.5x.
This rate is for 5 seconds, hence the constraint for x is 0 ≤ x ≤ 5, and the minimum depth attained by the submarine is:
f(5) = -50 - 10.5(5) = -102.5 ft.
Hence the constraint for y is given as follows:
-102.5 ≤ y ≤ -50.
What is the missing information?The complete problem is given by the image at the end of the answer.
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Write the quadratic equation whose roots are -6 and 5, and whose leading coefficient is 2 .
Answer: y = 2x² + 2x - 60
Step-by-step explanation:
We will write this in factored form since we are given the roots and leading coefficient. This will be written in the form y = c(x - a)(x - b) where c is the coefficient and a & b are the roots.
y = c(x - a)(x - b)
y = 2(x + 6)(x - 5)
Now, we will distribute so we end up with the standard quadratic equation form.
y = 2(x + 6)(x - 5)
y = 2x² + 2x - 60
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Evaluate: - 2 to the third power - 45(15+10-23)
1. Remember
[tex]2^3[/tex]Means
[tex]2\times2\times2[/tex]Therefore,
[tex]2^3=2\times2\times2=8[/tex]2. Remember that we have to solve what's inside the parenthesis first. Therefore,
[tex]45(15+10-23)=45(2)=90[/tex]