Answer:
I believe it would be TRUE but sorry if I'm wrong!
Step-by-step explanation:
Answer: True
Step-by-step explanation:
I got it right on my lesson.
You want to have $2 million in real dollars in an account when you retire in 35 years. The nominal return on your investment is 9.94% and the inflation rate is 3.2%. What is the real amount you must deposit each year to achieve your goal?
a. $20,403.
b. $7,482.
c. $16,017.
d. $18,887.
e. $19,711.
Answer:
b. $7,482.
Step-by-step explanation:
20,403 nets $5,996,106 after 35 years.
7,482 nets $2,198,837 after 35 years.
$7,482 is over 2 million and the smallest amount, so you don't have to solve for the other ones.
The real amount that must deposit each year to achieve your goal is $16,017 option (c) is correct.
What is invested amount?An investment is a payment made to acquire the securities of other firms with the intention of making a profit.
First, we will calculate the real rate of interest:
r = [(1+nominal rate)/(1+inflation rate)] - 1
Nominal rate = 9.94% = 0.094
Inflation rate = 3.2% = 0.032
r = [(1+0.094)/(1+0.032)] - 1
After calculating,
r = 0.0653 or 6.53%
Deposit amount each year:
Future value = PV[(1+r)ⁿ - 1]/(r)
2000000 = PV[(1+0.0653)³⁵ - 1]/(0.0653)
After calculating,
PV = $16020.544
The value $16020.544 is near the $16,017.
Thus, the real amount that must deposit each year to achieve your goal is $16,017 option (c) is correct.
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i nee help so bad math
Answer:
2L - the third picture
2W - the fifth picture
4 - the first picture
L+2 - the 6th picture
W - the 7th picture
Step-by-step explanation:
2L - the third picture
2W - the fifth picture
4 - the first picture
L+2 - the 6th picture
W - the 7th picture
please help for this question. Thank you
Answer:
A. 8.3
B.18.7
C. 10.4
D. 1.04
Step-by-step explanation:
p(x) = 0.03x² + 0.56x + 6.35
A. Determination of p(3)
p(x) = 0.03x² + 0.56x + 6.35
x = 3
p(3) = 0.03(3)² + 0.56(3) + 6.35
p(3) = 0.03(9) + 1.68 + 6.35
p(3) = 0.27 + 1.68 + 6.35
p(3) = 8.3
B. Determination of p(13)
p(x) = 0.03x² + 0.56x + 6.35
x = 13
p(13) = 0.03(13)² + 0.56(13) + 6.35
p(13) = 0.03(169) + 7.28 + 6.35
p(13) = 5.07 + 7.28 + 6.35
p(13) = 18.7
C. Determination of p(13) – p(3)
From A and B above,
p(13) = 18.7
p(3) = 8.3
p(13) – p(3) = 18.7 – 8.3
p(13) – p(3) = 10.4
D. Determination of p(13) – p(3) / 13 – 3
From C above,
p(13) – p(3) = 10.4
p(13) – p(3) / 13 – 3 = 10.4/ 13 – 3
= 10.4 / 10
= 1.04
If f(x) = 2x + 3 and g(x) =4x - 1, find f(4).
Solve the "f" function with substitute 4 and solve the "g" function with what we get for the "f" function.
f(4) = 2(8) + 3
f(4) = 16 + 3
f(4) = 19
g(19) = 4(19) - 1
g(19) = 76 - 1
g(19) = 75
Best of Luck!
can someone help ? i only have 36 min
Answer:
[tex] \boxed{ \bold{{ \boxed{ \sf8 {x}^{7} + 3 {x}^{6} + {x}^{5} + 5 {x}^{4} - 2 {x}^{3} }}}}[/tex]
Step-by-step explanation:
Here, we have to arrange the polynomial from higher power to lower power.
So, Option C is the correct option
Hope I helped!
Best regards! :D
40.7 is the same as 4.07
Answer:
That would be false
Step-by-step explanation:
if you look at where the decimal is, 40.7 would be bigger
Find the distance between (-7,-2) and (11,3)
Answer:
The answer is
[tex] \sqrt{349} \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-7,-2) and (11,3)
The distance between the points is
[tex]d = \sqrt{ ({ - 7 - 11})^{2} + ({ - 2 - 3})^{2} } \\ = \sqrt{ ({ - 18})^{2} + ({ - 5})^{2} } \\ = \sqrt{324 + 25} \\ [/tex]We have the final answer as
[tex] \sqrt{349} \: \: units[/tex]Hope this helps you
Please help me how to convert fraction to decimal? easy method plz.
Given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3
Answer:
-15
Step-by-step explanation:
start from the inside and go out.
So first plug in -3 into g(x)
g(-3) = -3 - 7 = -10
then plug in -10 into f(x)
f(-10) = 2(-10) + 5 = -15
so f(g(x)) = -15
Answer:
The answer is - 15Step-by-step explanation:
f(x) = 2x + 5
g(x) = x − 7
To find f(g(x)) substitute g(x) into f(x) that's replace every x in f(x) by g(x)
That's
f(g(x)) = 2(x - 7) + 5
= 2x - 14 + 5
f(g(x)) = 2x - 9
When x = - 3
Substitute - 3 into f(g(x))
That's
f(g(3)) = 2(-3) - 9 = - 6 - 9 = - 15Hope this helps you
Is 0.4/0.8 rational or irrational ?
Answer:
[tex]\Huge \boxed{\mathrm{ Rational }}[/tex]
Step-by-step explanation:
Rational numbers can be expressed as fractions with whole numbers as the numerator and the denominator.
[tex]\displaystyle \frac{0.4}{0.8}[/tex]
Multiply both the numerator and the denominator by 10.
[tex]\displaystyle \frac{4}{8} =\frac{1}{2}[/tex]
The result is a simplified fraction with both the numerator and the denominator being whole numbers. The result is rational.
Calculate the producers' surplus for the supply equation at the indicated unit price p.(Round your answer to the nearest cent.) p = 120 + q; p = 165
Answer: ps = 1012.5
Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5
Step-by-step explanation:
Given that;
p = 120 + q ; p = 165
Now to find the producer's surplus for supply equation p=f(q) at the indicated unit price; we find p
so from p = 120 + q ; p = 165, if we substitute for q
120 + q = 165
q = 165 - 120 = 45
so
ps = ⁴⁵∫₀ ( 165 - (120+q) dq
ps = ⁴⁵∫₀ ( 45 - q) dq
USING THE EXPRESSION [ xⁿdx = xⁿ⁺¹ / n+1]
ps = [45q - q²/2]₀⁴⁵
ps = [45(45) - 45²/2] [45(0) - (0)²/2]
ps = [2025 - 1012.5] - [0]
ps = 1012.5
Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5
Subtract 5y ^2−6y−115, y, squared, minus,
Answer:
y^2+8y+16
Step-by-step explanation:
6y^2 +2y +5 - ( 5y^2 -6y-11)
Distribute the minus sign
6y^2 +2y +5 - 5y^2 +6y+11
Combine like terms
y^2+8y+16
Which of the following is equal to 5% of 55% of 555?
Answer:
Step-by-step explanation:
The correct answer is 15.15.
The solution is 15.2625
The value of the equation 5% of 55% of 555 is A = 15.2625
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as n = 555
Now , let the equation be represented as A
The value of A = 5% of 55% of 555
On simplifying the equation , we get
55 % of 555 = 555 x ( 55/100 )
55 % of 555 = 555 x 0.55
55 % of 555 = 305.25
Now , 5% of 55% of 555 = A
A = 5 % of 305.25
The value of A = 305.25 x ( 5/100 )
The value of A = 305.25 x ( 0.05 )
The value of A = 15.2625
Hence , the value of the equation is A = 15.2625
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Find the largest value of $n$ such that $5x^2+nx+48$ can be factored as the product of two linear factors with integer coefficients.
Answer:
[tex]n = 241[/tex]
Step-by-step explanation:
Given
[tex]5x^2 + nx + 48[/tex]
Required
Determine the highest value of n
From the given equation, 5 is a prime number;
So, the factors of x² is 5x and x or -5x and -x
Since [tex]5x^2 + nx + 48[/tex] has all shades of positive terms, we'll make use of 5x and x
The factorized expression can then be:
[tex](5x + a)(x + b)[/tex]
Open the brackets
[tex]5x^2 + ax + 5bx + ab[/tex]
Equate this to the given expression
[tex]5x^2 + ax + 5bx + ab = 5x^2 + nx + 48[/tex]
[tex]5x^2 + (a + 5b)x + ab = 5x^2 + nx + 48[/tex]
By direct comparison;
[tex]5x^2 = 5x^2[/tex]
[tex](a + 5b)x = nx[/tex]
[tex]a + 5b = n[/tex] ---- (1)
[tex]ab = 48[/tex] --- (2)
From (2) above, the possible values of a and b are:
[tex]a = 1, b = 48[/tex]
[tex]a = 2, b = 24[/tex]
[tex]a = 3, b = 16[/tex]
[tex]a = 4, c = 12[/tex]
[tex]a = 6, b = 8[/tex]
[tex]a = 8, b = 6[/tex]
[tex]a = 12, b = 4[/tex]
[tex]a = 16, b = 3[/tex]
[tex]a = 24, b = 2[/tex]
[tex]a = 48, b = 1[/tex]
Of all these values; the value of a and b that gives the highest value of n is;
[tex]a = 1, b = 48[/tex]
So;
Substitute 1 for a and 48 for b in (2) [tex]a + 5b = n[/tex]
[tex]1 + 5 * 48 = n[/tex]
[tex]1 + 240 = n[/tex]
[tex]241 = n[/tex]
[tex]n = 241[/tex]
Hence, the largest value of n is 241
Answer:
Step-by-step explanation:
The two factors of $5x^2+nx+48$ must be in the form $(5x+A)(x+B)$. $A$ and $B$ must be positive integers to form the largest value of $n$. Therefore, $AB=48$ and $5B+A=n$. To form the largest value of $n$, $B$ must equal $48$. Therefore, $A=1$. \[5B+A=5(48)+1=\boxed{241}\]
(5x+3)(7x-7) how do find x
We can use the FOIL method to solve.
(5x + 3)(7x - 7)
(5x * 7x) + (5x * -7) + (3 * 7x) + (3 * -7)
35x - 35x + 21x - 21
0 + 0
0
Best of Luck!
The endpoints of a line segment graphed on a coordinate plane are (8, 5) and (10, 1). What are the coordinates of the midpoint of the line segment?
Answer:
(9,3)
Step-by-step explanation:
(8+10)/2. (5+1)/2
18/2. 6/2
9,3
A cash box of $1 and $5 bills is worth $45. The number of $1 bills is 3 more than the number of $5 bills. How many of each bill does it contain?
Answer:
There are 10 $1 bills and 7 $5 bills
Step-by-step explanation:
7($5 bills) x 5
=35
7+3 (3 more $1 bills)
=10
10+35
=45
Answer:
$1: 10
$5: 7
Step-by-step explanation:
To find out how many of each bill is in the cash box, create an expression
x = the dollar bills
This makes the $5 bills 5x and the $1 bills x (this can also be 1x)
When it says "The number of $1 bills is 3 more than the number of $5 bills" This means that the number of $1 is x + 3 and the number of $5 is 5x
When you put it together the expression will be x + 3 + 5x = 45
First add x and 5x, making it 6x
Next subtract 3 from each side, which makes the equation 6x = 42
Lastly, divide 6 from each side, this means that x = 7
To find out how many bills there are substitute 7 wherever there is an x
This mean that the number of $1 is 7 + 3 (10), and the number of $5 bills are 5x7 (35), but its just 7 because they are $5 each
15 points?
Solve
(7-w)(5w-8) = 0
(if there is more that one solution, separate them with commas.)
Please state what w is...
━━━━━━━☆☆━━━━━━━
▹ Answer
(w = 7, w = 8/5)
▹ Step-by-Step Explanation
(7 - w)(5w - 8) = 0
Separate:
7 - w = 0
5w - 8 = 0
Solve:
w = 7
5w - 8 = 0
(w = 7, w = 8/5)
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
w = 7, 8/5
Step-by-step explanation:
(7 - w) (5w - 8) = 0
(7 - w) × (5w - 8) = 0
7 × 5w - 7 × 8 - w × 5w + w × 8 = 0
35w - 56 - 5w² + 8w = 0
- 5w² + 43w - 56 = 0
5w² - 43w + 56 = 0
5w² - 35w - 8w + 56 = 0
5w(w - 7) - 8(w - 7) = 0
(w - 7) (5w - 8) = 0
w - 7 = 0 OR 5w - 8 = 0
w = 7 OR w = 8/5
Thus, the value of w is 7, 8/5
Factor xy−4y+4x−16 by grouping
Answer:
[tex](y+4)(x-4)[/tex]
Step-by-step explanation:
Given the expression:
[tex]xy-4y+4x-16[/tex]
[tex](xy-4y)+(4x-16)[/tex]
Take the common factor
[tex]y(x-4)+4(x-4)[/tex]
[tex](y+4)(x-4)[/tex]
The factored expression is (x - 4)(y + 4).
To factor the expression xy - 4y + 4x - 16 by grouping, we first group the terms in pairs and look for common factors:
xy - 4y + 4x - 16
Now, let's factor by grouping:
Step 1: Group the terms in pairs.
(xy - 4y) + (4x - 16)
Step 2: Factor out the common factor from each group.
In the first group, we can factor out "y" from the two terms:
y(x - 4)
In the second group, we can factor out "4" from the two terms:
4(x - 4)
Step 3: Notice that both groups have a common factor of (x - 4). Factor it out.
(x - 4)(y + 4)
So, the factored expression is (x - 4)(y + 4).
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Jenna bought a coat on sale for $120, which was 2/3 of the original price. What was the original price of the coat?
Answer:
$
180
Step-by-step explanation:
The original price is the quotient between $120 and 2/3, we get:
P = $180
What is the original price?
We know that 2/3 of the original price is $120, then to get the original price, we need to take the quotient between $120 and 2/3.
[tex]P = \frac{\$120}{2/3} = (3/2)*\$ 120[/tex]
By taking that quotient we will see that the original price of the coat is:
[tex]P = (3/2)*\$120 = $180[/tex]
We conclude that the original price of the coat is $120.
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How are the two angles the same?
Answer:
if ABCD is a rhombus then the diagonal of rhombus bisect it into two equal triangles.
Step-by-step explanation:
In triangles ABC and CDA,
AB= CD (S) because rhombus has equal sides.BC = AD (S) as as reason 1.AC= AC (S) being common side of both trianglesso the triangles are congruent to each other by S.S.S. fact/ axiom
PLZ HELP WILL MARK BRAINLIEST
What is the function g(x) created from f(x) = x2 by moving the graph left 7 units, adding vertical compression by a factor of 1 6 , and shifting the graph down 8 units?
Answer:
g(x) = (1/6)(x +7)^2 -8
Step-by-step explanation:
The transformation ...
g(x) = a·f(x -h) +k
represents vertical scaling by a factor of 'a', right shift by h units, and up shift by k units. You want the function g(x) for f(x) = x^2, a = 1/6, h = -7, and k = -8. Those transformations give you ...
g(x) = (1/6)(x +7)^2 -8
112,783 expanded form
Answer:
100,000 + 10,000+ 2,000+ 700+ 80+ 3
what I need to Know is 5003×5984= can you answer my question please thanks
Answer:
29,937,952 mark me as brainliest
Step-by-step explanation:
Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
z = \sqrt{x^2+y^2} and the sphere x2 + y2 + z2 = 32.
Answer: Find the answer in the attachment
Step-by-step explanation:
The volume constrained both by the cone and the sphere is [tex]21.905\pi[/tex] cubic units.
The volume of a solid in cylindrical coordinates ([tex]V[/tex]) can be determined by the following triple integral:
[tex]V = \iiint dz\,r\,dr\,d\theta[/tex] (1)
The solid is constrained by the following equations in cylindrical coordinates:
Sphere
[tex]r^{2}+z^{2} = 32[/tex] (2)
Cone
[tex]z = r[/tex] (3)
The integration limits can be identified by using the following intervals:
[tex]z \in [0, +\sqrt{32-4^{2}}][/tex], [tex]r \in [0,4][/tex], [tex]\theta \in [0,2\pi][/tex]
And the triple integral has the following form:
[tex]V = \int\limits_{0}^{2\pi}\int\limits_{0}^{4}\int\limits_{0}^{+\sqrt{32-r^{2}}} dz\,r\,dr\,d\theta[/tex] (4)
Now we proceed to integrate the expression thrice:
[tex]V = \int\limits_{0}^{2\pi}\int\limits_{0}^{4}\sqrt{32-r^{2}}\,r\,dr\,d\theta = 10.952\int\limits_{0}^{2\pi}\,d\theta = 21.905\pi[/tex]
The volume constrained both by the cone and the sphere is [tex]21.905\pi[/tex] cubic units.
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F = 2xi+3yj and σ is the cube with opposite corners at (0,0,0) and (3,3,3), oriented outwards. Find the flux of the flow field F across σ.
Answer:
the flux of the flow field F across σ = 135
Step-by-step explanation:
Given that :
F = 2xi + 3yj
and σ is the cube with opposite corners at (0,0,0) and (3,3,3) oriented outwards.
Using divergence theorem,
[tex]\iint \ F.ds = \iiint \ div. f \ dV[/tex]
[tex]div \ f = \dfrac{\partial }{\partial x}2x + \dfrac{\partial}{\partial y }(3y)[/tex]
f = 2 +3 = 5
where ;
F = 2xi + 3yj
Thus , the triple integral can now be ;
[tex]= \iiint 5.dV[/tex]
[tex]=5 \iiint \ dV[/tex]
[tex]= 5 \ \int^{3}_{0}\int^{3}_{0}\int^{3}_{0} \ dV[/tex]
= 5(3)(3)(3)
= 135
Convert the repeating decimal below into a fraction.
0.234
Answer:
the answer is 117/500 hop this helps:)
Step-by-step explanation:
0.234 = 117 / 500
as a fraction
To convert the decimal 0.234 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
0.234 = 0.234/1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 3 numbers after the decimal point, we multiply both numerator and denominator by 1000. So,
0.234/1
= (0.234 × 1000)
(1 × 1000)
= 234
1000
.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(234,1000) = 2. So,
(234÷2)
(1000÷2)
= 117/500
when reduced to the simplest form.
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
I would appreciate it!
A bricklayer is able to set 2.5 bricks in one minute. How many bricks can he set in 8 hours?
2,000
O 150
O 20
O
1, 200
0
120
Answer:
1200
Step-by-step explanation:
First we need to figure out how many bricks can be set in an hour, so you do 2.5*60, since there are 60 min. in an hour. That's 150.
Now we do 8 hours. You do 150*8, which is 1200.
Hope this helps.
Answer:
1200
Step-by-step explanation:
The reason behind this answer is because you first multiply 2.5 by 60 for the 60 minutes in an hour and ultimately get 150 then you multiply that answer by 8 to get 1200.
Which of the following is NOT a rational number?
7.11
4.333...
8/11
-2852664798743...
Answer:
A rational number is a number that can be written as a fraction.
A. 7.11
=> 711/100
So, the 1st option is a rational number.
B. 4.333....
=> 4 1/3
=> 13/3
So, the 2nd option is a rational number.
C. 8/11
=> This is in its fractional form.
=> So, the 3rd option is a rational number.
D. -2852664798743
=> This can't be written in a fractional form.
=> So, the 4th option is NOT a rational number.
Does a point have a location?
A point in geometry is a location.
It has no size, width, length or depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions.