The compounded interest is applied to the amount in the account at end
of a period specified in the rate of compounding.
The amount in the account at the end of 6 quarters is approximately $16,767.2Reasons:
The interest paid on the account = 4% compounding
Amount with which she opened the account = $10,000
Amount she makes as deposit at the end of each quarter = $1,000
Therefore;
The interest per quarter = 4% ÷ 4 = 1%
Amount in the account after the end first quarter, A₁, is therefore;
A₁ = 10,000 × 0.01 + 10,000 + 1,000 = 11,100
The amount in the second quarter, A₂, is given as follows;
A₂ = 11,100 × 0.01 + 11,100 + 1,000 = 12211
A₃ = 12211 × 0.01 + 12211 + 1,000 = 13333.11
A₄ = 13333.11 × 0.01 + 13333.11 + 1,000 = 14466.4411
A₅ = 14466.4411 × 0.01 + 14466.4411 + 1,000 = 15611.105511
At the end of the 6th quarter, we have;
A₆ = 15611.105511 × 0.01 + 15611.105511 + 1,000 = 16767.2165991
The amount in the account at the end of 6 quarters, A₆ ≈ $16,767.2
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PLZ HELP ME!! IF YOUR A GENUIS
The equation 4.05p+14.40=4.50(p+3) represents the number of p of pounds of penuts you need to make a trail mix. How many pounds of peanuts do you need for the trail mix?
Since "p" represents the number of pounds of peanuts and:
4.05p + 14.40 = 4.50(p + 3) [then by distributing we have:
4.05p + 14.40 = 4.50p + 13.5 [then by subtracting 13.5 from both sides we have:
4.05p + 0.9 = 4.50p [then by subtracting 4.05p from both sides we have:
0.9 = 0.45p [then by dividing both sides by 0.45 we have:
2 = p
So there are 2 pounds of peanuts needed for the trail mix.
There are 81 calories in a 0.75 cup serving of chicken noodle soup. How many calories are in a 2 cup serving?
Answer:
162Step-by-step explanation:
There are 81 calories in a 0.75 cup serving of chicken noodle soup. How many calories are in a 2 cup serving?
0.75*2=2 cups
81*2=162
Answer:
x = 216
Step-by-step explanation:
[tex]\frac{81}{0.75}[/tex] = [tex]\frac{?}{2}[/tex]
I hope this helps!!
What is this expression translated into words?
2n + 1
a
one plus 2 divided by a number n
b
2 times 1 added to a number n
c
two times a number n added to one
Answer:
C. two times a number n added to one
A store sells tents,sleeping bags,and campstools.A customer buys a tent, 2 sleeping bags, and 3 campstools for 212$.the price of the tent is 5 times the cost of a campstool.the cost of a sleeping bag is 6$more than the cost of a campstool.find the cost of was just item
The cost of each campstools, tent and sleeping bag is $20, $100 and $26
let
tent = 1
sleeping bags = 2
campstools = 3
Total cost = $212
tent = t
sleeping bags = s
campstools = c
If
t = 5c
s = c + 6
Total = t + 2s + 3c
212 = 5c + 2(c + 6) + 3c
212 = 5c + 2c + 12 + 3c
212 = 10c + 12
212 - 12 = 10c
200 = 10c
c = 200/10
c = 20
t = 5c
= 5 × 20
= 100
s = c + 6
= 20 + 6
= 26
Therefore, the cost of each campstools, tent and sleeping bag is $20, $100 and $26
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explain or show that the point (5,-4) is a solution to this system of equations
Answer:
You could substitute the point (5,-4) into each equation
Step-by-step explanation:
x=5 y=-4
3x-2y=23
3(5)-2(-4)=23
15+8=23
23=23
2x+y=6
2(5)+(-4)=6
10-4=6
6=6
The points go into each equation which proves that the point (5,-4) is the solution.
(i don't know if I did this right, I apologize if I didn't
.RP.1.3 | JoAnn bought 2 shirts for $13.50 each and a purse for $8.
The sales tax was 6%. What is the total she paid for her
purchase, including tax?
Answer:
The answer is $22.79. Hope this helped! If the answer is wrong i'm super sorry!
Step-by-step explanation:
$13.50 + $8 = $21.50
0.06 x 21.50 = $1.29
$1.29 + $21.50 = $22.79
An ice cream cup has 3 scoops of chocolate, 4 scoops of vanillas and 3 scoops of butter scotch ice cream. What is the probability that if you randomly sampled the ice cream that you will taste chocolate or vanilla ice cream?
Answer:
7 out of 10
Step-by-step explanation:
if you have 10 in the cup then you add
4 vanilla 3 chocolate = 7
and add all scoops together and you get 10
so your probability would be 7 out of 10
another way to say it is
the probability of getting chocolate or vanilla ice cream from the cup would be 7 out of 10
convert 3x-y=-5 to slope intercept form
Answer:
y=3x+5
Step-by-step explanation:
y=mx+b
-y=-5-3x
divide each term
y=5+3x
reorder 5 and 3x
answer:y=3x+5
Need help please if anyone one can help me now I will like that. Thanks
Triangle H J K is cut by line segment A B. Line segment A B goes from side H J to side H K. The length of H A is 5. 25 inches, the length of H B is 3 inches, and the length of B K is 5 inches. What is the length of Line segment A J if Line segment A B is parallel to lines segment J K? 8 in. 8. 75 in. 10. 25 in. 14 in.
The segments on triangle HJK are illustrations of equivalent ratios
The length of line AJ is 8.75 inches
The given parameters are:
[tex]H A = 5.25[/tex]
[tex]HB = 3[/tex]
[tex]BK = 5[/tex]
Because lines AB and JK are parallel lines, then we have the following equivalent ratios
[tex]HA:HB = AJ:BK[/tex]
Substitute values for length HA, HB and BK.
[tex]5.25:3 = AJ:5[/tex]
Express both ratios as fractions
[tex]\frac{5.25}{3} = \frac{AJ}5[/tex]
Multiply both sides by 5
[tex]\frac{5.25}{3} \times 5= AJ[/tex]
[tex]8.75= AJ[/tex]
Rewrite as:
[tex]AJ = 8.75[/tex]
Hence, the length of line AJ is 8.75 inches
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Thanks so very much!!
Answer:
yw
Step-by-step explanation:
help please anybody Mhm
Answer:
B
Step-by-step explanation:
Answer:
Your answer would be C
Step-by-step explanation:
Because its a ratio of integers with a nonzero denominator.
The square of a number minus twice the number is 48. Find the number.
Answer: 8 or -6
Step-by-step explanation:
x^2 - 2x = 48
x^2 - 2x - 48 = 0
(x-8)(x+6) = 0
x = 8 or -6
System practice problems
Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
Find the area, in square inches, of a square with a side length 1/4 in.
Answer:1/16 squared
Step-by-step explanation:
1/4*1/4
4*4=16
1/16
Someone please help me with this
PLEASE HELP!
Determine the value of X.
Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Step-by-step explanation:
The figure below shows the number of dots in each of the first four terms of a pattern.
image 3946d177031641899e8a9055b29f185e
Which of these can be used to determine
N
, the number of dots, given
t
, the number of the term in the pattern?
N
=
4
(
t
−
1
)
N = 4 ( t − 1 )
N
=
3
t
+
1
N = 3 t + 1
N
=
3
(
t
−
1
)
+
1
N = 3 ( t − 1 ) + 1
N
=
3
t
+
2
Answer:
there is nothing just a a codding log
Step-by-step explanation:
a movie rental service charges a $15 fee plus $1.50 per rental. suppose you have $40 to spend. how many movies can you rent
Answer:
16
Step-by-step explanation:
y = mx+b, where y is cost x is # of movies, m is $ per rental and b is the flat charge.
y = 1.50x+15
40 = 1.50x+15
25 = 1.50x
16.666... = x
You can rent about 16 movies
Hope that helps
Answer:
40 = 1.50x+15
25=1.50x
x=16
16 movies
Step-by-step explanation:
which of the following are equivalent
A total of 11 trucks was used to carry 126 tonnes of iron. Some of the trucks carry
16 tonnes each, and the rest carry 6 tonnes each. Form an equation and solve it to
find the number of 16 tonne trucks.
Step-by-step explanation:
x = number of trucks with 16 tonnes capacity
y = number of trucks with 6 tonnes capacity
x + y = 11
16x + 6y = 126
the first equation gives us
x = -y + 11
and we use that in equation 2 :
16(-y + 11) + 6y = 126
-16y + 176 + 6y = 126
-10y = -50
10y = 50
y = 5
x = -y + 11 = -5 + 11 = 6
the number of 16 tonne trucks was 6.
Which frequency table is consistent with the histogram of weights of 86 different students, below?
Answer:
B
Step-by-step explanation:
The incorrect tables each have at least one flaw that makes it not match the histogram.
A. The relative frequency associated with 4 of 86 is about 0.047, not 0.055. The relative frequencies are incorrect.
B. this table matches the histogram
C. The "bins" are not of uniform width, nor are they centered on the same values as shown in the histogram.
D. The values in a cumulative frequency table should be non-decreasing. The table value of 24 should be 54.
CD is a line parallel to AB and passes through the point (3, 5).
c. Find the equation of the line CD
Answer:
y=5/3x+b
Step-by-step explanation:
Supposing CD uses the equation y=mb (meaning CD passes through the origin) and passes through (3,5), we then know the slope if 5/3 and the y intercept is 0. We can then write CD's equation as y=5/3x+0, or just y=5/3x.
So if AB is parallel to CB, then their equation is y=5/3x+b, as we don't the y-intercept yet.
Thank you!
The price of an item has been reduced by 45%. The original price was $60. What is the price of the item now?
Answer:
the answer to the question is 15$
If you put $1000 in a savings account that yields an 7% annual rate of interest that is compounded weekly, how much would that be worth in 25 weeks
Answer:
A = $1034
Step-by-step explanation:
The relevant Amount function is A = P(1 + r/n)^(n*t), where r is the annual interest rate as a decimal fraction, n is the number of compounding periods per year, and t is the number of years.
There are 52 weeks in a year. Hence, n = 52, and 25 weeks = 25/52 year, or 0.481 year.
The accumulation (value of the savings) would be
A = ($1000)(1 + 0.07/52)^(52*[25/52]), or approximately
A = ($1000)(1.0013)^25, or approximately A = $1034
1. Calculate the equation of the line through the points (1, 1), (4, 3), (10, 7) and (40, 27).
Answer:
y = (2/3)x + 1/3
Step-by-step explanation:
Check that a single straight line will actually go through all four of these points. Going from (1, 1) to (4, 3), the 'rise' is 2 and the 'run' is 3, which would make the slope, m, equal rise/run = 2/3. Going from (4,3) to (10, 7), m = rise/run = 4/6 = 2/3 (again).
Let's find the slope-intercept form of the equation of this line: y = mx + b
Arbitrarily choose the point (1, 1). Here x = 1, y = 1 and m = 2/3. Then
we have
1 = (2/3)(1) + b, or 1 = 2/3 + b, so that b must be 1/3.
The equation in question is y = (2/3)x + 1/3
Find the area of the triangle
[tex] =( \frac{1}{2} \times 10.4 \times 16.9) {ft}^{2} \\ = (5.2 \times 16.9) {ft}^{2} \\ = 87.88 {ft}^{2} [/tex]
Answer:
The area of the triangle is 87.88 square feet.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Anyone know how to solve 28?
Answer:
i need help too
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
x = - 3 is a vertical line parallel to the y- axis.
A line perpendicular to it will therefore be a horizontal line parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (6, - 4 ) with y- coordinate - 4 , then
y = - 4 ← equation of perpendicular line
HELP It's due in 15 minutes
Answer:
L
Step-by-step explanation:
Find the polynomial function in standard form that has the zeros listed. 1(multiplicity 2), -2(multiplicity 3)
Answer:
f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8
Step-by-step explanation:
If p is a zero, then (x -p) is a factor. The multiplicity of the zero tells you how many times that is a factor (its exponent).
f(x) = (x -1)²(x +2)³ = (x² -2x +1)(x³ +6x² +12x +8)
f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8
_____
Additional comment
You can use the distributive property to write out the 12 terms of the product of the two expanded factors, or you can do a little mental arithmetic based on what you know about the exponent of a product term. (It is the sum of the exponents of its factors.)
The mental exercise can be made easier by writing the coefficients of the factors as though they were two cubics. It works well to write them in two rows:
[tex]\left[\begin{array}{cccc}0&1&-2&1\\1&6&12&8\end{array}\right][/tex]
The columns are in order of decreasing powers of x. A relatively simple and symmetrical pattern of sums of cross products is used to find the coefficients of the final polynomial. Working in order of decreasing exponents, we have ...
coefficient of x^6 = (0)(1) = 0
coefficient of x^5 = (0)(6) +(1)(1) = 1
coefficient of x^4 = (0)(12) +(1)(-2) +(1)(6) = 4
coefficient of x^3 = (0)(8) +(1)(1) +(1)(12) +(6)(-2) = 1
coefficient of x^2 = (1)(8) +(6)(1) +(-2)(12) = -10
coefficient of x^1 = (-2)(8) +(12)(1) = -4
coefficient of x^0 = (1)(8) = 8