Answer:
[tex]\begin{array}{ccl}Year&&End \ of \ year \ balance\\1&&\$4,483.18\\2&& \$3,088.68\\3&&\$1,596.57\\4&&0\end{array}[/tex]
Step-by-step explanation:
The initial amount invested, P = $1,600
Danny's age at which the amount, A, is to be used for his college, t = 19 years
The number of equal annual payments, m, to be withdrawn from the amount = 4
The compound interest on the account, r = 7% = 0.07
Let, A, represent the amount at the year the annual withdrawals starts to be made, we have;
[tex]A = P \times \left(1+\dfrac{r}{n} \right)^{n \times t}[/tex]
n = The number of times the interest is applied annually = 1
Therefore;
[tex]A = 1,600 \times \left(1+\dfrac{0.07}{1} \right)^{1 \times 19} \approx 5,786.444[/tex]
The amount, m, is withdrawn at start of Danny's first year in college to give the amount in the account = A - m
The amount in the account at the end of the first year with compound interest, r = (A - m)×(1 + r)¹ = (A - m)×(1 + r)
At the stat of the second year, the second withdrawal is made to give the starting amount = (A - m)×(1 + r) - m
The amount in the account at the end of the second year = ((A - m)×(1 + r) - m)×(1 + r)
At the start of the third year, the amount in the account = ((A - m)×(1 + r) - m)×(1 + r) - m
At the end of the third year, we have the amount in the account = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r)
At the start of the forth year, the last yearly installment is withdrawn from the account and we have 0 balance in the account.
Therefore, on the fourth year, we have the amount in the account = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r) - m = 0
(A - m)×(1 + r)³ - m×(1 + r)² - m × (1 + r) - m = 0
A×(1 + r)³ - m×(1 + r)³ - m×(1 + r)² - m × (1 + r) - m = 0
A×(1 + r)³ = m×(1 + r)³ + m×(1 + r)² + m×(1 + r) + m = m × ((1 + r)³ + (1 + r)² + (1 + r) + 1)
A×(1 + r)³ = m × ((1 + r)³ + (1 + r)² + (1 + r) + 1)
m = A×(1 + r)³/((1 + r)³ + (1 + r)² + (1 + r) + 1)
∴ m = 5,786.444×(1 + 0.07)³/((1 + 0.07)³ + (1 + 0.07)² + (1 + 0.07) + 1) ≈ 1,596.56
The amount withdrawn annually, m ≈ $1,596.56
The amount in the account at the end of the each year is given as follows;
First year = (A - m)×(1 + r) = (5,786.444 - 1,596.56)×(1 + 0.07) ≈ 4,483.17588
Second year = ((A - m)×(1 + r) - m)×(1 + r) = ((5,786.444 - 1,596.56)×(1 + 0.07) - 1,596.56)×(1 + 0.07) = 3,088.68
Third year = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r) = (((5,786.444 - 1,596.56)×(1 + 0.07) - 1,596.56)×(1 + 0.07) - 1,596.56) × (1 + 0.07) = 1,596.57
At the end of the first year, we have $4,483.17588
At the end of the second year, we have $3,088.68
At the end of the third year, we have $1,596.57
At the end of the fourth year, we have 0
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8. The two diagonals of a parallelogram meet at a 60° angle. The diagonals are 10 cm and 6 cm long. Find the lengths of the sides of the parallelogram.
Target due: 1/14/22 52% 5
10 cm
0 14 cm, 8.7 cm
4.4 cm, 2.8 cm
CLASS INFO
O 4.4 cm, 4.4 cm
7 cm, 4.4 cm
818-572-
ak:
tnp-
2 01:15:20
9514 1404 393
Answer:
7 cm, 4.4 cm
Step-by-step explanation:
The side lengths can be found from the law of cosines. Each triangle has legs 3 cm and 5 cm. The angle between these will be 60° or 120°. Then the two sides of the parallelogram are ...
s = √(a² +b² -2ab·cos(C))
s = √(3² +5² -2·3·5·(±1/2)) = √(34 ±15) = {√49, √19}
The two side lengths are 7 cm and about 4.4 cm.
What is the measure of n
Answer:
Step-by-step explanation:
This is a geometric means problem. Namely, n is the geometric mean between the 2 smaller triangles within that larger one. Set up the problem accordingly:
[tex]\frac{28}{n}=\frac{n}{7}[/tex] and cross multiply:
[tex]n^2=196[/tex] so
n = 14
Instructions: Find the missing side. Round your answer to the nearest tenth.
54°
29
Answer:
x = 23.5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 54 = x / 29
29 sin 54 = x
x=23.46149
To the nearest tenth
x = 23.5
I need the answer to his question soon, please help!
Answer:
b=x+1
Step-by-step explanation:
The equation is:
[tex]2x^2}+x-1=\frac{1}{2} b(4x-2)[/tex]
Isolate b by subtracting and dividing.
You end up with b= x+1
How do I do this question it is really hard
Answer:
Step-by-step explanation:
Given the following coordinates the glide reflection transformation
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A (4, 2 ) → A' (4, - 2 )
B (7, 0 ) → B' (7, 0 )
C (9, 3 ) → C' (9, - 3 )
A translation of a shift to the left of 3 units is a horizontal shift.
This means subtracting 3 fro the x- coordinate and leaving the y- coordinate
A' (4, - 2 ) → A'' (4 - 3, - 2 ) → A'' (1, - 2 )
B' (7, 0 ) → B'' (7 - 3, 0 ) → B'' (4, 0 )
C' (9, - 3 ) → C'' (9 - 3, - 3 ) → C'' (6, - 3 )
What quadratic formula do I need to use to solve 3x(x+6)=-1
Answer:
[tex]\Large \boxed{x_1=\frac{9+\sqrt{51} }{3} \ \ ; \ \ x_2=\frac{9-\sqrt{51} }{3} }[/tex]
Step-by-step explanation:
[tex]\displaystyle \Large \boldsymbol{} 3x(x+6)=-10 \\\\3x^2+18x=-10 \\\\3x^2+18x+10=0 \\\\D=324-120=204 \\\\ x_{1;2}=\frac{18\pm2\sqrt{51} }{6} =\frac{9\pm\sqrt{51} }{3}[/tex]
A plane flies from London to Dubai and to Colombo. it leaves London at 01:50 and the total journey takes 13 hours and 45 minutes. The local time in Colombo is 7 hours ahead of London. Find the arrival time in Colombo
Answer:
11:35
Step-by-step explanation:
add 13 hour and 45 minutes to 1:50 giving you 4:35 and since the time is 7 hours ahead add another 7 hours and tada
The arrival time in Colombo is 10:35 pm.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Now, First, we need to convert 13 hours and 45 minutes to just hours.
We can do this by dividing the minutes by 60:
45 minutes ÷ 60 = 0.75 hours
So the total flight time is,
13 + 0.75 = 13.75 hours.
Next, we need to add the time difference between London and Colombo. Since Colombo is 7 hours ahead of London, we need to add 7 hours to the total flight time:
13.75 hours + 7 hours = 20.75 hours
Now we need to convert this to a time.
Since the flight left at 01:50, we can add 20 hours and 45 minutes to find the arrival time in Colombo:
01:50 + 20:45 = 22:35
So, the arrival time in Colombo is 10:35 pm.
Learn more about the addition visit:
https://brainly.com/question/25421984
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10. Both x and y vary inversely with each other. When x is 10, y is 6,which of the following is not a possible pair of corresponding values of x and y? (A) 12 and 5 (B) 15 and 4 (C) 25 and 2.4 (D) 45 and 1.2
expain me
mods plz answer
9514 1404 393
Answer:
D) 45 and 1.2
Step-by-step explanation:
The "varies inversely" relationship is described by the equation ...
y = k/x . . . . . . y varies inversely with x (and vice versa)
The value of k can be found from known values of x and y:
xy = k . . . . . . multiply the above equation by x
(10)(6) = k = 60 . . . . using the given values
__
To check if a given pair of numbers satisfies ...
y = 60/x
you can multiply them together to see if the product is 60.
(A) 12×5 = 60
(B) 15×4 = 60
(C) 25×2.4 = 60
(D) 45×1.2 = 54 . . . . . not a possible pair of corresponding values.
45 and 1.2 are not a possible solution for x and y.
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your
answers as radicals in simplest form.
Answer:
x = 10
y = 5
Step-by-step explanation:
Applying Trigonometry ratio
sin∅ = opposite/hypotenuse
cos∅ = Adjacent/hypotenuse
From the diagram,
sin60° = 5√3/x
make x the subject of the equation
x = 5√3/sin60°
But, sin60° = √3/2
x = 5√3/(√3/2)
x = (5√3)(2/√3)
x = 10.
Also, applying
cos60° = y/x
Where x = 10, cos60° = 1/2
y = xcos60°
y = 10(1/2)
y = 5
What is the length of leg s of the triangle below?
45
32
907
4
O A. 16
B. 32
OC. VA
D. 22
E. 4
F. 1.5
SOM
The question is not well formatted. A ell formatted version of the question type is attached and solved below :
Answer:
10
Step-by-step explanation:
Using trigonometry :
Taking the angle 45°
From trigonometry :
Sin θ = opposite / hypotenus
Opposite = s ; hypotenus = 10√2
Sin 45 = s / 10√2
Recall :
Sin 45 = 1/√2
We have ;
1/√2 = s / 10√2
s = 10√2 * 1/√2
s = 10√2 / √2
s = 10
10 points please help im confused
What is the volume of the prism?
103.8 cubic inches
114.9 cubic inches
140.6 cubic inches
110.5 cubic inches
Answer:
110.5 cubic inches
Step-by-step explanation:
Base is parallelogram, so area is
A = 4.7×5 = 23.5
Height(h) is 4.7, so volume is,
V = A×h
= 23.5×4.7
= 110.45 ≈ 110.5
Answered by GAUTHMATH
The volume of a gas in a container varies inversely with the pressure on the gas. If a gas has a volume of 450 cubic inches under a pressure of 3 pounds per square inch, what will be its volume if the pressure is increased to 5 pounds per square inch
Answer: [tex]270\ in.^3[/tex]
Step-by-step explanation:
Given
Volume of a gas varies inversely with pressure i.e.
[tex]V\propto \dfrac{1}{P}\\\\PV=\text{constant}[/tex]
Initially, [tex]V_1=450\ in.^3,P_1=3\ psi[/tex]
Then, pressure increases to [tex]P_2=5\ psi[/tex]
[tex]\therefore P_1V_1=P_2V_2\\\Rightarrow 3\times 450=5\times V_2\\\Rightarrow V_2=3\times 90\\\Rightarrow V_2=270\ in.^3[/tex]
Thus, volume decreases to [tex]270\ in.^3[/tex].
Janice's age was two-third of her elder sister's age now. If Janice's elder sister was x years old three years ago, determine Janice's age three years later in terms of x.
Answer: Her sister's age 3 years ago = x
so, her age now = x+3
so Janice's present age = 2/3 of (x+3) {as Janice's present age is two-third of her sister's age now}
Therefore, Janice's age determining the value of x is 2/3 of (x+3).
can i get some help please
Answer:
66 degrees
Step-by-step explanation:
The value of an external angle is the sum of the other two angles of the triangle of which that external triangle is sharing with.
This means that angle 4, or 123 is equal to angle 1 plus angle 3, which is 57 degrees.
We have this equation:
[tex]x+57=123[/tex], where x is the value of angle 1.
Subtracting 57 from both sides, we have
[tex]x = 66[/tex]
Please hurry I will mark you brainliest
Question’s Picture included*
Answer:
when you have 32 pennies the total mass will be 185
Full working out for this question please.
On Monday Farmer Tom collected 6 times as many eggs as Farmer Jack. On Tuesday, Farmer Tom sold 425 eggs. Farmer Jack then had three times as many eggs as Farmer Tom. How many eggs did farmer Jack have?
a.150
b.175
c.125
d.25
e.75
Answer:
75
Step-by-step explanation:
Let farmar jack collected x eggs, then farmar Tom collect 6x eggs
farmar Tom sold 425 eggs, so he left with 6x-425 eggs, now farmar jack has 3 times of what farmar Tom has, so
3(6x-425)=x
or, x=75
so farmar jack had 75 eggs
Answered by GAUTHMATH
Meg initially has 3 hours of pop music and 2 hours of classical music in her collection. Every month onwards, the hours of pop music in her collection is 5% more than what she had the previous month. Her classical music does not change. Which function shows the total hours of music she will have in her collection after x months
Answer:
The answer is "[tex]f(x) = 3(1.05)x + 2[/tex]".
Step-by-step explanation:
She starts off with 3 hours with pop music.
Next month, she will have 3 hours she has had and + 3*0.05.
3hrs + 3*0.05hrs = 3*1.05 hrs
We add 2 hours of classical music to the 3 * 1.05 hours to achieve 3 * (1.05) hours + 2 hours of classical music.
Answer: f(x):2(0.05)^x+3
Please help me this on the picture
Answer:
Step-by-step explanation:
WILL GIVE BRAINLIEST. Given: SLant Prism, m
Hi! I ran into a similar problem so i will try, but sorry if i get it wrong, so basically all you do i
Simplify 6 - (-2) - 3(-5).
-11
-7
19
23
Answer:
23
Step-by-step explanation:
6-(-2)-3(-5)
you first have to multiply the signs
a negative×a negative is a positive.positive times negative is negative, positive times positive is positive.
so for this question
6+2+15
23
I hope this helps
In the diagram, which two angles are corresponding angles with angle 12?
Answer:
∠8 and ∠16.
Step-by-step explanation:
Given the diagram we have to find the angles which are corresponding angles with ∠12. Those angles which are on the same side of traversal called corresponding angles. By definition of corresponding angles the angles which are corresponding to ∠12 are ∠8 and ∠16.
I just need the number can anyone give me them please ???
Answer:
here are the points (0,-6), (-2,1), (2,2), (6,3)
Step-by-step explanation:
you just use the rise over run rule, which means that the top number is the rise and the bottom number is the run. In this case the rise is 1 and the run is 4. So, you would move up one space then move 4 spaces to the right, but because the graph is cut off you can reverse it and it would be the same thing, it would just be in a different area of the graph. So you go, down 1 and left 4 instead. hope this helps :)
Penelope earned $50 in May. She earned $60 in June.
What is the percent increase or decrease in Penelope's monthly earnings?
O A. 30% decrease
O B. 25% increase
O C. 20% decrease
O D. 20% increase
Answer:
20% Increase
Step-by-step explanation:
Percentages can be put vice versa. So 20% Of 50 = 50% Of 20 Which Equals 10.
Mark me as brainliest please
Find the measure of the indicated angle to the nearest degree
A physical therapist has 2400 minutes available for patients next week,
Patients have already made appointments for 1490 minutes. If the variable p
stands for the time the physical therapist has left, which units could apply to
that variable?
Answer: 910 minutes
Step-by-step explanation:
Since the physical therapist has 2400 minutes available for patients next week, and the patients have already made appointments for 1490 minutes, then the time that the physical therapist has left will be:
p + 1490 = 2400
p = 2400 - 1490
p = 910
Therefore, the physical therapist will have 910 minutes left
Which number line shows the solution set for StartAbsoluteValue 8 minus 2 p EndAbsoluteValue = 6?
A number line going from negative 1 to positive 7. Points are at positive 1 and positive 7.
A number line going from negative 4 to positive 4. Points are at negative 1 and positive 1.
A number line going from negative 8 to positive 8. Points are at negative 7 and positive 7.
A number line going from negative 7 to positive 1. Points are at negative 7 and positive 1.
Answer:
A number line going from negative 1 to positive 7. Points are at positive 1 and positive 7.
Step-by-step explanation:
We have the equation:
|8 - 2*p| = 6
Remember that the equation:
|f(x)| = A
with A > 0
means that:
f(x) = A
or
f(x) = -A
Then for our case, we can rewrite:
|8 - 2*p| = 6
as:
(8 - 2*p) = 6
or
(8 - 2*p) = -6
Now we can solve these two equations to find the two possible values of p.
From the first one, we get:
8 - 2*p = 6
8 - 6 = 2*p
2 = 2*p
2/2 = p = 1
so one solution is p = 1
Now from the other equation, we can get the other solution:
(8 -2*p) = -6
8 - 2*p = -6
8 + 6 = 2*p
14 = 2*p
14/2 = p = 7
So the two solutions are p = 1 and p = 7
Then the correct option is:
"A number line going from negative 1 to positive 7. Points are at positive 1 and positive 7."
hello help please
Express
[tex] \frac{3}{5} [/tex]
of a right angle triangle to radian measure and can some anybody help me by looking one old question from my profile help please
a right angle is 90°, or 1/4 of a circle.
3/5 * 1/4 = 3/20
radian measure is the length of the circumference of this part of the circle.
a full circumference of a circle would be 2*pi*r, also expressed as 2 rad * r
now let's multiply the full thing with the 3/20 from earlier to just get the desired fraction:
6/20 rad * r
= 3/10 rad * r
of course a solution in cm or inch still depends on the radius here, wich could be just plugged in at will
Answer:
[tex]\frac{3\pi }{10}[/tex]
Step-by-step explanation:
To express degrees in radians
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]
[tex]\frac{3}{5}[/tex] of a right angle
= [tex]\frac{3}{5}[/tex] × 90° = 54° , then
radian = 54 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{54}{180}[/tex] × π = [tex]\frac{3}{10}[/tex] × π = [tex]\frac{3\pi }{10}[/tex]
f(x)=−4x
2
+5x
\text{Find }f(6)
Find f(6)
Answer:
-114
Step-by-step explanation:
f(x) = -4x^2 +5x
Let x = 6
f(6) = -4(6)^2 +5(6)
= -4(36) +30
- 144+30
= -114
What is the simplified form of V 100x35 ?
Answer:
answer is 3500.
answer is 3500
answer is 3500
