Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Monthly deposit= $100
Interest rate= 0.06/12= 0.005
Number of periods= 12*5= 60 months
a)
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {100*[(1.005^60) - 1]} / 0.005
FV= $6,977
b) If the deposit is at the beginning of the month, the interest is compounded one more period. We need to use the following formula:
FV= {A*[(1+i)^n-1]}/i + {[A*(1+i)^n]-A}
FV= 6,977 + {[100*(1.005^60)] - 100}
FV= 6,977 + 35
FV= $7,012
Find the value of the variable.
Answer:
[tex]90 \sqrt{2} [/tex]
Step-by-step explanation:
This is a 45°-45°-90° right triangle, so the length of the hypotenuse is √2 times the length of a leg. Since both legs have length 90, the hypotenuse has length 90√2. So y=90√2.
4n^2+16n+15 factor completely
Answer:
(2n+3)(2n+5)
Step-by-step explanation:
HELP ASAP Find the equation of a line that goes through the points (8, -9) and (-4, 15).
Answer:
Your answer is: y= -2x+7
Step-by-step explanation:
Hope this helped : )
The equation of a line that goes through the points (8, -9) and (-4, 15) is y = -2x + 7
The formula for calculating the equation of a line is expressed as y = mx+ b
m is the slope of the line
b is the y-intercept
Given the coordinate points (8, -9) and (-4, 15)
Get the slope of the line;
[tex]m =\frac{15-(-9)}{-4-8}\\m=\frac{24}{-12} \\m = -2[/tex]
Get the y-intercept of the line
Recall that y = mx + b
15 = -2(-4) + b
b = 15 - 8
b = 7
Get the required equation in the form y = mx + b
y = -2x + 7
Hence the equation of a line that goes through the points (8, -9) and (-4, 15) is y = -2x + 7
Learn more here: https://brainly.com/question/17003809
7 — 8п what is the answer
Answer:
-8n+7
Step-by-step explanation:
Answer:
-8n+7
Step-by-step explanation:
(#10) How do I check if this is right for Hugo?
you're correct that, since Hugo is charging Johnny $2000, so the amount invested will be 98000.
[tex]~~~~~~ \stackrel{\textit{\Large Hugo}}{\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 &\$98000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &15 \end{cases}[/tex]
[tex]A=98000\left(1+\frac{0.06}{4}\right)^{4\cdot 15}\implies A=98000(1.015)^{60}\implies A\approx 239435.54 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\Large Hector}}{\textit{Compound Interest Earned Amount}}[/tex]
[tex]A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$100000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases} \\\\\\ A=100000\left(1+\frac{0.055}{12}\right)^{12\cdot 15}\implies A=100000\left( \frac{2411}{2400} \right)^{180}\implies A\approx 227758.38[/tex]
well, seems that even though Hugo is charging some Johnny, the returned amount is more than with Hector, so Johnny should give Hugo a call.
The volume of a cube is 7,077.888 cubic meters. What is the length of each side of the cube?
Answer:
19.2
Step-by-step explanation:
Take note:
a = edge
v = volume
Equations for a Cube
[tex]v=a^{3}[/tex]
[tex]a=v^{\frac{1}{3} }[/tex]
We are given V. Plug 7,077.888 into the second equation.
[tex]a=7077.888^{\frac{1}{3} }[/tex]
[tex]a=19.2[/tex]
Find the equation of the parabola with a focus at the point (2,5), and a directrix of y=3.
A). y=x^2/2-x+3
B).y=x^2/4-x+3
C).y=x^2/2-x+5
D).y=x^2/4-x+5
Ayden collects football, baseball, and Pokémon cards. He has four times as many baseball cards as football cards. His Pokémon cards contain 7 more cards than his baseball collection. If he has 106 cards all together, how many of each type does he have?
Answer: Ayden has 11 football cards,44 baseball cards and 51 Pokemon cards which totals 106 cards all together
Step-by-step explanation:
STEP 1 :
Let x represent number of football cards
He has four times as many baseball cards as football cards, let baseball cards be = 4x
Pokémon cards contain 7 more cards than his baseball collection,let Poke mon cards = 4x +7
Step 2 :
Putting in equation we have that
Football cards + Baseball cards + Pokemon cards = 106 cards
Therefore,
x + 4x + 4x+7 = 106
9x + 7 = 106
9x = 106-7
9x = 99
x =99/9 = 11
therefore football cards , x = 11 football cards
baseball cards = 4x = 4 x 11 = 44 baseball cards
Pokemon cards = 4x+7= 4x11 +7 = 44 +7 =51 Pokemon cards
The time it takes to complete a certain job is directly proportional to the number of units produced. If it takes 22 minutes to proficiently 18 units, how many units are produced in 33 minutes?
Answer:
27 units
Step-by-step explanation:
let t represent time and n represent number of units
given t is directly proportional to n then the equation relating them is
t = kn ← k is the constant of proportion
to find k use the condition t = 22, n = 18 , then
22 = 18k ( divide both sides by 18 )
[tex]\frac{22}{18}[/tex] = [tex]\frac{11}{9}[/tex] = k
t = [tex]\frac{11}{9}[/tex] n ← equation of variation
when t = 33 , then
33 = [tex]\frac{11}{9}[/tex] n ( multiply both sides by 9 )
297 = 11n ( divide both sides by 11 )
27 = n
27 units are produced in 33 minutes
Ray QS bisects PQR and mPQR =57°
Find mPQS
Answer:
The measure of angle ∠PQS is 28.5°
Step-by-step explanation:
If a ray bisects an angle, then it divides it into two equal angles in measures and the measure of each one is half of the measure of this angle.
In our question
∵ Ray QS bisects ∠PQR
→ That means it divides it into two angles PQS and SQR
∴ m∠PQS = m∠SQR = [tex]\frac{1}{2}[/tex] m∠PQR
∵ m∠PQR = 57°
→ Multiply its measure by [tex]\frac{1}{2}[/tex] to find the measures its parts
∴ m∠PQS = [tex]\frac{1}{2}[/tex] × 57°
∴ m∠PQS = 28.5°
∴ The measure of angle ∠PQS = 28.5°
What is the area of a rectangle with length 4 cm and width 12 cm?
16 cm2
48 cm2
3 cm2
32 cm2
Answer:
option 2 = 48 cm ²
12 × 4 = 48
cm × cm = cm²
answer = 48 cm²
can someone please simply this and show the work ?
Answer:
it's one of this two. if it's exactly how you have written it , it's the first picture.
Answer:
12[tex]\sqrt{5}[/tex]x^5
Step-by-step explanation:
Apply exponent rule
Add the numbers
Multiply the numbers
Factor integer
:)Hope you enjoy this:)I need help..
5x-3+3x+7 if x=3
Answer:
28
Step-by-step explanation:
Replace x with 3, and multiply the number next to it.
5(3)= 15
3(3)=9
so, 15-3+9+7=28
Answer:
28
Step-by-step explanation:
To solve this, replace every x with (3). If x is next to a number, that means you multiply that number and the value of x. This gives us the equation 5(3)-3+3(3)+7. When a set of parentheses are next to a number, you multiply. 5 times three is 15, and 3 times 3 is 9. This gives us 15-3+9+7. 15 - 3 is 12. 12 + 9 is 21. 21 + 7 is 28. 28 is your answer.
What is "A" in this problem equal to? 4/5 = 24/A. Explain your answer! *
Answer:
A = 30
Step-by-step explanation:
cross multiply to get A out from the denominator
4/5 = 24 /A
4A = 24 x 5
4A = 120
4A/4 = 120/4 divide
A = 30
16c-8d equivalent expression
Answer:
8(2c - d)
Step-by-step explanation:
16c - 8d ← factor out 8 from each term
= 8(2c - d)
What is the approximate value of x in the equation below. log subscript three-fourths baseline 25 = 3 x minus 1
Answer:
12123
Step-by-step explanation:
Answer:
A.) -3.396
Step-by-step explanation:
On edg ;)
Question is in the pic
Help please I need help with this
Answer:
π/6 ≈ 11/21 cubic units
Step-by-step explanation:
Use the given values in the formula for the volume of a sphere:
V = 4/3πr³
V = (4/3)(22/7)(1/2)³ = 4·22/(3·7·8) = 11/21 . . . . cubic units
We know,
[tex]{\qquad { \longrightarrow \pmb {\sf Volume_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3} }}}[/tex]
Here,
Radius of the sphere is [tex] \sf\dfrac{1}{2} .[/tex] We will take the value of π as [tex] \sf\dfrac{22}{7} .[/tex]⠀
Substituting the values in the formula :
[tex] { \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times \dfrac{22}{7} \times {\bigg(\dfrac{1}{2} \bigg)}^{3} }}}[/tex]
[tex] { \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times \dfrac{22}{7} \times \dfrac{1}{8} }}}[/tex]
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{ \cancel4}{3} \times \dfrac{22}{7} \times \dfrac{1}{ \cancel8} }}}[/tex]
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{ 1}{3} \times \dfrac{22}{7} \times \dfrac{1}{ 2} }}}[/tex]
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{22}{3 \times 7 \times 2} }}}[/tex]
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{22}{42} }}}[/tex]
[tex]{ \longrightarrow {\qquad {\bf Volume_{(Sphere)} = \dfrac{11}{21} }}}[/tex]
⠀
Therefore,
Radius of the sphere is [tex] \bf \dfrac{11}{21} [/tex] units³.2. Mr. Rivera revealed that 70% of the students got an A on the vocabulary quiz in ELA this.
week. If there are 100 students in Mr. Riverds class, create a model that represente bo
many students got an A.
Answer:
143 to the nearest Whole #
Step-by-step explanation:
100/0.70=142.59
Anthony's father is going to put a tile border around this square fish pond. The pond is 1
yard on each side. The tiles are squares that are 1 foot on each side. How many tiles will
Mr. Chen need?
Answer:
12 tiles
Step-by-step explanation:
1 yard = 3 feet, so 3*4 = 12, because it makes four yards in total with each side being a yard.
Express the following equation in the form of ax^2+bx+c=0.
(4a+3)^2 = (a+5)(a-2)
Answer:
15a² + 21a + 19 = 0
Step-by-step explanation:
(4a + 3)² = (a + 5)(a - 2)
16a² + 24a + 9 = a² + 3a - 10
15a² + 21a + 19 = 0
need the answer asap
Answer:
22
Step-by-step explanation:
Mr. Chen started a new exercise program and is walking four days a week last week he walked the same distance each day for a total of 21 miles if W represents the number of miles he walked each day which equation can be used to find the value of W
Answer:
it's 21/4
Step-by-step explanation:
on time 4 learning
p.s. stream sour by Olivia Rodrigo
Katrina bought new shoes for $55.00, jeans for $29.99, and a new blouse for $27.79. Sales tax in her area is 7 percent. What was the total charge for her purchases?
Answer:
$120.67
Step-by-step explanation:
1. 55+29.99+27.79 = 112.78
2. 7% of 112.78 is 7.89
:)
Peyton is a salesperson who sells computers at an electronics store. She makes a base pay amount of $60 per day regardless of sales and she earns a commission of 2.5% of the dollar amount of all sales that she makes. Write an equation for P,P, in terms of x, representing Peyton's total pay on a day on which she sells xx dollars worth of computers.
Answer:
Step-by-step explanation: if Peytons base pay= $60 plus she earns commission on $x (computers sold)
P= $60+ (0.025x)
You would multiply by 0.025 as this equals 2.5%
Remember PEMDAS- parentheses, exponents, multiplications, division, addition, subtraction
(20 POINTS!!!!) The expression 14₆÷ 14₄ is equal to _____. (The small numbers are supposed to be the exponents or something?)
Awnsers
14 ₂
1
2
14 ₁₀
Answer:
14^2
Step-by-step explanation:
i just plugged into calculator lol
Given expression:
14⁶ / 14⁴
Using the exponent rule;
[tex]\frac{x^{n} }{x^{m} }[/tex] = [tex]x^{n-m}[/tex]
So;
x = 14
n = ⁶6
m = 4
So;
[tex]\frac{14^{6} }{14^{4} }[/tex] = 14⁶⁻⁴
= 14²
Sled dogs have thick fur to keep them warm. But they can overheat while running if it’s too warm outside. The maximum temperature the dogs can run in is 71º higher than their minimum of -71ºF. What is the maximum temperature that they can run in?
Answer:
-71 + 71 =0 so 0°
Step-by-step explanation:
I hate the fact that it needs to be 20 letters
Common multiple of 12 and 20
Answer:
4
Step-by-step explanation:
Answer: 60
Step-by-step explanation:
write down the 12 times table
12 , 24, 36, 48, 60, 72, 84, 96, 108, 120
20, 40, 60, 80, 100, 120, 140, 160, 180, 200
Now you can see that 60 is the multiple that comes up first in both of the times tables which means it is the lowest common factor.
Mother is three times as old as her daughter. Three years ago she was four times as old as her daughter was. Find their present ages.
Answer:
daughter = 9yrs
mother = 27yrs
Step-by-step explanation:
let age of daughter be x
age of mother = 3x
by qsn,
three yrs ago,
4 (x-3) = 3x-3
4x-12 = 3x-3
4x-3x = -3+12
× = 9 yrs (age of daughter )
3x = 3×9 = 27 yrs ( age of mother)
how do you solve
10^-3
Answer:
0.001
Step-by-step explanation:
Answer:
[tex]\frac{1}{1000}[/tex]
Step-by-step explanation:
[tex]10^{-3}[/tex]
[tex]= \frac{1}{10^{3}}[/tex]
[tex]= \frac{1}{1000}[/tex]