A prize fund is setup with a single investment of £4000 to provide an annual prize of £150. The fund accrues interest at 5% p.A. Paid yearly. If the first prize is awarded one year after the investment, find the number of years for which the full prize can be awarded.
The invested amount, A=£4000
Rate of interest on this amount, r=5% per annum.
Total interest on the amount £4000 after 1 year
[tex]= 5\% \;\text{of} \;\£ 4000=0.05\times \£4000=\£200[/tex].
The total amount after 1 year, P=£4000+£200=£4200
Amount remains after an annual prize of £150=£4200-£150=£4050.
Note that after providing the annual prize the amount remains is £4050 which is more than the invested amount of £4000 as the prize money is less than the interest gained.
Now, for the 2nd year, the 5% interest is on the principal amount of £4050, which will have more interest as compared to the interest of 1st year.
Again, after prize distribution, the total amount remains for the principal amount of 3rd year will be more than the principal amount of 2nd year. This sequence repeated every year and the total amount will increase every year.
So, it will never end, the full prize money can be awarded for infinitely many years.
What is the opposite of -6 on a line graph
Answer:
6
Step-by-step explanation:
|-6| = 6
3. Two fire towers are 30 kilometers apart, tower A being due
west of tower B. A fire is spotted from the towers, and the
bearings from A and B are E 14° N and W 34° N, respectively.
Find the distance d of the fire from the line segment AB.
Answer:
Step-by-step explanation:
From the attachment we have a triangle ABD, but sum of angle in a triangle is 180 which means angleABD=180
Angle A=14
Angle B= 34
Then angle D= 180-(14+34)=132deg.
From trigonometry
a/sinA=b/sinB = c/sinD
a/sin14 = b/sin34= 30/sin132
But sin(14)=0.991
Sin(132)= 0.0531
Then substitute we have
a/0.991 = 30/0.0531
Then cross multiply we have
0.0531×a=30× 0.991
a= 29.73/0.0531
a=9.77km
Therefore, the distance d of the fire from the line segment AB is 9.77km
1. It takes the earth 24 h to complete a full rotation. It takes Mercury approximately 59 days, 16 h, and 40 min to complete a full rotation. How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.
Answer:
It takes Mercury approximately 1,432 hours and 40 min. to make a full rotation.
Step-by-step explanation:
59*24=1416
1416+16=1432
Then add the 40 min
and you get 1,432 hours and 40 min
Which best proves why the expressions 4 (x + 3) + 2 x and 6 (x + 2) must be equivalent expressions?
When x = 3, both expressions have a value of 30.
When x = 5, both expressions have a value of 42.
When x = 1, both expressions have a value of 18, and when x = 8, both expressions have a value of 60.
When x = 2, both expressions have a value of 15, and when x = 6, both expressions have a value of 39.
Answer:
When x=1
Step-by-step explanation:
Solving for both equations by putting them both equal to each other.
f(x) = x2 + 1 and g(x) = x + 1 Which of the following best represents
f(g(x)) ?
Answer:
Step-by-step explanation:
Since you haven't given us any choices, I will just give an answer. You can match it.
f(g(x) = (g(x))^2 + 1
That means that wherever you see an x in f(x) you put g(x) in on the right.
f(g(x)) = (x + 1)^2 + 1
f(g(x)) = x^2 + 2x + 1 + 1
f(g(x)) = x^2 + 2x + 2
Answer: [tex]f(g(x)) = x^2+2x+2[/tex]
=========================================
Work Shown:
[tex]f(x) = x^2 + 1\\\\f(x) = ( x )^2 + 1\\\\f(g(x)) = ( g(x) )^2 + 1 \ \text{ replace every x with g(x)}\\\\f(g(x)) = ( x+1 )^2 + 1 \ \text{ plug in } g(x) = x+1\\\\f(g(x)) = ( x+1 )( x+1 ) + 1\\\\f(g(x)) = x^2+2x+1 + 1 \ \text{ use FOIL rule}\\\\f(g(x)) = x^2+2x+2\\\\[/tex]
What is the discount of a baseball hat that is $34 with a 28% discount?
Answer:
12 bucks
Step-by-step explanation:
Write £5 as a percentage of £10
Answer:
50%
Step-by-step explanation:
5/10*100
=50%
Find x if AC = -7+2x, BC =9, and AB = -27 + 3x
Answer:
x = -4
Step-by-step explanation:
AB + BC = AC
-27 + 3 + 9 = -7 + 2x
-27 + 3 + 9 + 7 = 2x
-8 = 2x
x = -8/2
x = -4
how do you write this in number form five million, eight hundred twenty-two thousand, nine hundred forty-three
Answer:
5,822,943
Step-by-step explanation: lol
Answer:
5,822,943
Step-by-step explanation:
5,000,000 + 800,000 + 20,000 + 2,000 + 900 + 40 + 3 = 5,822,943
I need help with this. How does one make 4 DIFFERENT equations for the SAME four points.
Answer:
y +3 = 3/4(x +8)
y = 3/4(x +4)
y -3 = 3/4x
y -6 = 3/4(x -4)
Step-by-step explanation:
Each point differs from the one to its left by 4 units horizontally and 3 units vertically. The "rise/run", or slope, is 3/4. With this and the four point coordinates, you can make four equations in the point-slope form:
y -k = m(x -h) . . . point-slope form of equation through (h, k) with slope m
y +3 = 3/4(x +8)
y = 3/4(x +4)
y -3 = 3/4x
y -6 = 3/4(x -4)
__
You can also write equations in slope-intercept form:
y = 3/4x +3
and in standard form:
3x -4y = -12
4y - 9 = 3 what is y
Help me out please thank u
Answer:
Three points determine a plane.
:)
Answer:
Three
Step-by-step explanation:
Evaluate the Expression 44 - [x] when x= -10
Answer:
54
Step-by-step explanation:
44−(−10)
=44−(−10)
=44+10
=54
An account executive receives a base salary plus a commission. On $20,000 in monthly sales, an account executive would receive compensation of $1,900. On $40,000 in monthly sales, an account executive would receive compensation of $2,700. Determine a linear function that yields the compensation y (in dollars) of a sales executive for x dollars in monthly sales.
Answer:
The equation is y = 0.04x + 1100
Step-by-step explanation:
The computation of the linear function is as follows
Here the slope-intercept form could be used i.e.
y = mx + b
where,
x = monthly sales
and, y = compensation
x_1 y_1 x_2 y_2
($20,000, $1,900) ($40,000, $2,700)
Now
m = (y_2 - y_1) ÷ (x_2 - x_1)
= ($2,700 - $1,900) ÷ ($40,000 - $20,000)
= ($800) ÷ ($20,000)
= 2 ÷50
= 4%
Now for determining the b one of the ordered pairs could be chosen and then placing it into the above equation
y = mx+b.
Let use (x_2, y_2) or ($40,000, $2,700)
y = mx+b
$2,700 = 0.04 ($40,000)+b
$2,700 = $1,600 + b
b = $1,100
So,
The equation is y = 0.04x + 1100
What is the decimal equivalent to the fraction 7/20?
Answer:
0.35 (is the answer i have too type this so i can send it. i have to type 20 charters to send it)
What are the solutions of this quadratic equation? 2^2=16x-65
Answer:
x= 4.3125
Step-by-step explanation:
2^2 = 16x - 65
4= 16x- 65
+65 +65
69 = 16x
69/16 =16x/16
4.3125 = x
What is the value of k?
Answer:
k = 10
Step-by-step explanation:
The triangles angels added up must equal 180 degrees, and the top angle is 65 degrees by the 180 degree rule.
So 10k + 15 must equal the remaining 115
subtract 15 from each side and you get 10k = 100
divide each each by 10 and you get the answer of k = 10
If the co-ordinates of middle point of line segment joining ( 2 , 1 ) and ( 1 , -3 ) are [tex] \sf{( \alpha \:, \: \beta ) }[/tex] , prove that [tex] \sf{6 \alpha \: + \: \beta \: - 8 \: = 0}[/tex]
By the midpoint formula,
[tex]\alpha = \frac{2+1}{2}=\frac{3}{2}\\
\beta =\frac{1+(-3)}{2} = \frac{-2}{2} = -1[/tex]
Substitute the values in given equation:
$\text{LHS} = 6 \Big( \frac{3}{2}\Big) + (-1)-8$
$\implies \text{LHS}= 9-1 -8 =0 =\text{RHS}$
Since both sides are equal, this proves the equation $\sf{6 \alpha \: + \: \beta \: - 8 \: = 0}$
convert into a mixed fraction 2/5+4/5=
Answer:
1 1/5
hope this helps! :D
what is 10.0 as a whole number-
The tallest building in Franklin is two-thirds the
height of the tallest building in Mayville. If the
tallest building in Mayville is 80 i feet, find
the height of the tallest building in Franklin.
Answer:
53 7/8
Step-by-step explanation:
turn the mixed number into an improper fraction
divide the numerator by 3
multiply quotient by 2
simplify
The tallest building in Franklin is 53.3 feet.
The tallest building in Franklin is two-thirds the height of the tallest building in Mayville which is 80 feet high.
The tallest building in Franklin is therefore:
= 2/3 x 80
= 160 / 3
= 53.3 feet
The tallest building in Franklin is therefore 53.3 feet.
Find out more at https://brainly.com/question/24544202.
Given the replacement set {0. 1. 2. 3. 4). solve 4x - 5 = 11.
0 X=0
0 X = 3
0 X = 4
Answer:
It's 4
Step-by-step explanation:
4x-5=11
4x=11+5
4x=16
Divide by 4
X=4
What is the measure of X?
Answer:
68
Step-by-step explanation:
let the angleAGF be y
then,
y+22=90
y=90-22
y=68
y=x(being vertically oppsite angle
what is the answer to the inequality 3t + 9 ≥ 15
Answer:
t ≥ 2
Step-by-step explanation:
3t + 9 ≥ 15
3t ≥ 6
t ≥ 2
I hope this helped!
what is 14.3- 32.24=127.92
14.3p - 32.24 + 32.24 = 127.92 + 32.24
14.3p = 160.16
p=?
Answer: p=11.2
Step-by-step explanation:
14.3p- 32.24 =127.92
14.3p - 32.24 + 32.24 = 127.92 + 32.24
14.3p = 160.16
p = 160.16 ÷ 14.3
p = 11.2
Hope this can help you :)
Answer:
p = 11.2
Step-by-step explanation:
Given equation is :
2.6(5.5p – 12.4) = 127.92
Using the distributive property :
14.3p - 32.24 = 127.92
Using addition property :
14.3p - 32.24 + 32.24= 127.92 + 32.24 (adding 32.24 to the both sides)
14.3p = 160.16
Using division property :
So, the value of p is 11.2
please help me
solve 3x+1/2=3/8+x
Answer:
x= -[tex]\frac{1}{32}[/tex]
Step-by-step explanation:
First move the x on the right side the the left side. Now your equation is
2x+[tex]\frac{1}{2}[/tex]=[tex]\frac{3}{8}[/tex] Next move 1/2 to the right side. Now your equation is 4x=[tex]\frac{-1}{8}[/tex]. Next divide both sides by 4 to isolate "x." Now your equation is x= -[tex]\frac{1}{32}[/tex]
Hope this helped and have a great day.
(brainliest please)
8x-9(x-9)=-(9x-16)+9(x-1)
Answer: X=74
if you want to be shown step by step comment below
how to write out m/3=3(2m+1)
Answer:
m divided by three equals 3 times two m plus 1.
Step-by-step explanation:
Answer:
a number m divided 3 equals to 3 times the sum of 2 and the number m and one.a number divided by 3 equals to 3 multiplying the sum of that particular number and 2 + 1.HELP PLEASE DUE IN 10 MINUTES!!!!! 15 POINTS
Enter your answer in scientific notation.
1. 3.6 × 10^3 + 7.3 × 10^4 =
2. 8 × 105 − 5.7 × 105 =
Answer:
1. 7.66 x 10^4 (76,600)
2. 2.415 x 10^2 (241.5)
Step-by-step explanation:
1. First just do (3.6 x 10^3) and (7.3 x 10^4) to get 3600+73000 = 76600. In Scientific notation it would be 7.66 x 10^4
2. First do (8 x 105) and (5.7 x 105) to get 840-598.5 = 241.5. In Scientific notation it would be 2.415 x 10^2
