Paddy and Anna each invest $2000 for 5 years.
Paddy earns simple interest at a rate of 1.25% per year.
Anna earns compound interest at a rate of r% per year.
At the end of 5 years, Paddy's investment is worth the same as Anna's investment.
Calculate the value of r.
Answer: r= 1.22
Step-by-step explanation:
Formula for amount with simple interest = [tex]P(1+rt)[/tex]
, where
P= principal value , r= rate of interest , t = time.
Given: P= $2000, t= 5 years, r= 1.25% = 0.0125
[tex]A=2000(1+0.0125\times5)\\\\=2000(1.0625)=2125[/tex]
Formula to compute compound amount : [tex]P(1+r)^t[/tex]
[tex]=2000(1+r)^5[/tex]
When both have same worth then
[tex]2000(1+r)^5=2125\\\\\\ (1+r)^5=\dfrac{2125}{2000}\\\\\\ (1+r)^5=1.0625[/tex]
taking log on both sides , we get
[tex]5\ln (1+r)=\ln 1.0625\\\\\\ 5\ln (1+r)=0.0606246\\\\\\ \ln (1+r)=0.012125\\\\\\ 1+r=e^{0.005266}\\\\\\ 1+r=1.0122\\\\ r=0.0122\\\\ \\ r=1.22\%[/tex]
Hence, Value of r= 1.22
help me please thank you
Answer:
b)30 boys c)1425 beats
Step-by-step explanation:
Answer:
Step-by-step explanation:
b and g are the number of boys and girls, respectively.
b:g = 3:4
b = 3x, g = 4x
3x+4x = 70
x = 10
There are 30 boys.
:::::
(380 beats)/(4 minutes) = (380/4 beats)/minute = (95 beats)/minute
15 minutes × (95 beats)/minute = 1425 beats
An arithmetic sequence has a 2nd term equal to 3 and 10th term equal to -13.
Find the term of the sequence that has value -93. please answer asap.
Answer:
50th term
Step-by-step explanation:
Second term, a + d = 3
Tenth term, a + 9d = -13
a + d = 3 (1)
a + 9d = -13 (2)
Subtract (1) from (2) to eliminate a
9d - d = -13 - 3
8d = -16
d = -16/8
d = -2
Substitute d = -2 into (1)
a + d = 3 (1)
a + (-2) = 3
a - 2 = 3
a = 3 + 2
a = 5
Find the term of the sequence that has value -93.
nth term = a + (n -1)d
-93 = 5 + (n - 1) -2
-93 = 5 + (-2n + 2)
-93 = 5 - 2n + 2
-93 = -2n + 7
-93 - 7 = -2n
-100 = -2n
n = -100/-2
n = 50
50th term = -93
Help would suffice
Answer: Yes
Step-by-step explanation:
x = 9 in (9, 8)
The inequality is x is less than or equal to 9
x = 9 so the point satisfies the inequality.
Yes
ANSWER THIS PLZ PLZ PLZ!!!
Answer:
answer is D
Step-by-step explanation:
window seat and the front are 8/12 which simplifies to 2/3. hope it helps
Answer:
2/9 is the probability that the passenger wants a window seat in the front of the plane
explainatio:
8 people want that particular seat and there are 36 passengers on the plane so 8/36= 2/9
Which represents the series in sigma notation?
-5+(-1)+3+7+11
Answer:
The third answer is correct
when you plug 1 into the equation
4(1)-9= -5
4(2)-9 = -1
4(3)-9= 3
Step-by-step explanation:
The sigma notation of the given series is [tex]\sum _{j=1}^5\:\left(4j-9\right)[/tex], option C is correct.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given series is -5+(-1)+3+7+11
The sigma notation of the given series is [tex]\sum _{j=1}^5\:\left(4j-9\right)[/tex]
Now let us check by plugging j values from 1 to 5
When j =1,
4(1)-9= -5
When j =2
4(2)-9 = -1
when j=3
4(3)-9= 3
Hence, the sigma notation of the given series is [tex]\sum _{j=1}^5\:\left(4j-9\right)[/tex], option C is correct.
To learn more on Sequence click:
https://brainly.com/question/21961097
#SPJ2
Dan buys a car for £700.
It depreciates at a rate of 5.5% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate
Answer:
£469
Step-by-step explanation:
Given the following
Original cost of car = £700.
Depreciation rate = 5.5%
Depreciation amount after 1 year = 5.5% * 700
Depreciation amount after 1 year = 0.055 * 700
Depreciation amount after 6 year =6 * 38.5 = £231
Worth after 6 years = £700 - £231
Worth after 6 years = £469
The correct answer is:
£498.53
show your work please :)
Step-by-step explanation:
yphñotdtowtkstlstoyosotstlstlstosupfhñznx$*□◇○}₩○¥■○♧■▪︎■♧○¥□•¥{•£{•£{{£•{¥{¥•£□•□£●£•●£$>£|•
Write an equation in point-slope form for the line that passes through each point with the given slope (-1,-2) m= 3
Answer:
y + 2 = 3(x + 1)Step-by-step explanation:
The Point-Slope form of equation of a line with slope of "m" and passing through point (x₁, y₁) is: y - y₁ = m(x - x₁)
m = 3
x₁ = -1
y₁ = -2
Therefore the equation:
y - (-2) = 3(x - (-1))
y + 2 = 3(x + 1)Consider JKL below. Determine whether each equation is correct. Select correct or incorrect next to each question.
From the options equation A and D are correct answers.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given triangle JKL, JK=25, JL=7 and LK=24.
We know that, sin θ= Perpendicular/Hypotenuse
tan θ= Perpendicular/Base
A) Now, sin J=LK/JK
sin J= 24/25
B) tan J=LK/JL
tan J=24/7
C) sin K=JL/JK
sin K=7/25
D) tan K=JL/LK
tan K=7/24
Therefore, from the options equation A and D are correct answers.
Learn more about the trigonometric ratios here:
brainly.com/question/25122825.
#SPJ2
Find the coordinates of the midpoint of a segment with the given endpoints.
(4-6) (-3,-6)
Make sure your type your answer in as an ordered pair
Please explain how you found the answer
Answer:
Please mark as Brainliest if this helps :)
Step-by-step explanation:
PLEASE HELP ME QUICK!!
Answer:
D
Step-by-step explanation:
Corresponding angles are the same angles for both sides.
Example: if a= 12, then b also = 12.
Im positive it's alternate interior because they are both inside on alternative sides
You need to rent a bowling lane. On Friday nights, you have two options. Option A is a $20 lane rental plus $3 per game. Option B is a $35 lane rental with a maximum of 10 games. For what number of games is the total cost the same for each option. This is Algebra 1 by the way
Answer:
Option B
Step-by-step explanation:
Answer:
3 games to be equivilent
Step-by-step explanation:
to be the same, on the 20 dollar lane you can play 5 3 dollar games for the same price to play on the 35 dollar lane with 10 games.
Hope this helps
A clothing store manager uses a 12 percent markup on the merchandise. At what price will he sell pants that were purchased for $40?
Answer:
i think this is right $4.80
Step-by-step explanation:
Jenny is 9 years younger than Sammie. Five years ago Sammie was 4 times older than Jennie. How old is each now?
Pls Help Need Answer By 7:00.
Jenny is 8 years old and Sammie 17 is years old.
Given that:Jenny is 9 years younger than Sammie.Five years ago, Sammie was 4 times older than Jennie.To find:Current age of Jennie and Sammie
Calculation and Explanation.Let the current age of Jennie be x.
Let the current age of Sammie be y.
Then from given data we have:
[tex]x = y-9\\4(x-5) = (y-5)[/tex]
We'll substitute value of x from equation 1 in equation 2:
[tex]4(y-9-5) = (y-5)\\3y = 51\\y=17[/tex]
Thus, from equation 1 and y = 17, we have:
[tex]x=y-9\\x=17-9\\x=8[/tex]
Thus, Jenny is 8 years old and Sammie 17 is years old.
Learn more about age difference related posts here:
https://brainly.com/question/4159273
Answer:
Jenny is 8 years old and Sammie 17 is years old.
Notes:
Please make me the brainliest! I worked hard on this.
PLEASE HELP... WILL GIVE BRAINLIEST
Answer:
the answer is B.
Step-by-step explanation:
hope this helps!
if the point (x,y) is on the x-axis is it x=0 y=0
Answer:
You know that y must have to equal 0. x can be anything though.
Step-by-step explanation:
The x-axis is a straight line in the center of the y-axis where y = 0.
the interval between 3:15 p.m. to 8 p.m. is
Answer:
4 hours and 45 minutes
Step-by-step explanation:
The only thing you have to do is subtract 8 by 3:15 which is 4:45. 4:45 means that it its 4 hours and 45 minutes.
Hope this helps
$1,200 in sales with 4% commission
Answer: 48 dollars
Step-by-step explanation:
Select the equation that is equivalent to the equation y-3=2(x+5)
Bernard built 15 model cars one year. He did not build as many model cars as his sister, Abby. In the inequality, n represents the number of model cars Bernard needed to build to have more than Abby.
Which number of model cars did Bernard need to build to have more model cars than Abby?
A.1
B.2
C.3
D.4
Answer:
The answer is 1
Step-by-step explanation:
Which is true about the position of A on the number line?
A. It is less than -1
B. It is greater than 0
C. It is less than -8/3
D. It is greater than 3/4
Acellus
Meg has 11 hats and she buys 1 new hat
every month. Fanny has 1 hat, but plans
to buy 3 every month. How many months (m)
will it be until Fanny has as many hats as Meg?
h = m +11
h = 3m +1
[?] months
Enter
[tex]\\ \sf\Rrightarrow m+11=3m+1[/tex]
[tex]\\ \sf\Rrightarrow m-3m=1-11[/tex]
[tex]\\ \sf\Rrightarrow -2m=-10[/tex]
[tex]\\ \sf\Rrightarrow m=-10/-2 [/tex]
[tex]\\\sf \Rrightarrow m = 5[/tex]
There are 15 neon tetras and 12 betta fish in a
fish tank. What is the ratio of betta fish to the
total number of fish? Write the ratio on simplest
form.
Read the question very carefully, notice the phrase "total number of fish"
HELP PLEASE
Answer:
4:9 or 4/9 depending on how your teacher or computer program wants it entered. Some use the colon (:) some use the slash (/).
Step-by-step explanation:
1. Betta fish = 12
2. Total fish = 27 (15 neon + 12 betta)
3. 12:27 or can be writte as 12/27 depending on your teacher or computer program.
4. Can be simplified by dividing by 3
12/3 and 27/3
5. 4:9 or 4/9
11 is the quotient of a number y and b
do I use area or what I'm confused?
Answer:
No you use the formula for perimeter (the perimeter should be 378)
Step-by-step explanation:
P = 2l + 2w, l is the length of the rectangle and w is the width of the rectangle
The l or length is (E-I) 119
The w or width is (N-T) 70 in total
the weight w of a steel frame is 9.2kg correct to 1 decimal place. complete the error interval for weight w
Answer:
9.5_<w<9.25
Step-by-step explanation:
how do you find the area of a trapezoid that is on a rectangle
Answer:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
Hope that helps!
two numbers have the ratio of 4:7 if their sum is 143 what are the numbers?
1.kind of proportion
2.write the proportion
3.first number answer
4second number answer
help me plss!
Answer:
52:91
Step-by-step explanation:
To find a ratio value you need to think of it more as two numerators that together equal one whole. 4+7 is 11 so that would be the denominator. If the sum is 143, then we divide by 11 since one number is 4/11s of 143, and the other is 7/11s of 143. 143/11=13
now we multiply both:
4(13)=52
7(13)=91
Check:
91+52=143
52/91 simplifies to 4/7 or 4:7
i hope this helps!
the area of rhombus is 60 square CM one diagonal is 10 cm The Other diagonal is
Answer:
area of rhombus=1/2d1d2
Step-by-step explanation:
60=1/2×10×d2
60×2=10×d2
120/10=D2
12=D2
therefore othr diagnol is 12
hope it helps!
