Elizabeth invested $970 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 % compounded daily. Matthew invested $970 in an account paying an interest rate of 6\tfrac{3}{4}6 4 3 % compounded continuously. After 8 years, how much more money would Matthew have in his account than Elizabeth, to the nearest dollar?
Using continuous compounding and compound interest, it is found that Matthew would have $17 more than Elizabeth in his account.
Compound interest:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
Continuous compounding:
[tex]A(t) = Pe^{rt}[/tex]
The parameters are:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For both of them:
Investment of $970, hence [tex]P = 970[/tex]Invested for 8 years, hence [tex]t = 8[/tex]Elizabeth:
Compounded daily, hence [tex]n = 365[/tex].Rate, as a percent, of [tex]6\frac{5}{8} = 6 + \frac{5}{8} = 6.625[/tex], hence [tex]r = 0.06625[/tex].Then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(8) = 970\left(1 + \frac{0.06625}{365}\right)^{365(8)}[/tex]
[tex]A(8) = 1648[/tex]
Matthew:
Rate, as a percent, of [tex]6\frac{3}{4} = 6 + \frac{3}{4} = 6.75[/tex], hence [tex]r = 0.0675[/tex].Then:
[tex]A(t) = Pe^{rt}[/tex]
[tex]A(8) = 970e^{0.0675(8)}[/tex]
[tex]A(8) = 1665[/tex]
The difference is:
1665 - 1648 = 17
Hence, Matthew would have $17 more than Elizabeth in his account.
A similar problem is given at https://brainly.com/question/24507395
A line includes the points (6,9) and (14, 17). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = x + 3
Step-by-step explanation:
Given: (6,9) (14, 17)
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{17-9}{14-6}=\frac{8}{8}=1[/tex]
slope, m = 1
Equation of line ⇒ y=mx+b
y = 9 , x = 6 , m = 1, b = ?
9 = 1*6 + b
9 = 6 + b
b = 9 - 6 = 3
Therefore, the equation of line will be:
y = 1x + 3
y = x + 3
The Cougars, a football team, must gain 10 yards in the next four plays to keep possession of
the ball. The Cougars gain 5 yards, lose 12 yards, gain 14 yards, and finally lose 8 yards. Do
the Cougars keep possession of the ball?
Answer:
No
Step-by-step explanation:
Gain 5= 5 to go
Lose 12= 7 to go
Gain 14= 7 to go
Lose 8=15 to go
What is a_50 of the arithmetic sequence 45, 40, 35, 30.
Answer:
5s
Step-by-step explanation:
45-5=40
solve for b please. last one 33 points
Answer:
32
Step-by-step explanation:
6^2= b^2 + 2^2
b^2 = 36- 4
b^2= 32
b= √32
Answer:
√32
Step-by-step explanation:
The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , is used to find the length of any side of a right triangle.
6² - 2² = b²
36 - 4 = b²
32 = b²
the choices for the first one is either x values or y-values
Answer:
x values
division
Step-by-step explanation:
Vertical lines are all "rise" and no "run"
therefor the difference in x values is always 0
division by 0 is undefined
Answer: y- values
Step-by-step explanation:
Please help me with this question
I can't figure it out and please answer all of it
Step-by-step explanation:
1. False
2. True
3. True
4. False
Answer:
a. false
b. true
c. true
d. false
Step-by-step explanation:
hope this is right
(if not tell me in the comments and i will try to help you best i can)
27 x 9^3x can be written in the form 3^k where k is an expression in terms of x. Find k
Answer:
27 x 9^3x = 3^3 x 9^3x = 3^3 x (3^3)^3x = 3^3 x 3^9x = 3 ^3+9x
3^3+9x = 3k
ln(3^3+9x) = ln(3^k)
3+9x(ln3)=k(ln(3))
k= 3(1+3x)/ln(3)
Step-by-step explanation:
ln(x^n) = n(ln(x))
what is 29,032 to the nearest thousands
Answer:
29,000
Step-by-step explanation:
Answer:
30,000 i believe
Step-by-step explanation:
if that isnt the right answer then its just 29,000
Factor the trinomial
10x^2+11X-6
Answer:
The expression is not factorable with rational numbers.
10x2+11X−6
Step-by-step explanation:
PLS Brainliest
Twelve square tiles, each measuring 5 inches
on a side, are laid side by side. What is the total
width of the tiles?
Answer:
pretty sure 60, 5 x 12
Step-by-step explanation:
just do 5 x 12 if there's 12 tiles and their measurement is 5 inches each
What dp they mean 2 to the fourth equal 16.
Answer:
See Below
Step-by-step explanation:
I think you mean 2 the the fourth power, showing 2, with an exponent of 4.
To calculate this, you multiply your base, 2, by itself as many times as the exponent states. Like, 2x2x2x2 because you are multiplying it 4 times by 2.
2x2=4, then 4x2=8, then 8x2= 16.
Hope this helps!
Rearrange v=u+at to make t the subject of formula.
A. t=(u-v)/(a)
B. t=(v-u)/(a)
C. t=(u+v)/(a)
D. t=(v+u)/(a)
Answer:
t=(v-u)/a
hope it will help you
Read the excerpt from the poem "Hide and Seek":
(21) I examine my hideout, the contours of the leaves,
(22) The blades of grass, a crawling caterpillar.
(23) The minutiae fascinate me, a world within my world.
(24) One touch from me, and the caterpillar lies curled.
(25) Isn't this a metaphor for life?
(26) I'm in a game within another game.
(27) We're all fascinated by ourselves, and our own life.
(28) How often do we acknowledge others' trouble and strife?
How does the point of view influence the description in lines 22-28?
A deeper connection is made and uses the setting to relate to life by the speaker.
A quick description of the hiding place is given at the end of the game by the speaker.
The other children's hiding spots are described by someone, not in the poem.
The setting is being described by someone who was not playing the game.
Answer:
A
Step-by-step explanation:
4.99 for 13lb find the unit rate
Answer:
$0.38 per lb.
Step-by-step explanation:
unit rate formula; cost / quantity
4.99 / 13 = 0.3838461538461
round to the nearest hundredth
Solve the slope for the table.
Answer:
The slope is 0
Step-by-step explanation:
All y-values are equal to 5 meaning the graph is a straight horizontal line. Slope is the rate at which a graph increases or decreases. Seeing as this graph doesn't do so, the slope is 0.
Help me I really don’t understand this and I can’t fail please just please help I will mark brainliest
Answer:this question is confusing but it's probably the last one, must be the one passing through
x=1
y=-1
Lee earns $17.00 per hour at her job. How much money will Lee earn if she works for 4 hours?
share 5,000 in the ratio of 1:2:3:4
Answer:
500 : 1000 : 1500 : 2000
Step-by-step explanation:
sum the parts of the ratio , 1 + 2 + 3 + 4 = 10 parts
Divide the amount by 10 to find the value of one part of the ratio
5000 ÷ 10 = 500 ← value of 1 part of the ratio , then
2 parts = 2 × 500 = 1000
3 parts = 3 × 500 = 1500
4 parts = 4 × 500 = 2000
5000 = 500 : 1000 : 1500 : 2000 in the ratio 1 : 2 : 3 : 4
what is 6.30 divided by 18
Answer:
6.3/18 = 0.35
Step-by-step explanation:
0.35 is your answer
after working out for 45 minutes, Juanita heartbeat at 75 beats in 30 seconds what equation represent the relatship of b and m
Answer:
abcdefghijklmnopqrstuvwxyz
someone please help me asap
Answer:
I only can see that one of them are B i don't know for the rest
Step-by-step explanation:
the rate of change is _____ inches of growth per week
Answer:
4.5 inches per week
Step-by-step explanation:
Easy conversions
Systems of elimination for
2w-3q=8
3w-7q=7
i guess is by multiplying 3by the first equation and multiply 2by the second equation
Write the equation of a line that
passes through the following points
:
Point 2: (0,-8)
Point 1: (-3,0)
Answer:
[tex]y = \frac{-8}{3}x - 8[/tex]
Step-by-step explanation:
Solving for the equation of the line with two points:
Let's remind ourself of the slope - intercept formula: [tex]y = mx + b[/tex]
We first have to find the slope of the line. This is found by using the formula :
[tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]
We have to find the change in y (Δy) and divide it by the change in x (Δx)
We then have to plug in a coordinate given to us, and use the point's x and y value to find the y - intercept
Step 1: SlopeLet's use the slope formula
[tex]\frac{0 - (-8)}{-3 - 0} = \frac{8}{-3}[/tex]
Slope = -8/3
Step 2: Y - InterceptTo find the y - intercept, we'll update our slope - intercept formula with the slope, and plugin a point. Let's use (-3,0)
[tex]y = \frac{-8}{3}x + b[/tex]
[tex]0 = \frac{-8}{3}(-3) + b[/tex]
[tex]0 = \frac{24}{3} + b[/tex]
[tex]0 = 8 + b[/tex]
[tex]b = -8[/tex]
Step 3: EquationLet's input our slope and y - intercept to the equation [tex]y = mx + b[/tex]
Slope = -8/3
Y - Intercept = -8
Equation: [tex]y = \frac{-8}{3}x - 8[/tex]
-Chetan K
Which expression is an equivalent expression for 2(6y – 4)?
A. 8x – 2
B. 12y – 8
C. 8y
D. 12y + 4
Answer:
B.
Step-by-step explanation:
Because you have to multiply 6y by 2 that is 12y and you have to multiply -4 by 2 that is - 8, you put it together and it's 12y - 8.
The degree of polynomial is ?
Line A is represented by the following equation: x + y = 2
What is most likely the equation for line B so the set of equations has no solution?
Answer:
[tex]ax+ay=k; a\ne0, k\ne2a[/tex]; line D in the options.
Step-by-step explanation:
The set of equations has no solutions if the two lines are parallel. A quick way to create a parallel line is to solve for y, put it in slope-intercept form. Else, as long as the cofficient of x and y are in the same ratio (in this case 1:1), the two lines are parallel, you just have to be careful not to pick the same line again!
The condition [tex]a\ne 0[/tex] makes sure you are still getting lines (else you would get rid of both x and y); the condition [tex]k\ne 2a[/tex] makes sure you're not picking line A again, just written in a different form.
Now that we have the options:
A and C have a different ratio for the coefficient of x and y (2:1 and 1:2) so are not good.
Choice B is just a more complicated way to write the same line, you can see by dividing both sides by 2 and get back x+y=2.
Line D is correct.
May ALG 1A Unit 5 Modified Discussion
A pattern that increases or decreases at a constant rate is a linear function
Question 1 represents a linear functionQuestion 2 and 3 represent a nonlinear functionQuestion 1
From the table, we see that:
As x increases by 25, The value of y decreases by 1The rate of increment/decrement is constant for both variables.
Hence, question 1 represents a linear function
Question 2
From the table, we see that:
As x increases by 2, The value of y increases at different ratesThe rate of increment is not constant for variable y.
Hence, question 2 represents a nonlinear function
Question 2
From the table, we see that:
As the steps (i.e. x) increases by 1, The number of blocks (i.e. the value of y) increases at different ratesThe rate of increment is not constant for variable y.
The complete table is:
[tex]\mathbf{Step\to Blocks}[/tex]
[tex]\mathbf{1 \to 2}[/tex]
[tex]\mathbf{2 \to 6}[/tex]
[tex]\mathbf{3 \to 12}[/tex]
[tex]\mathbf{4 \to 20}[/tex]
Hence, question 3 represents a nonlinear function
Read more about patterns and rates at:
https://brainly.com/question/22386004
four more than the price ,p