Using interest equations, it is found that it will take 1.08 year more for Lydia's money to triple than for Lily's.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
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.What is the amount in continuous compounding?It is given by:
[tex]A(t) = Pe^{rt}[/tex]
For Lily, the parameters are as follows: r = 0.065, with continuous compounding. The time to triple is t for which A(t) = 3P, hence:
[tex]A(t) = Pe^{rt}[/tex]
[tex]3P = Pe^{0.065t}[/tex]
[tex]e^{0.065t} = 3[/tex]
[tex]\ln{e^{0.065t}} = \ln{3}[/tex]
[tex]0.065t = \ln{3}[/tex]
[tex]t = \frac{\ln{3}}{0.065}[/tex]
[tex]t = 16.90[/tex].
For Lydia, using compound interest, the parameters are: r = 0.06125, n = 12, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]3P = P\left(1 + \frac{0.06125}{12}\right)^{12t}[/tex]
[tex](1.00510416667)^{12t} = 3[/tex]
[tex]\log{(1.00510416667)^{12t}} = \log{3}[/tex]
[tex]12t\log{(1.00510416667)} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{12\log{(1.00510416667)}}[/tex]
[tex]t = 17.98[/tex]
17.98 - 16.9 = 1.08, hence, it will take 1.08 year more for Lydia's money to triple than for Lily's.
More can be learned about interest equations at https://brainly.com/question/25781328
Evaluate the expression 24(20*14)
REE A manufacturer of window frames knows from past experience that 10 per cent of the production will have some type of minor defect that will require adjustment. Suppose 20 window frames are selected at random: a. How many window frames would you expect to have minor defects? (2 points) b. Calculate the standard deviation for the number of window frames to have minor defects in this random sample of 20 window frames. (2 points) c. Calculate the probability that exactly 2 window frames will need minor . adjustment. (2 points) d. What is the probability that more than 3 window frames will need minor adjustments? (7 points)
Answer:
10% to decimal is equal to 0.1.
Therefore 20 x 0.1 = 2
Step-by-step explanation:
Each window is independently probable for having minor defects. The expected number of window frames having minor defects = 2.
Other figures are:
Standard deviation for the number of windows frames to have minor defects in this random sample of 20 window frames = 1.34 approx.P(Exactly 2 windows will need minor adjustment) = 0.285 approx.P(More than 3 windows will need minor adjustment) = 0.1329 approx.How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np[/tex][tex]Var(X) = np(1-p)[/tex]For the considered case, we can assume that each window is independent of each other for having defects or being perfect.
Each window can be having defects (call it success) or no defects(call it failure).
Then, we can take:
X = number of windows out of 20 windows being perfect (no defect).
Then we get:
Success = window having defectn = 20p = 10% = 0.10 (as given in the problem)[tex]X \sim B(n=20,p=0.1)[/tex]Evaluating each sub parts one by one:
Case a: How many window frames would you expect to have minor defects?Expect number of defective windows = E(X) = np = 20 × 0.1 = 2
Case b: Calculate the standard deviation for the number of window frames to have minor defects in this random sample of 20 window frames.Standard deviation is the positive root of variance.
Standard deviation of number of windows (out of 20 windows of sample) having defects = [tex]\sqrt{Var(X)} = \sqrt{np(1-p)} = \sqrt{2(0.9)} \approx 1.34[/tex]
Case c: Calculate the probability that exactly 2 window frames will need minor adjustment.P(X = 2) = [tex]^{20}C_2(0.1)^2(0.9)^{18} \approx 0.285[/tex]
Case d: What is the probability that more than 3 window frames will need minor adjustments?P(X > 3) = 1 - P(X ≤ 3)
[tex]P(X > 3) = 1 -[ P(X = 0) + P(X = 1) +P(X= 2)+ P(X = 3)]\\\\P(X > 3) = 1- [^{20}C_0(0.1)^0(0.9)^{20} +^{20}C_1(0.1)^1(0.9)^{19} +\\\: \:\: ^{20}C_2(0.1)^2(0.9)^{18} +^{20}C_3(0.1)^3(0.9)^{17} ]\\\\P(X > 3) \approx 1-[ 0.1216 + 0.2702 + 0.2852 + 0.1901]=1-0.8671=0.1329 \\\\P(X > 3) \approx 0.1329[/tex]
Thus, the needed figures are:
Expected number of window frames having minor defects = 2Standard deviation for the number of windows frames to have minor defects in this random sample of 20 window frames = 1.34 approx.P(Exactly 2 windows will need minor adjustment) = 0.285 approx.P(More than 3 windows will need minor adjustment) = 0.1329 approx.Learn more about binomial distribution here:
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 36 and DC = 8, what is the length of BD in simplest radical form?
The length of BD is 16.97.
TrigonometryTo determine, given that right triangle ABC with altitude BD is drawn to hypotenuse AC, if AD = 36 and DC = 8, what is the length of BD in simplest radical form, the following calculation must be performed:
Hypotenuse AC = AD + DC = 36 + 8 = 44Altitude = square root of the multiplication of AD and DC√(36 x 8) = X√288 = X16.97 = XTherefore, the length of BD is 16.97.
Learn more about trigonometry in https://brainly.com/question/26719838
Which inequality compares 2/4 and 5/6?
Answer:
2/4 is greater
Step-by-step explanation:
if you reduce 2/4 its 1/2 and 5/6 cant be reduced so therefor 2/4 is greater
What is the slope intercept form of (-4,-5); and slope 1/2
Answer:
Step-by-step explanation:
Slope intercept form is y = mx + b where m is the slope and b is the y intercept.
We are given m = 1/2
Plug the point (-4,-5) in for x and y and the given slope in for m.
y = mx + b
-5 = 1/2(-4) + b
Now solve for b.
-5 = -2 + b
b = -3
Now plug m and b back in to get your slope intercept form.
y = 1/2x -3
Hope this helps!
20 Points for an answer! Please help! I have unlimited tries for the practice test, but I got this one wrong from an answer on here, Letter B doesn't work for the answer, I tried that already.
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
Question options:
A.) If segment AC ≅ segment BC, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
B.) If segment AD ≅ segment CD, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
This one is incorrect according to my practice test I took.
C.) If segment AC ≅ segment BC, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
D.) If segment AD ≅ segment CD, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Answer:
Well, according to the question, option D is the main answer
Find the area of the polygon.
Answer:
66 cm²
Step-by-step explanation:
As you know from the area formulas, the area of a triangle is equivalent to half the area of a rectangle with the same base and height. Another way to say that is the area of a triangle is equivalent to the area of a rectangle with the same base and half the height.
The triangle added to the side of the square is equivalent in area to a rectangle with the same 6 cm base (vertical dimension), and half the 10 cm height (horizontal dimension). That is, the total area of the polygon is the same as the area of one that is 6 cm high and 6+5 = 11 cm wide.
A = LW = (6 cm)(11 cm) = 66 square centimeters
__
If you want to figure the area more conventionally, it is the sum of the area of a 6 cm square and a 6×10 cm triangle:
6² +1/2(6)(10) = 36 +30 = 66 . . . square centimeters
Find the equation of the line with slope 25 and y-intercept (0,−2).
answer: Equation of line is : Y = mx +b
Y intercept is origin ( 0,0)
Therefore :
Y = 6/5 X
All lines passing through origin have equation:
Y = mX
Answer: y= 2x/5 -2
Step-by-step explanation:
y=mx+b
y=2/5x + (-2)
y=2x/5 -2
5x3x4x6
plz give me an answer quickly
Answer:
360
Step-by-step explanation:
5 * 3 * 4 * 6 = 5 * 4 * 3 * 6 = 20 * 18 = 360
Answer:
360
Step-by-step explanation:
5x3=15
15x4=60
60x6=36
1. Data with two variables is called *
A double data.
.
B bivariate data.
C split data
D bipedal data
Answer:
B. "bivariate data"
Quizlet fortunately had the same question with this answer, so here you go! :)
is encanto a good movie
Answer:
yes
Step-by-step explanation:
Answer:
Aah I don't like it but many people love it. It really depends on what kind of person you are
Determine the absolute value. Type the numerical answer only. |10|
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
The answer is 10 because:
1) Absolute value makes all negative or positive numbers positive (unless there is a negative sign outside the absolute value sign).
2) Therefore, the absolute value of 10 is positive 10.
Hope this helps! :D
The points (1, 6) and (r, -6) lie on a line with slope - 4. Find the missing coordinate r.
Answer:
49
Step-by-step explanation:
By the definition of slope, as vertical change over horizontal change, we get
[tex]-4=m = \frac{\Delta y }{\Delta x} = \frac{r-1}{-6-6} = -\frac{r-1}{12}[/tex]
By checking the first and the last step of that chain
[tex]-4=-\frac {r-1}{12} \rightarrow r-1=48\rightarrow r= 49[/tex]
PLEASE HELP ME ON THAT I REALLY NEEDED. Tell be the statement and the reason please also please do it in order because is on aleks. THANKS!
Answer:
CD = EC ⇒ proved down
Step-by-step explanation:
If a point lies on a segment, then it divides the segment into two parts, the sum of their length equals the length of the segment
Example:
If point Z lies on the segment XY, then Z divides XY into segments XZ and ZY, where XY = XZ + ZY
Let us use this fact to solve the question
∵ BD and EF intersected at point C
∴ C divides BD into two segments BC and CD
∴ C divides EF into two segments EC and CF
→ By using the fact above
∴ BD = BC + CD
∴ EF = EC + CF
∵ BD = EF ⇒ given
→ Equate their right sides
∴ BC + CD = EC + CF
∵ BC = CF ⇒ given
→ That means their adding segments are equal
∴ CD = EC ⇒ proved
What is the solution of the system of equations below?
y = x + 2
y = 3x
Answer:
x=1,y=3
Step-by-step explanation:
Which equation is a direct variation? PLEASE HELP
Does ARE NOT tell me to ADD or SUBTRACT?
Answer:
What is the question??
Step-by-step explanation:
Kady took 83 Tootsie Rolls to give to Mrs. Kilongkilong's 6th
grade class. After passing out one Tootsie roll to each student,
Kady had 25 left over. Which equation could Kady use to figure
out how many students are in Mrs. Kilongkilong's class?
8 = 83 x 25
8 = 83:25
S =
= 25 - 83
8 = 83 - 25
I need help
Step-by-step explanation:
83 - 25 should be the right answer
Suppose you borrow $1,000 for 5 years at an add-on interest rate of 6%, what is the approximate APR? Round your answer to one decimal place. Include the correct unit.
The approximate APR generated when you borrow $1,000 for 5 years at an add-on interest rate of 6%, = $300
Calculation of Annual percentage rateAnnual percentage rate is defined as the yearly interest generated by a sum that's charged to borrowers.
The formula for APR = p×t×r/100
The principal amount deposited (p)= $1000
Time (t) = 5 years
At the rate (r) = 6%
Therefore APR=
[tex] \frac{p \times t \times r}{100} [/tex]
[tex] \frac{1000 \times 5 \times 6}{100} [/tex]
[tex] \frac{30000}{100} [/tex]
APR = $300
Therefore, the approximate APR = $300
Learn more about APR here:
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A cylinder has a volume of 60cm what is the volume of a cone with the same radius and height.
Answer:
20 cm³
Step-by-step explanation:
Since the volume of a cylinder is 60 cm³, which we can express it as:
[tex]\displaystyle \large{\pi r^2 h=60}[/tex]
Keep in mind that [tex]\displaystyle \large{\pi r^2 h}[/tex] is the cylinder’s volume formula, and we want to find the volume of a cone with same radius and height. When they say same radius and height, they mean that the radius and height are the same as cylinders’.
But since no values of radius and height are given, we know that the volume of a cone is:
[tex]\displaystyle \large{\frac{1}{3}\pi r^2 h}[/tex]
Compare both formulas:
[tex]\displaystyle \large{\pi r^2h}[/tex] — cylinder’s volume
[tex]\displaystyle \large{\frac{1}{3}\pi r^2h}[/tex] — cone’s volume
See how they are quite similar except that cone’s volume has 1/3. That means cone’s volume is 1/3 of cylinder’s volume
Finding cone’s volume, multiply both sides by 1/3:
[tex]\displaystyle \large{\pi r^2h=60}\\\displaystyle \large{\frac{1}{3}\pi r^2h=\frac{1}{3}\cdot 60}\\\displaystyle \large{\frac{1}{3}\pi r^2h=20}[/tex]
Therefore, the volume of a cone with same radius and height from cylinder is 20 cm³.
__________________________________________________________
Summary
Volume (Cone) (1/3 of cylinder’s volume):
[tex]\displaystyle \large{V=\frac{1}{3}\pi r^2 h}[/tex]
Volume (Cylinder):
[tex]\displaystyle \large{V=\pi r^2h}[/tex]
They are quite related!
__________________________________________________________
Others
Let me know if you have any doubts about my answer, explanation or this question through comment!
3/5x3/5 as exponenttt help me
Answer:
i think it is 3/5 raised (^) to the 2nd
Step-by-step explanation:
obvioulsy if its an exponent and seeing that you put it 2 time you have the original number and just raise its power by how many times its being multiplied! its easy, you got this champ!
Please help!
Recently, the National Safety Council collected data on the leading causes of accidental death. The findings revealed that for people age 20, 30 died from a fall, 47 from fire, 200 from drowning, and 1950 from motor vehicle accidents. What percent of the accidental deaths were not attributed to motor vehicle accidents? Round to the nearest percent.
Answer:
10% were not attributed to motor vehicle accidents.
Step-by-step explanation:
Ray BD bisects ABC so that m
Answer:
Step-by-step explanation:
I hate this app! its so horrible rate me bad I dont care I hate YOU
What is the area of a section 10 ft wide and 50 yd long? Give your answer in square feet.
Answer:
1,500 square feet
Step-by-step explanation:
you have to convert yards to feet and multiply
Ms.Barton ate an impressive number of slices, but Mr.weaver ate eight more slices than Ms.Barton did. Mr.Fitzgerald ate fifteen Fewer slices than twice as many as Ms.Barton did. Mr.Lloyd’s total was more thirty than half of Ms.Barton’s
If the teachers ate a total of 176 slices of pie, what was the finishing order of the contest and how many slices did the winner eat?
Let:
Ms. Barton = b
Mr. Weaver = b + 8
Mr. Fitzgerald = 2b - 15
Mr. Lloyd = 1/2b + 30
Find b:
176 = b + b + 8 + 2b - 15 + 1/2b + 30
176 = 9/2b + 23
153 = 9/2b
b=34
Plug in 9 to b:
Ms. Barton = 34 slices (4th place)
Mr. Weaver = 34 + 8 = 42 slices (3rd place)
Mr. Fitzgerald = 2(34) - 15 = 53 slices (1st place)
Mr. Lloyd = 1/2(34) + 30 = 47 slices (2nd place)
in each linear equation, identify the slope (m) and the y-intercept (b)
Hey there!
Let's find the slope & y-intercept of each equation.
The first one is y=4x-5.
Please remember that
In slope-intercept equations. the slope is the coefficient of x (the number before x)Also, the y-intercept is the number/variable that's added/subtracted to/from the slope.In other words, in slope-intercept form (y=mx+b), m is always the slope and b is the y-intercept.
Therefore, the slope of the first linear equation is 4, and the y-intercept is -5.
or
m=4, b=-5 (option A)
Same with the other equation:
m=-1, b=2/3 (option C is the right option)
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
72 hundredths is ______ hundredths and _________hundredths, or 7 ________and 2 _____
Answer:
7 hundredths
2 tenths
Step-by-step explanation:
7 is in the hundredths place and there is no zero so then to would be in the tenths place
Consider a line whose slope is 6 and which passes through the point (8.–2).
3. Write the equation of the
4. Write the equation of the
line in point-slope form.
line in slope-intercept form.
Answer:
[tex]y=6(x-8)-2\qquad\text{point-slope form}[/tex]
[tex]y=6x-50\qquad\text{slope-intercept form}[/tex]
Step-by-step explanation:
The equation of a line can be written in several forms. Two of the most-used forms are the point-slope and the slope-intercept forms.
The point-slope form requires to have one point (xo, yo) through which the line passes and the slope m. The equation expressed in this form is:
[tex]y=m(x-xo)+yo[/tex]
The slope-intercept form requires to have the slope m and the y-intercept b, or the y-coordinate of the point where the line crosses the y-axis. The equation is:
[tex]y=mx+b[/tex]
The line considered in the question has a slope m=6 and passes through the point (8,-2). These data is enough to find the point-slope form of the line:
[tex]\boxed{y=6(x-8)-2\qquad\text{point-slope form}}[/tex]
To find the slope-intercept form, we operate the above equation:
[tex]y=6x-48-2[/tex]
[tex]\boxed{y=6x-50\qquad\text{slope-intercept form}}[/tex]
Use an area model to multiply (4x+3)(2x+5)
Fill in the blanks with the correct numbers.
Answer: [tex]12^{2}[/tex] + 43x + 35
Answer: I took the test and got 8x^2 + 26x + 15
I hope this helped!
what is the circumference of the circle if r = 3.5 feet? use 22/7 for pi
Answer:
22 feet
Step-by-step explanation:
the formula for the circumference of a circle is 2πr where r is the radius of the circle. this can also be written as πd where d is the diameter of the circle (because the diameter is 2×r)
2×3.5=7
(22/7)×7=22