Using compound interest and continuous compounding, it is found that it would take 2.61 years longer for Carter's money to triple.
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.For Carter, we have that the rate of interest and the number of compoundings are, respectively, r = 0.04875 and n = 12. The time to triple is t for which A(t) = 3P, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]3P = P\left(1 + \frac{0.04875}{12}\right)^{12t}[/tex]
[tex](1.0040625)^{12t} = 3[/tex]
[tex]\log{(1.0040625)^{12t}} = \log{3}[/tex]
[tex]12t\log{(1.0040625)} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{12\log{(1.0040625)}}[/tex]
t = 22.58.
What is continuous compounding?The amount of money is given by:
[tex]A(t) = Pe^{kt}[/tex]
For Jack, we have that the rate of interest is of k = 0.055, hence:
[tex]A(t) = Pe^{kt}[/tex]
[tex]3P = Pe^{0.055t}[/tex]
[tex]e^{0.055t} = 3[/tex]
[tex]\ln{e^{0.055t}} = \ln{3}[/tex]
[tex]0.055t = \ln{3}[/tex]
[tex]t = \frac{\ln{3}}{0.055}[/tex]
t = 19.97.
The difference is given by:
22.58 - 19.97 = 2.61
It would take 2.61 years longer for Carter's money to triple.
More can be learned about compound interest at https://brainly.com/question/25781328
Prove triangle ABC is congruent to triangle DEF.
Answer:
Step-by-step explanation:
Rotate triangle DEF 90° and translate it up 1 point, and left 2 points.
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Simplify the following expression: (52)^8
what is 5 2/3 x 13? I'm not really good with fractions
Answer:
The answer is 221/2 or 73 ⅔
Step-by-step explanation:
5 ⅔ = (3 × 5 + 2) ÷ 3 = 17/3
Now,
17/3 × 13 = 221/2 = 73 ⅔
Thus, The answer is 221/2 or 73 ⅔
2. A baby weighs 8 pounds, 1 ounce. How much does she weigh in ounces?
Answer:
97 oz
Step-by-step explanation:
12 oz per pound
8 pounds + 1 oz
(12 · 8)+ 1
97 oz
Hope this helps!
Which Expression represents the perimeter of the figure below?
А 5x+2y
B x + y +z
C 5x + 2y + 2
D (5+2 + 1)(x + y + 2)
Answer:
The C option is correct
TRUST ME
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEHow much will be in the jar?
Answer:
option B 1 1/6amount of paint:
1/2 * 1 + 1 * 3 + 1 1/2 * 1 + 1 * 27If divide into 6 jars:
7/61 1/6[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
let's solve ~
Total jars = 6
Total cups of blue paint :
[tex]\qquad \tt \dashrightarrow \: \frac{1}{2} + (1 \times 3) + 1 \frac{1}{2} + 2[/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{1}{2} + 3 + \frac{3}{2} + 2[/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{1 + 6 + 3 + 4}{2} [/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{14}{2} [/tex]
[tex]\qquad \tt \dashrightarrow \:7 \: cups[/tex]
So, teacher distributes all blue paint equally in each jar, then amount of paint in each jar is :
[tex]\qquad \tt \dashrightarrow \: \dfrac{7}{6} [/tex]
[tex]\qquad \tt \dashrightarrow \:1 \frac{1}{6} \: \: cups[/tex]
So, option B is correct
please help i need help
Answer:
the answer is 14
Step-by-step explanation:
so first you subtract 8- 2 over 2 then =1 over 8 then subract 2 over 2
8 x 2 - 2 = 16 - 2 = 14 = 2 x 7 = 7
1 x 2 - 2 = 2 = 2 = 2 x 1
then 1 x 2 = 2 = 7 over 1 next add 21 over 3 + 7 = 21 over 3 + 7 over 1 = 21 over 3 + 21 over 3 = 21 +21 over 3 = 42 over 3 = 3 X 14 over 3 x 1 = 14
hope this helps you have a good day
HELP PLEASEE !!! Only correct answers and please no links
An experiment consists of rolling a die and then flipping a coin.
The following tree diagram shows the possible outcomes.
A tree diagram in which a center point branches to numbers 1 through 6, which each branch to an H & T.
© 2018 StrongMind. Created using GeoGebra.
What is the probability of rolling an even number or flipping a tail?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
Both are 1/2
Step-by-step explanation:
Count just the tails, that's the numerator
Count all the heads and tails, that's the denominator.
And for the 2nd fraction:
Count just the evens, that's the numerator
Count all the even and odd numbers, that's the denominator.
Answer: The answer to this question is 3/4
Step-by-step explanation:
In this problem, there are 12 outcomes. Of those, 3 result in an even number and a tail, 3 more in an even number but not tail and 3 in a tail but an odd number, hence there are 9 desired outcomes.
Hence, the probability is given by: p=9/12=3/4
Find the exact value of the expression sin(sin225 - 120)
Step-by-step explanation:
I use desmos . com so it's easier.
A) 1.29
B) 0.91
C) 0.97
D) 1.05
Good Luck!
Which is the best buy?
Pack of 8 apples for £1.65
Pack of 6 apples for £1.25
Answer:
Pack of 6 apples for £1.65 is better because the price of 1 apple is less in this answer.
Divide - 5/4 by 25/13
13/25
hope it helps..!!!
Write a problem that represents the addition model shown above. Don't solve the problem.
15 points and Brainliest
Easy question! First one to answer gets brainliest!
X=5+7
x=12
.................
4) Debble uses 8 ounces of apples to make one serving of applesauce. How many servings
of applesauce can she make with 6 pounds of apples?
4) Hint: There are 16 ounces in 1 pound
Debble uses 8 ounces of apples to make one serving of applesauce.
12 servings of applesauce can she make with 6 pounds of apples.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Debble uses 8 ounces of apples to make one serving of applesauce.
There are 16 ounces in 1 pound
1 ounce = 1/16
8 ounces = 1/16 x 8
= 0.5 pounds
8 ounces of apples to make one serving of applesauce.
0.5 pounds apples = 1 serving of applesauce.
1 pound of apples = 1 / 0.5 serving of applesauce.
6 pounds of apples =
= [tex]\frac{1}{0.5} \times 6\\\\\frac{60}{5}\\ \\12[/tex]
Learn more about the unitary method;
https://brainly.com/question/23423168
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For circle h, jn = 5, nk = 4, ln = 2, and nm = x. solve for x. circle h with chords jk and lm intersecting at n inside the circle 10 2.5 1.6 7
The value of x for the circle h with chords jk and lm intersecting at n inside the circle is 10.
What is interseting chord theorem?The interseting chord theorem states that, when two chords in a circle intersect each other, then the product of their segment is equal.
For circle h in the given problem,
[tex]JN = 5, \\NK= 4, \\LN =2[/tex],
The value of segment NM is x. The figure of the circle h is attached below. In this figure, using the interseting chord theorem the chords can be given as,
LN×NM=JN×NK
2×x=5×4
x=20/2
x=10
Thus, the value of x for the circle h with chords jk and lm intersecting at n inside the circle is 10.
Learn more about the interseting chord theorem here;
https://brainly.com/question/5432495
four friends go out for lunch. Each person orders 1 drink for 1.50 and 3 tacos. the total cost for all 4 people is $24. what is the price of one taco? $_
Answer:
$1.50
Step-by-step explanation:
4(1.50 + 3x) = 24
4(1.50 + 3x) = 24/4
_________
1.50 + 3x = 6. subtract by 1.50 from both sides.
3x = 4.50
3x/3 = 4.50
____
3
x = 1.50
hope this helps!
Given point a = -7 and point b = 15, find the distance from point a to b. *
a. 8
b. -22
c. 22
and the solution would be appreciated
Answer:
c
Step-by-step explanation:
the distance between a to b is
| 15 - (- 7) | = | 15 + 7 | = | 22 | = 22
or
| - 7 - 15 | = | - 22 | = 22
there are 19 birds in a pond, all of which are ducks or geese. if the number of ducks in the pond is 1 more than twice the number of geese in the pond, how many geese are in the pond?
Answer:
its 9
Step-by-step explanation:
19-1 divided by 2
so 19-1=18
18/2 equals 9
and thats your answer
A dog is on the ground watching a cat on a 6-foot-
high wall. The angle of elevation from the dog to the
cat is 50º. About how far from the wall is the dog?
Answer:
5.0344
Step-by-step explanation:
tan=opposite
adjacent
Since you're trying to find the adjacent side to the angle 50, use tan.
So tan 50º= 6/x
Swap x and tan 50º , which puts tan 50º under the 6.
Use your calculator to find the approximate value of tan 50º (rounded to 4 decimals)
Then divide!
& What value of x satisfies the system of equations below!
x+2y= 11
4x - y = 8
Answer:
[tex]\boxed{\sf{x=3 \quad y=4}}[/tex]Step-by-step explanation:
Isolate the term of x and y from one side of the equation.
x+2y=11 and 4x-y=8⇒ x+2y=11
⇒ x=11-2y
Substitute.
4(11-2y)-y=8
Solve.
Distributive property:
⇒ A(B+C)=AB+AC
4(11-2y)
4*11=44
4*2=8
Rewrite the problem down.
44-9y=8
Subtract by 44 from both sides.
44-9y-44=8-44
Solve.
-9y=-36
Divide by -9 from both sides.
-9y/-9=-36/-9
Solve.
-36/-9=4
y=4
Substitute of y=4.
⇒ x=11-2*4
Use order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract11-2*4
Multiply.
2*4=8
Rewrite the problem down.
11-8
Subtract.
11-8=3
x=3
Therefore, the correct answer is x=3 and y=4.I hope this helps you! Let me know if my answer is wrong or not.
Complete the following sentence with the best phrase. A small P-value means:
A. The data provide strong evidence in favor of the null hypothesis
B. The data provide no evdence in favor of either hypothesis
C. The data provide little evidence in favor of the alternative hypothesis
D. The data provide strong evidence in favor of the alternative hypothesis
Answer:
d
Step-by-step explanation:
An angle is reflected across the y−axis. how is the measure of the reflected angle related to the measure of the original angle?the measure of the reflected angle is equal to the measure of the original angle.the measure of the reflected angle is equal to the measure of the original angle.the measure of the reflected angle is half the measure of the original angle.the measure of the reflected angle is half the measure of the original angle.the measure of the reflected angle is one-third the measure of the original angle.the measure of the reflected angle is one-third the measure of the original angle.the measure of the reflected angle is twice the measure of the original angle.the measure of the reflected angle is twice the measure of the original angle.
The measure of the reflected angle is equal to the measure of the original angle
Reflection of angles and coordinatesAn image or figure reflected are mirror images of each other. While the coordinate points of the vertices of a figure are affected by reflection, the angles remain the same.
Hence if an angle is reflected across the y−axis, the measure of the reflected angle is equal to the measure of the original angle
Learn more on reflection here: https://brainly.com/question/1908648
Jen and her friends would like a curved pit to be included in next year’s obstacle course. they found this equation to model their suggested curved pit using a computer simulation. in the equation, y is the depth of the pit in relation to the surface of the course, and x is the horizontal distance from the left edge of the entire obstacle course. both distances are in feet. y = 0.75x^2 − 13.5x + 57.75 select the correct answer from each drop-down menu. a robot traveling along the surface of the curved pit reaches a (maximum, minimum, or contrast) depth of (-3, -9, 4, or -7) feet
Considering the vertex of the quadratic function, it is found that:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the function is given by:
y = 0.75x² - 13.5x + 57.75.
Which means that the coefficients are a = 0.75 > 0, b = -13.5, c = 57.75.
Thus, the minimum value is given by:
[tex]y_v = -\frac{(-13.5)^2 - 4(0.5)(57.75)}{4(0.75)} = -22.25[/tex]
Thus:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967
A committee is to consist of two members. If there are seven people available to serve on the committee, how many different committees can be formed?
pls answer i give u anything
Answer:
the first one is 0.5 inches 1.27 centimeters
the second is 0.25 inches or 0.635 centimeters
Step-by-step explanation:
Sloane kicked a soccer ball off the ground at a speed of 48 feet per second. the height of the ball can be represented by the function h(t) = −16t2 48t, where t is the time in seconds. how many seconds did the ball travel before returning the ground? t = 0.33 seconds t = 3 seconds t = 16 seconds t = 48 seconds
Considering the function for it's height, it is found that the ball traveled for 3 seconds before returning to the ground.
What is the function for the ball's height?The height of the ball after t seconds is given by:
h(t) = -16t² + 48t.
It is at the ground at the instants of t for which:
h(t) = 0.
Hence:
-16t² + 48t = 0
-16t(t - 3) = 0.
We want t different of 0, hence:
t - 3 = 0 -> t = 3.
The ball traveled for 3 seconds before returning to the ground.
More can be learned about functions at https://brainly.com/question/25537936
Answer:
3 seconds is the answer
Step-by-step explanation:
Find the MEDIAN of his test scores.
Last semester, Mike got the following classwork grades in Math.
45, 54, 72, 89, 100, 26, 34, 100 , 92, 85, 76
Answer:
76
Step-by-step explanation:
The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median. If there are 2 numbers in the middle, the median is the average of those 2 numbers.
Choose the line plot that correctly shows this data about the growth of bean plants:
1/2,3/4,1/2,1/4,1/2,1/4,3/4,3/4,1/2
Answer:
It is the first one
Step-by-step explanation:
Hi, it is the first one because there is 4 - 1/2 3 - 3/4 and 2 - 1/4
A football team loses 5 yards on each of 3 consecutive plays.
What signed number represents the team's total loss of yards on the 3 plays? Write you
Part A
answer in the space provided.
Part B
Explain how you found your answer. Write your answer in the space provided.
Part A
Using proportions, it is found that the signed number -15 represents the team's total loss of yards on the 3 plays.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, in one play, the team lost 5 years, that is, the amount is -5. What is the amount on three plays? The rule of three is given by:
1 play - -5 yards
3 plays - n yards
Applying cross multiplication:
n = 3 x (-5) = -15.
The signed number -15 represents the team's total loss of yards on the 3 plays.
More can be learned about proportions at https://brainly.com/question/24372153
Name a number that is a factor of 20 and 18 but a multiple of 2.