After 14 years, Jane has accumulated approximately $1587.45, which means her initial investment of $500 has more than tripled due to the power of compound interest at a rate of 8.25%, compounded continuously.
Jane plans to invest $500 at 8.25% interest, compounded continuously. To find out how much money she has accumulated after 14 years, we use the formula for continuous compounding: [tex]A = Pe^{rt}[/tex], where:
For Jane's investment:
P = $500
r = 8.25% or 0.0825 (as a decimal)
t = 14 years
Plugging these values into the formula gets us:
[tex]A = 500e^{0.0825*14}[/tex]
Calculating this gives us:
[tex]A \approx 500e^{1.155} \approx 500 * 3.1749 \approx $1587.45[/tex]
Jane's money has more than tripled in 14 years. It has not quadrupled, but it has significantly grown beyond double the original investment.
The solution for the following system of equations is shown on the graph. What is the solution? y = 3x - 5 y = 1 3 x + 3 A) (3, 3) B) (3, 4) C) (4, 3) D) (4, 6)
Answer:3,4.b
Step-by-step explanation: Took the test.
what is y−2=−3(x−7) written in standard form?
Which professional needs the knowledge of statistics and geometry in order to comprehend maps, graphs and charts? Pilot, banker, fashion designer, or an architect?
Answer:
The correct answer is pilot. I took the test
Step-by-step explanation:
Solve 3x+11= k for x.
A. x=3k-11
B. x=k-11
C. k+11
x=———
3
D. k-11
x= ———
3
Answer: the correct option is (D) [tex]x=\dfrac{k-11}{3}.[/tex]
Step-by-step explanation: We are given to solve the following equation for the value of x :
[tex]3x+11=k~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for x, we need to take x on one side and all other terms on the other side of the equality.
The solution of equation (i) is as follows :
[tex]3x+11=k\\\\\Rightarrow 3x=k-11\\\\\Rightarrow x=\dfrac{k-11}{3}.[/tex]
Thus, the required value of x is [tex]x=\dfrac{k-11}{3}.[/tex]
Option (D) is CORRECT.
Jackson's kitten weighted 2 pounds and 3 ounces. A month later the kitten weighted 56 ounces. How much weight did the kitten gain in that month?
1 pound= 16 ounces
Batman is 4 times robins age. The sum has f their ages is equal to 45. How old is Batman and robin?
Answer:
Robin is 9 years old and Batman is 36 years old
Step-by-step explanation:
Batman: 4x
Robin: x
4x + x = 45
5x = 45
x= 9
please someone help..
ill give brainliest if ur answer is correct
Mitsu borrowed $1,250. She made 36 payments of $45.15 each. How
much did she pay in interest?
a. $375.40
b. $162.54
c. $1,625.40
d. $37.54
Find two numbers if their sum is 3 and their difference is 21
PLZ HELP!!!!
help me please !!! Surface area
Solve the equation for y. Then graph the equation.
5x – 4y = 12
A.
B.
C.
D.
Perform the indicated operation 7 1/8 times 5 2/3
Answer: The required result is [tex]40\dfrac{3}{8}.[/tex]
Step-by-step explanation: We are given to perform the following indicated operation :
[tex]E=7\dfrac{1}{8}\times5\dfrac{2}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To perform the given multiplication, first we need to convert the mixed fraction to improper fraction.
The simplification of the given operation is as follows :
[tex]E\\\\\\=7\dfrac{1}{8}\times5\dfrac{2}{3}\\\\\\=\dfrac{57}{8}\times\dfrac{17}{3}\\\\\\=\dfrac{19\times17}{8}\\\\\\=\dfrac{323}{8}\\\\\\=40\dfrac{3}{8}[/tex]
Thus, the required result is [tex]40\dfrac{3}{8}.[/tex]
What is the slope of this skateboard ramp if it rises 1.2 meters above the ground and runs 4 meters horizontally at the base?
Final answer:
The slope of the skateboard ramp, calculated using the rise over run formula, is 0.3. This is found by dividing the rise of 1.2 meters by the run of 4 meters.
Explanation:
The slope of a ramp is calculated as the rise divided by the run. To find the slope of the skateboard ramp, which rises 1.2 meters above the ground and runs 4 meters horizontally at the base, you would use the formula:
Slope (m) = Rise / Run
Here, the rise is the height the ramp rises above the ground, which is 1.2 meters, and the run is the distance along the ground, which is 4 meters horizontally. By substituting the given rise and run into the formula, you obtain:
Slope (m) = 1.2 m / 4 m = 0.3
So, the slope of the skateboard ramp is 0.3.
Describe the graph y=4[x+2] on [0, 3). Be specific in your description.
Answer: The description is mentioned in the below explanation.
Step-by-step explanation:
Since greatest integer function rounds down a real number to the nearest integer. for example, if f(x)=[x] and for x =1.3 f(x)= [1.3]= 1
or x= 0.9 f(0.9)= [0.9]= 0
Here, The given function, y=4[x+2]
Which is a greatest integer function and it is described on [0,3)
So, For the values of [tex]1 >x\geq 0[/tex],we take x=0 ⇒ y= 4(0+2)= 8
For, [tex]2>x\geq 1[/tex] , we take x=1, ⇒ y = 4(1+2)= 12
For, [tex]3>x\geq 2[/tex] we take x=2, ⇒ y = 4(2+2)=16
The graph description for the open or close interval, is mean describe values of variable for the interval. The graph [tex]y=4[x+2][/tex] is described and the values of y we get are 8,12, and 16 for the values of x as 0,1 and 2.
How to graph integer on a number line?Integer keeps the values as positive or the negative and graphed at the number line.
Given information-
The function of the graph given in the problem is,
[tex]y=4[x+2][/tex]
This function need to be describe on the points [0,3).
The close bracket is used in left side means the value 0 is included and the open bracket is used in right side means the value 3 is excluded.
Thus find the value of variable y for the different intervals o x,
The interval is,
[tex]0\leq x<3[/tex]
When the value of x is 0 at interval [tex]0\leq x<1[/tex],
[tex]y=4(0+2)\\y=4\times2\\y=8[/tex]
When the value of x is 1 at interval [tex]1\leq x<2[/tex],[tex]y=4(1+2)\\y=4\times3\\y=12[/tex]
When the value of x is 2 at interval [tex]2\leq x<3[/tex],[tex]y=4(2+2)\\y=4\times4\\y=16[/tex]
The graph of the given point is attached below.
Thus the graph [tex]y=4[x+2][/tex] is described and the values of y we get are 8,12, and 16 for the values of x as 0,1 and 2.
Learn more about the graph integer on a number line here;
https://brainly.com/question/90983
a square parking lot has an area of 225 yards.There is a sidewalk along one side of the parking lot.How long is the sidewalk
Answer: 56.25
Step-by-step explanation:
Since there are four sides to a square and the area is 225 yards you would -
225 yards/ 4 sides
= 56.25 yards per side
If you were solving a system of equations and you came to a statement like 4 = 4, what do you know about the solution to the system? (1 point) The solution is (4, 4) The solution is x = 4 and y = 4 There is no solution There are infinitely many solutions
Answer:
There are infinitely many solutions.
Step-by-step explanation:
While solving a system of equations, if we get a true statement like 1=1, then there will be "infinitely many solutions" and if we get a false statement like 1=2, then there will be "no solution".
Here the statement is 4=4, which is a true statement.
So, there are infinitely many solutions.
PLEASE HELP ASAP
The solutions to a certain quadratic equation are x=-4 and x=3. Write the equation in standard form below.
First correct answer will receive brainiest !!
Isaac made all these rectangles with 24cm lengths of string. This implies that the perimeter of all these rectangles are equal
Final answer:
When Isaac uses 24cm of string to make rectangles, no matter the individual dimensions, the sum of the length and width of these rectangles must always be 12 cm. This is a direct result of the fixed perimeter, which requires that the combined measurements of length and width halves the total perimeter to maintain the consistent total string usage.
Explanation:
Isaac made all these rectangles with 24cm lengths of string, which implies that the perimeter of all these rectangles is equal. The observation about the sum of the length and the width of these rectangles is that regardless of the individual measurements of the length and width, their sum must always be half the total perimeter of the rectangle. Given a fixed perimeter of 24cm, the formula for the perimeter of a rectangle (P) is
P = 2(l + w),
where l is the length and w is the width. Since the perimeter is given as 24cm, this simplifies to
24 = 2(l + w), or 12 = l + w.
This equation means that the sum of the length and width of the rectangles must always equal 12 cm. This is because the total loop made by the string when forming the rectangle has to be divided into four edges, two lengths, and two widths, which totals the provided 24cm of string. Therefore, if we adjust either the length or the width, the other measurement must adjust in such a way that their sum remains constant at 12 cm to maintain the total perimeter as 24cm.
What is the area of this polygon?
Enter your answer in the box.
Eliza paints a circle on her bedroom wall as part of a mural. After she paints it, she decides that she wants a much bigger circle. So, she multiplies her original radius by four and repaints the circle. Which statement best describes Eliza's solution?
a.) The area of the new circle is two times larger.
b.) The area of the new circle is four times larger.
c.) The area of the new circle is eight times larger.
d.) The area of the new circle is 16 times larger.
Answer: d.) The area of the new circle is 16 times larger.
Step-by-step explanation:
Let the radius of the original circle be r.
Then the area of the original circle will be :-
[tex]\text{A}_1=\pi r^2[/tex]
When she multiplies her original radius by four and repaints the circle.
The new radius = [tex]R=4r[/tex]
Then the area of the new circle will be :-
[tex]\text{Area}=\pi R^2\\\\\Rightarrow\ \text{Area}=\pi (4r)^2\\\\\Rightarrow\ \text{Area}=\pi (16r^2)\\\\\Rightarrow\ \text{Area}=16\pi r^2\\\\\Rightarrow\ \text{Area}=16(\pi r^2)\\\\\Rightarrow\ \text{Area}=16A_1[/tex]
Hence, The area of the new circle is 16 times larger.
Leonardo da Vinci drew a portrait of a young woman. The portrait is shaped like a rectangle. It is 13.5 inches long and 10 inches wide. What is the length of a diagonal that connects one corner of the portrait to the other? Round the answer to the nearest tenth of an inch.
Adam and Kevin are standing 35 metres apart, on opposite sides of a flagpole. From Adam’s position, the angle of elevation of the top of the flagpole is 36°. From Kevin’s position, the angle of elevation is 50°. How high is the flagpole?
a sperm whale can stay underwater 7 times longer than a sea cow can.how long can a sperm whale stay underwater?
The sperm whale's underwater duration is seven times that of the sea cow, showcasing remarkable breath-holding abilities, likely adapted for deep-sea foraging and hunting.
The relationship between the underwater durations of a sperm whale and a sea cow suggests that the sperm whale's capability is sevenfold that of the sea cow. Let's denote the sea cow's duration as "x." Accordingly, the sperm whale's underwater duration would be 7 times x.
In practical terms, if we assume the sea cow can stay submerged for 10 minutes (x = 10), then the sperm whale, being seven times more proficient, can stay underwater for 7 times 10, which is 70 minutes (7x = 7 * 10 = 70). This sevenfold difference implies a significant contrast in their breath-holding abilities.
The numerical representation extends universally; if the sea cow can endure underwater for "x" units of time, the sperm whale can endure for 7 times "x" units of time. This relationship showcases the remarkable adaptation of the sperm whale to extended submersion, likely linked to its deep-sea foraging behavior and hunting strategies.
In essence, the sperm whale can stay underwater for a duration that is seven times longer than that of the sea cow, highlighting its remarkable breath-holding capacity.
A sperm whale can stay underwater for 7 times longer than a sea cow, so it can stay underwater for 7 times the duration of a sea cow.
If a sperm whale can stay underwater 7 times longer than a sea cow, we can express this relationship as:
Time a sperm whale can stay underwater = 7 * Time a sea cow can stay underwater
So, if we let the time a sea cow can stay underwater be represented by 'x', then the time a sperm whale can stay underwater is:
7 * x
Therefore, a sperm whale can stay underwater for 7 times longer than a sea cow, which means it can stay underwater for 7x.
Bill and Greg are walking in opposite directions with speeds of 45 and 75 feet per minute. When they started, the distance between them was 20 feet. What will be the distance between them in 2.5 min?
Answer:
The distance between them in 2.5 min will be 320 ft
Step-by-step explanation:
Let
x--------------> Bill distance after 2.5 min------- > speed 45 ft/min
y--------------> Greg distance after 2.5 min------> speed 75 ft/min
z-------------> distance between them in 2.5 min
we Know that
z=x+y+20
Remember that
To find the distance multiply the speed by the time
so
x=45*2.5=112.5 ft
y=75*2.5=187.5 ft
therefore
z=x+y+20-----------> 112.5+187.5+20=320 ft
Final answer:
Bill and Greg's total distance apart after 2.5 minutes is 320 feet, calculated by adding their initial distance of 20 feet to the distance they covered in 2.5 minutes at their combined speed of 120 feet per minute.
Explanation:
Bill and Greg are walking away from each other with speeds of 45 and 75 feet per minute, respectively.
Since they are moving in opposite directions, their relative speed is the sum of their individual speeds, which is 45 + 75 feet per minute, or 120 feet per minute.
To find the distance between them after 2.5 minutes, we multiply their relative speed by the time elapsed. Therefore, the distance is:
Distance = Speed × Time = 120 feet/minute × 2.5 minutes = 300 feet.
We must also include the initial distance between them, which was 20 feet, so the total distance after 2.5 minutes is:
Total distance = Initial distance + Distance covered in 2.5 minutes = 20 feet + 300 feet = 320 feet.
Convert the rectangular coordinates (4, –4) into polar coordinates.
Which figure is the image of figure P after a rotation of 270° clockwise? Assume that the center of rotation is the origin.
A.
figure A
B.
figure B
C.
figure C
D.
figure P
On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: a2 = b2 + c2 – 2bccos(A)
options are in the pics
Answer: The correct option is 4.
Explanation:
The formula of law of cosine is,
[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]
Where a,b,c are sides of the triangle and A is the interior angle of vertex A.
Reason for correct option:
From the above formula we can easily conclude that to find an unknown angle measure we need the length of all sides of the triangle.
In figure 4 all sides are given, so the correct option is 4.
Reason for incorrect option:
In figure 1,2 and three all sides are not known, so we can apply the cosine rule to mind the unknown angle measure.
Therefore option 1,2 and 3 are incorrect.
Factor 1-3
1. X to the second power -14x+45
2.X to the second power -15x+36
3.X to the second power -7x-44
***Need answered ASAP***... PLEASE
What happens to the temperature of the remaining liquid when some if the liquid evaporates?
A. Increases
B. decreases
C. Does not change
D. The change cannot be determine
PLEASE FULL ANSWERS! need all the help I can get