Jimmy invests $2,936 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 18 years?
A) $6,599.86
C) $6,534.19
B) $7,221.39
D) $6,869.20
Answer:
B) $7,221.39
Step-by-step explanation:
Given data
Principal=$2,936
Rate=5%
n=12
Time = 18 years
The expression for compound interest is
A=P(1+r/n)^nt
substitute
A= 2936(1+0.05/12)^12*18
A= 2936(1+0.00416)^12*18
A= 2936(1.00416)^12*18
A= 2936(1.00416)^216
A= 2936*2.45149
A=7197.57464
Hence the approximate amount is B) $7,221.39
A system of equations is shown.
y = 3x - 2
y = x2
What are the solutions to the system of equations?
Answer:
x = 1, y = 1
x = 2, y = 4
Step-by-step explanation:
substitution method:
x² = 3x - 2
x² - 3x + 2 = 0
(x - 2)(x - 1) = 0
x = 2
x = 1
Kant's sister has 150 red marbles and 360 pink marbles and she wants the same number of marbles on each row, what is the least number of rows she can make ?
Answer:
We know that Kant's sister has 150 red marbles and 360 pink marbles.
She separates the marbles in rows, such that each row must have the same number of marbles.
The least number of rows she can make is when she puts N marbles in each row, such that N is the greatest common factor between 150 and 360.
To find the greatest common factor between 150 and 360 we can write them as the product of prime numbers.
150 = 15*10 = (3*5)*(2*5)
360 = 36*10 = (6*6)*(2*5) = (2*3*2*3)*(2*5)
Here we can see that the factors: 2, 3, and 5 appear (at least) one time in each number, this means that the greatest common factor between 150 and 360 is the product of these 3 factors:
GCF = 2*3*5 = 30
This means that we need to make rows with 30 marbles each.
and we will have:
150/30 = 5 rows of red marbles
360/30 = 12 rows of pink marbles.
A total of 5 + 12 = 17 rows.
if 2 bags of nuts cost $5.50, how much will 7 bags cost
Answer:
$19.25
Step-by-step explanation:
Find the cost of one bag.
5.50/2=2.75
Multiply bag of one by the amount of bags wanted.
2.75*7=19.25
Therefore, the answer is $19.25
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Cost of 7 bag of nut using the unitary method is $19.25
What is Cost?A cost is the value of money that has been used up to produce something or deliver a service
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Cost of 2 bags of nuts = $5.50
Cost of 1 bag of nuts =[tex]\frac{5.50}{2} =2.75[/tex]
Cost of 7 bags of nuts =7×2.75= $19.25
Hence, the cost of 7 bags of nuts is $19.25
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Matt earns $5 for each lawn he does. He wants to earn at least $100. Which inequality represents his situation?
Answer:
$100 is less than or equal to x
At City Burger, 4 of the last 8 customers wanted cheese on their burgers. What is the experimental probability that the next customer will want cheese on his or her burger?
help fast please!!!
find the distance between two points 5,5 and -4,6
Answer:
19.06
Step-by-step explanation:
Put the points into the distance formula:
[tex]d=\sqrt{(-4-5)^2+(6-5)^2}[/tex]
Solve:
[tex]d=\sqrt{(-9)^2+(1)^2}[/tex]
[tex]d=\sqrt{82}[/tex]
[tex]d=9.055385[/tex]
Answer:
[tex]\displaystyle d = \sqrt{82}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (5, 5)
Point (-4, 6)
Step 2: Solve for d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in coordinates [Distance Formula]: [tex]\displaystyle d = \sqrt{(-4-5)^2+(6-5)^2}[/tex][Distance] [√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{(-9)^2+(1)^2}[/tex][Distance] [√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{81+1}[/tex][Distance] [√Radical] Add: [tex]\displaystyle d = \sqrt{82}[/tex]Look at this table:
-4
10
81
-3
10
27
10
-2
9
-1
10
3
0
10
Write a linear (y = mx + b), quadratic (y = ax?), or exponential (y = a(b)") function that
models the data.
y =
Omar is driving to Denver. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Omar has 55 miles to his destination after 44 minutes of driving, and he has 41.5 miles to his destination after 62 minutes of driving. How many miles will he have to his destination after 74 minutes of driving?
Answer:
After 74 minutes of driving, he still has 32.5 miles to his destination.
Step-by-step explanation:
A linear relationship can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that a line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Now let's go to the question.
We know that the distance to his destination is a linear function of his total driving time.
We know that he has 55 miles to his destination after 44 minutes of driving. We can write this as the point (44 min, 55mi)
We know that he has 41.5 miles to his destination after 62 minutes of driving, we can write this as (62 min, 41.5mi)
Then the slope of this equation will be:
a = (41.5mi - 55mi)/(62min - 44min) = -0.75 mi/min.
Then the linear equation is something like:
y = (-0.75 mi/min)*x + b
to find the value of b we can use the fact that this line passes through the point (44 min, 55mi)
This means that when x = 44 min, we must have y = 55mi
Then:
55mi = (-0.75 mi/min)*44min + b
55mi + (0.75 mi/min)*44min = b
88mi = b
Then the equation is:
y = (-0.75 mi/min)*x + 88mi
Now we want to know how many miles will he have to his destination after 74 minutes of driving, then we need to replace x by 74 min.
y = (-0.75 mi/min)*74min + 88mi
y = 32.5mi
After 74 minutes of driving, he still has 32.5 miles to his destination.
The circumference of a circular garden is 138.16 feet. What is the radius of the garden? Use 3.14 for it and do not round your answer.
Il feet
?
Answer:
11 feet
Step-by-step explanation:
The radius of the circular garden is approximately 22 feet.
The formula to calculate the circumference of a circle is given by:
C = 2πr
where C is the circumference and r is the radius of the circle.
We are given the circumference as 138.16 feet, so we can set up the equation:
138.16 = 2 * 3.14 * r
To solve for the radius (r), we can rearrange the equation:
138.16 = 6.28r
Dividing both sides of the equation by 6.28:
138.16 / 6.28 = r
r ≈ 22
Therefore, the radius of the circular garden is approximately 22 feet.
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Are they similar?
Or not?
Answer:
They look similar but their not
Step-by-step explanation:
because of their length and
The first triangle is a Scalene because all the side are different and
The second triangle is a isosceles because it has to side of equal length.
A triangle has one angle of 120 degrees what must be true about the other two angles A- the sum of the two angles must be equal to 120 degrees. B- the two angles must be the same measure C- the sum of two angles must be 60 degrees
Answer:
C
Step-by-step explanation:
A triangles sum of all the angles will be 180, so since we already have one as 120, then that least 60. So the sum of the two extra angles has to be 60.
A club has members from three grades.
It has 36 members from sixth grade, 24 members from seventh grade, and 30 members from eighth grade.
What is the ratio of the club's seventh graders to eighth graders?
5. Each of 5 gift bags contains x pencils. Tyler adds 3 more pencils to each bag.
Altogether, the gift bags contain 20 pencils. Create an equation comparing the
number of pencils in each gift bag to the total. Then find the original number of
pencils in each bag before Tyler added 3 more.
Answer:
Answer: x=20-3
Step-by-step explanation:
On the main floor of the Kodak Hall at the Eastman Theater, the number of seats per row increases at a constant rate. Lucas counts 31 seats in row 3 and 37 seats in row 6. How many seats are there in row 20?
67
61
63
65
Answer:
67
Step-by-step explanation:
There are 65 seats in row 20, option D is correct.
Given that number of seats in row 3 are 31.
Number of seats in row 6 are 37
We need to find the rate of increase, we can calculate the difference in the number of seats between row 6 and row 3 and divide it by the number of rows in between:
Rate of increase = (Number of seats in row 6 - Number of seats in row 3) / (6 - 3)
Rate of increase = (37 - 31) / (6 - 3)
Rate of increase = 2
So, the number of seats increases by 2 seats per row.
To find the number of seats in row 20, we can use the rate of increase:
Number of seats in row 20 = Number of seats in row 3 + (Rate of increase × (20 - 3))
Number of seats in row 20 = 31 + (2× (20 - 3))
= 31 + (2 × 17)
= 31 + 34
= 65
Therefore, there are 65 seats in row 20.
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(-2)x(+4)x(+3)x(-1)=
Can you help me please?
Pode me ajudar por favor?
Podría ayudarme por favor?
Answer:
-24
Step-by-step explanation:
-2×4= -8
-8×3= -24
-24×1= -24
I hope this helps ^-^
What is the measure of angle N?
Answer:
42.7+90+N=180
132.7+N=180
N=180-132.7
Angle N =47.3°
The side length of a triangle or 12.5 inch 4.4 inch and 11.72 which statement best describes the triangle formed using these
side lengths
Answer:
scalene
Step-by-step explanation:
12.5, 4.4, and 11.72 are all different measurements
i hope this helped
Graph the
equation.
y = 3x+4
Answer:
Plot the following points:
(-2,-2)
(-1,1)
(0,4)
(1,7)
(2,10)
Step-by-step explanation:
Just plug any random number in for x to solve for y.
Which of the following statements correctly describes the evidence shown by
the structures in the accompanying image?*
Whale
Frog
Porce
Bird
VARROW
O c. The human and the bat share analogous bone structures in their forelimbs
b. Only the human and the frog share homologous bone structures
a. The bat and the frog share analogous bone structures in their forelimbs
d. All the species shown share homologous structures in their forelimbs
All the species shown share analogous
ructures in
forelimbs
O
This is a required question
Name the polygon. Then tell whether it is a regular polygon or not a regular polygon.
Answer:
not a regular polygon
Step-by-step explanation:
A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center
This is about pi and 25 is NOT the answer. If you choose 25, have a link, an answer that isn't even near the answer to the question (ex. "Hhhhjjhf thank you" isn't a real answer) you will be reported. Thank you guys need explanation for brainliest but is optional.
Answer: 19.625in
Step-by-step explanation:
3.14*1.25*1.25 = 4.90625
4.90625*4 = 19.625in
Answer: 19.625in
Step-by-step explanation:
Explain your answer please ;w; : Change -2Y - 2X = -6 to the slope intercept form of the equation of a line.
Answer:
y = -x + 2
Step-by-step explanation:
The desired equation must have the form y = mx + b.
Start with -2Y - 2X = -6 and solve for y: y + x = 2
Now solve this result for y:
y = -x + 2
[tex]\frac{1-(-5)}{7-2}[/tex]
Answer:
2
Step-by-step explanation:
Find the solution to the following system using substitution or elimination:
Please help this is my 5th time asking this question
C. (1, 10)
10=3(1)+7
10=3+7
10=10
Select the correct answer
A scientist is studying the motion of waves by measuring the distance between the crests and troughs of waves in a particular area. He set up a
series of buoys at equal intervals, and attached a depth detector to each buoy.
After gathering data, the scientist modeled the positions of the buoys at a specific instance with the
given function, where x is the horizontal
distance, in feet, from the first buoy and 1() is the depth of the water, in feet, at that location.
f(3) = 2cos(61) + 13
Select the correct representation of the buoy positions modeled by function f.
Answer:
i got it right on the test
Step-by-step explanation:
The correct representation of the buoy positions is modeled by function f shown in picture (B) option (B) is correct.
What is cos function?It is defined as a function that is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.
We have:
A scientist studying the motion of waves by measuring the distance between the crests and troughs of waves in a particular area.
The equation he set up:
f(x) = 2cos(πx/8) + 13
As we know the cos function has a maximum value is 1 and a minimum value is -1
The maximum value:
f(0) = 2(1) + 13
f(0) = 2 + 13
f(0) = 15
The minimum value:
f(8) = 2(-1) + 13
f(8) = -2 + 13
f(8) = 11
Thus, the correct representation of the buoy positions is modeled by function f shown in picture (B) option (B) is correct.
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What is the solution to this equation?
- 4
A. Y = 4
B. X= 8
C. X= 2
D. X= 16
Answer:
The correct answer is C. X= 2
pls help ill give brainliest if correct
pic is attached
Answer:
option 3
Step-by-step explanation:
can someone help me with this pleaseee ill give you brainliest and points :)
Eric's team won 20 games last season and James team won 6 games. Which equation will find how many more games Eric's team won than James team?
A.) y + 6=20
B.) 6y=20
C.) y-6=20
D.) Y/6=20
Answer:
A) y + 6 = 20Step-by-step explanation:
Let the difference is y.
Then it is:
y = 20 - 6Equivalent equation is:
y + 6 = 20Correct choice is A