When dante was born, his grandparents deposited $10,000 into a special college fund that paid 4% annual interest, compounded monthly. how old was dante when the balance in the account reached$13,000? round your answer to the nearest tenth of a year.
Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.
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.In this problem, we have that the parameters are given as follows:
A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.
Hence the time in years is found as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]
[tex](1.0033)^{12t} = 1.3[/tex]
[tex]\log{(1.0033)^{12t}} = \log{1.3}[/tex]
[tex]12t\log{1.0033} = \log{1.3}[/tex]
[tex]t = \frac{\log{1.3}}{12\log{1.0033}}[/tex]
t = 6.6
More can be learned about compound interest at https://brainly.com/question/25781328
#SPJ1
Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture celebrating education. The sculpture is to be created from sheets of tempered spring steel, it will be hollow, and the supporting cone will not include a base.
Calculate the amount of steel Kassidy will need to create the sculpture if the base of the sculpture is 4-feet tall and has a 2-foot diameter.
Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture, the amount of steel Kassidy will need is mathematically given as
SA=16.094711 ft^2
What is the amount of steel Kassidy will need to create the sculpture if the base of the sculpture is 4-feet tall and has a 2-foot diameter.?Generally, the equation for the surface area of a cone is mathematically given as
SA=πr(rπ+√(h^2+r^2))
Therefore
SA=πr(rπ+√(h^2+r^2))
SA=π*1(1+√(4^2+1^2))
SA=16.094711 ft^2
In conclusion, the amount of steel Kassidy will need is
SA=16.094711 ft^2
Read more about surface area
https://brainly.com/question/2835293
#SPJ1
Which rule describes the relationship between the x- and y-coordinates in the following table?
Y
1
6
4
15
6
21
Choose 1 answer:
A
Multiply by 6 to get y.
B
Multiply by 3. Then add 3 to the result to get y.
8
Answer: B
Step-by-step explanation:
We will test the options and see if they apply to the given values.
[A] ✗
1 * 6 = 6 ✓
4 * 6 ≠ 15✗
[B] ✓
1 * 3 = 3, 3 + 3 = 6 ✓
4 * 3 = 12, 12 + 3 = 15 ✓
6 * 3 = 18, 18 + 3 = 21 ✓
[C] ✗
1 * 8 = 8, 8 - 2 = 6 ✓
4 * 8 = 32, 32 - 2 = 30, 30 ≠ 15 ✗
Question 10 of 20
Which polynomial shows the difference of (4x² + 3x - 2) and (x²+2x+4)?
OA. 3x²+x-8
B. 3x²+x+2
OC. 3x² + 5x+2
OD. 3x²+x-6
Answer:
D.3x²+x-6
Step-by-step explanation:
4x²-x²+3x-2x-2-4
3x²+x-6
Find the roots of:
[tex]1.\ &2x^3-7x^2+8x-3=0\\ 2. \ & x^3-x^2-4=0\\ 3. \ &6x^3+7x^2-9x+2=0 \end{align*}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:
| 2 -7 8 -3
1 | 2 -5 3
| 2 -5 3 0
1 | 2 -3
2 -3 0
So the factorization is (x-1)² (2x-3)=0. So:
[tex]\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:
| 1 -1 0 -4
2 | 2 2
1 2 2 0
So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.
[tex]\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}[/tex]
Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:
| 6 7 9 2
-2 | -12 10 -2
6 -5 1 0
So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:
[tex]\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}[/tex]
Graph the function f(x) = 5(0.21)x.
Answer: A
Step-by-step explanation: BIG BRAIN
4 x 12 = 6 x n 4
6
8
12
Answer:
2 I believe
Step-by-step explanation:
you do 4x12 then divide it by 6x4 then it would be n equals 2
Mary measured the heights of two different plants every day. Plant A was 1 inch tall when
Mary began her measuring, and it grew 0.5 inch per day. Plant B was 3 inches tall, and it grew
0.25 inch per day. On which day were plant A and plant B the same height?
A day 5
B.
day 8
C. day 12
D.
day 16
The heights of plant A and plant B will be equal on the day 8.
How to find the heights of the trees?The height of the tree can be found as follows:
The equation for plant A can be described as follows:
y = 1 + 0.5x
where
x = number of days
y = height
The equation for plant B can be described as follows:
y = 3 + 0.25x
Therefore, for the height to be equal
1 + 0.5x = 3 + 0.25x
1 - 3 = 0.25x - 0.5x
-2 = -0.25x
x = 2 / 0.25
x = 8 days
learn more on height here: brainly.com/question/16959984
#SPJ1
multiply (x^2 - 5x)(2x^2 + x - 3)
Answer:
[tex]\textbf{C.}~2x^4 -9x^3-8x^2 +15x[/tex]
Step-by-step explanation:
[tex]~~~~(x^2 -5x)(2x^2 +x-3)\\\\=2x^4+x^3 -3x^2 -10x^3 -5x^2 +15x\\\\=2x^4 -9x^3-8x^2 +15x[/tex]
Part 1: Come up with and describe two scenarios: one that models a direct variation situation and one that models an inverse variation situation. Do not state explicitly which scenario is which, but provide at least four data pairs for each situation. Your classmates will have to determine which of the scenarios is a direct variation and which is an inverse variation, and the value of k for each.
Answer:
1. I went to a store four days in a row and only bought chocolate bars each day. All chocolate bars were the same and cost the same. On the first day, I bought 2 chocolate bars for $2.38. On the second day I bought 1 chocolate bar for $1.19. On the third day, I bought 10 chocolate bars for $11.90. On the fourth day, I bough 4 chocolate bars for $4.76.
2. A sink is full. It contains 20 gallons of water. The stopper is removed and water starts draining out. One minute after the stopper is removed, the volume of water in the sink is 18 gallons. Two minutes after the stopper is removed, the volume of water in the sink is 16 gallons. Four minutes after the stopper is removed, the volume of water in the sink is 12 gallons. Ten minutes after the stopper is removed, the sink is empty.
A dishwasher was advertised at $640 with a further $175 for installation. Calculate the total purchase and installation costs if the cost of the dishwasher (excluding installation) is reduced by 18% due to minor scratching.
Answer:
$699.80
Step-by-step explanation:
$640 - 18% = 524.80
(640x18)/100 = 115.20
640-115.20 = 524.80
524.80+175 = 699.80
Answer:
$699.80
Step-by-step explanation:
640(18%)
640 x 18
100
reduce fraction
640 x 9
50
simplify
64 x 9
5
576
5. or 115 1
5. of 115.20
640 - 115.20 = 524.80 (dishwasher)
524.80 + 175 = 699.80 (total including installation)
6x-2=8x-8 please i forgot how you do this
Answer:
x = 3
Step-by-step explanation:
6x - 2 = 8x - 8 ( subtract 8x from both sides )
- 2x - 2 = - 8 ( add 2 to both sides )
- 2x = - 6 ( divide both sides by - 2 )
x = 3
Answer:
x=3
Step-by-step explanation:
If 50% of all federal inmates are serving time for extortion and a random sample of 16 federal inmates is selected, then what is the expected number of inmates serving time for extortion? A)
18 B)12 C) 9 D) 8
Part b
what is the area of the target that earns at least 30 points on a throw?
select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
An equation in the form ax2+bx+c=0 is solved by the quadratic formula. The solution to the equation is shown below.x=−7±√ "572" What are the values of a, b, and c in the quadratic equation?
A: a= 1, b= -7, c = -2
B: a = 1, b= 7, c = -2
C: a = 2, b = -7, c = -1
D: a = 2, b = 7, c = -1
Question has errors in typing that 572 should be √57/2
Because if it's 572 then 2a=1 so
a=1/2Also
-7=1/2bb=-7(2)b=-14c also comes different
If it's like what I said
then
2a=2a=1and
-b=-7b=7By putting values
c=-2Option B can be correct
Answer:
B: a = 1, b= 7, c = -2
Step-by-step explanation:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Given:
[tex]x=\dfrac{-7\pm\sqrt{57}}{2}[/tex]
Comparing the terms of the given x-value with those of the quadratic formula:
[tex]\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}=\dfrac{-7\pm\sqrt{57}}{2}[/tex]
Therefore:
[tex]2a=2 \implies a=1[/tex][tex]b = 7[/tex][tex]b^2-4ac=57[/tex]Using the found values of a and b to solve for c:
[tex]\implies b^2-4ac=57[/tex]
[tex]\implies (7)^2-4(1)c=57[/tex]
[tex]\implies 49-4c=57[/tex]
[tex]\implies -4c=57-49[/tex]
[tex]\implies -4c=8[/tex]
[tex]\implies c=-2[/tex]
In summary: a = 1, b = 7, c = -2
[tex]\implies x^2+7x-2=0[/tex]
Therefore, option B is the correct solution.
The sum of 3 times one number, x, and 6 times a second number, y, is 111. If the sum of the two numbers is 27, find the two numbers.
Enter a system of equations to represent the situation, then solve the system.
Step-by-step explanation:
using elimination method because this is a simultaneous equation
3×x+6×y=111
x+y=27
1×[3x+6y=111]
3×[x+y=27]
3x+6y=111—equation 1
3x+3y=81—equation 2
substrate equation 1 from equation 2
3y=30
divide both sides by 3
y=10
substitute 10 for y in equation 1
3x+6y=111
3x+6(10)=111
3x+60=111
3x=111-60
3x=51
divide both sides by 3
x=17
a letter is chosen from the nine letters in the word "bumblebee." what is the probability the letter is a b or an e?
statistics and probability
Answer:
2/3
Step-by-step explanation:
Probability (b or e) :
⇒ There are 3 b's and 3 e's in the word "bumblebee"
⇒ P (b or e) = No. of b's and e's / Total letters
⇒ P (b or e) = 3 + 3 / 9
⇒ P (b or e) = 6/9
⇒ P (b or e) = 2/3
( geometry) Find the area of a regular hexagon whose sides are 22.6 cm, and whose apothem is 19.6 cm.
Answer:
1328.88 cm^2
Step-by-step explanation:
Area = 6 * 1/2 * 22.6 * 19.6
= 1328.88 cm^2
find the 5th term of the GP is 48 and it 8th term is 384. find the first term and the common
Answer:
[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]
The angle by which turns clockwise about point b to coincide with is degrees. if from point b, a point e is drawn directly opposite point c so that b, e, and c are on the same straight line, the angle by which turns counterclockwise to coincide with is degrees.
The first drop-down menu answer is 63.9 And the second drop-down menu answer is 116.1
The complete question is as given below:-
The angle by which turns clockwise about point B to coincide with is degrees. If from point B, a point E is drawn directly opposite point C so that B, E, and C are on the same straight line, the angle by which turns counterclockwise to coincide with is degrees.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
I have attached the figure for this problem and there are two questions for this problem. The first is the angle needed for AB to turn to coincide with BC.
Simply, get add the measures of the angles ABD and DBC. So,
33.3 + 30.6 = 63.6 degrees
The second question is the angle needed for AB to turn to coincide with EB. Angle EBA is complementary with angle ABC. So,
180 - 63.6 = 116.4 degrees
Therefore for first drop-down menu answer is 63.9 And the second drop-down menu answer is 116.1
To know more about an angle follow
https://brainly.com/question/25770607
#SPJ1
Answer:
90
Step-by-step explanation:
90
Whats the equation of the line that passes through the points (-8,4) and (0,22)
Answer:
d
Step-by-step explanation:
your answer to your question is D
i need help finding out the answer
Answer:
D) 5.7 cmStep-by-step explanation:
Let the shorter sides be x.
Given:Isosceles and acute triangle.Longer side is 8 cm.To find:The length of the shorter sides, rounded to the nearest tenth.Solution:The angle at common vertex of congruent sides is less than 90°, since it is acute triangle.
It means the other congruent angles are greater than 45°, according to angle sum theorem.
The vertical bisector divides the triangle in half, with base 8/2 = 4 cm and hypotenuse x.
It gives us the inequality:
4/x < cos 45° ⇒ x > 4 / cos 45° = 5.656 x ≥ 5.7 cmCorrect choice is D
Jamaal and his father have 1,920 stamps from around the world. They want to place the stamps in display cases that each hold 72 stamps. How many display cases can Jamaal and his father completely fill with the stamps?
Answer:
26 display cases
Please give brainliest!
Hope this helps :)
if Jamaal has 1920 stamps, and he wants to place them in diplay cases that can each hold 72 stamps, we figure out how many display cases can be filled with stamps by finding out 1920/72
This gives us 26 2/3, but 2/3 isn't 1.
he can fill 26 cases
Which graph shows the information in the table?
Calories in Salad Dressing
Number of Ounces of Salad Dressing
Total Calories
2
300
3
450
4
600
5
750
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (2, 300) and (4, 600).
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (300, 2) and (600, 4).
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (1, 200) and (2, 300).
On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (200, 1) and (300, 2).
The graph that shows the information on the table is On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (2, 300) and (4, 600).
How can the information on the table be represented?The independent variable is the number of ounces of salad dressing which means that it will be shown on the x axis.
The total calories is the dependent variable which means that it will be on the y axis.
The line drawn will pass through the points on the table of (2,300) and (4 ,600) so option A is correct.
Find out more on constructing linear graphs at https://brainly.com/question/1889064.
#SPJ1
Please help
Why is this not an equilateral triangle?
The given shape in the image is not an equilateral triangle.
What is an equilateral triangle?The triangle with all three sides equal and all the angles equal is called an equilateral triangle.
In the given figure we can see a triangle this triangle is not an equilateral triangle because the figure is formed between a square grid now if you see closely the base of the triangle can not be equal to the two sides of the triangle.
Because these two sides are the hypotenuse for the remaining right-angle triangle. So the base of the highlighted triangle can not be equal to the other two sides of the triangle.
Therefore given shape in the image is not an equilateral triangle.
To know more about triangles follow
https://brainly.com/question/17335144
#SPJ1
For melions birthday she wanted to make fruit punch that had 2 1/2 gallons of orange juice, 4 quarts of cranberry juice, and 3 quarts of apple juice. how much did she make in all?
Answer:
4.25 gallons of juice
Step-by-step explanation:
4 quarts = 1 gallon
3 quarts = 3/4 gallon
2 1/2 + 1 + 3/4 = 3 2/4 + 3/4 = 3 5/4 = 4 1/4
4 1/4 = 4.25
give brainliest please
hope this helps :)
Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide. saif is building a second pen that is 75% the length of the original and 125% the width of the original. write an equation to determine the length of the second pen. what is the length of the second pen? . .
The length of the second pen is 11.25 units.
What is a Rectangle ?A rectangle is a polygon with four sides , the opposite sides are parallel and equal .
it is given in the question that
Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide
length new = 75% length initial
Length new = (75/100) * 15
Length new = 0.75 * 15
Length new = 11.25 units
The length of the second pen is 11.25 units.
To know more about Rectangle
https://brainly.com/question/15019502
#SPJ1
please help me asap urgent grade 11 math
Answer:
choose option 1
Step-by-step explanation:
option one is going to take a longer time to pay off but option 2's annual fees are going to make you spend at least $200 more dollars than option 1
A line passes through the points (6, 8) and (4, 2). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=3x-10
Step-by-step explanation:
Slope: (y2-y1)/(x2-x1)
(2-8)/(4-6)
slope= -6/-2 = 3
Point: (6,8)
Slope-intercept: y-y1=m(x-x1)
y-8=3(x-6)
y-8=3x-18
y=3x-10
Please help! 30 points!
Answer:
it would be a vertical shift of 5 down
Step-by-step explanation:
I'm learning the same thing rn and that's right