Using compound interest, it is found that the annual rate of increase was of 3.10%.
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 this problem, the parameters are given as follows:
t = 9, A(t) = 6, A(0) = 4.5, n = 12.
Hence we solve for r to find the interest rate as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]6 = 4.5\left(1 + \frac{r}{12}\right)^{12 \times 9}[/tex]
[tex]1 + \frac{r}{12}\right)^{108} = 1.33[/tex]
[tex]\sqrt[108]{1 + \frac{r}{12}\right)^{108}} = \sqrt[108]{1.33}[/tex]
[tex]1 + \frac{r}{12} = (1.33)^{\frac{1}{108}}[/tex]
1 + r/12 = 1.0026.
r/12 = 0.0026
r = 12 x 0.0026
r = 0.031.
The annual rate of increase was of 3.10%.
More can be learned about compound interest at https://brainly.com/question/24924853
#SPJ1
To find the x-intercept from an equation, you substitute ___ for the variable ___
and solve for ___
.
To find the y-intercept from an equation, you substitute ___ for the variable __
and solve for ___
.
To find the x-intercept from an equation, you substitute 0 for the variable y
and solve for x
To find the y-intercept from an equation, you substitute 0 for the variable x
and solve for y.
How to find x-intercept and y-intercept in an equation?The x-intercept is where a line crosses the x-axis.
In other words, the x-intercept is the value of the x coordinate of a point where the value of y coordinate is equal to zero.
The y-intercept is the point where the line crosses the y-axis.
In other words, the y-intercept is the value of the y coordinate of a point where the value of x coordinate is equal to zero.
Hence,
To find the x-intercept from an equation, you substitute 0 for the variable y
and solve for x
To find the y-intercept from an equation, you substitute 0 for the variable x
and solve for y.
learn more on x-intercept and y-intercept here: https://brainly.com/question/20661614
#SPJ1
Pre-Calc: Perform the operation and write the result in standard form. (Simplify completely)
[tex]\left( \sqrt{-27} \right)^2\implies \left(\sqrt{(-1)(27)} \right)^2\implies \left( \sqrt{-1}\cdot \sqrt{27} \right)^2\implies \left( \sqrt{-1} \right)^2 \left( \sqrt{27} \right)^2 \\\\\\ i^2\cdot 27\implies -1\cdot 27\implies -27[/tex]
A cyclist rode at an average speed of 15 mph for 30 miles. how long was the ride? 0.5 hours 0.5 hours 1 hour 1 hour 2 hours 2 hours 3 hours
Answer:
2 hours
Step-by-step explanation:
Answer: 2 hours
Step-by-step explanation:
using the relationship distance = speed × time, the time = 2 hours
i need help with this question
Answer:
x = 1 and x = -3
Step-by-step explanation:
if y = f(x) and f(x) = -5, this means y = -5
draw a horizontal line at y = -5 and see write the x values for where the line intersects with the graph.
The x values are:
x = 1 and x = -3
How do you know the value of x is positive?
It depends on the answer and the number of y
What is the coefficient of the term of degree 1 in the polynomial 2x^8-5^2+3x+4
Answer:nk it is the letter A
Step-by-step explanation:
Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.)
Line segment VW is the segment bisector is true based on the diagram
as it is showed in the diagram that the line segment vw divides segment TU in two equal parts so line segment VW is segment bisector
line segment VW cannot be a perpendicular bisector because it is not mentioned that Line segment VW divides side TU at right angle that is at 90°
line segment VW cannot be a angle bisector because Line segment VW does not lie on any angle
v is not the vertex of pair of congruent angles and w is not the vertex at the right angle
to know more about line segments - https://brainly.com/question/25727583
#SPJ9
2/3 of the sum of nine and p
The resulting expression for 2/3 of the sum of nine and p is 2/3(9+p)
Translating expression to wordsAccording to the question, we are to write the given statement as an expression
Let the unknown variable be p such that the sum of nine and p is 9 + p
Since "of" means multiplication, hence;
2/3 of the sum of nine and p will be expressed as;
2/3 of (9 + p)
2/3 * (9 + p)
2/3(9+p)
Hence the resulting expression for 2/3 of the sum of nine and p is 2/3(9+p)
Learn more on expression here; https://brainly.com/question/723406
#SPJ1
Consider the pair of points below.
(-5, -4)
(-1,8)
Find the slope of the line passing through the pair of points.
m =
Suppose that both of the events you have just analyzed are partly responsible for the increase in the price of pizzas. Based on your analysis of the explanations offered by the two groups of students, how would you figure out which of the possible causes was the dominant cause of the increase in the price of pizzas?.
The supply curve swings left along the demand curve, raising the price of the pizza shops to close. If individuals just have a greater interest in beer, the demand curve will shift to the right, which will cause the price to rise as the supply curve is moved to the right. Apply this knowledge to the rest of the analysis.
If the price increase was modest, then the movement in supply in the pizza market must have outweighed the shift in demand. The supply shift in the pizza market must have been greater than the demand shift if the equilibrium amount of pizzas declines. The price of pizzas must have changed as a result of whichever modification happened first. If the amount of pizzas in the equilibrium market falls, the demand shift must have been greater than the supply shift.
The demand curve changes to its proper position. It happens as a result of people switching to eating pizza instead of pizzas. The new equilibrium price rises as a result of the new demand curve and the existing supply curve.
A rise in supply and a decline in demand will result in a decrease in the equilibrium price, but the impact on the equilibrium quantity cannot be predicted. Consumers now place less significance on price for any quantity, and producers are willing to simply accept a lower price; as a result, the price will decrease.
learn more about supply and demand:
https://brainly.com/question/26424586
#SPJ4
Simplify -|3-5|² + 4 • 3²
Answer:
32.
Step-by-step explanation:
-|3-5|² + 4 • 3²
= - 2^2 + 4*9
= -4 + 36
= 32.
Answer:
32
Step-by-step explanation:
Subtract
5
from
3
.
−
|
−
2
|
2
+
4
⋅
3
2
The absolute value is the distance between a number and zero. The distance between
−
2
and
0
is
2
.
−
2
2
+
4
⋅
3
2
Raise
2
to the power of
2
.
−
1
⋅
4
+
4
⋅[tex]3^{2}[/tex]
Multiply
−
1
by
4
.
−
4
+
4
⋅
3
2
Raise
3
to the power of
2
.
−
4
+
4
⋅
9
Multiply
4
by
9
.
−
4
+
36
Add
−
4
and
36
.
32
»
What number is equivalent to
32 +6 (14-5×2) ÷ 4
A 23/1
B 10/
C 14
D 15
The result of the given equation is 14.
This is an problem of simplification. And for simplification we need to understand the rule of BODMAS.
BODMAS means we have to first solve B for bracket, O for of, D for divide, M for multiplication, A for addition and S for subtraction.
The rule of BODMAS has to be followed in order to solve any equation in simplification method.
Here the problem is;
32+6(14-5×2)÷4
⇒32+6(14-10)÷4
⇒32+6(4)÷4
⇒32+24÷4
⇒56÷4
⇒14
So, the solution of the given equation gives 14 as the answer.
To learn ore about simplification and BODMAS visit the link:
https://brainly.com/question/2804192
#SPJ9
HELP ME ASAP FOR MATHS
Answer:5 higher and 1 horizontal
Step-by-step explanation:
In the figure, m/3= (3x+15)° and mZ8= (x+100)°. Find the value of x. Then calculate the measure of Z4.
Value of x = 42.5 ° and measure of angle 4 = 37.5 ° .
measure of angle 3 = measure of angle 8
( 3 x + 15 ) ° = ( x + 100 ) °
2 x = 85
x = 42.5 °
measure of angle 3 + measure of angle 4 = 180 °
measure of angle 3 = ( 3 x + 15 ) °
= ( 3 * 42.5 ) + 15
= 142.5 °
Hence , measure of angle 4 = 180 - 142.5 ° = 37.5 ° .
To learn more on transversal follow link :
https://brainly.com/question/26961508
#SPJ9
Let the graph of g be a translation 4 units left followed by a horizontal shrink by a factor of 1/3 of the graph of f(x)=x²+x. Write a rule for g
The transformed function is:
g(x) = (3*(x + 4))² + (3*(x + 4))
How to write the transformed function?Here we have the function:
f(x) = x² + x
Now we want to apply a translation of 4 units to the left, followed by a horizontal shrink by a factor of 1/3.
First, the translation is written as:
g(x) = f(x + 4)
Now the shink will give:
g(x) = f( 3*(x + 4))
Replacing the actual function we will get:
g(x) = (3*(x + 4))² + (3*(x + 4))
If you want to learn more about transformations:
https://brainly.com/question/4289712
#SPJ1
What is the product of 1.6 × 10³ and 2.9 × 10³ expressed in scientific notation?
Answer:
4.64x10^6
Step-by-step explanation:
6. x+1<-3 I need this done tonight I don’t know how to solve this.
Answer:
x<-4
Step-by-step explanation:
You just subtract the 1 from both sides and the sign stays the same UNLESS you are dividing by a negative number, then it will change. Good luck on your hw :)
Suppose a/b c/d and e/f represent three rational numbers. If a/b is less than c/d and c/d is less then e/f compare a/b and e/f explain
We get that a / b will also be less than e / f.
A rational number means a number that can be written in the form of p / q.
We are given the three rational numbers:
a / b , c / d and e / f.
We are also given that:
a / b < c / d …(1)
c / d < e / f …(2)
Multiply (1) and (2), we get that:
a / b × c / d < c / d × e / f
Dividing both sides by d / c, we get that:
a / b < e / f
So, a / b will also be less than e / f.
Therefore, we get that a / b will also be less than e / f.
Learn more about less than here:
https://brainly.com/question/7879375
#SPJ9
What is the correct answer
Answer: distance is the answer
5 Complete the table. Rounded to the nearest 10 100 1,000 10,000 100,000 1,000,000 3,147,283 68,547 69,000 1,656,908 900,571
The completion of the table by rounding the numbers to the nearest 10, 100, 1,000, 10,000, 100,000, and 1,000,000 is as follows:
Rounded to Numbers
the nearest 3,147,283 68,547 1,656,908 900,571
10 3,147,280 68,550 1,656,910 900,570
100 3,147,300 68,500 1,656,900 900,600
1,000 3,147,000 69,000 1,657,000 901,000
10,000 3,150,000 70,000 1,660,000 900,000
100,000 3,100,000 100,000 1,700,000 900,000
1,000,000 3,000,000 0.068547 2,000,000 1,000,000
What is a rounding number?Rounding a number involves, making it simple and very close to its true value, sometimes, using zeros or scientific notations.
Rounding a number is also known as an approximation, which is an estimate before the actual calculation is carried out.
Rounded to Numbers
the nearest 3,147,283 68,547 1,656,908 900,571
10 3,147,280 68,550 1,656,910 900,570
100 3,147,300 68,500 1,656,900 900,600
1,000 3,147,000 69,000 1,657,000 901,000
10,000 3,150,000 70,000 1,660,000 900,000
100,000 3,100,000 100,000 1,700,000 900,000
1,000,000 3,000,000 0.068547 2,000,000 1,000,000
Learn more about rounding numbers at https://brainly.com/question/28707100
#SPJ1
what are the blocked words?
Answer:
In the order they appear in the paragraph: different, measurement, coversions, world.
Step-by-step explanation:
"Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems."
The paragraph would not make sense if the words were in incorrect places.
Which of these number sentences are true?
A) 12.02 < 6.54 x 10^2
B) 12.02 > 6.54 x 10^2
The 12.04< [tex]6.54 * 10^2[/tex] number sentences are true.
Option (A) is correct.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.
Given:
The given number is
12.02 and [tex]6.54*10^2[/tex]
We have to choose the sentences are true.
According to given question we have
The greater-than sign is a mathematical symbol that denotes an inequality between two values.
6.54 x 10^2
When we can multiply the value of 6.54*100 we get
654
The number is greater than 12.02
i.e 654>12.04
It is written as
12.04< [tex]6.54 * 10^2[/tex]
Therefore, the 12.04< [tex]6.54 * 10^2[/tex] number sentences are true.
Learn more details about integer here:
https://brainly.com/question/15276410
#SPJ1
The MyTunes song app sells music downloads. Over the past few years, the service
has lowered its prices. The table shows the price per song and the number of songs
downloaded per day at that price.
Price per
Song
$0.89
$0.79
$0.69
$0.59
$0.49
$0.39
Number of Downloads (in
thousands)
1,212
1,704
1,760
1,877
1,944
2,011
The approximate number of downloads at a price of $0.54 per song is ______
The approximate number of downloads at a price of $0.54 per song is 1910.5
As the problem given we have The table shows the price per song and the number of songs downloaded per day at that Price per Song.
Price per song number of songs
downloaded per day at that price
$0.89 1,212
$0.79 1704
$0.69 1760
$0.59 1877
$0.49 1944
$0.39 2011
The formula for the linear interpolation process y = y1 + ((x – x1) / (x2 – x1)) * (y2 – y1), where x is the known value, y is the unknown value. x1 and y1 are the coordinates that are below the known x value, and x2 and y2 are the coordinates that are above the x value.
here x1= 0.49 y1= 1944 x2= 0.59 y2=1877 x=0.54
y=1944+((0.54-0.49)/(0.59-0.49))*(1877-1944)
y=1944-33.5=1910.5
Learn more about linear interpolation here:
https://brainly.com/question/18768845
#SPJ9
Kiara is covering part of this rectangular box with duct tape. she is covering the four sides but not the top or bottom. 4 in. 4 in. 20 in. what is the total area that kiara will cover with duct tape? show your work.
160 square inches duct tape is needed to cover.
The mentioned box is rectangular according to the question and Kiara have to cover top and the bottom part with this duct tape .
Thus we have to find the area of the box , where 4 inch is the width of this box and 20 in. is the length . To find the area we will use the formula , (Area = length × width)
∵ The area is , ( 4 × 20 ) square inches = 80 square inches
for the top part it is 80 inc² and for the bottom it's again 80 inch² , so she have to cover total ( 80+ 80) inc² = 160 in.²
To know more about area of a rectangle visit ,
https://brainly.com/app/ask?q=area+of+a+rectangle
#SPJ4
160 square inches duct tape is needed to cover.
The mentioned box is rectangular according to the question and Kiara have to cover top and the bottom part with this duct tape .
Thus we have to find the area of the box , where 4 inch is the width of this box and 20 in. is the length . To find the area we will use the formula , (Area = length × width)
∵ The area is , ( 4 × 20 ) square inches = 80 square inches
for the top part it is 80 inc² and for the bottom it's again 80 inch² , so she have to cover total ( 80+ 80) inc² = 160 in.²
160 square inches duct tape is needed to cover.
To know more about area of a rectangle refer to the link:
https://brainly.com/question/2607596
#SPJ4
what is the radical expression that is equivalent 27 ⅕?
Answer:
[tex]\sqrt[5]{27}[/tex]
Step-by-step explanation:
27^(1/5) = [tex]\sqrt[5]{27}[/tex]
Describe three different ways you can determine that an angle is a right angle.
The three different ways you can determine that an angle is a right angle are as follows:
B) You can determine whether an angle is right if it is marked with a right angle symbol.
D) You can determine whether an angle is right if the angle is a vertical pair with a right angle.
E) You can determine whether an angle is right if the angle forms a linear pair with a right angle.
What is a right angle?A right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angle has a measure of 90 degrees.
In conclusion, we can reasonably infer and logically deduce that all right angles are marked with a right angle symbol and they are formed as a linear pair.
Read more on right angle here: https://brainly.com/question/28453423
#SPJ1
Complete Question:
Describe three different ways you can determine that an angle is a right angle.
A) You can determine whether an angle is right if the angle is congruent to the complement of the angle.
B) You can determine whether an angle is right if it is marked with a right angle symbol.
C) You can determine whether an angle is right if it is formed by two lines that appear to be perpendicular.
D) You can determine whether an angle is right if the angle is a vertical pair with a right angle.
E) You can determine whether an angle is right if the angle forms a linear pair with a right angle.
Which two of the calculations give the same answer?
12 ÷ 3
1.4 +2.6
1.4 x 3
2.1+2.4
Answer:
A and B
Step-by-step explanation:
Amy studied 3- hours for her Biology test. She studied half as long for her math test as she did for her biology test. How long did she study for her math test?
Answer:
90 minutes or 1 hour and 30 minutes
Step-by-step explanation:
Hey there!
In order to find out how long Amy studied for her math test, all we need to do is divide 3 hours by 2
First of all, we can convert 3 hours to 180 minutes since there are 60 minutes in 1 hour
Now, we divide 180 and 2
180/2 is 90
This means, Amy studied 90 minutes or 1 hour and 30 minutes for her math test
HII NEED HELP PLEASE! I DON'T UNDERSTAND
Answer: f(-2)=3
Step-by-step explanation:
f(-2)=(-2-1)^2+3(-2)
=9-6
=3
This is the only true statement out of the questions.
So the answer would be -2.
How much of the daily value must a snack meet in order for the fda to consider it a ""good source"" of nutrients? 10 percent to 19 percent 10 percent to 19 percent 25 percent to 35 percent 25 percent to 35 percent 30 percent to 40 percent 30 percent to 40 percent 50 percent to 59 percent
10 percent to 19 percent of daily value must a snack meet in order for the FDA to consider it a ""good source"" of nutrients.
The Food Manufacturer or Distributor is responsible for ensuring their food product labeling complies with FDA regulations. FDA will not review or approve food labels. If the labels do not comply with FDA requirements, the FDA will consider the product as misbranded and may take regulatory action, including detention.
LMG's Label review service will help you confirm your product labels comply with FDA requirements. We have designed three types of label review services; you can choose the best service which fits your products.
( Food Label Compliance : FDA , Food and Drug administration)
To know more about FDA ,
https://brainly.com/question/19891116?referrer=searchResults