We have been given that you invest $100,000 in an account earning 8% interest compounded annually. We are asked to find the time it will take the amount to reach $300,000.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
[tex]8\%=\frac{8}{100}=0.08[/tex]
[tex]300,000=100,000(1+\frac{0.08}{1})^{1\cdot t}[/tex]
[tex]300,000=100,000(1.08)^{t}[/tex]
[tex]\frac{300,000}{100,000}=\frac{100,000(1.08)^{t}}{100,000}[/tex]
[tex]3=(1.08)^{t}[/tex]
[tex](1.08)^{t}=3[/tex]
Let us take natural log on both sides of equation.
[tex]\text{ln}((1.08)^{t})=\text{ln}(3)[/tex]
Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:
[tex]t\cdot \text{ln}(1.08)=\text{ln}(3)[/tex]
[tex]\frac{t\cdot \text{ln}(1.08)}{\text{ln}(1.08)}=\frac{\text{ln}(3)}{\text{ln}(1.08)}[/tex]
[tex]t=\frac{1.0986122886681097}{0.0769610411361283}[/tex]
[tex]t=14.274914586[/tex]
Upon rounding to nearest tenth of year, we will get:
[tex]t\approx 14.3[/tex]
Therefore, it will take approximately 14.3 years until the account holds $300,000.
Solve the system using substitution and describe your steps
x = y - 3
2x + y = 12
Answer:
[tex]x=3\\y=6[/tex]
Step-by-step explanation:
[tex]x=y-3\\2x+y=12[/tex]
We have already defined that x = y - 3, replace x for this value.
[tex]2x+y=12\\2(y-3)+y=12[/tex]
Distribute 2.
[tex]2y-6+y=12[/tex]
Add 6.
[tex]2y+y=12+6[/tex]
Combine like terms;
[tex]3y=18[/tex]
Divide by 3.
[tex]y=\frac{18}{3}\\ y=6[/tex]
After having found a variable value, in this case y, replace it in the other equation; x = y - 3, to find x.
[tex]x=y-3\\x=6-3\\x=3[/tex]
Fill in the blank.
A rectangular prism has a length of 11 centimeters, a width of 9 centimeters, and a height of 3 centimeters. Its volume is
a0 cubic centimeters.
Answer:
297 cubic centimeters
Step-by-step explanation:
volume is LWH
11*9*3 = 297
Answer:
297 cubic centimeters
Step-by-step explanation:
mark me brainy plz!
what is the greatest common factor of the expression below?
22x^5 + 20x
Answer:
the answer is 2x
Step-by-step explanation:
The greatest common factor of the expression 22x^5 + 20x is 2x. Both the numerical values and the variable components are considered to determine this.
Explanation:To find the greatest common factor of the expression, we need to identify the highest number and the highest power of variable that evenly divides both terms. In the case of the expression 22x^5 + 20x, the numerical part of the greatest common factor can be found by examining 22 and 20. The greatest common factor of 22 and 20 is 2. Next we need to look at the variables in each term, in this case 'x'. The highest power of 'x' that will divide both 'x^5' and 'x' is 'x' itself.
So, combining these two elements, the greatest common factor of the expression is 2x.
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A report issued by the mayor's office states that city residents support building a new baseball
stadium. The report is based on a survey of 150 city residents who were shopping at a sporting
goods store. Participants were asked the question, "Do you think the city should replace its outdated
stadium with a more modern stadium?"
Select all statements that correctly evaluate the report
question is not biased
The sample is biased because it does not represent the population
The sample is not biased,
The question is biased toward a Yes response.
The question is biased toward a No response.
Next
Hey, sorry for the late answer but just in case some one else needs help on the problem here it is.
Answer:
"the sample is biased because it does not represent the population." and "The question is biased toward a Yes response."
Step-by-step explanation:
The sample is biased because they people being surveyed are shopping at a sporting shop so most of them are going to support it.
The question is biased because it says "outdated" and "modern" to try to get people to support it.
I took this quiz and this is correct :) hope I can help some one.
one third of an interger
Which represents a perfect cube? 6 times 6 times 6 6 + 6 + 6 3 times 3 times 3 times 3 3 + 3 + 3 + 3 + 3
Answer:
6 times 6 times 6
Step-by-step explanation:
6 x 6 = 6²
Therefore 6 x 6 x 6 = 6³
Answer: 6 times 6 times 6
Step-by-step explanation: I did it on edg :)
A stadium holds a total of 7,500 people. A random survey of 150 people finds that 17 of them are under 21 years old.
Enter the total number of people predicted to be in the stadium under 21.
Answer: 850 people
Step-by-step explanation:
Stadium capacity = 7,500 people.
A random survey was done for 150 people and it was found out that 17 of them are under 21 years old. This can be expressed as a fraction as:
= 17/150
The total number of people that are predicted to be in the stadium of under 21 will be:
= 17/150 × 7500
= 17 × 50
= 850 people
Photo is attached please help ASAP super easy geometry
Answer:
Volume = 280 cm
Step-by-step explanation:
V=(lwh)/3
length: 10
width: 7
height: 12
V= (10*7*12)/3
V= 840/3
V= 280cm
Which triangle is both scalene and acute?
Answer:
Top right.
Step-by-step explanation:
For it to be an acute triangle, none of the angles can be greater or equal to 90°.
In the case of the top right triangle, none of them are:
51°, 58° , 71°
The definition of a scalene triangle, is that none of the sides must have the same measurements (no sides are congruent). This is true, all measurements are different:
8.3 ft, 9 ft, 10 ft
Top Right choice is your answer.
~
Find the value of x in ⊙Q .
Answer:
x= 5
Step-by-step explanation:
both lines are the same length
5x-6=2x+9
-2x -2x
3x-6= +9
+6 +6
3x = 15
÷3 ÷3
x= 5
The value of x is 5.
To find the value of [tex]\(x\)[/tex] in the given circle, we need to use the properties of the circle and the given information about the segments.
1. Given:
PM is a chord of the circle with center [tex]\(Q\)[/tex].
[tex]\(NL\)[/tex] is the perpendicular bisector of [tex]\(PM\)[/tex].
[tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], and [tex]\(T\)[/tex] lies on [tex]\(NL\)[/tex].
[tex]\(MT = 5x - 6\)[/tex] and [tex]\(TP = 2x + 9\)[/tex].
2. Key Properties:
Since [tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], we have [tex]\(PT = TM\)[/tex].
The perpendicular bisector of a chord passes through the center of the circle, so [tex]\(NL\)[/tex] passes through [tex]\(Q\)[/tex].
3. Equating the Segments:
Since [tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], we have:
[tex]\[ PT = TM. \][/tex]
Using the given expressions for [tex]\(MT\)[/tex] and [tex]\(TP\)[/tex]:
[tex]\[ MT = 5x - 6 \quad \text{and} \quad TP = 2x + 9. \][/tex]
Because [tex]\(T\)[/tex] is the midpoint, [tex]\(PT = TM\)[/tex].
Therefore, we have:
[tex]\[ PT = TM = 2x + 9. \][/tex]
Since [tex]\(MT = 5x - 6\)[/tex], and [tex]\(PT = TM\)[/tex], we have:
[tex]\[ 5x - 6 = 2x + 9. \][/tex]
4. Solving for [tex]\(x\)[/tex]:
[tex]\[ 5x - 6 = 2x + 9. \][/tex]
[tex]\[ 3x - 6 = 9. \][/tex]
[tex]\[ 3x = 15. \][/tex]
[tex]\[ x = 5. \][/tex]
You are in charge of the city carnvial committee. You have $8,096.35 to spend. You have already purchased: Decorations $894.60. Tent rental
$1.009.99, new popcorn and cotton candy machines $658.50
How much money do you have left to spend to rent carnival rides for the kids?
Step-by-step explanation:
Total amount to spend = 8096.35
Amount already spent = 894. 60 + 1009.99 + 658.50 = 2563.09
Amount left to spend = 5533.26
find the exact length of the third side
Answer:
X is 8
Step-by-step explanation:
[tex]100^{2} =6^{2} +x^{2}[/tex]
[tex]x=8[/tex]
Answer:
8
Step-by-step explanation:
This is a right triangle, and we know this because of the little square in the corner. Therefore, we can use the Pythagorean theorem.
a^2+b^2=c^2
a and b are the legs, and c is the hypotenuse.
We know the 6 and the unknown side are the legs, since they form the right angle. We also know that 10 is the hypotenuse, since it is opposite the right angle.
6^2+b^2=10^2
Evaluate the exponents
36+b^2=100
Now, we need to solve for b. To do this, we need to get by itself. First, subtract 36 from both sides
36-36+b^2=100-36
b^2=64
Take the square root of both sides
[tex]\sqrt{b^2}=\sqrt{64}[/tex]
b=8
So, the the unknown side is 8
Given AQRS - AXYZ, what is the value of tan(Q)?
A) 3/5
B) 3/4
C) 4/5
D) 4/3
) Perry earns $13 per hour. Last week, he worked 6 hours on Monday, 5 hours on
Tuesday, and 9 hours on Wednesday. He had Thursday off, and then he worked 7 hours on
Friday. How much money did Perry earn in all last week?
Which describes the cross section of a square prism that passes through vertices A. B. and C?
A. a triangle with three equal sides, all measuring 8 inches
B.a triangle with three equal sides, all longer than 12 inches
C. a triangle with only two equal sides one side measures 8 inches and two sides measure 12 inches
D. a triangle with only two equal sides; one side is longer than 8 inches and two sides of equal length that are longer than 12 inches.
Please answer now, I’m on a timer.
Answer:
c
Step-by-step explanation:
there are 150 students in the marching band, and 30 of them play the trumpet. Which number line represents the percent of the srudents in the marching band who play the trumpet?
Answer:
30 is 20% of 150 i.e. 20% of total 150 students in the marching bank play the trumpet.
Step-by-step explanation:
Draw two number lines:
One number line to represent number of students from 0 to 150. For convenience, divide the number line into intervals of 15 so that 30 is also present on the line.Second number line to represent percentage and divide it in intervals from 1 to 100.Now, place the other number line just below the other number line and draw a vertical line as shown the attached figure.
We find out that 30 is at 20% of 150.
It means that 20% (30 of total 150) of total 150 students in the marching band, play trumpet.
30 is 20% of 150 i.e. 20% of total 150 students in the marching bank play the trumpet. Step-by-step explanation:
The steps below show the incomplete solution to find the value of x for the equation.
The answer is 4x=24 because the next step is to add 4 to both sides
Most likely to the next step is option 1) [tex]4x=24[/tex]
The given equation is [tex]7x-3x-4=-1+21[/tex]
and it's already given the step 1, step 2 , step 3 in the question.
Let's simplify the given equation ,
[tex]7x-3x-4=-1+21\\\\7x-3x-4=20\\4x-4=20[/tex]
Taking [tex]4[/tex] to the other side,
[tex]4x=20+4\\4x=24[/tex]
To know more about finding the value of x type question,
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onsider the system of equations. y = –2x + 4, 3y + x = –3 Which statement is true of this system of equations? Both equations are in slope-intercept form. The first equation converted to slope-intercept form is y + 2x = 4. The second equation converted to slope-intercept form is .y = negative one-third x minus 1 Neither equation is in slope-intercept form.
Answer:
The second equation converted to slope-intercept is y = -1/3 x - 1.
Step-by-step explanation:
take the second equation:
3y + x = -3
3y = -x - 3
y = 1/3 x - 1. <----- Slope-intercept form.
Answer:
its c
Step-by-step explanation:
im dumb as heck so plez halp
The bases of a 39-foot pole and a 15-foot pole are 45 feet apart, and both poles are perpendicular to the ground. The ground is flat between the two poles. What is the length of the shortest rope that can be used to connect the tops of the two poles?
Answer: 51 feet
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:
x^2 = a^2 + b^2
Where x is the hypotenuse of the triangle (in this case length of the rope) and a and b are the other sides.
The difference between the poles' heights is equal to one side of the triangle (39-15=24), the other side of the triangle is the distance between poles (45).
Replacing with the values given:
x^2 = 24^2 + 45^2
x^2 = 576+2,025
x^2 = 2,601
x = √2,601
x = 51 feet
Feel free to ask for more if needed or if you did not understand something.
What is 2 divided by 3 written as fractions?
1/3 with a line over the answer ( 0.66666666666...)
The fraction form of the expression ''2 divided by 3'' would be 2/3.
Used the concept of the fraction that states,
A fraction is part of a whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that the statement is,
''2 divided by 3''
Now it can be written in fraction form as,
''2 divided by 3''
= 2 ÷ 3
= 2 / 3
Therefore, the fraction form is 2/3.
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Question shown in images
find the distance of the line segment joining the two points (4,-3) and (12,3) 3 10 6 5
Answer:D or 4 square root 3
Step-by-step explanation:
using distance formula -12 square rooted - 2 square root 3 = -4squareroot3. So, after that you would square giving 48 then square root giving 4 square root 3. (-4 square root 2 and -32 square rooted cancel out giving 0)
pls help! will give brainlist!
Answer:
Since this is a transversal, I am using certain rules to figure this out.
For example, angles 1 & 2 should equal 180 when added together, in the same way angles 11 & 12 should do the same thing!
Therefore, since angle 1 is 140°, angle 2 should be 40°, to complete it. This is the same for the other side!
Answer:
Angle2: 40
Angle11: 60
Step-by-step explanation:
ang1+ang2=180 (Linear pair)
140+ang2=180
ang2=40
ang2+ang9+ang11=180 (angle sum property)
40+80+ang11=180
ang11=180-120
ang11=60
Hope this helps...Pls mark as Brainliest!!
Noah scores n points in a basketball game.
a. What does 15 < n mean in the context of the basketball game?
Answer: Noah scores more than 15 points.
Step-by-step explanation:
Hi, to answer this question we have to analyze the inequality:
15 < n
Where n are the scored points on a basketball game.
< means greater than.
So, in the context of the basketball game, it means that Noah scored more than 15 points.
Feel free to ask for more if needed or if you did not understand something.
The correct interpretation of 15 < n in the context of the basketball game is that Noah scores more than 15 points.
The inequality 15 < n indicates that the number of points Noah scores, represented by n, is greater than 15. This means that the actual number of points Noah scores must be any number that is a increment above 15, but cannot be 15 itself. For example, if Noah scores 16 points, 17 points, or any number of points greater than 15, the inequality 15 < n would be satisfied. It is a mathematical way of stating that Noah's score exceeds 15 points.
- Which of the following is the least?
A).27
B) 1/4
C) 3/8
D) 2/11
E) 11%
Step-by-step explanation:
A) 0.27
B) 1/4 = 0.25
C) 3/8 = 0.375
D) 2/ 11 = 0.1818
E) 11% = 0.11
E is the correct answer
Answer:
E
Step-by-step explanation:
2/11= .18
3/8= .375
1/4= .35
11%= .11
.27= .27
Write an equation of the circle with center (-3, 4) and radius 6.
Answer:
(x+3)²+(y-4)²=36.
Step-by-step explanation:
For this, we need to use the equation of a circle which is:
(x-h)²+(y-k)²= r²
Simply substitute the center values for 'h,k', and the radius for 'r'.
This will give you:
(x+3)²+(y-4)²=36.
What is -78.6% (-2.4)? A. -188.64 B. -32.75 C. 32.75 D. 188.64
Answer:
D
Step-by-step explanation:
hope this helps
Answer:
188.64
Step-by-step explanation:
-78.6%(-2.4) =
-0.786(-2.4) =
1.8864
1.8864 * 100 = 188.64
So, your answer letter choice D.
Abby used 10 ounces of dried pineapple, 20 ounces of dried cranberries, and 18 ounces of pecans to make a trail mix. Which statement is a true statement?
Estimate the sum by first rounding each
mixed number to the nearest whole number
and then adding:
4 7/12 + 2 1/3
[?]+[] = []
Answer:
7
Step-by-step explanation:
4.583 + 2.333 = 6.916 = 7(to the nearest whole number)