Answer: 12.6 years
Step-by-step explanation:
Hi, to answer this question we have to apply the compounded interest formula:
A = P (1 + r/n) nt
Where:
A = Future value of investment (principal + interest)
P = Principal Amount
r = Nominal Interest Rate (decimal form, 4/100= 0.04)
n= number of compounding periods in each year (1)
t = years
Replacing with the values given
8200= 5000(1+ 0.04/1)^1(t)
Solving for t
8200 =5000 (1.04)^t
8200/5000 =(1.04)^t
1.64 =(1.04)^t
log 1.64 =log (1.04)^t
log 1.64 = t log (1.04)
log 1.64/ log (1.04) =t
t = 12.6 years
Question 16 (5 points)
The first two terms of an arithmetic sequence are a1 = 2 and a2 = 5. Find a6, the
sixth term of the sequence.
OA) 27
B) 20
OC) 14
D) 17
Answer:
D. 17.
Step-by-step explanation:
The nth term of an arithmetic sequence (an) is a1 + d(n - 1) where a1 = first term and d = the common difference.
In this sequence d = a2 - a1 = 5 - 2 = 3.
a6 = 2 + 3(6 - 1)
= 2 + 3*5
= 17.
Answer:
Step-by-step explanation:
probably 17
\frac{h^{2}-1 }{h+3} when h=5
Answer:
3
Step-by-step explanation:
[tex]\frac{h^{2}-1 }{h+3}[/tex]=
[tex]\frac{5^{2}-1 }{5+3}[/tex]=
[tex]\frac{25-1}{8}[/tex]=
[tex]\frac{24}{8}[/tex]=
3
I need help on this.
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
hopefully this helps
Please help with this
Answer:
C is correct
Step-by-step explanation:
1 and 2 add up to 90,
so does 3 and 4
Quadrilateral ABCD has coordinates A (3, 1), B (4, 4), C (7, 5), D (6, 2). Quadrilateral ABCD is a
Answer:
Rhombus
I hope I helped!!!
Please make me brainliest
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = -16t^2 + 120t + 10. How long does it take to reach maximum height? What is the boulder's maximum height? What is the boulder's maximum height? Round to the nearest hundredth, if necessary.
Answer:
See below in bold.
Step-by-step explanation:
h = -16t^2 + 120t + 10
To find the height and time for maximum we convert to vertex form:
h = -16(t^2 - 7.5t) + 10
h = -16 [(t - 3.75)^2 - 14.0625] + 10
h = -16(t - 3.75)^2 + 225 + 10
h = -16(t - 3.75)^2 + 235
So the time to reach maximum height is 3.75 seconds and the maximum height = 235 ft.
QUICK!!!!! Which question is best modeled with a division expression?
A: How much does it cost to buy 3 and one-half pounds of apples at $2 per pound?
B: How many apples are needed for 2 pies if the recipe uses 3 and one-half apples per pie?
C: How many more apples are needed if a recipe uses 3 and one-half apples and you only have 2 apples?
D: How many apples are in each pie if a total of 3 and one-half apples were used to bake 2 pies?
Answer:
D
Step-by-step explanation:
[tex]\frac{2}{3.5}[/tex]
Which is about .57
What are the missing amounts in this statement.
20% of $30= 40% of $____
Pls help me
Answer:
Step-by-step explanation:
20% of $30 = 40% of x
0.20 * 30 = 0.40 * x
[tex]\frac{0.2}{0.4}*30=x\\[/tex]
x = 15
Which is the constant term in the equation given in standard from 5x+3y=15
Answer:
15
Step-by-step explanation:
The constant is the term without the variable
5x+3y=15
15 is the constant
Lavern just turned 40 years old, so her credit score rose from 555 to 623,
According to the following table for a $150,000 mortgage, how much less per
year would Lavern have to pay on a $150,000 mortgage with the new credit
score?
FICO
Interest Monthly
Score
Rate Payment
720-850
5.59% $860
700-719
5.71% $872
675-699
6.25% $924
620-674
$1039
560-619
8.53% $1157
500-559
9.29% $1238
7.40%
A. $199
ООО
B. $1238
C. $1039
O D. $2388
Answer:
D
Step-by-step explanation:
($1238-$1039)×12=$2388
If f(1) = 7 and f(n) = 5(n-1) + 2, then f(4) =
Answer:
f1 =7
f2 = 5(7) + 2 = 37
f3 = 5(37) + 2 = ?
f4 = 5(?) + 2 = ____
914
hopefully this makes sense
Which subsets of real numbers does 2 1/3 belong to?
Answer:
rational numbers set
Step-by-step explanation:
rational numbers are fractions and 2 1/3 = 7/3
Please help me
Two exponential functions, fand g, are shown in the graph where g is a transformation of f.
Which of the rules given below shows the transformation of f?
A. g(x) = f(x-2)
B. g(x) = f(x) + 2
C. g(x) = f(x + 2)
D. g(x) = f(x) - 2
Make x the subject:
y = 6x-7 / 3x-8
Answer:
I. x=y-7
6
Step-by-step explanation:
y=6x-7
6x-7=y
6x=y-7
6x=y-7
6. 6
x=y-7
6
Answer:
x = [tex]\frac{8y-7}{3y-6}[/tex]
Step-by-step explanation:
Given
y = [tex]\frac{6x-7}{3x-8}[/tex] ( multiply both sides by 3x - 8 )
y(3x - 8) = 6x - 7 ← distribute left side
3xy - 8y = 6x - 7 ( subtract 6x from both sides )
3xy - 6x - 8y = - 7 ( add 8y to both sides )
3xy - 6x = 8y - 7 ← factor out x from each term on the left
x(3y - 6) = 8y - 7 ← divide both sides by (3y - 6)
x = [tex]\frac{8y-7}{3y-6}[/tex]
What is the value of x in the equation -2.4x = 8.4?
-20.16
-3.5
3.5
20.16
Answer:
Step-by-step explanation:
x = 8.4/-2.4 = -84/24 = -3.5
The value of x in the equation is -3.5.
What is the value of x?
Division is the process of parting a number into equal parts using another number. The sign used to denote division is ÷.
In order to determine the value of x, divide 8.4 by -2.4
x = 8.4 / -3.5 = -3.5
To learn more about division, please check: https://brainly.com/question/13281206
Please help this is due at midnight!!!!!!!!!
Describe how to optimize a function given a set of constraints.
The setup for this problem is written as l(x,y)= f(x,y)+λg(x,y)
For example, a common economic problem is the consumer choice decision. Households are selecting consumption of various goods. However, consumers are not allowed to spend more than their income (otherwise they would buy infinite amounts of everything!!). Let’s set up the consumer’s problem:
Suppose that consumers are choosing between Apples (A) and Bananas (B). We have a utility function that describes levels of utility for every combination of Apples and Bananas.
11
A 2 B 2 = Well being from consuming (A) Apples and (B) Bananas.
Next, we need a set of prices. Suppose that Apples cost $4 apiece and Bananas cost $2 apiece. Further, assume that this consumer has $120 available to spend. The income constraint is
$2B+$4A≤$120
However, the problem requires that the constraint is in the form g(x, y)≥ 0. In
the above expression, subtract $2B and $4A from both sides. Now we have 0≤$120−$2B−$4A
g(A, B) Now, we can write out the lagrangian
11
l(A,B)= A2 B2 +λ(120−2B−4A)
f (A, B) g(A, B)
Step II: Take the partial derivative with respect to each variable We have a function of two variables that we wish to maximize.
Therefore, there will be two first-order conditions (two partial derivatives that are set equal to zero).
To know more about function follow
https://brainly.com/question/22340031
#SPJ2
Bob and Sally's mortgage payment increases to $1632.00. Their roof starts to leak and they need to replace it. They budget $500 per month (replace the old student loan charge with roof expense).
Answer:
List of expenses is attached below.
Total Income = $160 + $6245 = $6405
1) Do Bob and Sally have a surplus or deficit?As mortgage payment has increased, we replace $1580 with $1632 in the table
Replace student loans with roof expense, we replace $544 with $500 in the table.
Find Total Expenses by adding all the values from the table.
Total Expenses = $6660.17
Total Income =$6405
They have a deficit
2) By how much?Deficit = $6660.17 - $6405 = $255.17
Deficit = $255.17
3) They decide to stop putting money in savings. How much their balance be?Savings = 10% of income = 10% OF $6405
Savings = (10/100)· $6405 = $640.5
New total expenses = $6660.17 - $640.5
New total expenses = $6019.67
Balance = Total income - New total expenses = $6405 - $6019.67
Balance = $295.33
4) Do you agree with them removing the savings to create surplus?
Yes, they had to remove the savings to fulfill their expenditures. Otherwise, they would have been spending more than their income, which couldn't last very long
What is the value of 2x3+12-13
Answer:
5
Step-by-step explanation:
According to PEMDAS the answer is five.
2x3+12-13
6+12-13
18-13
5
you don't have to answer number 15. but pls answer the rest!
is 3kg equal to less than or greater than 3,000
there are more in the picture pls help ASP
BEST ANSWER GETS BRAINLESST AND FOLLOW ASP HURRY!!
Answer:
13) >
14)=
15)>
16)=
17)>
18)<
Step-by-step explanation:
how do you solve the height?
Answer:
If you know the base and area of the triangle, you can divide the base by 2, then divide that by the area to find the height. To find the height of an equilateral triangle, use the Pythagorean Theorem, a^2 + b^2 = c^2.
im really tired and my brain isnt working right please help i need help with part b
Answer:
hello! the answer is 2.5 hours :)
Answer:
the answer is 2.5 hours
Step-by-step explanation:
I’m confused :( I will mark as Brainliest and give you points
Answer:
123.5 square inches
Step-by-step explanation:
Given: To find the area of a rectangle, you have to multiply base times height.
To find the area of a triangle, you have to do base times height devided by 2.
Finding the area: Let's break up this shape into polygons. At the bottom there is a rectangle. We know that to find the area of the rectangle you have to do base times height. 13in•7in will give you 91in square for the rectangle.
Now for the triangle. If you can see, if you break the triangle in half, there are 2 right triangles. Let's look at the right one for now. Since we know that to find the area of a triangle you have to do base times height divided by 2, you do 5in•6.5in=32.5in. 32.5in divided by 2 is 16.25in square which is the area of one triangle. You might be wondering why i did 5•6.5, and that's because at the bottom of the rectangle you can see it's 13in, and 13in÷2=6.5in.
We already found the area of the rectangle and one triangle. The other triangle is equal to it so we can just do 16.25+16.25=32.5in square for both of the triangles.
Now we add it all up: 32.5+91=123.5 square inches
The area of a triangle is 30 square inches. The base of the triangle is 10
in. What is the height of the triangle? *
I will mark as Brainliest and give extra points help
Answer:
6 inches
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
30 = 1/2 (10) h
30 = 5h
Divide each side by 5
30/5 = 5h/5
6 = h
Answer:
Step-by-step explanation:
we know area of a triangle = 1/2 * base * height
1/2*10* height = 30
5* height =30
height = 30/5 = 6inches
hope it helps
b) A fruit seller bought some mangoes for Rs 500. He sold them at 10% loss. If he wants to make a profit of 12.5% without increasing the selling price, by how much should the cost price of the mangoes be reduced?
Answer:
New CP = Rs 387.5
Step-by-step explanation:
Cost Price = Rs. 500
Loss %age = 10% of 500
So, Loss = Rs 50
Finding the selling price:
Selling Price = CP - Loss
SP = 500 - 50
SP = Rs 450
Now, The fruit seller wants to gain a profit of 12.5% without changing the selling Price:
Firstly, Let's talk about the Profit :
Profit %age = 12.5% of 500
Profit = 12.5 * 5
Profit = Rs 62.5
He wants to gain a profit of Rs 62.5
So, The cost Price
The cost price would be reduced by Rs 62.5
New CP = 450 - 62.5
New CP = Rs 387.5
The diagram shows a circle centre O work out the size of angle X work out the size of angle y
Answer:
x = 116° , y = 20°
Step-by-step explanation:
The angles are x = 116° & y = 20°
what is the circle theorem?When two angles are subtended by the same arc, the angle at the centre of a circle is twice the angle at the circumference i.e ∠O=2∠A
let the Points on the circumference be A,B,C then we have two traingles namely ΔABC & ΔOBC.
Given here ∠A=58°
therefore, by the circle theorem we get ∠O=116°
Again in ΔOBC it is a isosceles triangle with its two sides equal to the radius of the circle, so ∠OBC = ∠OCB
∠OCB +∠OBC+∠BOC=180°
2 ∠OBC=180°-116°
2 ∠OBC=64°
∠OBC=32°
Again, in ΔABC ∠C = 32° + 38° = 70° & ∠B= y +32°
therefore, y + 32° + 70° + 58° = 180°
y= 20°
Hence, the angles are x = 116° & y = 20°
Learn more about the circle theorem:
https://brainly.com/question/19906313
#SPJ5
T&L - Math 7 - Volume 7.4 -19-20
Directions: Type your answer in the box below
A cube with an edge length of 8 must be filled completely. How many cubic centimeters will
be needed? Type your answer in the box
The diameter and height of a cylindrical container are shown.
Answer: You would need 512 cubic centimetres
Step-by-step explanation: The first approach to this question would be to understand the properties of the shape given in the question.
If a cube has an edge with length 8 cm, then all edges measure 8 cm as well. That is one property of a cube. Hence, the length, width and height all measure 8 cm each.
The volume of a cube is given as follows;
V = L x W x H (and the answer is expressed as V³)
Since the length , width and height all measure 8 cm, the volume can simply be expressed as
V = L x L x L
V = L³
V = 8³
V = 512 cm³
Therefore to completely fill a cube with edge length of 8 cm you would need 512 cubic centimetres.
what’s 38,000 * 16 please help me
Answer:
608,000
Step-by-step explanation:
Using the following image, solve for x
Step-by-step explanation:
Vertical angles are always equal
4+6x= 70°
6x =70-4 = 66°
x= 11°
We know the angles have a vertical angle and we know that vertices angle are Intercept lines.
Let's set up the equation.
[tex]4+6x=70[/tex]
We will subtract 4 from both sides and get
[tex]6x=66[/tex]
Divide by 6 on both sides
[tex]x=11[/tex]
How much would 1 case of each fruit cost together? Grid in tori answer as dollars.cents
Answer:
35.00
Step-by-step explanation:
4a+8p=220
2a+5p=130
if we want to add them we must multiply the 2nd equation by -2
4a+8=220
-4a-10p=-260
0=20
after plugging 20 in, the apples should cost 15
15+20=35
If 15 x a = 90, then a=
Answer:
A = 6
Step-by-step explanation:
to find a, divide 90 by 15
90 / 15 = 6