Answers
Answer:
$321562.50
Step-by-step explanation:
Exponential growth can be modeled by the formula [tex]y = a(1+r)^{x}[/tex] , with y representing the final value, a being the starting value, r being the growth rate, and x being the number of time intervals passed.
To figure out the rate, we must use the values given from the months we have data of. Our starting value is 60,000 , ending value is 105,000 , and given that monthly sales are given, we can assume that sales grew exponentially each month. There were 4 years, or 48 months, that the store had to grow. Our formula is thus
[tex]105000 = 60000(1+r)^{48}\\[/tex]
To solve for r, we can first divide both sides by 60,000 , then put each side to the power of 1/48, resulting in
[tex]105000/60000 = (1+r)^{48}\\1.75 = (1+r)^{48}\\\\1.75^{1/48} = 1+r[/tex]
Since we know our rate, and there are 8 years/96 months between January 2005 and January 2013, we can make our starting value 105,000 , plug (1.75)^(1/48) for r and 96 for x in [tex]y = a(1+r)^{x}[/tex], and go from there.
Our final value is then
[tex]y = 105000(1.75^{1/48})^{96}\\y = 105000(1.75^{2})\\y = 321562.5[/tex]. We were able to turn 1.75^(1/48)^(96) into 1.75² using the exponent rule stating that x^y^z = x^(y*z)
Related Questions
Please help me on this question
Answers
Answer:
8π
Step-by-step explanation:
A=180/360×π(4^2)
A=1/2×16π
A=8π
Find the different between compound interest payable anually and half anually for a amount Rs14000 at the rate of 12•\•per annum for 2 yrs.
Answers
Answer:
$113.08
Step-by-step explanation:
The formula for calculating future value:
FV = P (1 + r/m)^mn
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
14,000(1.12)^2 = 17,561.60
14,000 ( 1 + 0.12/2)^(2x2) = 17674.68
Difference : 17674.68 - 17,561.60 = $113.08
13. Which equation represents the line that passes through the point (4,-5) and is
perpendicular to y = 1/2x + 8?
Answers
Answer:
y = - 2x + 3
Step-by-step explanation:
since the line passing through ( 4, - 5 ) is perpendicular to y = 1/2 x + 8, product of the slope of the lines will be - 1.
That is ,
[tex]m_1 \times m_ 2 = - 1[/tex] [tex][ \ where \ m_ 1 = \frac{1}{2} \ ][/tex]
[tex]\frac{1}{2 } \times m_2 = - 1 \\\\m_ 2 = -1 \times 2 = -2[/tex]
Find the equation the line perpendicular to the given line :
[tex]( y - y_2 ) = m_ 2 ( x - x_ 2 ) \ , [ \ where \ (x_2 , y_2 ) = ( 4 , -5 ) \ ][/tex]
[tex]( y - ( -5)) = -2 ( x - 4)\\\\( y + 5 ) = - 2 x + 8\\\\y = -2x + 8 - 5 \\\\y = -2x + 3[/tex]
Select the elements in H.
Let H = {cube numbers}
A-8
B-49
C-3
D-125
E-1
F-100
G-25
H-12
Answers
Answer:
H={8,125,1}
Step by step explanation:
8 is the cube of 2125 is the cube of 51 is the cube of 125 points ! :)
Can anyone solve this ? with explanation?
[tex]A brick of weight 20N and dimensions 20 cm x1Ocm x Scm is placed once on its largest surface area and then on its smallest surface area on the ground. Find out the ratio of the pressure exerted by the brick.}}[/tex]
Answers
Answer:
1 : 4
Step-by-step explanation:
[tex]Pressure = \frac{F}{A}[/tex]
[tex]P_1 = Pressure \ on \ the \ largest \ surface \ area[/tex]
[tex]=\frac{F}{20 \times 10 \times 20}[/tex]
[tex]P_2 = Pressure \ on \ small \ surface \ area[/tex]
[tex]=\frac{F}{20 \times 10 \times 5}[/tex]
[tex]\frac{P_1 }{P_2 }= \frac{20 \times 10 \times 5}{20 \times 10 \times 20} = \frac{5}{20} = \frac{1}{4}[/tex] [tex][ \ \ \frac{F}{20 \times 10 \times 20}\ \div\ \frac{F}{20 \times 10 \times 5} => \frac{F}{20 \times 10 \times 20} \times \frac{20 \times 10 \times 5}{F} \ ][/tex]
Therefore ,
[tex]P_1 : P_2 = 1 : 4[/tex]
The dimensions of the brick are :
20 cm10 cm5 cmSolution :[tex]\large\boxed{\boxed{\mathrm{pressure = \frac{Force}{Area}}}}[/tex]
The largest surface area would be : -
[tex]➢ \: \: 20 \times 10[/tex]
[tex]➢ \: \: 200 \: \: cm {}^{2} [/tex]
[tex]➢ \: \: 0.02\: \: m {}^{2} [/tex]
(product of two greater sides)
pressure applied by greatest surface area of brick :
[tex]➢ \: \: \dfrac{20}{0.02} [/tex]
[tex]➢ \: \: \dfrac{20}{2} \times 100[/tex]
[tex]➢ \: \: 1000 \: \: pascals[/tex]
The smallest surface area would be : -
[tex]➢ \: \: 10 \times 5[/tex]
[tex]➢ \: \: 50 \: \: cm {}^{2} [/tex]
[tex]➢ \: \: 0.005 \: \: m {}^{2} [/tex]
(product of two Smaller sides)
pressure applied by smallest surface area of brick :
[tex]➢ \: \: \dfrac{20}{0.005} [/tex]
[tex]➢ \: \: \dfrac{20}{5} \times 1000[/tex]
[tex]➢ \: \: 4000 \: \: pascals[/tex]
Let's find the ratio :
[tex]➢ \: \: \dfrac{1000}{4000} [/tex]
[tex]➢ \: \: \dfrac{1}{4} [/tex]
[tex]➢ \: \: 1 : 4[/tex]
[tex]\mathrm{✌TeeNForeveR✌}[/tex]
Help mark complete the pairs of expressions
Answers
if u do the equation on the calculator for the equation C,u will get the B
which statement is true regarding the functions on the graph?
Answers
Answer:
where's the graph?
Step-by-step explanation:
Answer:
f(2) = 0 and g(2) = 0
f(2) = g(2) TRUE
b) f(0) = 2 and g(0) = -2
f(0) = g(0) FALSE
c) f(2) = 0 and g(0) = -2
f(2) = g(0) FALSE
d) f(0) = 2 and g(2) = 0
f(0) = g(2) FALSE
Which property of exponents must be used first to solve this expression? (iy2)1/3
Answers
Step-by-step explanation:
"must be used first" is a very hard phrasing. multiplication is commutative.
and I am not sure that the problem is stated correctly.
I read here
(i×y²) to the power of 1/3.
i is the imaginary constant sqrt(-1) ?
exponents brought themselves to the power of something else multiply.
e.g.
[tex]({2}^{3})^{4} = {2}^{12} [/tex]
exponents in multimedia expressions of the same base simply add up.
e.g.
[tex] {2}^{3} \times {2}^{4} = {2}^{7} [/tex]
a negative exponent means that the expression with the same positive exponent is just at the bottom of a division.
e.g.
[tex] {2}^{ - 3} = 1 \div {2}^{3} [/tex]
and a fraction as exponent specifies a root to be taken.
e.g
[tex] {2}^{1 \div 3} = \sqrt[3]{2} [/tex]
so, I would do all the exponent multiplications to simplify the expression.
[tex] \sqrt[3]{i \times {y}^{2} } = ({i \times {y}^{2} })^{1 \div 3} = [/tex]
[tex] = ( { - 1}^{1 \div 2} \times {y}^{2} ) ^{1 \div 3} [/tex]
1/2 × 1/3 = 1/6
2 × 1/3 = 2/3
[tex] = { - 1}^{1 \div 6} \times {y}^{2 \div 3} = \sqrt[6]{ - 1} \times \sqrt[3]{ {y}^{2} } [/tex]
so, as we can see, we can move freely from multiplying the fraction exponents to converting them into root expressions and vice versa.
A sick person takes 10 ml of medicine three times a day how much medicine does the person take in 15 days
Answers
Answer:
450 mL
Step-by-step explanation:
Given that :
Amount in mL of medicine taken at a time = 10mL
Number of times taken per day = 3 times
Amount in mL taken per day = 3 * 10mL = 30mL
Total amount in mL of medicine taken in 15 days :
Amount in mL taken per day * 15 days
= 30mL * 15
= 450mL
Answer 2 questions about equations A and B.
A. 5x−2+x=x-4
B. 5x+x=x−4
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Add/subtract a quantity to/from only one side
(Choice B)
B
Add/subtract the same quantity to/from both sides
(Choice C)
C
Rewrite one side (or both) using the distributive property
(Choice D)
D
Rewrite one side (or both) by combining like terms
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
Answers
Step-by-step explanation:
Given that,
Two equations,
A. 5x−2+x=x-4
B. 5x+x=x−4
1.
The RHS of both the equations is same. To make them equal we need to remove the difference.
If we add 2 to the left side of equation A, then we get equation B.
The correct option is (A) i.e. Add/subtract a quantity to/from only one side.
2.
As the equations are not same, they will have different solutions. The answer choice is (b) "No".
Hey There Answer Add/subtract a quantity to/from only one side
And No
Step-by-step explanation:
how long is each side of a square with a perimeter of 12.32 centimeters
Answers
Step-by-step explanation:
Let each side of square be x
So, x+x+x+x = 12.32
4x = 12.32
x = 12.32/4
x = 3.02 cm
I need help with my math! Can you please help me!!
Answers
Answer:
[tex]y=-|x-1|+3[/tex]
Step-by-step explanation:
The graph of the function ([tex]y=|x|[/tex]) can be described as a perfect (v) shape composed of two lines with the equation ([tex]y=x[/tex]) and ([tex]y=-x[/tex]) with a range of ([tex]y\geq 0[/tex]). In the depicted graph, this function has undergone some transfomrations. The general format for a transformation of an absolute value function is the following;
[tex]y=(+-)n|x-k|+h[/tex]
The function can be inverted if the sign of (n) is (-). As per the given graph, the function is inverted, thus the answer will have a (-) sign in front of it. One can see that the (n) value has to be (1) or rather not present since the function has no scaling factor.
[tex]y=-|x|[/tex]
The function has been shifted (k) units to the right, one can see that the given function's vertex is (1) unit to the right, thus the equation of the function has a (1) in the position of (k).
[tex]y=-|x-1|[/tex]
The function is shifted (3) units up, thus the position of (h) is occupied by a (3).
[tex]y=-|x-1|+3[/tex]
Therefore the following answer choice is correct, as it fits all of the requirements;
[tex]y=-|x-1|+3[/tex]
Help i dont know what this is
Answers
Answer:
Use a permitation :D
P(4,2)= 4x3=12
D, 1/12
What is true about the sides of KNM?
KN = NM
KN + NM = KM
KM = 2(NM)
KN = One-halfKM
Answers
Answer:KN = NM
Step-by-step explanation:
you desperate anyways that’s why you here
Answer:
its the first one
Step-by-step explanation:
i did it
please mark me brainliest
6. Find the slope and y-intercept of the line.
y = 7/4x-10
Answers
Answer:
Slope= 7/4
y-intercept = (0, -10)
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify
y = 7/4x - 10
↓ Compare to y = mx + b
Slope m = 7/4
y-intercept b = -10
Answer:
slope = 7/4
y-intercept = -10
Step-by-step explanation:
slope intercept form :
y = mx + b
m = slope
b = y-intercept
Simplify Negative two and one-third minus negative ten and one-sixth
Answers
Answer:
7 5/6
Step-by-step explanation:
-2 1/3 - (-10 1/6)
-7/3 + 61/6 (subtract neg = add positive)
-14/6 + 61/6 = 47/6 = 7 5/6
Answer:
[tex]-2\frac{1}{3} - (-10\frac{1}{6} )[/tex]
Minus minus is plus so:
[tex]-2\frac{1}{3} + 10\frac{1}{6} [/tex]
Make improper:
[tex]-\frac{7}{3} + \frac{61}{6} [/tex]
Common denominator:
[tex]-\frac{14}{6} + \frac{61}{6} [/tex]
Equals=
[tex]\frac{47}{6} [/tex]
Solve for x. (have to add extra letters so the question works)
PLEASE ADD STEPS AND EXPLAIN IT IN ANY WAY POSSIBLE SO I CAN LEARN
Answers
Answer:
x=11°
Step-by-step explanation:
-Sum of angles of a triangle should alway be 180 degrees
35+110+2+3x=180
-Add all known values
147+3x=180
-Subtract 147 from both sides
3x=33
-Isolate x by divind both sides by 3
x=11°
Use the law of cosines to find the length of a
Answers
Answer:
Step-by-step explanation:
You don't need the Law of Cosines, the Law of sines if what you need. You can't use the Law of Cosines because in order to find side a, you would need the length of side c and you don't have it. Using the Law of Sines is appropriate, knowing that angle B = 55:
[tex]\frac{sin55}{175}=\frac{sin42}{a}[/tex] and solving for a:
[tex]a=\frac{175sin42}{sin55}[/tex] so
a = 143.0
(6x+15)°
63° triangle
Answers
Answer:
x = 2
Step-by-step explanation:
The sum of the 3 angles in the triangle = 180°
Sum the 3 angles and equate to 180
6x + 15 + 90 + 63 = 180
6x + 168 = 180 ( subtract 168 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
What is the measure of each exterior angle of a regular hexagon?
40°
45°
60°
72°
Answers
The measure of each exterior angle of a regular hexagon ( six sided regular polygon is 60°.
Option C)60° is the correct answer.
What is a polygon?A polygon is simply a two-dimensional a plane shape enclosed by line segments called sides.
The formula for calculating the exterior angles of a polygon is;
E = 360° ÷ number of sides
Given the data in the question;
The polygon in question is a regular hexagonA regular hexagon has six sides, n = 6So we substitute the value for number of sides into the expression above.
E = 360° ÷ number of sides
E = 360° ÷ 6
E = 60°
The measure of each exterior angle of a regular hexagon ( six sided regular polygon is 60°.
Option C)60° is the correct answer.
Learn more about polygons here: brainly.com/question/22408868
#SPJ2
Answer: (C) 60°
Just took it on edge
what do i put for y and x , need help asap!!!
Answers
For ex- y = -1 and x = -3
AT&T has a family plan of four lines for $125 and additional lines are $15 each per month. If Jason wants to spend at most $200 per month on cell phone expenses, how many additional lines can he afford? Which inequality represent the given situation. please help for my final
Answers
Given:
Cost of four lines = $125
Cost of each additional line = $15
Jason wants to spend at most $200 per month on cell phone expenses.
To find:
The inequality for the given situation.
Solution:
Let [tex]x[/tex] be the number of additional line.
Cost of one additional line = $15
Cost of [tex]x[/tex] additional line = [tex]\$15x[/tex]
Total cost = Fixed cost + Addition cost
= [tex]125+15x[/tex]
It is given that Jason wants to spend at most $200 per month on cell phone expenses. It means the total cost must be less than or equal to 200.
[tex]125+15x\leq 200[/tex]
Therefore, the correct option is C.
)) A farmer placed an order for 16 2/3 tons of fertilizer. He calculates that the corn fields
will require 8 5/6 tons of it. How much fertilizer will the farmer have left for his other crops?
Answers
Answer:
7 5/6
Step-by-step explanation:
16 2/3 - 8 5/6
16 4/6- 8 5/6
7 5/6
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
I really need help :(
Answers
Answer:
Value of x = 3√2 unit
Step-by-step explanation:
Given:
Hypotenuse of given triangle = 6 unit
Length of equal side = x units
Find:
Value of x
Computation:
Using pythagorean theorem
Hypotenuse² = Perpendicular² + Base²
Hypotenuse of given triangle² = Perpendicular² + Base²
6² = x² + x²
36 = 2x²
x² = 36/2
x² = 18
x = √18
x = 3√2
Value of x = 3√2 unit
Triangle AEB is similar to triangle CBD by
Answers
Answer:
SAS
Step-by-step explanation:
Based on your observations, what conclusion can you draw about the lengths of AB DB AE EC
Answers
Answer:
The ratio of AD to DB is equal to the ratio of AE to EC. In other words, the pairs of lengths are proportional.
Step-by-step explanation:
Sample answer from plato
which graph shows the solution to this system of linear inequalities?
Answers
Answer:
c or b
tep-by-step explanation:
can someone answer my question.........
Answers
Answer:
Rhombus
Energy used
Step-by-step explanation:
A rhombus is formed fromm the intersection, since the stick have equal length, Hence, all the sides will be equal and the opposite side will be parallel.
If a person exercises more and more, more energy is utilized, the dependemt variable here is the amount of energy utilized because it is the measured variable whose value is based on the amount or level of exercise the body is subjected to. The amount of exercise is the dependent variable as it gives influences the amount of energy expended
The profit for a car company can be represented by the function P=−0.5 x² +4 x+ 12,
where P is the profit in hundred thousands of dollars and x represents the number of cars sold in thousands. What is the maximum profit the company can make?
Answers
Answer:
3x+12
Step-by-step explanation:
-0.5x*2+4x+12
Multiply 0.5x*2=x
= -x+4x+12
Add similar elements -x+4x+12
= 3x+12
y <= - 1/3 * x + 2; y > 2x - 3 linear inequalities
Answers
Step-by-step explanation:
Given
Inequalities are [tex]y\leq -\dfrac{1}{3}x+2[/tex] and [tex]y>2x-3[/tex]
Take the inequality as two equations to get the intersection point
[tex]y=-\dfrac{1}{3}x+2\ and\ y=2x-3[/tex]
Equate the value of y
[tex]\Rightarrow -\dfrac{1}{3}x+2=2x-3\\\Rightarrow 5=\dfrac{7x}{3}\\\\\Rightarrow x=\dfrac{15}{7}[/tex]
[tex]\therefore y=1.286[/tex]
The common region gives the required regions for inequalities.