The interest earned on a [tex]$\$ 50,000$[/tex] deposited for 6 years at [tex]$4\frac{1}{8 }\%$[/tex] in compounded continuously is [tex]$\$ 14040.97$[/tex].
Continuous compounding is the mathematical limit of the number of periods across which compound interest can be calculated and reinvested into the account balance. Although it is impractical, the concept of endlessly compounded interest is important in finance. This is an extreme example of compounding because most interest is compounded on a monthly, quarterly, or semiannual basis.
The given amount is [tex]$\$ 50,000$[/tex].
It will be deposited for 6 years.
With [tex]$4\frac{1}{8 }\%$[/tex] interest,
The formula for compounded continuously is
[tex]$$\begin{aligned}&A=P e^{r t} \\&P=50000 \\&r=4 \frac{1}{8}=\frac{33}{8}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}r &=0.04125 \\t &=6\end{aligned}$$[/tex]
Substitute all the values
[tex]$$\begin{aligned}&A=50000 e^{0.04125 \times6} \\&A=50000 e^{0.2475} \\&A=50000\times 1.28081\\&A=64040.96811\end{aligned}$$[/tex]
[tex]$\mathrm{I}=\mathrm{A}-\mathrm{P}$[/tex]
Interest [tex]$=64040.96811-50000=14040.9681$[/tex]
Hence, Interest [tex]$=\$ 14040.97$[/tex]
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Some values of linear functions A and B are shown in the table and graph.
Which of the following describes the intercepts of the two functions?
A
The y−y-y−intercept of Function A is equal to the y−y-y− intercept of Function B.
B
The y−y-y−intercept of Function A is 111 unit less than the y−y-y− intercept of Function B.
C
The y−y-y−intercept of Function A is 111 unit greater than the y−y-y− intercept of Function B.
D
The y−y-y−intercept of Function A is 222 units greater than the y−y-y−intercept of Function B.
Answer:
C) The y-intercept of Function A is 1 unit greater than the y-intercept of Function B
Step-by-step explanation:
The y-int of Function A is (0,1), while the y-int of Function B is (0,0).
Answer:
C
Step-by-step explanation:
For Function A, the y-intercept occurs at 1. For B, it occurs at 0. Therefore, the y-intercept of Function A is 1 unit greater than the y-intercept of Function B.
At a store, apples cost $0.80 each and oranges cost $0.95 each. Harry buys some apples and oranges and spends $9.55 . He buys a total of 11 pieces of fruit.
A system of linear equations to describe this situation is given by:
A + O = 11.
0.80A + 0.95O = 9.95.
Harry bought six (6) apples and five (5) oranges from this store.
How to write a system of linear equations?In order to write a system of linear equations to describe this situation, we would assign variables to the amount of apples and oranges respectively, and then translate the word problem into algebraic equation as follows:
Let the variable A represent the amount of orange Harry bought.Let the variable O represent the amount of apple Harry bought.Since Harry bought a total of 11 pieces of fruit, we have:
A + O = 11 .....equation 1.
Since the cost of apples is $0.80 each and oranges cost $0.95 each, we have:
0.80A + 0.95O = 9.95 .....equation 2.
Part B.From equation 1, we have:
O = 11 - A .....equation 3.
Substituting equation 3 into equation 2, we have:
0.80A + 0.95O = 9.95
0.80A + 0.95(11 - O) = 9.95
Apples, A = 0.90/0.15
Apples, A = 6.
For the number of oranges, we have:
Oranges, O = 11 - A
Oranges, O = 11 - 6
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Complete Question:
At a store, apples cost $0.80 each and oranges cost $0.95 each. Harry buys some apples and oranges and spends $9.55 . He buys a total of 11 pieces of fruit.
Part a. Write a system of linear equations to describe this situation.
Part b. How many of each fruit did Harry buy?
solve for x
m = -12bx - 3 + 9x
3. An object is launched at 190.6 meters per second (m/s). The equation for the object's height
s at time t seconds after launch is s(t) = -4.9t^2 + 190.6t + 58.8, where s is in meters.
a. What was the initial height of the object?
b. At what time will the object first hit the ground?
c. What was the maximum height reached by the object?
Considering the quadratic equation, it is found that:
a) The initial height of the object is of 58.8 meters.
b) The object first hits the ground after 39.2 seconds.
c) The maximum height reached by the object is of: 1912 meters.
What is the quadratic equation?The quadratic equation that models the projectile's height is defined as follows:
s(t) = -4.9t² + 190.6t + 58.8.
Which has the coefficients given as follows:
a = 4.9, b = 190.6, c = 58.8.
The initial height is obtained as follows:
s(0) = -4.9(0)² + 190.6(0) + 58.8 = 58.8 meters.
It hits the ground at the positive root for which s(t) = 0, hence, using a quadratic equation calculator, this root is of:
t = 39.2 seconds.
The maximum height obtained by the object is the y-coordinate of the vertex, hence:
hMAX = -(b² - 4ac)/4a = -(190.6² - 4(-4.9)(58.8))/(4(-4.9)) = 1912 meters.
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The graphs below have the same shape. f(x)=x2².
What is the equation of the graph of g(x)?
O A. g(x)=x²+2
OB. g(x)=(x-2)²
O C. g(x)=x2²-2
OD. g(x) = (x + 2)²
According to the concept of translation, the function of g(x) = x² + 2.
Translation:
The concept of translation is defined by using the function f(x) then f(x + a) is a horizontal translation of f(x)
If the value of a > 0 then a shift to the left of a units
If the value of a < 0 then a shift to the right of a units
Given,
Here we have the function f(x) = x².
Now, we have to find the equation of the graph of g(x) and how it change in corresponds to f(x).
While we looking the graph, the function f(x) has curved on the origin (0, 0).
Where the function g(x) has curved the point (2,0).
Which tells the the graph is move left side by 2 units.
So, according to the rule of translation, the value of a is 2.
Then the function g(x) is written as,
=> g(x) = x² + 2.
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[dd] meaning in mathematics
Answer:
Roman numeral representing thousand (1000)
I need h e l p
△ABC has a right angle at C, BC=9.2 centimeters, and m∠A=63∘.
What is CA ?
Enter your answer rounded to the nearest tenth in the box.
Answer:
17.8
Step-by-step explanation:
You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3
What is 247.968 rounded to the nearest cent
Answer: 247.97
Step-by-step explanation:
The nearest cent is two decimal places.
Simplify this expression. If the answer contains exponents, all exponents should be positive.
Answer:
below
Step-by-step explanation:
(7p^9)^-4 a negative exponent means move the number up or down in the fraction
= 1 / [ (7 p^9) ^4 ]
= 1 / ( 7^4 p^36) = 1/(2401 p^36) <===don't omit the parentheses!
Can you please help me
A number line which represents the given inequality (-1 ≥ x) is: number line C.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Next, we would determine a solution for the given inequality (-1 ≥ x) in order to graph it on a number line:
-1 ≥ x
x ≤ -1
In conclusion, we can logically deduce that the value of x is less than or equal to -1 as shown in number line C, which is shaded because of the less than or equal inequality symbol.
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Find how many quarts of 5% butterfat milk and 2% butterfat milk should be mixed to yield 90 quarts of 3% butterfat milk.
The mixture should contain ___ quarts of the 5% butterfat milk.
Answer:
The mixture should contain 30 quarts of the 5% butterfat milk.Step-by-step explanation:
Let the required amount of 5% milk is x quartz, then the amount of 2% milk is 90 - x quartz.
Set equation for the fat content:
5% of x + 2% of (90 - x) = 3% of 900,05x + 0.02(90 - x) = 0.03*900.05x + 1.8 - 0.02x = 2.70.03x = 2.7 - 1.80.03x = 0.9x = 0.9/0.03x = 30while exploring a volcano, Zane heard some rumbling, so he decided to climb up out of there as quickly as he could.
Zane's elevation relative to the edge of the inside of the volcano (in meters) as a function of time (in seconds) is graphed.
The time that it took Zane to reach the edge of the volcano is of:
35 seconds.
Where is the edge of the volcano?The variables that are graphed in this problem are listed as follows:
x-axis: Time.y-axis: Elevation relative to the volcano.The edge of the volcano is the point at which the elevation relative to the volcano is of 0, hence the coordinate is:
y = 0.
y = 0 is the x-intercept of the function, which is the value of x at which the function crosses the x-axis.
Hence, looking at the graph, the time that it took Zane to reach the edge of the volcano is of:
35 seconds.
(as 35 is the x-intercept of the graph, and we previously explained that the edge of the volcano is the x-intercept).
Missing informationThe question is:
How long did it take Zane to reach the edge of the volcano?
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The length of a rectangle is five times its width.
If the area of the rectangle is 245 ft^2 , find its perimeter.
Answer:
P = 84
Step-by-step explanation:
Area = length* width or A = lw
We know that the length is 5 times its width which can also mean
[tex]l = 5*w[/tex] or [tex]l=5w[/tex]
Use the formula for area and replace [tex]l[/tex] with [tex]5w[/tex] and the total area with 245
[tex]A = lw\\245=5w(w)[/tex]
Multiply:
[tex]245=5w^{2}[/tex]
Divide by 5
[tex]49=w^2[/tex]
Square root of [tex]w^2[/tex]
[tex]\sqrt{49}=\sqrt{w^2}[/tex]
Simplify
[tex]7=w[/tex]
Now that we know w = 7 we can input this into the Perimeter formula
(P = 2l +2w)
P = 2(5*7)+2(7) // Note: Remember [tex]l[/tex] = 5*w and w = 7
P = 84
There is also a formula for this type of problem, but this explanation is for when you forget. Hope that explains things :)
Weekend: The product of the two numbers is 144 and their difference is 10. What is the sum of the two numbers?
Answer:
There are two pairs of numbers:
-8 -18
and
18 8
Step-by-step explanation:
a * b = 144 EQ. 1
a - b = 10 EQ. 2
From EQ. 2:
a = 10 + b EQ. 3
Replacing EQ. 3 in EQ. 1:
(10+b)b = 144
10*b + b*b = 144
b² + 10b - 144 = 0
b = {-10±√((10²)-(4*1*-144))} / (2*1)
b = {-10±√(100+576)} / 2
b = {-10±√676} / 2
b = {-10±26} / 2
b₁ = {-10-26} / 2 = -36/2 = -18
b₂ = {-10+26} / 2 = 16/2 = 8
a₁ - b₁ = 10
a₁ - (-18) = 10
a₁ + 18 = 10
a₁ = 10 - 18
a₁ = -8
a₂ - b₂ = 10
a₂ - 8 = 10
a₂ = 10 + 8
a₂ = 18
Check:
a₁ * b₁ = -8 * -18 = 144
a₂ * b₂ = 8 * 18 = 144
The plates that Mom bought are very fragile and expensive. She paid $16.68 per plate and there are eight plates. How much money did she spend on the plates? Show work.
The money spent on the plates which are very expensive is: $133.44
Given,
The plates that mom bought are very fragile and expensive.
Each plate costs $16.68.
Total plates bought by her mom are = 8
we are asked to determine the total cost of the plates bought = ?
let y represent the total cost of the plates.
and x represent the number of plates bought.
based on the conditions, we can formulate:
total cost pf plates = 16.38(number of plates bought)
⇒ y = 16.68x
we know that plates bought = 8
⇒ total cost is:
⇒ y = 16.68(8)
⇒ y = 133.44
Hence total cost of 8 plates is $133.44
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Help answer this question
Write down an expression in terms of x, for the area of this trapezium.
x cm
8 cm
(3x + 2) cm
The area of the given trapezium is 16x + 8
Area of trapezium:
The general formula to calculate the area (A) of a trapezium is written as,
A = ½ (a + b) h where,
where
a, b = bases of trapezium, and,
h = height
Given,
Here we have the figure of trapezium and the measures are written in it.
Now, we have to find the area of the trapezium.
According to the formula of the area of the trapezium,
We need the value of base and height.
By looking into the given figure, we have identified the value of
a = x cm
b = 3x + 2 cm
h = 8 cm.
Then the area of the trapezium is calculated as,
A = ½ (x + (3x +2)) 8
A = ½ (4x + 2) 8
A = 4 (4x + 2)
A = 16x + 8
Therefore, the area of the trapezium is 16x + 8.
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Find the local maximum of the function.
2.
f(x)=2x3+15x2−36x+1
Please help! Thank you :D
The minimum and maximum of the function f(x)=2x³+15x²-36x+1 are 38 and 39 respectively
The maximum value of a function f(x) is also called the absolute maximum value, or the greatest value of the function f on the closed interval [0, 1]. on the other hand, the minimum value of f(x) at x = 0 is called the absolute minimum value, or least value of the function f on the closed interval [0, 1)
How to find the minimum and maximum functions?
From the function f(x) = 2x3 − 15x2 + 36x + 1.
Using differential calculus , dy/dx = 6x2 - 30x + 36
= 6(x2 - 5x + 6)
f(x) is a maximum when x = 2 and the maximum value of f(x) = f(2).
This implies that f(2) = 2(23) − 15(22) + 36(2) + 11 = 39
d2y/dx2|x=3 = 12 x 3 - 30 = 6 > 0
This also implies that f(x) is a minimum when x = 3 and the minimum value of f(x) = f(3) = 2(3)3 − 15(3)2 + 36(3) + 11 = 38
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Round 8.879 to the nearest tenth.
Round 8.879 to the nearest tenth is 8.9.
Rounding to the nearest tenth:
The combination of a whole number and a fraction, separated by a decimal point, is known as a decimal number in mathematics. The place value of the digits is divided by 10 starting from left to right. Determining the place values of tenths, hundredths, and thousands will therefore be aided by the decimal place value. For instance, the definition of the place value tenth is 1/10.
Think about the decimal 12.345.
Tenth place value in this case is 3.
By substituting the actual number with an approximation, the decimal value can be rounded. To the nearest integer, the decimal number 5.8 is rounded to 6, for instance. The decimal number can also be rounded to the nearest tenths place value. The first integer that appears after the decimal point is the tenth place value. Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.
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At a music store in New York City, 70 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 70, 18 chose rock, 20 chose
country, 8 chose classical and 24 chose something other than rock, country, or classical.
a) Determine the empirical probability that the next person entering the store favors rock music.
b) Determine the empirical probability that the next person entering the store favors country music.
c) Determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music
a) The empirical probability that the next person entering the store favors rock music is
(Simplify your answer.)
b) The empirical probability that the next person entering the store favors country music is
(Simplify your answer.)
c) The empirical probability that the next person entering the store favors something other than rock, country or classical music is
The probability of the person favoring rock music is 0.257, favoring country music is 0.285, and favoring something other than rock, country, or classical music is 0.342.
Given that:
Total people = 70
Chose rock = 18
Chose country = 20
Chose classical = 8
Chose something other than rock, country, or classical = 24
a) The empirical probability that the next person entering the store favors rock music is = Total people choosing rock music/ Total people
= 18/70 = 9/35 = 0.257
b) The empirical probability that the next person entering the store favors country music is = Total people choosing country music/ Total people = 20/70 = 2/7 = 0.285
c) The empirical probability that the next person entering the store favors something other than rock, country, or classical music is = Total people choosing something other than rock, country, or classical music/ Total people = 24/70 = 12/35 = 0.342.
Hence, the empirical probability that the next person favors rock music is 0.257, favors country music is 0.285, and favors something other than rock, country, or classical music is 0.342.
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find a function whose graph is a parabola with vertex (-3,-9) and that passes through the point (-2,-6)
your answer is f(x)= ____
The function is y = 3(x+3)^2-9
The equation of a parabola is
y=a(x-h)^2+k
where (h,k) are the coordinates of the vertex and a, is a constant.
From the question, we have
(h,k)=(-3,-9)
⇒y=a(x+3)^2-9
To find a, substitute x=-2,y=-6
-6=a(-2+3)^2-9
⇒a=3
The equation, y=3(x+3)^2-9
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Find the equation of the linear function represented by the table
below in slope-intercept form.
X 0,1,2,3,4 y 6,8,10,12,14
to get the equation of any straight line, we simply need two points off of it, let's use those two in red in the picture below
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 2 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \\\\\\ y-6=3x-3\implies {\Large \begin{array}{llll} y=3x+3 \end{array}}[/tex]
2. Ms. Graham buys 8 feet of copper wire for a science experiment. Each experiment requires
foot of copper wire. How many experiments can Ms. Graham conduct?
Answer:8 experiments
Step-by-step explanation:
she has 8 feet of copper and she needs one foot for each experiment she can do 8 experiments.
i am trouble finding out what 2(-4)
Answer:-8
Step-by-step explanation:
You are basically adding -4+(-4)
Answer:
Step-by-step explanation:
2(-4)
2 x -4
answer: -8
A pipe has a diameter of 2.5 inches and a length of 15 inches. The plumber also wants to know how much water can flow through his pipe at one time. To the nearest tenth, what is the volume of the pipe?
Answer:
volume is approximately 73.6 to the nearest tenth
Step-by-step explanation:
The volume of a pipe is volume = π * radius² * length
diameter = 2.5
radius = 2.5/2 = 1.25 inches
volume = π * 1.25² * 15
volume = π * 1.5625 * 15
volume = π * 23.4
which is approximately 73.6 to the nearest tenth
In triangle XYZ, m∠Z = (3m − 12)° and the exterior angle to ∠Z measures (2m + 2)°. Determine the value of m.
m = 38
m = 20
m = 15
m = 14
Answer:
[tex]m=38[/tex]
Step-by-step explanation:
An interior angle and its corresponding exterior angle are supplementary, so:
[tex]3m-12+2m+2=180 \\ \\ 5m-10=180 \\ \\ 5m=190 \\ \\ m=38[/tex]
Which graph represents the polar curve r = 3 – 2cos(θ)?
The graph of the polar curve r = 3 – 2cos(θ) is in the attachment
What is a graph?A graph is a diagram representation on a coordinate system.
What is a polar curve?A polar curve is a curve represented by the equation r = a + bcosθ where
a and b are constants and θ = the argument of the curveHow to find the graph of the polar curve r = 3 – 2cos(θ)?To find the graph of the polar curve r = 3 – 2cos(θ), we need to determine its maximum and minimum values and also the value as it crosses the axis.
The maximum value of rSince r = 3 – 2cos(θ), the maximum value of r is obtained at the minimum value of cos(θ) = -1 at θ = π
So, substituting this into the equation, we have
r = 3 – 2cos(θ)
r = 3 – 2(-1)
r = 3 + 2
r = 5
The minimum value of rSince r = 3 – 2cos(θ), the minimum value of r is obtained at the maximum value of cos(θ) = 1 at θ = 0
So, substituting this into the equation, we have
r = 3 – 2cos(θ)
r = 3 – 2(1)
r = 3 - 2
r = 1
The value of r at the originSince r = 3 – 2cos(θ), the value of r at the origin is when θ = π/2 and θ = 3π/2
So, substituting this into the equation, we have
r = 3 – 2cos(θ)
r = 3 – 2cos(π/2)
r = 3 – 2(0)
r = 3 - 0
r = 3
So, in polar form, the points we require for the polar curve graph are
(5, π), (1, 0), (3, π/2) and (3, 3π/2)Find the graph of the polar curve in the attachment
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Answer:
C: The third graph.
Step-by-step explanation:
Took the quiz
how many miles per gallon of gasoline would a car get if it gets 24 kilometers per liter?
Answer:
160.1 divided by 22.3 = 7.179 miles per litre.
This is 7.179 x 4.544 = 32.62 miles per gallon.
hope that will help
keeping in mind that there are about 1.609 Km in 1 mile and that there are about 3.78L in 1 gallon(US)
[tex]\cfrac{24~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{mile}{1.609~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{3.78~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{gallon(US)} \\\\\\ \cfrac{24(3.78)}{1.609}\cfrac{mile}{gallon(US)} ~~ \approx ~~ 56.38\frac{mile}{gallon}[/tex]
4) During a school carnival, students from the middle school raised money by selling crafts, food, game tickets, and school play admissions. Of each dollar earned, $0.15 came from games. Craft sales earned 3 times as much as games. Food sales were 4 times the amount earned from the play.
Crafts-blank
Play-blank
Games-$0.15
Food-$0.32
If the total sales were $500, then:
How much was earned from the craft sales?
How much was earned from the play?
$225 was earned from the craft sales
and $40 was earned from the play.
Given, During a school carnival, students from the middle school raised money by selling crafts, food, game tickets, and school play admissions.
Of each dollar earned, $0.15 came from games. Craft sales earned 3 times as much as games. Food sales were 4 times the amount earned from the play.
Let the amount earned by play be x,
Now, Games earned = 0.15×500 = $75
Also, crafts earned 3×75 = $225
Now, as play earned x, then food earned 4x.
According to question,
x + 75 + 225 + 4x = 500
5x + 300 = 500
5x = 200
x = 40
So, the amount earned by Play be, $40
and the amount earned by Food be $160.
Hence, $225 was earned from the craft sales
and $40 was earned from the play.
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Find the area of the shaded region. 3 1/4 and 4
Answer:
Step-by-step explanation:
7 1/4 is what i think