It will take 4.63 years to double the principal.
The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously after t years is-
A = P[tex]e^{rt}[/tex]
Here r = 6.5%
= 0.065
Let the principal amount be P,
then the amount after t years = 2P
A = P[tex]e^{rt}[/tex]
2P = P[tex]e^{rt}[/tex]
2P/P = [tex]e^{rt}[/tex]
2 = [tex]e^{0.065t}[/tex]
Taking log on both sides-
Log 2 = log [tex]e^{0.065t}[/tex]
Log 2 = 0.065t log e
Log 2 = 0.065t
0.65t = Log 2t
= log 2/ 0.065t
= 0.301/ 0.065 t
= 4.63
Thus, it will take 4.63 years to double the principal.
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Name a line that contains point b
Answer:
I think the answer is c.CB
the Martinez family has 3/4 a gallon of orange juice in the refrigerator. How many cups
of orange juice are in the refrigerator
Answer:
There are 12 cups of juice in the refrigerator.
Step-by-step explanation:
The conversion --> 1 gallon = 16 cups.
Therefore, [tex]\frac{3}{4}[/tex] a gallon x [tex]\frac{16 cups}{1 gallon}[/tex] = 12 cups.
--
Have a nice day!
You can spend at most $48 at the fair. Game tickets cost $1 each, and ride
tickets cost $3 each. You want to buy at least 4 game tickets and more than 3
ride tickets. Which system of linear inequalities represents the situation?
Answer:b i think
but im not sure
Step-by-step explanation:
According to the question, equation 3r + g ≤ 48 where r > 3 and g ≥ 4 represents the given situation.
What are linear inequalities?When two mathematical expressions or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.
Given, A maximum of $48 can be spent during the show. Each game ticket (g) costs $1, while each ride ticket (r) costs $3. At least 4 game tickets and more than 3 transportation tickets are what you want to purchase. From that, we can drive that sum of 3 times of ride ticket and game ticket cost should be at least greater than 48. Hence,
$3 * ride cost + $1 * game cost ≤ 48
Therefore, The above circumstance is represented by the equation
3r + g ≤ 48, where r > 3 and g ≥ 4.
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Set up a proportion and use it to solve for x.
The value of x is 7.
what is proportion?A proportion is an equation in which two ratios are set equal to each other.
Now, setting up the proportion we have
6/4 = x+6 / 4+8
3/2 = x+6 / 12
12*3 = 2(x+6)
36 = 2x + 12
2x = 36-12
2x= 14
x=7
Hence, the value of x is 7.
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Need answer asappppp
The Perimeter of the composite figure = 44.2 units.
How to Find the Perimeter of a Composite Figure?The perimeter of the composite figure = TU + UV + VW + WX + XQ + QR + RS + ST.
Length of TU = 3 units
Length of UV = 11 units
VW = 9 units
XQ = 5 units
QR = 2 units
Use the distance formula, d = [tex]\sqrt{(y_2 - y_1)^2 - (x_2 - x_1)^2}[/tex], to find the lengths of WX, RS, and ST.
W(-2, -6)
X(-5, -3)
R(-3, 2)
S(0, 0)
T(4, 5)
WX = √[(−5−(−2))² + (−3−(−6))²]
WX = √18 ≈ 4.2
RS = √(0−(−3))² + (0−2)²]
RS = √13 ≈ 3.6
ST = √[(0−4)² + (0−5)²]
ST = √41 ≈ 6.4
Perimeter of the composite figure = 3 + 11 + 9 + 5 + 2 + 4.2 + 3.6 + 6.4
Perimeter of the composite figure = 44.2 units.
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What is 23 divided by 2746
what is the interval notation for the compound inequality x is less than or equal to -5 or x > 4
Answer:%
Step-by-step explanation:
Divide.
−5 5/8÷5
Responses
−118
, , negative 1 and 1 over 8
−58
, , negative 5 over 8
58
5 over 8
118
The simplified value of the expression −5 5/8 ÷ 5 is −1 1/8
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
−5 5/8 ÷ 5
Convert the mixed fractions to improper fractions
So, we have
−5 5/8 ÷ 5 = −45/8 ÷ 5
Express the quotient as a product
So, we have
−5 5/8 ÷ 5 = −45/8 x 1/5
Evaluate the product of the numerators in the above expression
So, we have
−5 5/8 ÷ 5 = −45/8 x 1/5
Evaluate the product of the denominators in the above expression
So, we have
−5 5/8 ÷ 5 = −45/40
Simplify the result
So, we have
−5 5/8 ÷ 5 = −9/8
Express as a mixed number
So, we have
−5 5/8 ÷ 5 = −1 1/8
Hence, the simplified value of the expression −5 5/8 ÷ 5 is −1 1/8
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Recycling Center A processes aluminum at a rate of 100 pounds per hour, while Recycling Center B processes aluminum at a rate of 2 tons per week. Assuming that both centers operate all day every day, which center processes aluminum faster, and why?
1: Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 12 pounds per hour.
2: Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 24 pounds per hour.
3: Recycling Center B processes aluminum faster; its rate is about 120 pounds per hour.
4: Recycling Center B processes aluminum faster; its rate is about 240 pounds per hour.
We need to know about unitary method to solve the given question. Option () is correct, Recycling Center A processes aluminium faster; Recycling Center B's rate is about 24 pounds per hour.
Unitary method is a method to find out the value for a single quantity and then derive the value for the asked quantity. Here is this question we know Center A processes aluminium at a rate of 100 pounds per hour and center B processes 2 tons per week, we need to know who processes aluminium faster. To find the answer we need to first find how much aluminium center B processes per hour, to find that we need to use unitary method.
1 ton=2000 pounds
so, 2tons=2x2000=4000 pounds
Thus Center B processes 4000 pounds per week
A day has 24 hours, a week has 7 days, we know that the centers operate all day every day so number of hours in a week is
7x24=168 hours
Center B processes 4000 pounds in 168 hours
Center B processes 4000/168 pounds in one hour
Center B processes about 24 pounds in one hour
Therefore, we can see that Center A processes aluminium faster and Center B's rate is about 24 pounds per hour, thus option (2) is right.
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Help please, I don't know what to do
The listed elements of the sets are as follows:
X = {1, 2, 3, 4, 5}Y = {2, 4, 6, 8 }U = {1, 2, 3, 4, 5, 6, 7, 8, 9}X ∪ Y = {1, 2, 3, 4, 5, 6, 8}X ∩ Y = {2, 4}X' = {6, 7, 8, 9}(X ∩ Y)' = {1, 3, 5, 6, 7, 8, 9}How to list elements of a sets in a Venn diagram?Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
The sets in the Venn diagram are U, X and Y.
Therefore, let's find the elements of the sets.
X = {1, 2, 3, 4, 5}Y = {2, 4, 6, 8 }U = Universal sets = {1, 2, 3, 4, 5, 6, 7, 8, 9}X ∪ Y = {1, 2, 3, 4, 5, 6, 8}X ∩ Y = {2, 4}X' = {6, 7, 8, 9}(X ∩ Y)' = {1, 3, 5, 6, 7, 8, 9}learn more on Venn diagram here: https://brainly.com/question/10608955
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The equation y = 2.391x +57.420 models the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving.
What does the y-intercept of the equation represent in context of the situation?
A cereal with 0 grams of sugar has a rating of about 57.
A cereal with 0 grams of sugar has a rating of about 2.391.
The average number of grams of sugar is 57.
The average number of grams of sugar is 2.
D
The y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
where -
m → slope of line
c → y-intercept of line
Given a equation → y = 2.391x + 57.420 that models the taste rating of a cereal 'y' and 'x' represents the number of grams of sugar per serving.
The y-intercept of the equation represents the point at which the graph of the equation cuts the y - axis. Now, the coordinates of the y-intercept is of the form (0, y). Therefore, the x-coordinate will be 0. Now, the equation given is -
y = 2.391x + 57.420
Comparing it with the general equation of line -
y = 2.391x + 57.420
y = mx + c
The y - intercept is c = 57.420
At x = 0, the equation becomes -
y = 2.391 x 0 + 57.420
y = 57.420
Now -
Number of grams of sugar per serving = 0
Taste rating of a cereal = y = 57.420
Therefore, the y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.
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The fraction n/16 is between 1/2 and 3/4. Write down all the possible values of n
Answer:
9,10,11 are the values of n
Write each expression in simplest form. 7∛2 x-3∛2 x
We write the expression in its simplest form and we are left with.
4∛2 x
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
If we want to express an expression in its simplest form we are talking about a simplification of it, in this case we have the difference of monomials:
7∛2x - 3∛2x.
As both have the same variable, then the way of reduction is only the subtraction operation
4∛2x
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The mean of the 5 observations in the following table is 5. 1. Fill in the missing values. X = X 14 3 -10 12 6 Download CSV 2. Determine the following sums: Σ(-x) = Σ(x - x)² = xx 3. Sample variance, s² = (x − x)² 4. Report the sample standard deviation accurate to 2 decimal places. Sample standard deviation, s =
The mean, summation of (x - μ), summation of (x - μ)², variance, and standard deviation will be 5, 0, 360, 72, and 8.49, respectively.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation. The standard deviation is given as,
[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]
The data set is given below.
14, 3, -10, 12, 6
The mean of the data will be
μ = (14 + 3 - 10 + 12 + 6) / 5
μ = 25 / 5
μ = 5
The summation of the (x - μ) will be
∑(x - μ) = (14 - 5) + (3 - 5) + (- 10 - 5) + (12 - 5) + (6 - 5)
∑(x - μ) = 9 - 2 - 15 + 7 + 1
∑(x - μ) = 0
The summation of the (x - μ)² will be
∑(x - μ)² = (14 - 5)² + (3 - 5)² + (- 10 - 5)² + (12 - 5)² + (6 - 5)²
∑(x - μ)² = (9)² + (-2)² + (-15)² + (7)² + (1)²
∑(x - μ)² = 81 + 4 + 225 + 49 + 1
∑(x - μ)² = 360
Then the standard deviation (σ) will be
σ = √(360 / 5)
σ = √72
σ = 8.49
Then the variance (σ²) will be
σ² = 8.49²
σ² = 72
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Three pins are inserted into a cork mat at points c, e, and d. the three pins are collinear. how much string is needed to reach from the pin at e to the pin at d and then to the pin at c? leave your answer as a decimal to the nearest tenth.
Answer:2.7 - 1.1 = 1.6
Let u=(-1,3), v= (2,4) , and w = (2,-5) . Find the component forms of the following vectors. -3 v
Given u = (-1, 3), v = ( 2, 4) , and w = (2, -5), by applying scalar multiplication of vectors, -3v = -3.( 2, 4) = (-6, -12)
In the two-dimensional coordinate system, vectors can be split into x-component and y-component.
We can write, for example, a vector s = (4,–2), which means:
x-component = 4
y-component = –2
Some vector operations:
Addition / subtraction of vectors: Just add or subtract the corresponding components.In the given problem:
u = (-1, 3), v = ( 2, 4) , and w = (2, -5)
Then,
-3 v = -3 . (2, 4)
= ( -3 . 2, -3 . 4)
= (-6, -12)
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What is solution of the equation -16=x²+8 x ?
After solving, the factor of equation -16 = x²+8x is:
(x+4)What is an equation, exactly?A mathematical statement composed of two representations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We obtain the value for the variable x as x = 7 after solving this equation.So,
Given equation: -16 = x²+8x
Then,
-16 = x²+8xx²+8x+16x²+x( + ) +16x²+x(4+4)+16x²+4x+4x+16x(x+4)+4(x+4)Factors are: (x+4) and (x+4)
Therefore, after solving, the factor of equation -16 = x²+8x is:
(x+4)Know more about equations here:
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At the end of the summer, I decide to drain the swimming pool. I noticed that it drains
faster when there is more water in the pool. That was interesting to me, so I decided to measure the rate at which it drains. I found that it was draining at a rate of 3% every 5
minutes. How many gallons are left in the pool after 50 minutes? About how many minutes will it take to have less than 1000 gallons in the pool? Justify your answer with a
mathematical model of the problem situation.
An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = eˣ
Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 - r)^t
Where:
P(t ) represents the volume of water in gallons.t represents the time or number of years.I represents the initial volume of water.r represents the decay rate.Substituting the given parameters into the formula, we have;
P(t) = I(1 - r)^t
P(50) = 1500 × (1 - 0.3)^0.2{50}
P(50) = 1500 × (0.97)^10
P(50) = 1,106 gallons.
Therefore, there would be 1,106 gallons of water left in the pool after 50 minutes.
Next, we would determine the amount of time it would take to have less than 1000 gallons in the pool:
P(t) = I(1 - r)^t
1000 = 1500 × (1 - 0.3)^0.2t
1000 = 1500 × (0.97)^0.2t
1000/1500 = (0.97)^0.2t
2/3 = (0.97)^0.2t
Taking the log of both sides, we have:
log0.97(0.2t) = log(2/3)
t = log(2/3)/(0.27log0.97)
Time, t = 66.6 minutes.
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Complete Question:
A pool drains at a rate of 3% every 5 minutes. If it starts with 1500 gallons, how many gallons are left in the pool after 50 minutes? About how many minutes will it take to have less than 1000 gallons in the pool? Justify your answer with a mathematical model of the problem situation.
Solve for x .
23≥3x−4 or 32<3x−4
Responses
9 12 or x≤9
Answer:
1. x≤9
2. x>12
Step-by-step explanation:
1. Rewrite so x is on the left side of the inequality.
3x−4≤23
Move all terms not containing x to the right side of the inequality.
3x≤27
Divide each term in 3x≤27 by 3 and simplify.
x≤9
2. Rewrite so x is on the left side of the inequality.
3x-4>32
Move all terms not containing x to the right side of the inequality.
3x>36
Divide each term in 3x>36 by 3 and simplify.
x>12
What is the solution to the system of equations?
Y=2/3+3
y
x = -2
The solution to the given system of equations will be x = -2, y = 5/3. That is (-2, 5/3)
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given system of equation is;
y = 2/3 x + 3 ----------- (1)
x= -2 ----------- (2)
The value of x has been given in the second equation.
Now, we need to determine the value of y
From the second equation, we have that;
x = -2
Now Substitute the value of x into the first equation,
y = 2/3 x + 3
y = 2/3 (-2) + 3
y = -4/3 + 3
y = 5/3
Hence, the solution to the given system of equations will be x = -2, y = 5/3. That is (-2, 5/3)
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On a coordinate plane, a function has four connecting lines. The first line goes from (0, 0) to (2,2), the second line goes from (2, 2) to (3, 1), the third line goes from (3, 1) to (5, 3), and the fourth line is horizontal to the x-axis at 3. This graph shows a portion of an even function. Use the graph to complete the table of values. x f(x) −1 −3 −5 −6
Considering that the function is even, the numeric values are given as follows:
x = -1, f(x) = 1.x = -3, f(x) = 1.x = -5, f(x) = 3.x = -6, f(x) = 3.What are even and odd functions?In even functions, we have that f(x) = f(-x) for all values of x.In odd functions, we have that f(-x) = -f(x) for all values of x.If none of the above statements are true, the function is neither.In this problem, we have that the function is even, hence:
The first line goes through points (0,0) and (2,2), hence y = x, then when x = 1, y = 1 and when x = -1, y = 1, because f(x) = f(-x).f(3) = 1, hence, f(-3) = 1.f(5) = 3, hence f(-5) = 3.Due to the horizontal line, f(6) = 3, hence f(-6) = 3.More can be learned about even functions at https://brainly.com/question/3964641
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Answer:
1,1,3,3
Step-by-step explanation:
on edge
find the coordinates of the missing endpoint if b is the midpoint of ac
C(-5,4) B(-2,5)
step by step explanation
thank you!
Answer: (1,6)
Step-by-step explanation:
Let the coordinates of A be (x,y).
[tex]\frac{x-5}{2}=-2 \implies x=-4 \implies x=1\\\\\frac{y+4}{2}=5 \implies y+4 =10 \implies y=6\\\\\therefore A=(1, 6)[/tex]
Select the expression that matches the scenario correctly. On January 1, the high temperature was 81 F in Kona, Hawaii the low temperature was -29 F in Barrow, Alaska. What was the difference between the two temperatures?
A. -29 + 81
B. |89 - 21|
C. |81 - (-29)|
D. 36 divided 6
The difference between the two temperatures is mathematically given as
|81 - (-29)| Option C
This is further explained below.
What was the difference between the two temperatures?Generally, the equation is mathematically given as
h-l=d
Therefore
81-(-29)=d
81+29=d
d=110
In conclusion,, in magnitude form
|81 - (-29)|=|81 +29|=|110|=110
|81 - (-29)|
Option C is correct
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Louie drove 50 1/8 miles and used 2.5 gallons
of gas. find the number of miles driven per
gallon of gas.
The number of miles driven per gallon is 401/20
How to calculate the number of miles ?Louie drove 5- 1/8 miles
He used 2.5 gallons for this journey
Therefore the number miles per gallon can be calculated as follows
401/8 = 2.5
x= 1
Cross multiply both sides
2.5x= 401/8
x= 401/8 ÷ 2.5
x= 401/8 × 1/2.5
= 401/20
Hence the number of miles per gallon is 401/20
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whats are equivalents to 9y +5y +4y
PLEASE HELP ME WITH THIS
The correct way of using the equation is:
$25,475 = (1 - m)*$27,000
And with that we will get that the markdown is of the 5.6%
Which is the correct way of use the given formula?We know that the original price of the car is $27,000, and there is a markdown such that the new price of the car is $25,475.
Then, if m represents the markdown, we can write the equation:
$25,475 = (1 - m)*$27,000
Now we can solve this for m to get:
1 - $25,475/$27,000 = m = 0.056
If we want this in percentage form, we need to multiply it by 100%.
0.056*100% = 5.6%
the markdown in the price is of the 5.6%
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Determine whether each function is an example of exponential growth or decay. Then find the y -intercept.
y=0.6(1/10)x
The function y = 0.6 × ( 1/10)ˣ is a form of exponential decay and the value of y-intercept is 0.6.
The term "exponential decay" refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)ˣ, where x is the amount of time that has passed, a is the initial amount, b is the decay factor, and y is the final amount.
Consider the function,
y = 0.6 × ( 1/10)ˣ
This equation is a form of exponential decay because the number being raised in the power is a fraction, and whenever a fraction is raised to a positive power, the result decreases.
In order to determine the y-intercept of the function, we substitute the value of x as zero and find the value of y. Whenever a number is raised to zero power, the answer is always one.
Therefore,
y = 0.6 ( 1/10)ˣ
y = 0.6 × ( 1/10 )⁰
y = 0.6 × 1
y = 0.6
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Given the function, find f(-1) and f(3).
The value of function f(x) at x = - 1 and x = 3, will be -
f(-1) = 3
f(3) = 3
We have a function f(x).
We have to evaluate it at x = -1 and x = 3.
What is a function ?A function in mathematics is a relation between a dependent and independent variables [y and x respectively]. In a function, the dependent variable (y) always depends on independent variable (x) for its value. It is denoted by - y = f(x).
According to the question, we have -
f(x) = [- x + 2 , x ≤ 1] and f(x) = [x² - 4x + 6, x > 1]
Now, for x = -1, f(x) will be -
f(- 1) = - (-1) + 2 = 3
and
for x = 3, f(x) will be -
f(3) = 3² - 4 x 3 + 6 = 3
Hence, the value of function f(x) at x = - 1 and x = 3, will be -
f(-1) = 3
f(3) = 3
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The per capita consumption (in pounds) of all poultry in a country is approximated by the function C(x) = 2.49x +93.19, where x is the number of years since 2001. Find and interpret C(1), and
estimate the per capita consumption of all poultry in the country in 2010.
a. Find and interpret C(1).
The value at intercept C(1) is 95.68 pounds
The estimated per capita consumption in the year 2010 will be 115.6 pounds
Part a:
Per capita consumption of all the poultry in a country is given by the function C(x) = 2.49x + 93.19
Finding intercept C(1):
For C(1) the value of x will be 1
C(1) = 2.49(1) + 93.19
C(1) = 95.68
Hence, the value at intercept C(1) is 95.68 pounds
Part b:
Finding the per capita consumption in the year 2010:
where x will be 9, as the time period from 2001 to 2010 is 9 years
C(2010) = 2.49(9) +93.19
= 22.41 + 93.19
= 115.6
Hence, the estimated per capita consumption of all the poultry in the country will be 115.6 pounds in the year 2010
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Evalute1111011 ×1101 in base tow
Step-by-step explanation:
11dvccvgtgcgt5cjuuhh