For both cases time needs to double the invested money is 7.7016 years
What is continuous compounding?It is a mathematical expression define that interest can be compounded at any time even within any smallest period of time.
How do we calculate compounded continuously doubling money?When annual interest rate is given in a data along with invested money, we can calculate the years required to get doubled money by using the formula A= Pe∧(rt)
A is the double money of the investment
P is the investment
r is the annual interest rate
t time in years
as per question A=2P, r=0.09
2P =Pe∧(0.09t)
2= e∧(0.09t)
㏑2=0.09t
t= 7.7016 years
hence, it takes 7.7016 years to get double money
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Question
Eli caught three fish. The weights of the fish were 2 lb 4 oz, 1 lb 11 oz, and 4 lb 14 oz,. What was the total weight of the
three fish?
Answer:
8 lbs. 13 oz.
Step-by-step explanation:
2 lb. 4 oz.
+ 1 lb. 11 oz.
4 lb. 14 oz.
__________
7 lbs. 29 oz.
Since there are 16 oz in one pound, subtract 16 from 29 to get 13 oz and don’t forget to add that pound to the 7, so your final answer should be 8 lbs. 13oz.
The ________ could be used to describe a data set by itself, while ___________ would almost never be used to describe a data set by itself.
A. mean ; interquartile range
B. range ; mean
C. interquartile range ; mean
D. mean ; range
The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.
What is Descriptive statistics?These are operations which are used to summarize certain characteristics a set of data has.
Mean and range deals with the full set of data while interquartile range measures just the middle half of the data and is denoted as option A.
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A slot machine has 3 dials each dial has 30 positions one of which is jackpot. To win jackpot all three dials must be in jackpot position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot
Answer:
3/90
Step-by-step explanation:
1 slot is 1/30
2 slot is 1/30
3 slot is 1/30
this gives you that 3/90 when you had them
Answer:
D) 1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Step-by-step explanation:
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
The percent error of the house of the pizza would be 2.
The difference between the estimated and actual values in comparison to the actual value is expressed as a percentage. In other words, the relative error multiplied by 100 equals the percent error.
How to calculate the percent error?Percent errors indicate the magnitude of our errors when measuring something in an analysis process. Lower percentage errors indicate that we are getting close to the accepted or original value.
Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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\((x - 3)(x + 4)(x - 2) = 0\)
Answer:
Step-by-step explanation:
x-3 = 0
x = 3
x + 4 = 0
x = -4
x - 2 = 0
x = 2
x = 3, -4, 2
What is the probability of choosing a factor of 16?
Answer:
I think it could be 2/8 but sorry if I'm wrong
the size of an impala population is represented by the function r(t)=10+2cos(pi/6 t), where t is time in months since the beginning of the year and R(t) is measured in thousands. After 3 months, the population is ______ at a rate of _____ thousand per month. Round to 2 decimal places.
The population of impalas at t = 3 months is decreasing at a rate of \(-(\frac{\pi}{3})\) thousand per month, or approximately -1.05 thousand per month.
What is derivative?The derivative is a mathematical concept that represents the rate of change of a function with respect to its input.
To find the population of impalas after 3 months, we can substitute t = 3 into the given function;
\(R(t)=10+2Cos(\pi t/6)\)
\(R(3)=10+2Cos(\pi *3/6)\)
\(= 10 + 2cos(\pi/2)\) = 10
Therefore, the population of impalas after 3 months is 10,000 (since R(t) is measured in thousands).
To find the rate of change of the population at t = 3 months, we can take the derivative of the function R(t) with respect to t:
\(R(t)=10+2Cos(\frac{\pi t}{6} )\)
\(R'(t)=-\frac{\pi}{3} Sin (\frac{\pi t}{6} )\)
Substituting t = 3 into the derivative, we get:
\(R'(3)=-\frac{\pi}{3} Sin (\frac{\pi}{2} )\\\)
\(= -\frac{\pi}{3}\)
Therefore, the population of impalas at t = 3 months is changing at a rate of \(-(\frac{\pi}{3})\) thousand per month, or approximately -1.05 thousand per month (rounded to 2 decimal places).
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how did the greeks defend themselves from dorian rules?
Answer: the Dorians were far less advanced then the Mycenaean Greeks; economy collasped and trade stopped
What is the maximum of f(x)=sin(x)
Answer:
1
Step-by-step explanation:
The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2. If you look at a graph of
y = sin(x) you can see this.
Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.
Step-by-step explanation:
Property of Sine function:
Sin(x)=0 when x=90°,180°,360°The maximum and Minimum value of Sin(x) is 1 and -1 respectively, when and x=270° respectively.The range of values of sin(x) is -1 to 1.Read more on the Sine function:
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Please help me asap I’m really stuck
Answer:
Step-by-step explanation:
el
Talia sells educational software for a yearly salary of $65,000 plus a 2.65% commission on her total sales. If Talia sells $2.5 million of software during one year, what are Talia’s earnings for that year?
Answer:
$131250
Step-by-step explanation:
Talia's earnings during one year are equal to her base yearly salary ($65000) added to her commission. Now, to know the commission it is necessary to find the 2.65% of her total sales ($2.5 million)
Step 1. Divide the total sales or 2,500,000 by 100 considering this represents the total or 100%
2,500,000 ÷ 100 = 25000
Step 2. Multiply this number by the specific percentage (2.65)
25000 x 2.65 = 66250
Now add the commission and the yearly salary
65000 + 66250 = 131250
Hence, total earnings of Talia were $131250
Find the slope intercept form of the equation parallel to the line of Y =6x+72 and with coordinates of (8-9).Then find the slope intercept form of the equation Perpendicular to the line Y=5x-1/2 and with the coordinates of (25,-11).
the slope -intercept form of the equation of a line is
\(\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ b\text{ is the y-intercept} \end{gathered}\)so
Step 1
find the slope of the line:
2 lines that are parellel has the same slope , so the slope of the line we are looking for must equal to the slope of
\(\begin{gathered} y=6x+7 \\ y=6x+7\Rightarrow y=mx+b \\ so \\ m=slope=6 \end{gathered}\)so
slope=6
Step 2
now, we need to use the point-slope formula , it says
\(\begin{gathered} y-y_1=m(x-x_1) \\ where \\ m\text{ is the slope and } \\ P1(x_1,y_1)\text{ is a well known of the line} \end{gathered}\)so
a) let
\(\begin{gathered} slope=6 \\ P1(8,-9) \end{gathered}\)b) now, replace and solve for y
\(\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-(-9)=6(x-8) \\ y+9=6x-48 \\ subtract\text{ 9 in both sides} \\ y+9-9=6x-48-9 \\ y=6x-57 \end{gathered}\)therefore, the answer is
\(y=6x-57\)I hope this helps you
Find the area of the curve y= f(x) = x between x = 5 and x = 10
Answer:
the area of the curve y= f(x) = x between x = 5 and x = 10
\(A=\frac{75}{2}\)
Step-by-step explanation:
Finding the area of the curve y = f(x) = x between x = 5 and x = 10Using the Area formula
\(A=\int _a^b\:f\left(x\right)dx\)
As the area of curve lies between x = 5 and x = 10
so
a = 5, b = 10so the integral expression becomes
\(A=\int _5^{10}xdx\)
\(\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\)
\(A=\left[\frac{x^{1+1}}{1+1}\right]^{10}_5\)
\(=\left[\frac{x^2}{2}\right]^{10}_5\)
\(=\frac{1}{2}\left[10^2-5^2\right]\)
\(=\frac{1}{2}\cdot \:75\)
\(=\frac{75}{2}\)
Therefore, area of the curve y= f(x) = x between x = 5 and x = 10
\(A=\frac{75}{2}\)
Can u guys please give me the correct answer
Answer:
∠ 3 = 65°
Step-by-step explanation:
∠ 2 and 115° are a linear pair and sum to 180° , that is
∠ 2 + 115° = 180° ( subtract 115° from both sides )
∠ 2 = 65°
∠ 2 and ∠ 3 are corresponding angles and and are congruent , then
∠ 3 = 65°
to spend to much traveling and country the day she arrived the exchange rate was 1.4 country a dollars Per country B dollars if she exchange 500 country B dollars when she arrived how many country eight dollars she receive
Answer:
She receives 700 country A dollars.
Step-by-step explanation:
This question is solved by proportions, using a rule of three.
1.4 country a dollars Per country B dollar
She exchanges 500 country B dollars, so:
1.4 country A dollars - 1 country B dollar
x country A dollars - 500 country B dollars
Applying cross multiplication:
\(x = 1.4*500 = 700\)
She receives 700 country A dollars.
in 2009 Larry's gross pay was $275,800 in that year the maximum taxable for Social Security was 118500 and the Social Security was 62.2%.
Based on the maximum taxable amount for social security in 2009, and the social security tax rate, the social security tax that Larry paid was $7,347.
How much did Larry pay in social security taxes?The total amount paid by Larry as Social security tax can be found as;
= Maximum amount allowable for social security tax x Social security tax rate
The social security tax rate was 6.2% not 62.2%.
The social security tax was therefore:
= 118,500 x 6.2%
= $7,347
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When you add a positive number and a negative, how
Answer:
The answer would be B. When you add a negative and a positive it equals a negative, Like when adding a positive and a negative. But, adding two that are the same, like a positive and a positive equals a positive.
Step-by-step explanation:
Marvin was buying soil for his flower garden. What would be the most reasonable amount of soil he would need to buy for a flower garden? A. 6 grams B. 60 liters C. 60 kilograms D. 6,000 kilograms
Answer:
60 liters
Step-by-step explanation:
Answer:
C. 60 kilograms
Step-by-step explanation:
The person above me is incorrect because liters is used on liquids
Yolanda used her graphing calculator to graph y= 3x. Her graph is shown at right. Do you think she
did it correctly? Explain.
What do you add to 17/4 to make 5?
The number that can be added to 17/4 to make 5 is 3/4
How to add fractionsGiven
Add to 17/4 to make 5
let
x = number addedx + 17/4 = 5
x = 5 - 17/4
x = (20-17) / 4
x = 3/4
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What is the equation of this line?
A. y= x - 3 =
B. y=-x-3 =
C. y= -2x - 3
D. y=2x-3 - - 3
lve for m.
-3 + m
9 = 10
A.
-30
B.
63
C.
87
D.
93
The value of m that satisfies the equation -3 + m = 9 is m = 12.
To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.
-3 + m = 9
To move -3 to the other side, we can add 3 to both sides of the equation:
-3 + 3 + m = 9 + 3
Simplifying, we have:
m = 12
Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.
None of the provided answer options (A, B, C, D) match the correct solution.
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in 1932, giuseppe momo was commissioned to build the famous vatican museum double spiral staircase. suppose that it takes you one hour to stroll at a constant speed up one spiral of this staircase, which has a radius of 19 feet and a height of 40 feet and makes 4 revolutions. (a) assuming the spiral staircase is centered about the -axis, find a vector parametric equation for the helical path you take from the point to the point that makes revolutions during the time interval .
where r = 19 feet, h = 40 feet, and θ varies from 0 to 8π (4 complete revolutions) as t varies from 0 to 4.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, which are separated by an equals sign (=). An equation can have variables, constants, coefficients, and operators. The variables are represented by letters, and their values can change depending on the context of the problem. The constants are fixed values, and the coefficients are the numbers that multiply the variables. The operators are mathematical symbols that indicate the operation to be performed, such as addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^). Solving an equation means finding the value(s) of the variable(s) that satisfy the equation.
Given by the question.
Let's start by defining the necessary parameters. The radius of the staircase is given as 19 feet, and the height is given as 40 feet. The staircase makes 4 complete revolutions, so the total height of the staircase is 4 times the height of one revolution, which is 40 feet.
To find a vector parametric equation for the helical path, we need to consider the circular motion around the center axis, as well as the motion along the axis. Let's define the following parameters:
r: radius of the staircase (19 feet)
h: height of one revolution (40 feet)
θ: angle of rotation around the center axis (in radians)
z: height along the center axis
The circular motion around the center axis can be described by the following parametric equation:
x = r cos(θ)
y = r sin(θ)
z =???
To find the equation for z, we need to consider the motion along the center axis. Since it takes one hour to stroll up one revolution, and there are 4 revolutions in total, the time it takes to stroll up the entire staircase is 4 hours. Therefore, we can use t as a parameter that varies from 0 to 4, and define z as:
z = (h/4) t
Note that we divide h by 4 to scale the parameter t to the interval [0,4].
Putting it all together, the vector parametric equation for the helical path is:
r(t) = <r cos(θ), r sin(θ), (h/4) t>
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2 to the 3rd power times 2 to the 4th power simplified answer
2 raised to the third power is equal to 2^3 = 8.The value of 2 to the 4th power i.e., 2^4 is 16.
What is exponent?
The exponent of a number shows how many times the number is multiplied by itself.
2 to the 3rd power can be written as 2^3 = 2 × 2 × 2, as 2 is multiplied by itself 3 times.
Here, 2 is called the "base" and 3 is called the "exponent" or "power."
In general, xn means that x is multiplied by itself n times.
2^3 = 2 × 2 × 2 = 8
Thus, 2 raised to the third power = 2^3 = 8.
According to the Power Rule of Exponents,
am = a × a × a... m times
Thus, 2^4 can be written as 2 × 2 × 2 × 2 = 16
Thus, the value of 2 to the 4th power i.e., 2^4 is 16.
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PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
Do it in this order
Step-by-step explanation:
5 3 1 2 4 6
Find the area of the shape
The area of the given figure is 27.5 square centimeter which has a rectangle and triangles
The given figure has a rectangle and triangles
The area of rectangle is length times width
Area of rectangle =5×4
=20 square centimeter
Area of triangle =1/2×base×height
=1/2×2.5×3
=7.5/2
=3.75 square centimeter
As there are two triangle = 2(3.75)
=7.5 square centimeter
Total area = 7.5+ 20
=27.5 square centimeter
Hence, the area of the given figure is 27.5 square centimeter
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There are 8 ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon.
1 L ≈ 0.26 gallons
6 kL ≈ fl oz
6 kiloliters are approximately equal to 202,884.14 fluid ounces.
We have,
To convert 6 kiloliters (kL) to fluid ounces (fl oz), we need to use the conversion factor between these two units.
The conversion factor states that 1 kiloliter is equal to 33814.0227 fluid ounces.
This means that for every kiloliter, there are 33814.0227 fluid ounces.
To convert 6 kiloliters to fluid ounces, we multiply the given value (6 kL) by the conversion factor (33814.0227 fl oz/kL).
= 6 kL x 33814.0227 fl oz/kL
= 202884.1362 fl oz
Therefore,
6 kiloliters are approximately equal to 202,884.14 fluid ounces.
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18) Solve for side AC.
A) 1.10
B) 8.24
C) 9.50
70
C
3
B
Step-by-step explanation:
tan0=opp/adj
where opposite =3,adjacent =x,=70
tan 70=3/x
2.7474=3/x
2.7474x=3
divide both sides by 2.7474
x=3/2.7474
x=1.0919
x=1.10 to 1 d.p
A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is /6, this angle is decreasing at a rate of /3 rad/min.
How fast is the plane traveling (in km/min) at that time? (Round your answer to two decimal places.)
Answer:
# rad u cant take 67 from it its going 35 mps
Step-by-step explanation:
Please help answer my question
Answer:
x = 6
Step-by-step explanation:
This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:
(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²
From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.
3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²
3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²
Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:
8x - 20 = 5x - 2
Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.
8x - 20 = 5x - 2
8x - 20 - 5x = 5x - 2 - 5x
3x - 20 = -2
3x - 20 + 20 = -2 + 20
3x = 18
3x/3 = 18/3
x = 6
Hopefully that's helpful! Let me know if you need more help. :)