you invested 1,000 in an account with interest rate at 2% compounded continuously. how long until 1400 is in your account?
Answers
Answer:20 months
Step-by-step explanation:
2% of 1000 is 20 1000-1400=400
400/20=20 so 20 months
Related Questions
Question 6 C= < Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z> c) = 0.0304, find c. Submit Question >
Answers
The value of c, given that P(z > c) = 0.0304 for a standard normal distribution with a mean of 0 and a standard deviation of 1, is approximately 1.89.
To find the value of c given P(z > c) = 0.0304, where z-scores are normally distributed with a mean of 0 and a standard deviation of 1, we can use the standard normal distribution table or a statistical calculator.
Using a standard normal distribution table, we need to find the z-score that corresponds to a cumulative probability of 0.0304 in the upper tail. This means we need to find the value of c such that P(z > c) = 0.0304.
From the standard normal distribution table, we look for the closest probability value to 0.0304, which is 0.0306. The corresponding z-score is approximately 1.89.
Therefore, c ≈ 1.89.
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if he rolls a non-4 on the first throw, the player is paid $5. the player is paid $10 if he rolls a 4 followed by a non-4; $20 if he rolls two 4s followed by a non-4; $30 if he rolls three 4s followed by a non-4; and $50 in all other cases. what is the expected amount paid to the player?
Answers
$7.50
The expected amount paid to the player is $7.50. This is calculated by taking the probability of each outcome multiplied by the amount paid for that outcome, and then summing them all together. The probabilities are as follows:
The expected amount paid is therefore: (0.75 x $5) + (0.0625 x $10) + (0.0039 x $20) + (0.0001 x $30) + (0.00001 x $50) = $7.50
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. If sin(x + y)=sin x.cos y+cos x.sin y, then find the value of sin 75 degrees
Answers
Answer:
\(\sf \dfrac{\sqrt{6}+\sqrt{2}}{4}\)
Step-by-step explanation:
Trigonometry:75 = 45 + 30
Sin (x + y) = Sin x *Cos y + Cos x * Sin y
Sin (45 + 30) = Sin 45 * Cos 30 + Cos 45 * Sin 30
\(\sf =\dfrac{1}{\sqrt{2}}*\dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}* \dfrac{1}{2}\\\\\\=\dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}\\\\\\=\dfrac{\sqrt{3}*\sqrt{2}}{2*\sqrt{2}*\sqrt{2}}+\dfrac{1*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\\\=\dfrac{\sqrt{6}}{2*2}+\dfrac{\sqrt{2}}{2*2}\\\\\\=\dfrac{\sqrt{6}+\sqrt{2}}{4}\)
How do you write an equation from a line of best fit on a graph?
Answers
Answer:
find y intercept and slope
Step-by-step explanation:
Adrian bought 20 chicken wings for $44.00. How much does each wing cost?
Answers
Answer:
my crushes name is Adrian but the answer is $2.20
Step-by-step explanation:
determine the periodic solutions, if any, of the system x˙ = y x p x 2 y 2 (x 2 y 2 − 2), y˙ = −x y p x 2 y 2 (x 2 y 2 − 2).
Answers
The periodic solutions of the system are:
(0, 0),
(±√2, ±√2).
These points represent periodic orbits in the phase space of the system.
To determine the periodic solutions, if any, of the system:
ẋ = yx^p(x^2y^2 - 2),
ẏ = -xy^p(x^2y^2 - 2),
we need to find values of x and y for which the derivatives ẋ and ẏ are equal to zero simultaneously. These points represent potential periodic solutions.Setting ẋ = 0 and ẏ = 0, we have:
0 = yx^p(x^2y^2 - 2),
0 = -xy^p(x^2y^2 - 2).
From the first equation, we can see that either y = 0 or x^2y^2 - 2 = 0.
If y = 0, then the second equation implies that x = 0. Therefore, (0, 0) is a solution.
If x^2y^2 - 2 = 0, then x^2y^2 = 2.
Taking the square root of both sides, we get xy = ±√2.Considering the second equation, we have -xy^p(x^2y^2 - 2) = 0.
Substituting xy = ±√2, we find that this equation holds true.
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One side of each pentagon lies along a side of the octagon.
AB is a side of the octagon.
AC is a side of one of the pentagons.
BC is a side of the other pentagon.
Work out the size of angle y.
Show your working clearly.
Answers
Answer:
The size of angle y is 126°
Step-by-step explanation:
From the diagram of the regular polygons, we have;
One side of each pentagon lies along a side of the octagon
The interior angle of the octagon > The interior angle of the pentagon
Each interior angle of a regular pentagon = 108°
Each interior angle of a regular octagon = 135°
Therefore, ∠ABC = 135° - 108° = 27°
Similarly, ∠BAC = 135° - 108° = 27°
Therefore, by triangle the angle sum theorem, we have;
∠y = ∠ACB = 180° - ∠BAC - ∠ABC = 180° - 27° - 27° = 126°
The size of angle y, ∠y = 126°.
Last question can someone help?
Answers
Answer:
The answer is y= - 2x - 14
Step-by-step explanation:
Slope intercept form is y=mx+b so the answer is y= - 2x - 14
You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.7. Prepare a decision tree and use it to calculate the expected value of the buy new option. The payoff table is provided below (+ for profits and - for losses).
When entering the answer, do not use the $ symbol. Do not enter the thousand separator. Enter up to 2 decimal places after the decimal point. For example, $6,525.35 must be entered as 6525.35
N1: Prosperity ($) N2: Recession ($)
A1 (Buy New) $1,035,332 $-150,000
A2(Modify) $823,625 $293,648
Answers
The expected value of the "Buy New" option is 724732.60.
Decision Tree:
To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:
Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:
Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)
Substituting the given values in the above formula, we get:
Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60
Therefore, the expected value of the "Buy New" option is 724,732.60.
Conclusion:
To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.
The expected value of the "Buy New" option is 724,732.60.
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36
Four times my number is 36. What is my number?
The variable, n, represents
The bar diagram demonstrates that four of the
unknown numbers together make
4 = 36
72
n
n
n
The number is
Answers
Answer:
i know ima lil late but heres the answer
Step-by-step explanation:
Answer:
its a, d, b, b
Step-by-step explanation:
hope you pass!!
MY NOTES ASK YOUR TEACHER Find the local maximum and minimum values and saddle point(s) of the function. If you have three dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter NONE In any unused answer blanks.) fx, y)-8-2x+4y-²-4² maximum " (smaller x value) (larger x value) " minimum " (smaller x value) " (larger a value) saddle points Submit Answer ) (smallest x value) ) (largest x value)
Answers
The local maximum and minimum values of the function are as follows: maximum at (smaller x value), minimum at (larger x value), and there are no saddle points.
To find the local maximum and minimum values of the function, we need to analyze its critical points, which occur where the partial derivatives are equal to zero or do not exist.
Let's denote the function as f(x, y) = -8 - 2x + 4y - x^2 - 4y^2. Taking the partial derivatives with respect to x and y, we have:
∂f/∂x = -2 - 2x
∂f/∂y = 4 - 8y
To find critical points, we set both partial derivatives to zero and solve the resulting system of equations. From ∂f/∂x = -2 - 2x = 0, we obtain x = -1. From ∂f/∂y = 4 - 8y = 0, we find y = 1/2.
Substituting these values back into the function, we get f(-1, 1/2) = -9/2. Thus, we have a local minimum at (x, y) = (-1, 1/2).
There are no other critical points, which means there are no local maximums or saddle points. Therefore, the function has a local minimum at (x, y) = (-1, 1/2) but does not have any local maximums or saddle points.
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How many millimeters of solution B does she use, if the resulting mixture is a 5% alcohol solution
Answers
Let a represent the volume of solution A. If it contains 2% of alcohol, then the amount of alcohol that A contains is 2/100 * a = 0.02a
If A = 200, then the amount of alcohol in A is 0.02 * 200 = 4
Let b represent the volume of solution B. If it contains 7% of alcohol, then the amount of alcohol that B contains is 7/100 * a = 0.07b
The total volume of solution A and B is (a + b)
If the volume of A = 200, then the total volume or resulting mixture is 200 + b
If the mixture contains 5% alcohol, the the amount of alcohol in the mixture is
5/100 * (200 + b)
0.05(200 + b)
By equating the concentrations, we have
4 + 0.07b = 0.05(200 + b)
4 + 0.07b = 10 + 0.05b
0.07b - 0.05b = 10 - 4
0.02b = 6
b = 6/0.02
b = 300
She needs to use 300 milliliters of solution B
how do I compare 6.098 and 6.908
Answers
6.908 is greater than 6.098 as the second digit from the left is greater.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, are two numbers 6.098 and 6.908.
Now, starting from left both the numbers have the same digit so we can't
differentiate.
The digit after the decimal place to the first number is 0 and on the second it is 9 so definitely, the second number is greater.
∴ 6.098 < 6.908.
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What is the value of the expression: 2/10 ÷ 5/4?
1/50
4/10
8/50
1/2
Answers
Answer:
8/50
Step-by-step explanation:
2/10 x 4/5 = 8/50
Hope that helps!
The length of a rectangle i 2cm greater than the width of the rectangle. The perimeter of the rectangle i 24cm
Answers
The length of the rectangle is 7 cm and the width is 5 cm.
Perimeter of a rectangle:The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.
The formula for the Perimeter of the rectangle is given by
Perimeter = 2( Length + Width )Here we have
The length of a rectangle is 2cm greater than the width of the rectangle
And perimeter of the rectangle = 24 cm
Let x be the width of the rectangle
From the given data,
Length of the rectangle = (x + 2) cm
As we know Perimeter of rectangle = 2(Length+width)
=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)
From the given data,
Perimeter of rectangle = 24cm
=> 2(2x +2) = 24 cm
=> (2x +2) = 12 [ Divided by 2 into both sides ]
=> 2x = 12 - 2
=> 2x = 10
=> x = 5 [ divided by 2 into both sides ]
Length of rectangle, (x+2) = 5 + 2 = 7 cm
Therefore,
The length of the rectangle is 7 cm and the width is 5 cm.
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Samantha has 52 jelly beans. She decides that she will eat 4 jelly beans per minute, and she wants to create an expression that represents how many jelly beans she has left after x minutes. Which of the following expressions correctly models this situation?
Select one:
A. 4x + 52
B. x + 52
C. -x + 52
D. -4x + 52
~and also if whoever answers doesn't mind, please put an actual explanation since I just wanna be able to fully understand the concept! It would be greatly appreciated! ~
Answers
Answer:
-4x+52
Step-by-step explanation:
So we know that Samantha has 52 jelly beans and that she'll eat 4 jelly beans per minute in X minutes.
It'd be 4*x=4x
Usually, it'd be 52-4x
But you can create an equivalent
Lets say x=5
So she'd eat 20 jelly beans
52-20=32
BUT
-20+52=32
So, the answer would be D
5. Which expression is equivalent to
(3x^2y-4)^0?
Answers
Answer:
1
Step-by-step explanation:
It is 1 because the laws of exponents state that anything raised to the power of 0 is 1.
Help yalll I really need help major time
Answers
Answer:
Annalise is correct because the outputs are closest when x = 1.35
Step-by-step explanation:
The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.
Three artificial flaws in type 316L austenitic stainless steel plates were fabricated using a powderbed-based laser metal additive manufacturing machine. The three artificial flaws were designed to have the same length, depth, and opening.
Flaw A is a simple rectangular slit with a surface length of 20 mm, depth of 5 mm, and opening of 0.4 mm, which was fabricated as a reference.
Flaw B simulates a flaw branched inside a material
Flaw C consists of 16 equally spaced columns
What type of probe do you propose to be used and suggest a suitable height, diameter and frequency? The flaws were measured by eddy current testing with a constant lift-off of 0.2 mm.
Draw the expected eddy current signals on the impedance plane and explain, in your words, why the eddy current signals appear different despite the flaws having the same length and depth
Answers
Step 1: The proposed probe for flaw detection in type 316L austenitic stainless steel plates is an eddy current probe with a suitable height, diameter, and frequency.
Step 2: Eddy current testing is an effective non-destructive testing method for detecting flaws in conductive materials. In this case, the eddy current probe should have a suitable height, diameter, and frequency to ensure accurate flaw detection.
The height of the probe should be adjusted to maintain a constant lift-off of 0.2 mm, which is the distance between the probe and the surface of the material being tested. This ensures consistent measurement conditions and reduces the influence of lift-off variations on the test results.
The diameter of the probe should be selected based on the size of the flaws and the desired spatial resolution. It should be small enough to accurately detect the flaws but large enough to cover the entire flaw area during scanning.
The frequency of the eddy current probe determines the depth of penetration into the material. Higher frequencies provide shallower penetration but higher resolution, while lower frequencies provide deeper penetration but lower resolution. The frequency should be chosen based on the expected depth of the flaws and the desired level of sensitivity.
Overall, the eddy current probe with suitable height, diameter, and frequency can effectively detect the artificial flaws in type 316L austenitic stainless steel plates fabricated using a powderbed-based laser metal additive manufacturing machine.
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Which system of equations has the same solutions as the system below? `3x-y=7` `2x+3y=12`
Answers
Answer:
the system : 9x-3y =21
2x+3y = 12
Step-by-step explanation:
hello :
an system of equations has the same solutions as the system below
the system 3x-y=7
2x+3y=12
for exempl : 3×(3x-y)=3×7
2x+3y)=12
means :
9x-3y =21
2x+3y = 12
6x - 2y = 14, 2x + 3y - 6 = 6 has the same solution as the system of equations 3x - y = 7, 2x + 3y = 12
What are system of equations?A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
Given system of equations
3x - y = 7........................(1)
2x + 3y = 12...................(2)
Multiply equation 1 with 2
2(3x - y) = 2 × 7
6x - 2y = 14
Subtract 6 from equation 2
2x + 3y - 6 = 12 - 6
2x + 3y - 6 = 6
So, 6x - 2y = 14, 2x + 3y - 6 = 6 has the same solution as 3x - y = 7,
2x + 3y = 12
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It costs $46 for 8 people to go ice skating how much will it be for 11 people to go show your work please
Answers
Answer:
It will cost 63.25
Step-by-step explanation:
We can use a ratio to solve
46 dollars x dollars
--------------- = ---------------
8 people 11 people
Using cross products
46 * 11 = 8x
506 = 8x
Divide each side by 8
506/8 =8x/8
63.25 =x
It will cost 63.25
Answer:
$63.25
Step-by-step explanation:
46/8 = $5.75 each
11 x 5.75 = $63.25
. Mount Everest is 29,028 feet above sea level. The bottom of the Mariana Trench is 36,070 feet below sea level. What is the difference between these two elevations?
Answers
Explanation: In order to find the difference of those two you would have to subtract. so the equation would look like this: 29,028-(-36,070)
The difference between these two elevations is 7024 feet.
Given,
Mount Everest is 29,028 feet above sea level.
The bottom of the Mariana Trench is 36,070 feet below sea level.
We need to find out what is the difference between these two elevations.
How do we measure the distance above and below sea level?When we measure the distance above sea level we measure it as a positive distance but when we measure the distance below the surface we measure it as a negative distance.
Find the distance of Mount Everest above sea level.
= 29.028
Find the distance of the Mariana trench below sea level.
= 36,070
Find the difference in distance between them.
We are to find the difference in distance between them not the distance between them.
So,
Mariana trench is higher than Mount Everest by:
= 36,070 - 29,028
= 7024 feet
Thus the difference between these two elevations is 7024 feet.
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The points shown on the graph represent the numbers
in a geometric sequence.
What is the initial value of the sequence?
1
2
3
8
Answers
Task 4:
A Jesus Christ lizard is jumping across the water in search of
food. The equation h = -12t2 + 6t models the lizard's height
in feet above the water t seconds after he jumps.
A: How long after jumping is he back on the water?
0,3
22
B: How high is each jump?
-12(0.251
075 teet
C: How long does it take to get to
his highest point? 0.25
Answers
A: To determine when the lizard is back on the water, we need to find the time when the height (h) is equal to 0. So we set the equation -12t^2 + 6t = 0 and solve for t.
-12t^2 + 6t = 0
Factor out common terms:
-6t(2t - 1) = 0
Set each factor equal to 0:
-6t = 0 or 2t - 1 = 0
Solving each equation:
-6t = 0 --> t = 0
2t - 1 = 0 --> 2t = 1 --> t = 1/2
So the lizard is back on the water at t = 0 seconds and t = 1/2 seconds.
B: The height of each jump can be determined by substituting the time (t) values into the equation h = -12t^2 + 6t.
For t = 0 seconds:
h = -12(0)^2 + 6(0)
h = 0
For t = 1/2 seconds:
h = -12(1/2)^2 + 6(1/2)
h = -12(1/4) + 6/2
h = -3 + 3
h = 0
So each jump has a height of 0 feet.
C: To find the time it takes to reach the highest point, we need to find the vertex of the parabolic equation -12t^2 + 6t. The time at the vertex represents the highest point.
The formula for the x-coordinate of the vertex of a quadratic equation in the form ax^2 + bx + c is given by -b/(2a). In this case, a = -12 and b = 6.
t = -6/(2(-12))
t = -6/(-24)
t = 1/4
So it takes 1/4 seconds to reach the highest point.
Therefore, the answers are:
A: The lizard is back on the water at t = 0 seconds and t = 1/2 seconds.
B: Each jump has a height of 0 feet.
C: It takes 1/4 seconds to reach the highest point.
prove that the following set is countable using a diagram and a formula for the one-toone correspondence function. {±1^1 , ±2^2 , ±3^3 , ±4^4 , ±5^5 , . . .}
Answers
The set {±1^1, ±2^2, ±3^3, ±4^4, ±5^5, ...} is countable. It can be proven by constructing a one-to-one correspondence between the set and the set of positive integers.
To establish a one-to-one correspondence, we can define a function f: ℕ → {±1^1, ±2^2, ±3^3, ±4^4, ±5^5, ...} as follows:
f(n) = (-1)^n * n^n
This function maps each positive integer n to the corresponding element in the given set. It alternates the sign based on the parity of n and raises n to the power of n. The function is one-to-one because each positive integer is uniquely mapped to an element in the set, and no two distinct positive integers are mapped to the same element.
By defining this one-to-one correspondence, we establish that the set {±1^1, ±2^2, ±3^3, ±4^4, ±5^5, ...} is countable, as it can be put into a one-to-one correspondence with the set of positive integers.
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How many terms are in the expression 3x + 5a/2y
Answers
Answer: two
Step-by-step explanation:
the 3 three questions
Answers
Answer:
Step-by-step explanation:
#2 Should be many to one; the reason for this is when doing functions a proper one will have one input to one output.
#3 Should be D; same reasoning as above.
And sorry I am at a loss for #1.
Un cohete de juguete se lanzó al aire desde el techo de un granero. Su altura (h) sobre el suelo en yardas después de t segundos está dada por la función h(t) = −5t2 + 10t + 20¿Cuál era la altura inicial del cohete? *
Answers
Answer:
La altura inicial del cohete es de 20 yardas
Step-by-step explanation:
Los parámetros dados son;
La función que representa la altura en yardas del cohete es h (t) = -5 · t² + 10 · t + 20
Dónde;
t = El tiempo de duración después del cual se lanza el cohete
Por lo tanto, la altura inicial del cohete viene dada por la ecuación para la altura del cohete en el momento de inicio o de inicio cuando t = 0, que se da como sigue;
La altura inicial del cohete = h (0) = -5 × 0² + 10 × 0 + 20 = 20 yardas
La altura inicial del cohete = 20 yardas.
Can you find the value of X & Y?
What are the lengths OF each triangle what is the length of the vertical side, horizontal side, and vertical side divided by the horizontal side pls help or I’ll get a bad grade
ABC
CDE
FGH
PLS HELP FIND X AND Y PLS EXPLAIN WELL!!!
Answers
123456789012345678900987654321123456
Answer: the value of x is 9 and the value of y is 9 there you have your answer
Step-by-step explanation:
6-x / 3 = 8 I need help