The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)=x32 for x>1. Determine the following (round all of your answers to 3 decimal places): (a) P(X<5) (b) P(X>8) (c) P(610) (e) Determine x such that P(X
Answers
The value of P(x < 5) is 0.600. The value of P(x > 8) = 0.125The value of P(6 < x < 10) is 0.375. The value of P(x < 6 or x > 10) is 0.625. The value of x is 2.154
To solve the given problems, we'll use the probability density function (PDF) f(x) = 2/x^3 for x > 1.
a) To find P(x < 5), we need to integrate the PDF from 1 to 5:
P(x < 5) = ∫[1, 5] (2/x^3) dx = [-1/2x^2] evaluated from 1 to 5 = -1/2(5)^2 - (-1/2(1)^2) = 0.600.
b) To find P(x > 8), we integrate the PDF from 8 to infinity:
P(x > 8) = ∫[8, ∞] (2/x^3) dx = [-1/2x^2] evaluated from 8 to ∞ = -1/2(∞)^2 - (-1/2(8)^2) = 0.125.
c) To find P(6 < x < 10), we integrate the PDF from 6 to 10:
P(6 < x < 10) = ∫[6, 10] (2/x^3) dx = [-1/2x^2] evaluated from 6 to 10 = -1/2(10)^2 - (-1/2(6)^2) = 0.375.
d) To find P(x < 6 or x > 10), we subtract P(6 < x < 10) from 1:
P(x < 6 or x > 10) = 1 - P(6 < x < 10) = 1 - 0.375 = 0.625.
e) To determine x such that P(X < x) = 0.75, we set up the equation and solve for x:
∫[1, x] (2/t^3) dt = 0.75. Integrating the PDF, we get [-1/t^2] evaluated from 1 to x = -1/x^2 - (-1/1^2) = -1/x^2 + 1 = 0.75. Solving for x, we find x = 2.154.
In summary, the probability calculations are as follows:
a) P(x < 5) = 0.600
b) P(x > 8) = 0.125
c) P(6 < x < 10) = 0.375
d) P(x < 6 or x > 10) = 0.625
e) x = 2.154 for P(X < x) = 0.75.
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The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x > 1. Determine the following (round all of your answers to 3 decimal places):
a) P(x < 5)=
b) P(x > 8)=
c) P(6 < x < 10)=
d) P(x < 6 or x > 10)=
e) Determine x such that P(X < x) = 0.75
Related Questions
Serena is measuring the length of beetles for a science project 1 Beetle measures 4/5 cm and another measure 7/10 cm.what is the difference in the beatles length
Answers
The difference in the beatles length is 1/10 cm.
Given that Serena is measuring the length of beetles for a science project
Beetle measures 4/5 cm and another measure 7/10 cm.
We have to find the difference in the beatles length
Let us convert one fraction 4/5 to denominator 10 by multiplying numerator and denominator by 2
4/5=8/10
Now difference is 8/10 - 7/10
Which is 1/10
Hence, the difference in the beatles length is 1/10 cm.
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Which rule best describes the following pattern?
8, 4, 10, 6, 12, 8, 14, ...
Answers
Answer: It decreases by four then go up by six or increase by 6.
Step-by-step explanation:
It shows the alternating increased by 2
It decreases by four then go up by six or increases by 6.
We have given the pattern is
8, 4, 10, 6, 12, 8, 14, ....
We can see that
the first number is 8 and the second is 4
8>4
from 8 to 4 it is decreasing and the 4 to 10 it is increasing and again after 10 it is decreasing a.
What is the meaning of increasing?Increasing means there is a second number is greater than the first number third number is greater than the second number and so on.
There is two pattern
8,10,12,14....
Increasing by 2
4,6,8.....
Increasing by 2
Therefore it shows the alternating increased by 2.
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Perform the indicated operation.
6/y-z - 2/y-z
1. -4/y+z
2. -4/y-z
3. 4/y-z
4. 4/y+z
Answers
The value of the given expression 6/(y-z) - 2/(y-z) is 4/(y-z). Option 3 is the correct answer.
What are like terms?In algebra, like terms are those in which the same variable(s) are raised to the same power (s). Because they both have the same variable (y) raised to the same power, the expressions 2xy and -5y are similar (1). When combining terms that have similar coefficients, it's important to preserve the exponent and variable constants.
The given expression is 6/(y-z) - 2/(y-z).
Simplifying the expression by combining the like terms we have:
(6 - 2)/(y-z) = 4/(y-z)
Hence, the value of the given expression is option 3 4/(y-z).
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j^2+6j-40. factor helpppp
Answers
The expression is factorized to give j = -10 and j = 4
How to factor the expressionFrom the information given, we have the quadratic equation as;
j²+ 6j - 40
Using the factorization method, we have to mulitply the coefficient of j² by the constant.
After this, find the pair factors of the product that adds up to give 6
Substitute the values
Then, we have;
j² + 10j - 4j - 40
group the expression in pairs
(j² + 10j) - (4j- 40)
factor the common terms
j(j + 10) - 4(j + 10)
We have;
(j + 10) (j - 4)
j + 10 = 0
collect the terms
j = -10
j = 4
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A series of tile patterns is shown below. Consider the function that represents the number of whitetiles in each figureFigure 1Figure 2Figure 3Figure 4Select all statements that are true.
Answers
Solution
From the figures, the right options are
1) w(n) = 4n + 4 represents the function
To prove this
n = 1,2,3,4 for the different figures respectively.
w(1) = 4(1) + 4 = 8 white tiles in the first figure
w(2) = 4(2) + 4 = 12 white tiles in the second figure
w(3) = 4(3) + 4 = 16 white tiles in the third figure
w(4) = 4(4) + 4 = 20 white tiles in the fourth figure
Hence the first option is right.
2) Input value for the functions are natural numbers as we can see from n = 1,2,3,4 ..... substituted to find the number of white tiles.
3) The function is continuous as n = 1, 2, 3, 4, 5, 6, 7, 8..........
4) Figure 8 will have 36 white tiles.
w(8) = 4(8) + 4 = 32 +4 = 36 white tiles
A security car is parked 25 ft from a movie theater. Find at what speed the reflection of the security strobe lights is moving along the wall of the movie theater when the reflection is 30 ft from the car. The strobe lights are rotating with the speed 2 revolutions per second.
Answers
Answer:
v=20π ft/s
Step-by-step explanation:
Given:
Distance from the security car to the movie theater, D=25 ft
Distance of the reflection from the car, d=30 ft
Speed of rotation of the strobe lights, 2 rev/s
To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.
We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.
ω=2πf
=> ω=2π(2)
=> ω=4π rad/s
The distance between the security car and the reflection on the wall of the theater is...
r=30-25= 5 ft
The speed of reflection is given as (this is the linear velocity)...
v=ωr
Plug our know values into the equation.
v=ωr
=> v=(4π)(5)
∴ v=20π ft/s
Thus, the problem is solved.
The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.
To solve this problem, we can use the concept of related rates. Let's consider the following variables:
x: Distance between the security car and the movie theater wall
y: Distance between the reflection of the security strobe lights and the security car
θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights
We are given:
x = 25 ft (constant)
y = 30 ft (changing)
θ = 2 revolutions per second (constant)
We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.
Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:
x^2 + y^2 = z^2
Differentiating both sides of the equation with respect to time (t), we get:
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.
Plugging in the known values, we have:
2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)
Simplifying the equation, we find:
60(dy/dt) = 120π
Dividing both sides by 60, we get:
dy/dt = 2π ft/s
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Ayden is preparing for a job interview later today. He is deciding what to wear to the interview. He has 6 shirts, 4 pairs of pants, 3 ties, and 2 pairs of shoes. If an outfit consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes, how many different outfits can ayden make?.
Answers
If an outfit consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes, then 144 different outfits Ayden can make.
In the given question we have to find how many different outfits can ayden make.
Ayden has 6 shirts, 4 pairs of pants, 3 ties, and 2 pairs of shoes.
We have to choose outfit for interview consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes.
We have to choose 1 shirt and he has 6 shirts. So he can choose different shirts in 6 ways.
Similarly;
We have to choose 1 pair of pants and he has 4 pair of pants. So he can choose different pair of pants in 4 ways.
We have to choose 1 tie and he has 3 ties. So he can choose different ties in 3 ways.
We have to choose one pair of shoes and he has 2 pair of shoes. So he can choose different pair of shoes in 2 ways.
So the total different outfits that he select = 6*4*3*2 = 144
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A greengrocer buys 20 cases of oranges at a cost of $15 per case. Each case contains 10 kg of oranges. If he sells the oranges at $4/kg, how many kilograms must he sell before he makes a profit? If he sells all the oranges what will be his profit?
Answers
Answer:greengrocer should Dell 17 kg before profit. 500$ profit
Step-by-step explanation:
78. the probability that a marksman will hit a target each time he shoots is 0.89. if he fires 15 times, what is the probability that he hits the target at most 13 times?
Answers
The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.
Given that,
A marksman has a 0.89 percent chance of hitting the target each time he fires.
We have to find what is the probability that he will only hit the target 13 times out of 15 shots.
We know that,
The probability of getting exactly k successes in n trials is given by the probability mass function that is,
P(X=k)=\((\frac{n}{k} )p^{k}(1-p)^{n-k}\)
Where \((\frac{n}{k})= n!/k!(n-k)!\)
The probability that he hits the target at most 13 times is,
1-[P(he hits 14 times)+P(he hits 15 times)]
So, calculate the probability that he hits a target 14 times as follows:
P(X=14)=\((\frac{15}{14} )0.89^{14}(1-0.89)^{1}\)
P(X=14)=15×(0.89)¹⁴×(0.11)
P(X=14)=0.3228
And the probability that he hits a target 15 times is
P(X=15)=\((\frac{15}{15} )0.89^{15}(1-0.89)^{0}\)
P(X=15)=1×(0.89)¹⁵×(1)
P(X=15)=0.1741
And the required probability is
=1-[P(he hits 14 times)+P(he hits 15 times)]
=1-[0.3228+0.1741]
=0.5031
Therefore, The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.
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Select the correct answer from each drop-down menu.Some of the images in the diagram are images of polygon 1 from similarity transformations.ty2422B20১ম ৪ ৪ ০ ০ ২ ০18polygon 11614Do12Epolygonpolygon 486polygon 3polygon 5N02 4 6 8 10 12 14 16 18 20 22 24 26Polygon✓ and polygon
Answers
Solution
By definition of similar figures:
Similar figures are two figures having the same shape
The polygons that are similar to poly gone 1 are
Polygon 3 and Polygon 4
Diego is trying to find the value of X in 5 • x = 35. He draws his diagram but it’s not certain how to proceed. 1. Complete the tape diagram so represents the equation 5•x = 352. Find the value of x.Type the answer in the box belowX=__(Please use pictures or screenshots.
Answers
The tape diagram is:
Then we have that x times x equals to 35
What number multiplied 5 times is 35? The answer is 7
The answer to two is 7
We have the equation:
\(x\cdot5=35\)this means, that x is a number that multiplied by 5 is equal to 35. We can then divide both sides by 5:
\(x\cdot\frac{5}{5}=\frac{35}{5}\)By the multiplication table, we know that 5 *7 = 35. Thus:
\(x=7\)The answer is x = 7
The masses of the oranges on sale at a farm stand are normally distributed with a mean of 239 grams and a standard deviation of 25
grams.
Enter the Z-score of an orange that has a mass of 259 grams.
Answers
Answer:
0.8
Step-by-step explanation:
i just took the test
five hamburgers cost 5.25 at this rate what is the cost of 8 hamburgers
Answers
Answer: 8.4
Step-by-step explanation: 5.25 divided by 5 is 1.05. So 1.05 x 8 is 8.4
2. Price of 1 is 1.05
3. 1.05 multiply by 8 is 8.40
ANSWER: $8.40 for 8
the perimeter of a rectangle is 80x. the base is two times the height. in terms of x, what are the dimensions of the rectangle?
Answers
The perimeter of a rectangle is 80x. The base is two times the height. In terms of x, The width and length of the dimensions rectangle in terms of x are (80x/6) and (160x/6) respectively.
The dimensions of the rectangle in terms of x are as follows:
The perimeter of a rectangle is twice the sum of the length and the width. If the length and width of a rectangle are l and w, respectively, then the perimeter is 2(l + w).
According to the problem statement, the perimeter of a rectangle is 80x.
The width and length of a rectangle in terms of x are w and 2w, respectively. Because the base is two times the height.
Thus, we have the equation for the perimeter:
2 (l + w) = 80x Or,
substituting the value of l and w in terms of x, we have:
2 (2w + w) = 80x2(3w) = 80x6w = 80xw = 80x/6
The width of the rectangle, in terms of x is 80x/6. The length of the rectangle, in terms of x is 2(80x/6) or 160x/6.
Therefore, these are the dimensions of the rectangle.
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A salt mixture hss 7 parts water and 1 part salt. Suppose another part of salt is added. What is the new ratio of salt to water?
A) 7 to 1
B) 1 to 7
C) 2 to 7
D) 2 to 8
Answers
Answer:a
Step-by-step explanation:
Answer:
C) 2 to 7
Step-by-step explanation:
1 part salt:7 parts water
Add 1 part salt
2 part salt: 7 Parts water
Estimate the area of the following figure shown below. each square is 9ft
5.5 ft^2
6ft^2
49.5 ft^2
54 ft^2
Answers
Answer:
(c) 49.5 ft²
Step-by-step explanation:
We choose to estimate the area by comparison to the figure attached. Its area is (5.25)(9 ft²) = 47.25 ft². We don't believe the discrepancies are so large that we need to add another whole square to the area estimate.
Our choice is 49.5 ft².
In a level-C confidence interval about the proportion p of some outcome in a given population, the margin of error, m, is o the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population. the minimum distance between the sample statistic and the population parameter in C% of random samples of the same size from that population. o the maximum distance between the sample statistic and the population parameter in C% of random samples of the same size from that population. O the minimum distance between the sample statistic and the population parameter in any random sample of the same size from that population.
Answers
The margin of error in a level-C confidence interval is the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population
In a level-C confidence interval about the proportion p of some outcome in a given population, the margin of error (m) represents the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population.
The margin of error is a measure of the precision or uncertainty associated with estimating the true population proportion based on a sample. It reflects the variability that can occur when different random samples are taken from the same population.
When constructing a confidence interval, a level-C confidence level is chosen, typically expressed as a percentage. This confidence level represents the probability that the interval contains the true population parameter. For example, a 95% confidence level means that in repeated sampling, we would expect the confidence interval to contain the true population proportion in 95% of the samples.
The margin of error is calculated by multiplying a critical value (usually obtained from the standard normal distribution or t-distribution depending on the sample size and assumptions) by the standard error of the sample proportion. The critical value is determined by the desired confidence level, and the standard error accounts for the variability in the sample proportion.
The margin of error provides a range around the sample proportion within which we can confidently estimate the population proportion. It represents the uncertainty or potential sampling error associated with our estimate.
To summarize, the margin of error in a level-C confidence interval is the maximum distance between the sample statistic and the population parameter in any random sample of the same size from that population. It accounts for the variability and uncertainty in estimating the true population proportion based on a sample, and it helps establish the precision and confidence level of the interval estimation.
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Carlos is picking 6/384 apples. Mateo is picking oranges of 10. How much did Mateo pick?
Answers
Question might be incomplete or incorrect so we'd have to assume Mateo took apples
Answer:
5/189 apples
Step-by-step explanation:
If Carlos picks 6/384 apples then there must be 384 apples available to pick from. Amount of apples left after Carlos picks =384-6=378 apples
If Mateo picks 10 apples after Carlos then how much apples Mateo has taken would depend on the number of apples available, hence the fraction of apples Mateo has taken = 10/378
Reduce to lowest terms to get 5/189 apples
Whats the distance (7,0) and (-8,45)
Answers
Answer:
\(d = 15\sqrt{10}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra II
Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)Step-by-step explanation:
Step 1: Define
Point (7, 0)
Point (-8, 45)
Step 2: Find distance d
Substitute: \(d = \sqrt{(-8-7)^2+(45-0)^2}\)Subtract: \(d = \sqrt{(-15)^2+(45)^2}\)Exponents: \(d = \sqrt{225+2025}\)Add: \(d = \sqrt{2250}\)Simplify: \(d = 15\sqrt{10}\)explain why the columns of an n times nn×n matrix a are linearly independent when a is invertible.
Answers
The columns of an n x n invertible matrix A are linearly independent.
If a matrix A is invertible, it means that it has an inverse matrix A^-1, such that the product of A and A^-1 is the identity matrix I.
AA^-1 = A^-1A = I
Now, let's assume that the columns of A are linearly dependent. This means that there exist scalars c1, c2, ..., cn, not all zero, such that
c1A[:,1] + c2A[:,2] + ... + cnA[:,n] = 0
where A[:,i] represents the i-th column of A.
Multiplying both sides by A^-1, we get
A^-1(c1A[:,1] + c2A[:,2] + ... + cnA[:,n]) = A^-10
Since A^-1A = I, we can simplify the left-hand side to get
c1A^-1A[:,1] + c2A^-1A[:,2] + ... + cnA^-1A[:,n] = 0
c1I[:,1] + c2I[:,2] + ... + cnI[:,n] = 0
c1e1 + c2e2 + ... + cne_n = 0
where I is the identity matrix and ei is the i-th standard basis vector.
Since the ei's are linearly independent, it follows that c1 = c2 = ... = cn = 0. But this contradicts our assumption that the scalars are not all zero, which means that the columns of A cannot be linearly dependent. Therefore, the columns of an n x n invertible matrix A are linearly independent.
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You roll a standard number cube 7 times Assume that each number is equally likely to come up each time you roll To the nearest tenth of a percent the probability that number less than 3 comes up exactly 4 of the 7 times
Answers
Answer:
0.4%
Step-by-step explanation:
If we are looking to have a number less than 3 rolled 4 out of 7 times.
Our winning numbers are 1 and 2. Our losing numbers are 3, 4, 5, and 6.
This means that our winning percentage is 33.3% and our losing percentage is 66.6%.
We need to multiply these numbers together taking our number of rolls into account.
.333 * .333 * .333 * .333 * .666 * .666 * .666 = 0.0036
What is the slope of a line perpendicular to the line whose equation is 6x+3y=-63
Answers
Answer:
y=x/2−63
Step-by-step explanation: 6x+3y=-63 3y=6x-63= y=2/x-63
Answer:
The slope of a line perpendicular to the line whose equation is 6x+3y=-63 will be: 1/2
Step-by-step explanation:
We know that the slope intercept-form of the line equation is
\(y=mx+b\)
where m is the slope and b is the y-intercept
Given the equation
\(6x+3y=-63\)
simplifying the equation to write in the slope-intercept form
\(y=-2x-21\)
Thus, the slope = -2
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be:
\(\frac{-1}{-2}=\frac{1}{2}\)
Therefore, the slope of a line perpendicular to the line whose equation is 6x+3y=-63 will be: 1/2
Suppose, we need to differentiate numerically the following function f(x)=14x²+11.33x−11 Which differentiation rule (forward, backward, 3 point, or 5 point) would the most efficient to use in terms of computational performance and accuracy? Please explain.
Answers
The 3-point differentiation rule is computationally efficient because it requires evaluating the function at three points and performs a simple arithmetic calculation to estimate the derivative.
The 3-point differentiation rule, also known as the central difference method, provides a good balance between computational efficiency and accuracy. It approximates the derivative of a function using three points: one point on each side of the desired differentiation point.
In the 3-point differentiation rule, the derivative is calculated using the formula:
f'(x) ≈ (f(x + h) - f(x - h)) / (2h)
where h is a small step size.
Compared to other methods, such as the forward or backward difference rules, the 3-point rule provides better accuracy as it takes into account information from both sides of the differentiation point. It reduces the error caused by the step size and gives a more accurate approximation of the derivative.
Additionally, the 3-point differentiation rule is computationally efficient because it requires evaluating the function at three points and performs a simple arithmetic calculation to estimate the derivative. This makes it a practical choice for differentiating functions, providing a good trade-off between accuracy and computational performance.
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A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being odd numbers is 9 over 36.
If the experiment is repeated 140 times, predict the number of times both spins will be odd numbers.
140
70
36
35
Answers
So, based on the theoretical likelihood, we anticipate that 35 times out of 140 repeats, both spins will be odd numbers.
What is probability?Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.
Here,
The theoretical probability of both spins being odd numbers is 9 over 36, which means that for every 36 times the experiment is repeated, we expect 9 of those times to result in both spins being odd numbers.
If the experiment is repeated 140 times, we can use the theoretical probability to estimate the number of times both spins will be odd numbers as follows:
140 * (9/36) = 35
So, based on the theoretical probability, we predict that both spins will be odd numbers 35 times out of 140 repetitions.
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at what rate per annum should p2400 be invested so that it will earn an interest of p800 in 8 years?
Answers
The interest rate is 4.17%, according to the question.
What do you mean by interest rate?
An amount that a borrower must pay to a lender as interest during the course of a loan, stated as a percentage of the loan amount is called interest rate.
According to data in the given question,
We have the given values:
Amount to be invested/Principal: 2,400
Amount of Interest: 800
Time: 8 years
Now, we will calculate the rate,
Solve for the rate:
Interest = Principal × Rate × Time
Derive the equation for rate:
Rate = [Interest ÷ (Principal × Time)] × 100
Substitute the given values:
Rate = [800 ÷ (2,400 × 8)] × 100
Rate = [800 ÷ 19,200] × 100
Rate = 0.04167 × 100
Rate = 4.17 %
Therefore, the rate is 4.17%.
Check:
800 = 2,400 × 8 × 0.04167
800 = 800.064
800 = 800
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The price for 3 pounds of apples is $3.99. What is the unit rate?
Answers
Answer:
the unit rate is 1.33$ per pound of apples
Step-by-step explanation:
you can rewrite the word problem as
3x = 3.99.
now just divide both sides by 3.
3x / 3 = 3.99/3
x = 1.33
What is the numeric expression that matches 8 fewer than y?
Answers
Answer:
y-8
Step-by-step explanation:
Paula says that 2/3 is equivalent to 4/9 because 4 is a multiple of 2 and 9 is a multiple of 3. explain her error.
Answers
Answer:
Paula is wrong because, in order to be equivalent, the nominator and denominator of a fraction must have to be multiplied by the same number.
Step-by-step explanation:
Paula is wrong because, in order to be equivalent, the nominator and denominator of a fraction must have to be multiplied by the same number.
4/9 is basically obtained when we multiply the denominator of 2/3 by 2 and denominator by 3, which is wrong.
Thus, the correction is as follows:
Given the fraction
\(\frac{2}{3}\)
Multiply the nominator and denominator of the fraction by 2
\(\frac{2\times 2}{3\times 2}=\frac{4}{6}\)
Thus, the 4/6 is the correct equivalent expression of 2/3.
let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).
Answers
The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.
Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point
\(r(x) = f(g(x))\)therefore the derivative of r is given by \(r'(x) = f'g(x)\times g'(x)\)
\(r'(1) = f'(g(1))\times g'(1)\) from the graphs
r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0
Similarly s'(1) = g'(f(1))\times f'(1) from the graphs
f(1)=1.5, f'(1)
=\dfrac{ (3-0)}{(0-2)}
= -3/2 , g'(3/2) = 0
s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0
To learn more about derivative check the link below:
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Complete question:
let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).
Which equation is true for the value b = 10?
a 2(b + 4) = 16
b 2(b + 2) = 40
c 3(b – 2) = 24
d 2(8 + b)
Answers
explanation