General solution = CF + PS= c₁ cos 5x + c₂ sin 5x - (2/25) tan 5x= C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)), where C = c₂ and D = c₁.
Explanation:
The general solution of the given non-homogeneous differential equation: y"(x) + 25y(x) = 2tan 5x isy (x) = C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)).
First of all, we need to find the complementary function(CF) of the differential equation to find the general solution.To find the complementary function (CF),
we set the non-homogeneous term to 0.y" (x) + 25y (x) = 0T
his is a homogeneous differential equation with the characteristic equation: r² + 25 = 0Solving this quadratic equation gives:r = ± 5i
Hence, the complementary function is given by:CF = c₁ cos 5x + c₂ sin 5xwhere c₁ and c₂ are constants of integration.
Now, we find the particular solution (PS) of the given non-homogeneous differential equation using the method of undetermined coefficients.
Given, y" (x) + 25 y (x) = 2 tan 5x
For PS, we assume that y = A tan 5x + B
where A and B are constants to be determined.Substituting this in the given equation, we get:10A sec² 5x + 25(A tan 5x + B) = 2 tan 5x
Simplifying this equation, we get:10A sec² 5x + 25A tan 5x + 25B = 2 tan 5x⇒ 10A sec² 5x + 23A tan 5x + 25B = 0
Comparing the coefficients of tan 5x and sec² 5x on both sides, we get:A = -2/25 and B = 0
Hence, the particular solution is given by:PS = - (2/25) tan 5xNow, the general solution of the given non-homogeneous differential equation is given by
:GS = CF + PS= c₁ cos 5x + c₂ sin 5x - (2/25) tan 5x= C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)), where C = c₂ and D = c₁.
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let p value of our hypothesis testing problem is 0.10 with significance level of 0.05. what is the probability that null hypothesis is true?
Probability of the null hypothesis being true is greater than the significance level.
The probability that the null hypothesis is true depends on the significance level set before the hypothesis test. In this case, the significance level was set at 0.05 and the p-value obtained was 0.10. This means that the probability of the null hypothesis being true is greater than the significance level (0.10 > 0.05), so the null hypothesis cannot be rejected.
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1. How long does pia's journey take?
2. How much longer does Sam spend driving then Pia?
a) Pea's journey takes 2.25 hours.
b) Sam spends 0.25 hours longer driving than Pea.
a. To find Pea's journey time, we use the formula:
time = distance / speed
Substituting the values given, we get:
time = 180 km / 80 km/h
time = 2.25 hours
b. To find how much longer Sam spends driving than Pea, we can subtract the journey times.
time taken by Sam = distance / speed = 200 km / 80 km/h = 2.5 hours
Time difference = Sam's journey time - Pea's journey time = 2.5 hours - 2.25 hours = 0.25 hours
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Which of the cross sections described would result in a rectangle with a height of
inches (in.)?
A.A horizontal cross section through the center of a sphere with a radius of 4 in.
B. A horizontal cross section through the center of a cone with a radius of 4 and a height of 4 in.
C. A vertical cross section through the center of a cone with a radius of 4 and a height of 4 in.
D. A vertical cross section through the center of a cylinder with a radius of 4 and a height of 4 in.
Answer:B. A horizontal cross section through the center of a cone with a radius of 4 and a height of 4 in.
Step-by-step explanation:
a supply container dropped from an aircraft by parachute hits a target with a probability of 0.37. (a) what is the expected number of container drops needed to hit a target?
The given probability is 0.37 which is the probability of a supply container dropped from an aircraft by a parachute hitting a target. So the expected number of container drops needed to hit a target is approximately 2.7027.
To find out the expected number of container drops needed to hit a target, we can use the formula given below;
E(X) = (1/p) E(X)
= (1/0.37)E(X)
= 2.7027
Thus, the expected number of container drops needed to hit a target is approximately 2.7027.
An expected value is a statistical concept that represents the theoretical average value of a random variable. It is represented as E(X).
The expected value is calculated by multiplying each possible value of the random variable by its probability and then adding all of the products.
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What is the percent of decrease from 98.7 to 0?
Answer:
100% because it goes to zero which means 100% is decreased
if you're good at quadratics...
Therefore, the correct answer is: [tex](x+10)^2=82[/tex]. ( right hand side of the equation).
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically contains variables, which are represented by letters, and may also include constants and operators. The general format of an equation is:
expression = expression
For example, the equation x + 2 = 6 means that the expression x + 2 is equal to the expression 6. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.
To solve the quadratic equation by completing the square, Jamie needs to follow the steps:
Move the constant term to the right-hand side of the equation:
[tex]x^2 + 20x = -18[/tex]
Add and subtract the square of half the coefficient of x to the left-hand side of the equation:
[tex]x^2 + 20x + (20/2)^2 - (20/2)^2 = -18[/tex]
[tex](x+10)^2 - 100 = -18[/tex]
Simplify the right-hand side of the equation:
[tex](x+10)^2 = 82[/tex]
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Since the beginning of school, Steven has been saving money to buy a new phone. His bank balance is represented by the graph below.
a. According to the graph, about how much money had Steven saved after 2 weeks of school?
b. About how much money did Steven probably have after 4 weeks of school? How can you tell?
c. If he keeps saving at the same rate, how much will he have saved by Week 7? Explain how you know.
a. According to the graph, Steven had saved about $100 after 2 weeks of school.
b. According to the graph, Steven probably had about $200 after 4 weeks of school because the graph shows that he saves an average of $50 per week, so after 4 weeks, he would have saved $50 x 4 = $200.
c. If Steven keeps saving at the same rate, he will have saved $350 by Week 7. This is because he saves $50 per week, so after 7 weeks, he will have saved $50 x 7 = $350.
the annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches. find the probability that a randomly selected cedar tree will grow more than 8 inches in a given year. round your answer to four decimal places, if necessary
The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches. 0.8 is the probability that a randomly selected cedar tree will grow more than 8 inches in a given year.
The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.
To find the probability that a randomly selected cedar tree will grow more than 8 inches in a given year, the following steps should be followed:
Calculate the range of increase in height of cedar trees:
The range of increase in height is
(12 - 7) = 5 inches.
Calculate the probability that a cedar tree will grow more than 8 inches:
P(X > 8) = (12 - 8) / 5 = 0.8
where X is the annual increase in height of a cedar tree.
Round the answer to four decimal places:
Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is 0.8000 or 0.8 (rounded to four decimal places).
Probability can be defined as the measure of how likely an event is to occur.
The probability of an event ranges between 0 and 1, where 0 denotes that the event will not occur and 1 denotes that the event will certainly occur.
If a random variable X has a uniform distribution over an interval (a, b), then the probability of X falling between two values c and d is given by:
P(c < X < d) = (d - c) / (b - a)
In this problem, the annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.
Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is: P(X > 8) = (12 - 8) / (12 - 7) = 4 / 5 = 0.8 (rounded to four decimal places).
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Select the correct answer.
A graph with a y-axis and an x-axis in positive and negative planes. Two lines L I and I J are formed by connecting points (Negative 4,3), (5,3), and (5, Negative 3).
I(5, 3), J(5, -3), and L(-4, 3) are three vertices of rectangle IJKL. What are the coordinates of the fourth vertex, K, of rectangle IJKL?
A.
(-4, -3)
B.
(5, 3)
C.
(5, -3)
D.
(-4, 3)
The cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
Thus, οptiοn D is cοrrect.
What is the cοοrdinate geοmetry?Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetry using the principles οf algebra.
The rectangle IJKL is fοrmed by cοnnecting the pοints I, J, K, and L in a clοckwise οr cοunterclοckwise manner. Since I and J have the same x-cοοrdinate and are οn οppοsite sides οf the x-axis, and L and K have the same y-cοοrdinate and are οn οppοsite sides οf the y-axis, it fοllοws that the diagοnals οf the rectangle IJKL intersect at the οrigin (0,0).
Therefοre, the cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
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a container of hot liquid is placed in a freezer that is kept at a constant temperature of 25f. the initial temperature' of the liquid is 170f. after 4 minutes, the liquid's temperature is 70f. how much additional time (after 4 minutes) will it take for its temperature to decrease to 35f? round your answer to two decimal places.
The additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes is 21.54 minutes (rounded to two decimal places).
Given that: Initial temperature of the liquid, T₁ = 170°F.Final temperature of the liquid, T₂ = 35°F.Constant temperature of the freezer, T = 25°F.
Time taken to decrease the temperature of the liquid from 170°F to 70°F, t₁ = 4 minutes.
The rate of change of temperature, R = (T₁ - T) / t₁ = (170°F - 25°F) / 4 minutes = 111.25°F/minute.
In the freezer, the rate of change of temperature is constant. Hence, the rate of change of temperature after 4 minutes can be used to calculate the additional time it will take for the liquid's temperature to decrease from 70°F to 35°F:R = (T₂ - T) / t₂ = (35°F - 25°F) / t₂t₂ = (10°F / R) = (10°F / 111.25°F/minute) = 0.089728 minutes ≈ 5.38 seconds.
Adding this time to the initial 4 minutes, we have the additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes: t = t₁ + t₂ = 4 minutes + 0.089728 minutes ≈ 4.089728 minutes or 4 minutes 5.38 seconds.
The additional time it will take for the temperature of the liquid to decrease to 35°F after 4 minutes is 21.54 minutes (rounded to two decimal places).
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solve problems 3 and 4 in homework 2 by constructing confidence intervals about the parameters to be tested, rather than performing hypothesis testing. do you get the same results as before?
Confidence intervals provide more information than hypothesis tests as they give an estimate of the parameter value as well as a range of plausible values, whereas hypothesis tests only give a decision about the null hypothesis.
To solve problems 3 and 4 in homework 2 by constructing confidence intervals about the parameters to be tested, rather than performing hypothesis testing, we need to take the following steps:
Step 1: Calculate the sample mean and sample standard deviation from the given data.
Step 2: Calculate the standard error (SE) using the formula: SE = σ / √n`,
where `σ` is the population standard deviation (if known), or the sample standard deviation (if population standard deviation is unknown)
and `n` is the sample size.
Step 3: Calculate the margin of error (ME) using the formula: `ME = z * SE`,
where `z` is the z-score corresponding to the desired level of confidence.
Step 4: Calculate the confidence interval (CI) using the formula: `CI = sample mean ± ME.
Step 5: Interpret the confidence interval in the context of the problem.
Statement: Do you get the same results as before.
No, we do not get the same results as before.
When we construct a confidence interval, we obtain a range of plausible values for the parameter with a certain level of confidence, whereas in hypothesis testing, we either reject or fail to reject the null hypothesis based on the sample data at a certain level of significance.
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A ____ specifies which subjects and objects users or groups can access.
An access control list (ACL) specifies which subjects and objects users or groups can access.
What is Access Control List (ACL)?An Access Control List (ACL) is a term used to describe a security mechanism that regulates who has access to an object in a computing system. An Access Control List (ACL) is a type of file that contains the names of people or groups of individuals who are allowed or denied access to a system resource.
ACLs are one of the most widely used security measures in computer networks today, and they are used to establish access control policies for network resources such as files, folders, devices, or services. This list is compiled on the basis of the requirements and policies of the security team in place.
The access control list (ACL) is a security feature that allows administrators to define and manage the permissions and rights for different users or groups to access specific resources, such as files, directories, or applications. Implementing an ACL helps to ensure proper security and privacy in a system or network.
The access control list (ACL) is correct in the blanks.
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the estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line. True or false
The given statement "The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line" is true because it provides the best fit line.
The simple linear regression equation estimates the relationship between two variables - a dependent variable (y) and an independent variable (x) - by fitting a straight line through the data points.
The line is chosen so that the sum of the squared deviations (also known as the sum of squared errors or SSE) between the observed values of y and the predicted values of y on the line is minimized.
In other words, the simple linear regression equation finds the line that is closest to all the data points in terms of the vertical distance between the points and the line.
This line is chosen to minimize the sum of squared deviations because it provides the best estimate of the relationship between x and y, and it allows for the prediction of y values for a given x value.
Thus, minimizing the sum of squared deviations is a crucial aspect of the simple linear regression equation because it ensures that the line of best fit provides the most accurate estimate of the relationship between the variables.
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Which of these investments would be considered high-risk?
Stocks
Pension Plans
Certificate of Deposit
Annuities
Answer: Stocks
Step-by-step explanation: People mainly live on wim's so stocks at times can be unpredictable.
Gina Wilson All things Algebra Unit 10 Homework 6 answer key
Examining the figures of the circles, the values for x is calculated to be
11. x = 8
12. ED = 11
How to solve for xThe value of x in the two figure is solved using the relationship between secant and angle measures
11. The formula used here is
(2x + 7) = 0.5 * (78 - 32)
(2x + 7) = 0.5 * (46)
2x + 7 = 23
solving for x
2x = 23 - 7
2x = 16
x = 8
12.
11x - 9 = 0.5 ( (15x-39) - (9x-3) )
11x - 9 = 0.5 ( 15x - 39 - 9x + 3 )
11x - 9 = 0.5 ( 6x - 36 )
11x - 9 = 3x - 18
11x + 3x = -18 + 9
14x = -9
x = 14/9 = 1.56
solving for
ED = 9x - 3 = 9 * 14/9 - 3 = 14 - 3 = 11
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your neighborhood fast food restaurant only sells chicken nuggets in packs of five or seven. what is the largest number of nuggets that is impossible to order?
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven. This is because the restaurant only sells nuggets in packs of five and seven. This means that if you wanted to order eleven nuggets, it would not be possible.
To explain this mathematically, eleven can be written as 5+5+1, 7+4, or 3+3+3+2. As none of these can be made with just five and seven packs of chicken nuggets, it is impossible to order eleven.
If the restaurant sold chicken nuggets in packs of three and seven, then it would be possible to order eleven nuggets (3+3+3+2).
In conclusion, the largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
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I need some help please
Answer:
−18 x + 12
Step-by-step explanation:
multiply using the distributive property
Answer:
-2(9x-6)
-2 divided by 9x = - 18
-2 divided by - 6 = 12 (negative + negative =positive)
= - 18x +12
The product of two positive consecutive integers is 2 less than
twice their sum. Find the integers.
The two positive consecutive integers as required to be determined are; 3 and 4.
What are the integers which are as described?It follows from the task content that;
Let the positive consecutive Integers be; x and (x + 1).
Therefore, we have that;
x (x + 1) = 2 (x + x + 1) - 2
x² + x = 4x + 2 - 2
x² - 3x = 0
x = 0 or x = 3.
Since the integers are positive, Therefore, the integers in discuss are 3 and 4.
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the temperature at 12 noon was 10 degree Celsius above zero .if it decreases at the rate of 2 degree Celsius per hour until midnight ,at what time would the temperature be 8 degree Celsius below zero? what would be the temperature at midnight?
Answer:
The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.
What is the base, rate of change (incr/decr), and is it growth or decay
Y=3000(0.72)^x
The key features of the function are Base = 0.72, Rate = decrement and it decays
identifying the key features of the functionGiven that
y = 3000 * (0.72)ˣ
The given equation is in the form of exponential decay:
Base: The base of the exponential function is the constant term that is being raised to a power. In this case, the base is 0.72.
Rate of change: The rate of change is the factor by which the function is being multiplied or divided as the input variable increases.
Since the base is less than 1, the function is decreasing as x increases. The rate of decrease is given by the base, which is 0.72.
Growth or decay: As the base is less than 1, the function is decreasing, which means it is a decay function.
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What is the slope of the line parallel to the function: * y = 50 -0.5x 50 0.5 -0.5 02
The slope of the line parallel to the function: y = 50 - 0.5x include the following: C. -0.5.
What are parallel lines?In Mathematics and Geometry, parallel lines simply refers to two (2) lines that are always the same or equal distance apart and never meet.
Generally speaking, two (2) lines are considered as parallel under the following standard conditions:
Slope, m₁ = Slope, m₂.
From the function, we have:
y = 50 - 0.5x
Slope, m = -0.5
In this context, we can reasonably infer and logically deduce that the slope of the two lines would be equal and the same:
Slope of line 1 = Slope of line 2
-0.5 = -0.5
In conclusion, we can logically deduce that the slope of the given line is equal to -0.5.
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analysis of a pert problem shows the estimated time for the critical path to be 108 days with a variance of 64. there is a .90 probability that the project will be completed before approximately day: group of answer choices 108. 98. 115. 118. 109.
There is a .90 probability that the project will be completed before approximately day 118.
The given information can be solved by using the formula of z-score as follows:
Z = (X - μ)/σ
Where: Z = z-score
X = the time for project completion
μ = the mean time for the critical path
σ = standard deviation for the critical path
σ² = variance of the critical pathσ = √64
σ = 8
Given that the mean time for the critical path is μ = 108 days and σ = 8 days,
Therefore, the z-score of the completion of the project before 108 days is given by:
Z = (X - μ)/σ0.90
= P(Z < z)
= P(Z < (X - 108)/8)P(Z < (X - 108)/8)
= 0.90
Using a z-table or calculator, we find the z-value to be 1.28.
Then,1.28 = (X - 108)/8
Multiplying both sides by 8, we get:10.24 = X - 108
Adding 108 to both sides, we get: X = 118.24
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Solve each of the given inequalities for z. Which of the inequalities has 5 as a solution?
Inequality 1 Inequality 2
(4(2.8z + 1.75) > - 26.6) (2(1.9z + 1.5) <= 18.2)
Answer: Inequality 1
Step-by-step explanation: Let's solve each inequality first.
4(2.8z+175 )>-26.6
let's distribute the 4.
4(2.8z)+4(175)
11.2z+700>-26.6
Now let's isolate the variable by subtracting 700 on each side.
11.2z>-726.6
Now let's divide both sides by 11.2
z>-64.875
Oh? This one already has 5 as a solution as 5 is more than -64.875!
determine whether the property is true for all integers, true for no integers, or true for some integers and false for other integers. justify your answers. the average of any two odd integers is odd.
The property of the average of any two odd integers being odd is true for all integers.
This is because the sum of any two odd integers is always an even integer. For example, if we take any two odd integers, say 3 and 7, then the sum of these two is 10, an even integer. Therefore, the average of 3 and 7, which is (3 + 7)/2, is also an even integer, in this case, 5.
Since all even integers are divisible by 2, the average of any two odd integers must be an odd integer.
Therefore, the property is true for all integers.
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Consider the expression 2(3n + 6z)
Enter an expression that shows the sum of exactly two terms that is equivalent to 2(3n+6z)
Answer:
6n+12z
Step-by-step explanation:
then we got this bc we do like terms so 6n from 2 x3n then 12z bc 2x6
_______ is/are formed immediately after the union of sperm and ovum in the fallopian tube.
A Zygote is/are formed immediately after the union of sperm and ovum in the fallopian tube.
What is a zygote?A zygote is a cell formed when two gamete cells are fused by means of sexual reproduction. These cells contain a single set of chromosomes from both the father and the mother of the offspring. As a result, the zygote contains all of the genetic information required to create a completely new person. After the fertilization of the ovum by the sperm, the zygote is formed. The zygote will continue to divide into a multicellular embryo and eventually a fetus after fertilization has taken place.
The fusion of a sperm cell with an ovum in the fallopian tube leads to the formation of a zygote, which involves the combination of genetic material from both parents resulting in the creation of a single-celled zygote. This zygote then initiates the process of cell division and progresses into an embryo.
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 45.2 is the most accurate to use to show that they need more money.
The median of 49 is the most accurate to use, since the data is skewed.
The mean of 49 is the most accurate to use to show that they have plenty of money.
The mean of 45.2 is the most accurate to use, since the data is skewed.
The median of 49 is the most accurate to use, since the data is skewed.
What is distribution?Distribution refers to the pattern of variation in a dataset. Specifically, it refers to how the values in the dataset are spread out or clustered together.
According to question:The most appropriate measure of center to represent the data depends on the shape of the distribution. In this case, we can see from the histogram that the data is skewed to the right, with a longer tail of higher values.
In skewed distributions, the median is generally a more appropriate measure of center than the mean. This is because the mean can be influenced by extreme values in the tail of the distribution, whereas the median is more resistant to such outliers.Therefore, the correct answer is: the median of 49 is the most accurate to use, since the data is skewed. This represents the middle value of the data when it is arranged in order, and is less sensitive to the outliers at the high end of the distribution. Using the median can give a more accurate representation of the typical donations received by the charity.
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a spinner with the letters a, b, c, and d is spun. what is the theoretical probability of landing on the letter c?
The probability of the spinner landing on the letter C is 1/4
To understand the probability of the spinner landing on the letter C, we need to start by looking at the total number of possible outcomes. In this case, there are four possible outcomes, corresponding to the four letters A, B, C, and D.
Since each of the four quadrants on the spinner is equal in size, each of the four letters has an equal chance of being landed on. Therefore, the probability of the spinner landing on the letter C is the number of ways that the spinner can land on C, divided by the total number of possible outcomes.
Since there is only one way for the spinner to land on C, and there are four possible outcomes in total, the probability of the spinner landing on the letter C is 1/4
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The given question is incomplete, the complete question is:
A spinner with four equal quadrants labeled A, B, C, and D is spun. What is the theoretical probability of the spinner landing on the letter C
3.1.1) Determine the Accumulated amount for the investment at CAPITEC.
3.1.2) Determine the Accumulated amount for the investment at FNB.
3.1.3) Use the information you worked out to help Lebo decide which bank will give her the better investment. Explain your answer.
1. The accumulated amount for the investment at CAPITEC is R36,750.
2. The accumulated amount for the investment at FNB is R33,480.
3. Lebo will earn more interest if she invests her money at Capitec than at FNB.
What is the Accumulated amount for the investment at CAPITEC?The accumulated amount for the investment at Capitec with a principal amount of R30,000 invested at a simple interest rate of 7.5% for 3 years can be calculated as follows:
[tex]= Principal + (Principal * Rate * Time)\\= R30,000 + (R30,000 * 0.075 * 3)\\= R30,000 + R6,750\\= R36,750[/tex]
What is the Accumulated amount for the investment at FNB?The accumulated amount for the investment at FNB with a principal amount of R30,000 invested at a compound interest rate of 3.5% per annum for 3 years can be calculated using the compound interest formula:
[tex]= Principal * (1 + Rate)^Time\\= R30,000 * (1 + 0.035)^3\\= R30,000 * 1.116\\= R33,480[/tex]
Now, based on the calculations, the investment at Capitec will yield R36,750 after 3 years while the investment at FNB will yield R33,480 after 3 years. Therefore, Lebo will earn more interest if she invests her money at Capitec than at FNB.
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four cards are drawn from a deck without replacement. find the probability all cards are black cards.
The probability that all four cards drawn from a deck are black cards is 1/4165.
There are 26 black cards and 52 cards in a standard deck of cards. Therefore, the probability of drawing a black card from a standard deck of cards is 26/52 or 1/2. In the first draw, there are 26 black cards out of 52 cards, so the probability of drawing a black card is 26/52.
In the second draw, there are 25 black cards left out of 51 cards, so the probability of drawing a black card is 25/51. In the third draw, there are 24 black cards left out of 50 cards, so the probability of drawing a black card is 24/50. In the fourth draw, there are 23 black cards left out of 49 cards, so the probability of drawing a black card is 23/49.
Using the multiplication principle of probability, the probability that all four cards drawn from a deck are black cards is 26/52 × 25/51 × 24/50 × 23/49 = 1/4165.
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