The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.
The second derivative may be used to determine the local extrema of a function under certain conditions.
A function is said to have a local (relative) extremum at a critical point if the derivative of the function changes sign near that location. At the critical point, the function has a local (relative) maximum if the derivative switches from being positive (growing function) to negative (decreasing function). The function, however, has a local (relative) minimum at the critical point if the derivative switches from negative (decreasing function) to positive (growing function). The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.
Under certain circumstances, one can utilize the second derivative to identify the local extrema of a function. A function has a local minimum at this point if it has a critical point when f′(x) = 0 and the second derivative is positive. However, if the function contains a critical point at which the second derivative is negative and f′(x) = 0, then f has a local maximum at this location. The Second Derivative Test for Local Extrema is the name of this method.
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Step 1: Look at the first part of the word problem.
Cadence has a collection of 52 dolls that all have either blue eyes or green eyes.
Let b represent the dolls with blue eyes.
Let g represent the dolls with green eyes.
Write an equation for this part of the word problem.
The equation part of the given word problem is x+y=52 and y=x+16.
a) Let x = number of green eyed dolls
And let y = number of blue-eyed dolls
Now we are told the following:
x+y=52 → eq1
and
y=x+16 → eq2
b) substitute y = x+16 from eq2 into eq1:
x+x+16 = 52 subtract 16 from each side
x+x+16-16 = 52-16 collect like terms
2x = 36 divide each side by 2
x = 18 → number of green-eyed dolls
substitute x = 18 into equation2
y = 18+16 =34 → number of blue-eyed dolls
18+34=52
52=52
and
18+16=34
34=34
THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:
Let x = Number of green-eyed dolls
Then 52-x = Number of blue-eyed dolls
Now we are told that:
x+16 = 52-x add x to and subtract 16 from each side
x+x+16-16 = 52-16-x+x collect like terms
2x=36 → same as before
x = 18.
Hence, the equation part of the given word problem is x+y=52 and
y=x+16.
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Score: /1 Attempts: 30. For a perfectly symmetrical distribution, which relationship... For a perfectly symmetrical distribution, which relationship is always true? 9 Mean = median = mode Median= mode O Mean mode O Mean - median
For a perfectly symmetrical Distribution, the perfect relationship is
Mean = Median.
A symmetric distribution is when the values of a variable occur with regular frequency, often the mean, median, and mode all occurring at the same point. A line in the middle of the chart indicates that the two planes are mirror images of each other. In graphical form, symmetric distributions are displayed as normal (that is, bell-shaped) distributions. Symmetric distribution is a central concept in technical trading as it assumes that the price movements of an asset over time follow a symmetric distribution curve.
A symmetric distribution can be contrasted with an asymmetric distribution. Asymmetric distributions are probability distributions that are skewed or otherwise irregular in shape.
The Properties of Symmetrical distribution is :
Mean.MedianMode.Mean:
In mathematics, especially statistics, there are several kinds of instruments. Each average is used to summarize a particular group of data in order to better understand the overall values (magnitude and sign) of a particular data set.
For datasets, the arithmetic mean, also called the "arithmetic mean", is a measure of the central tendency of a finite set of numbers. More specifically, the sum of the values divided by the number of values. The arithmetic mean of a series of numbers x₁, x₂, ..., xₙ is usually given by the overhead bar. The dataset was based on a series of observations obtained by sampling from a statistical population. The arithmetic mean is the population mean is denoted by μ.
Median:
The median is the number in the middle of a sorted ascending or descending list of numbers that better describes the data set than the mean. This is the point above and below which half (50%) of the observed data lies, representing the midpoint of the data. Often compared to descriptive statistics.
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which logarithm bases can you use to solve for in the exponential equation ? (select all that apply.) log base x log base 25 log base 4 log base 10
The exponential equation may be solved using log base x and log base 10 logarithm bases. The right answer is D.
Finding the base of the logarithm that may be used to determine the value of x is necessary in order to solve an exponential equation with the form log base x (y) = z.
The equation log base x (y) = z applies here. Let's explore each possible logarithm base:
Log base x: The problem may be solved directly using this logarithm base. The value of x that the equation requires may be discovered using the logarithm base x.
Log base 25: The problem cannot be properly solved using this logarithm base. It does not work with the provided equation.
Log base 4: The equation cannot be properly solved using this logarithm base. It does not work with the provided equation.
Log base 10: The problem may be readily solved using this logarithm basis. To determine the value of x that the equation requires, use the logarithm base 10 function.
The logarithm bases that may be utilised to solve the exponential equation based on the provided parameters are log base x and log base 10.
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alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. how many calories are in one cookie?
Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.
A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.
Let x = calories in cookies.
y = calories in carrots.
Now, according to the question:
5x + 2y = 590 --------------------------------------- (1)
3x + 4y = 410 -------------------------------------- (2)
Multiplying equation(1) by 3 and equation(2) by 5:
15x + 6y = 1770 ---------------------------(3)
15x + 20y = 2050 ---------------------------(4)
Solving we get:
y = 280/14
or, y = 20 units.
Putting the value of y = 20 in equation (2)
3x + 4y = 410
⇒ 3x + 4 × 20 = 410
⇒ 3x = 410 - 80
⇒ x = 330/3
⇒ x = 110 Units
Therefore, the calories of cookies is 110 units .
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Which of the following is not a criteria for the construction of triangle ASA SSS AAA SAS?
Answer:
AAA
Step-by-step explanation:
There's no angle angle angle (AAA) because all triangle's angles add up to 180
the president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean sat score is lower than previous years. he took a sample of 30 of this year's entering students and found that their mean sat score is 1,501 with a standard deviation of 53. the university's record indicates that the mean sat score for entering students from previous years is $1,520. he wants to find out if his claim is supported by the evidence at a 5% significance level. which of the following best describes a type i error? the president concludes that the mean sat score of the entering students is lower than previous years when it is indeed not lower the president concludes that the mean sat score of the entering students is higher than previous years when it is indeed higher the president concludes that the mean sat score of the entering students is not lower than previous years when it is indeed lower the president concludes that the mean sat score of the entering students is lower than previous years when it is indeed lower
The result is not statistically significant.
To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level.
The null hypothesis is
H₀ : μ ≥ 1520
The alternative hypothesis is
Hₐ : μ ≤ 1520
then the test statistic is,
t = (x - μ)/(s/√n)
= (1501 - 1520)/(53/√20)
t = - 1.603
The t-test statistic is - 1.603.
Degree of freedom n - 1 = 20 - 1 = 19
Hence the t-critical value is -1.792.
The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance. There is insignificance evidence indicates that the mean SAT score is less than 1520.
The result is not statistically significant.
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Brent is a member of the school's basketball team. Brent is 74 inches tall, the mean height of the
players on the team is 76 inches. Brent's height translates to a z-score of -0. 85 in the team's height
distribution. What is the standard deviation of the team members' heights?
Round to 2 decimal places
The standard deviation of the team members' heights is 2.35.
A z-score is a number that indicates how far an observation deviates from the mean and in which direction.
A z-score is a common name for a standardized number.
The standardized value of x is: If x is an observation from a distribution with known mean and standard deviation :
z = (x - mean) / Standard Deviation
Given in question,
z = -0.85
x = 74
mean = 76
Let the Standard deviation be s.
By putting the values in the equation,
-0.85 = (74 - 76)/s
s = -2/-0.85
= 2/0.85
= 2.35
Hence, the standard deviation of the team members' heights is 2.35.
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based on your site data sheet and your sample identification, do you feel that you determine an appropriate stream rating? (why or why not). do you feel using macroinvertebrates is a good method to evaluate stream conditions?
When collecting quantitative data you can use a statistical formula to give you a rough estimate of the sample size you will need. When collecting qualitative data, however, the rule of thumb is to have as representative of a sample as possible that will allow you to exhaust the knowledge you could learn from the population.
Macroinvertebrate sampling provides a relatively easy way to assess the water quality of a stream. The types and numbers of macroinvertebrates (mostly insect larvae/nymphs) that form the biological community at a particular stream location are shaped by both the nature of the stream and the quality of water that drains into the stream.
A paper cup is in the shape of a cone, with a diameter of 2 cm and a height of 5 cm. what is the volume of a paper cup?
In April, Anthony's shop made a daily profit of $400 in 12 days and a daily loss of $300 in the rest of the month. It is given that his shop opened every day in April. Find the average daily profit or loss of Anthony's shop in April.
please use directed numbers to solve
The average daily loss of Anthony's shop in April is $20.
How is the average daily loss determined?The average daily loss is the total net profit (loss) divided by the number of days in April.
An average is the mean of the value in a data set, which is determined as the quotient between the total value and the number of items.
Days in April = 30
Daily profit in 12 days = $400
Daily loss in 18 days (30 - 12) = $300
Total daily profit = $4,800 ($400 x 12)
Total daily loss = $5,400 ($300 x 18)
Net daily loss = $600 ($5,400 - $4,800)
Average daily loss = $20 ($600/30)
Thus, in April, Anthony's shop incurred an average daily loss of $20.
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How do you simplify (2+i)/(1−)i completely?
Multiply the numerator and denominator by the conjugate of the denominator to simplify (2+i/(2-i)).
To determine, multiply the denominator's conjugate by the numerator and denominator.
[tex]\frac{2+i}{1-i} = \frac{1}{2} +\frac{3}{2}i[/tex]
The complex number a + bi has the conjugate a-bi. A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.
[tex]\frac{2+i}{1-i} = \frac{(2+i)(1+i)}{(1-i)(1+i)} \\=\frac{2+2i+i-1}{1+i-i+1} \\=\frac{1+3i}{2} \\=\frac{1}{2} +\frac{3}{2} i[/tex]
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Michael picks cucumbers from his garden and bags them up to give to his neighbors. He starts with 40 bags of cucumbers and gives out 8 bags per hour until there are none left. Use the Segment tool to plot a graph representing the number of bags of cucumbers Michael has left to give away from the time he starts giving them away until he has no bags left.
You would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.
What is a line graph?
An informational shift over time is graphically represented by a line graph. It is a graph that was created by connecting points with line segments.
Michael starts with 40 bags of cucumbers and gives out 8 bags per hour until there are none left.
Michael starts giving them away until he has no bags left.
To create the graph we need coordinate points to locate on the graph.
So initially he has 40 bags and gives away 8 bags for every 1 hour.
The number of bags will be represented on the y-axis, and the number of hours will be represented on the x-axis.
The coordinates are:
x-axis y-axis
0 40
1 32
2 24
3 16
4 8
5 0
Hence, you would start at points (0, 40) and then move to (1, 32), (2, 24), (3, 16), (4, 8), and (5, 0) because he gives out 8 bags per hour.
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the monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). the monthly cost for 45 minutes of calls is $14.40 and the monthly cost for 102 minutes is $19.53. what is the monthly cost for 66 minutes of calls?
The monthly cost for 66 minutes of calls will be $15.84.
Monthly cost is the payment or the bill amount that needs to be paid at the end of the month.
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes)
The monthly cost for 45 minutes of calls = $14.40
The monthly cost for 102 minutes = $19.53
The above values can be paired in groups so as to satisfies the coordinates of a linear function
(45,14.40) and (102,19.53)
Finding the slope of the graph using these points
slope, m=Δy/Δx
m=Δy=19.53 - 14.40 = 5.13
Δx=102 - 45 = 57
m = 5.13/57 =0.09
Finding the equation of the linear function using m = 0.09, and point (45,14.40)
m=Δy/Δx
0.09=y-14.40/x-45
0.09(x-45)=y-14.40
0.09x-4.05=y-14.40
0.09x-4.5+14.40=y
y=0.09x + 9.9
So for 66 minutes, the cost will be;
x = 66, y = ?
y=0.09*66 + 9.9
y=5.94+9.9 = $15.84
The monthly cost for 66 minutes of calls is $15.84.
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in a basket of red and green apples, green apples are only 1/3 as common as red apples. if there are 60 apples in total, how many are green? you answered 20, which is incorrect.
If there are 60 apples in total, then green are 15 .
Given:
in a basket of red and green apples, green apples are only 1/3 as common as red apples.
if there are 60 apples in total, how many are green = ?
x is the number of red apples
y is the number of green apples
x/3= y;
x=3y
x+y= 60
3y+y=60;
4y=60;
that means y=60/4
y = 15
Hence there are 15 green apples.
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Which histogram depicts higher standard deviation? L Choose the correct answer below Histogram depicts the higher standard deviation, because the distribution has more dispersion Histogram depicts the higher standard deviation, because the bars are higher than the average bar in b Histogram depicts the higher standard deviation since is more bell shaped_ D. Histogram depicts the higher standard deviation because the distribution has more dispersion
The histogram that depicts the higher standard deviation is the one that has a wider spread of data, meaning the distribution has more dispersion.
This can be seen by the points in the histogram being more spread out and having a larger range of values. The bars may be higher than the average bar in b, but that does not necessarily mean it has a higher standard deviation. Similarly, a more bell-shaped distribution does not necessarily indicate a higher standard deviation.The histogram that depicts the higher standard deviation is the one that has a wider spread of data, meaning the distribution has more dispersion. This is because a higher standard deviation indicates that the data points are more spread out, and the range of values is larger. This can be seen by looking at the histogram and observing that the points are more spread out and have a larger range of values. The bars in the graph may be higher than the average bar in b, but this does not necessarily mean that it has a higher standard deviation. Similarly, a more bell-shaped distribution does not necessarily indicate a higher standard deviation.
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Question 1
What is their rate of change (speed) in Section A? Remember to include units.
Question 2
What is the rate of change of (speed) in section B? Remember to included units
Question 3
What is their rate of change of (speed) in section D (hours 7-10)? Remember to include units
Question 4
During which section was the person moving at the highest speed? What was their speed? Defend your answer
Question 5
During which section did the person travel the farthest? How did they travel?
Question 6
BONUS: write a short (paragraph) scenario that tells the story about where on the graph came from. You can be as creative as you want!
Please only comment if you will give me all these answers thank you!
Answer:
On attached woksheet
Step-by-step explanation:
The graph has units of time (sec) on the x axis and distance (meters) on the y. The lines in the graph represent a change in distance from the origin as a function of time. The slopes of these lines represent the speed, in m/sec., for that line. Since they are straight lines, the speed is not changing for that time period. A flat, horizonal, line represent a stationary object. Distance does not change with time. Steeper lines represnt faster speeds - the distance changes more quickly for the same time period.
See attached worksheet.
relationship between integers and zero
The difference is zero lies in the middle of the number line and it is itself an additive identity.
What is number line?
A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.
An integer is positive if it exceeds zero and negative if it falls below zero. Zero is described as being neither positive nor negative.
Hence, The difference is zero lies in the middle of the number line and it is itself an additive identity.
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simplify value of 3a-2
Nothing further can be done with simplifying the given expression.
How do you solve 2^x=20?
Answer:
x=4.321928
Here’s your explanation
Let's solve your equation step-by-step.
2^x=20
Solve Exponent.
2^x=20
log(2^x)=log(20) (Take log of both sides)
x*(log(2))=log(20)
x=log(20)
log(2)
Then you get your answer x=4.321928
Step-by-step explanation:
Take the log of both sides:
log2(2^x) = log2(20)
xlog2(2) = log2(20)
x(1) = log2(20)
x = log2(20) ≈ 4.322
“Let me give so much time to the improvement of myself that I shall have no time to criticize others.” what do you think about this one small paragraph please
Answer: I believe that this statement is very true. People shouldn’t be pushing others down when instead they could be pushing themselves up, improving them to be better.
Step-by-step explanation:
Answer:
THAT VERY RIGHT INSTEAD OF PEOPLE HELPING THEMSELVES THEY SPEND THEIR TIME CRITICIZING OTHERS KUDO TO U
Which of the following is quadratic equations √ 3x² - 2x + 1/2 = 0?
The following equation √ 3x² - 2x + 1/2 = 0 is quadratic
What is quadratic?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.
Is a quadratic 2 or 4?Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."
As the expression √ 3x² - 2x + 1/2 = 0 has square root so it is a quadratic equation.
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Which of the following describes the nature of the solutions of the quadratic
equation-2x^2-x-1=0?
A. One real, rational solution
B. Two real, rational solutions
C. Two real, irrational solutions
D. Two complex conjugate solutions
Answer:
D
Step-by-step explanation:
To find the solutions, let's calculate the determinant:
Δ = (-1)²-4(-2)(-1) = 1-8 = -7
the solution is: (1 ±√-7)/(-4)
√-7 indicates there are two complex solutions
Rewrite in simplest terms: 6(0.7y+0.8z)−4z−6(−0.1z−0.6y)
deltamath is killing me aaaa
The expression into an equivalent form 6(0.7y+0.8z)−4z−6(−0.1z−0.6y) would be; 7.8y + 1.4z
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
We need the expression into an equivalent form;
6(0.7y+0.8z)−4z−6(−0.1z−0.6y)
This expression could also be given by;
6(0.7y+0.8z)−4z−6(−0.1z−0.6y)
Now, we know that:
4.2y + 4.8z - 4z + 0.6z + 3.6y
Now
7.8y + 1.4z
Hence, the expression into an equivalent form 6(0.7y+0.8z)−4z−6(−0.1z−0.6y) would be; 7.8y + 1.4z
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a farmer wants to decide if he should plant beets or sweet potatoes. no matter what he plants he will get either a good, average, or bad crop yield. for beets, a good yield will give him a profit of $5,000, average will profit $3,000 and, and a bad yield will give a profit of $1,000. for sweet potatoes, the profit for good, average, and bad yields are as follows: $6,000, $3,000, and $0. for either crop, the probability of good yield is 0.4, the probability of average yield is 0.5 and the probability of a bad yield is 0.1. what are the outcomes for beets?
The outcomes for beets or plants beet is $ 5000 , $3000 and $1000.
Given :
a farmer wants to decide if he should plant beets or sweet potatoes. no matter what he plants he will get either a good, average, or bad crop yield.
For beets, a good yield will give him a profit of $5,000, average will profit $3,000 and, and a bad yield will give a profit of $1,000. for sweet potatoes, the profit for good, average, and bad yields are as follows: $6,000, $3,000, and $0. for either crop, the probability of good yield is 0.4, the probability of average yield is 0.5 and the probability of a bad yield is 0.1.
Outcomes of beets = good yield , average and bad yield.
so
= $ 5000 , $3000 and $1000
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How do you solve 8^x=1000?
Solution of 8^x=1000 is x ≈ 3.322 .
Use the
law of logarithms
[tex]log x^{n} = nlogx[/tex]
The word algorithm does not appear in data protection law. But an algorithm often results in an automated decision (or algorithmic decision making). It is code that decides something. There is a law that deals with automated individual decision-making and this is very relevant to algorithms.
An algorithm is a set of rules or a computational procedure that is typically used to solve a specific problem.
Applies to logarithms to any base.
Take the ln ( natural log) of both sides.
log 8^x = log 1000
An algorithm is a procedure used for solving a problem or performing a computation. Algorithms act as an exact list of instructions that conduct specified actions step by step in either hardware- or software-based routines. Algorithms are widely used throughout all areas of IT.
Using the above law
x log 8 = log 1000
dividing both side by log 8
[tex]\frac{xlog8}{log8} = \frac{log1000}{log8}[/tex]
x = ㏒8 (1000)
[tex]log_{a} b = \frac{log_{c}b }{log_{c}a }[/tex]
[tex]x = log_{10} 1000/log_{10} 8[/tex]
x ≈ 3.322 to 3 decimal places
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One last question the floor of Raj’s classroom has an area of 525 feet.The ceiling is 12 feet high.What is the volume of Raj’s classroom?
Answer:
6300 ft
Step-by-step explanation:
Answer:
The volume of Raj's classroom would be 6,300 cubic feet which is the multiplication of the floor area and the height of the room.
What is the volume of the cuboid?
The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.
The volume of a cuboid is length × breadth× height
Raj's classroom floor area measures 525 square feet. The ceiling height of the room is 12 feet.
The volume of Raj's classroom is the multiplication of the floor area and the height of the room.
The volume of Raj's classroom = the floor area × the height of the room
The volume of Raj's classroom = 525 × 12
The volume of Raj's classroom = 6,300 cubic feets
Thus, the volume of Raj's classroom would be 6,300 cubic feet.
Graph the function f(x) = -3 log₂ (-x-4) - 8 on the
axes below. You must plot the asymptote and any two points
with integer coordinates.
The graph of the function is attached below:
The asymptote of the function is:
(-3 log(-x-4)/log2)-8 →∞ as x→ -4
What is meant by a function?Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. The sets X and Y are referred to together as the function's codomain and domain, respectively.
Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who are credited with developing the earliest known approach to the concept of function. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. The idea was developed historically with the infinitesimal calculus towards the end of the 17th century, and until the 19th century, the functions that were taken into consideration were differentiable.
Given function is,
f(x)= -3 log₂ (-x-4) - 8
The graph of the function is attached below:
The asymptote of the function is:
(-3 log(-x-4)/log2)-8 →∞ as x→ -4
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8) if 2 to the power (x + 2) = k, what is the value of x in terms of k ?
and how
if (x+2)² = k , making x the subject is x = √k - 2
What is subject of formula?The subject of a formula is the variable that is being worked out. It can be recognised as the letter on its own on one side of the equals sign.
For example, if V = πr²h and we want to make r the subject of the formula, we make r in place of V.
Therefore r² = V/πh
r = √ (V/πh)
Similarly
(x+2)² = k
when we square root both sides
x+2 = √k
Collecting like terms
x = √k - 2
therefore making x the subject in the formula (x+2)² = k in terms of k is x = √k - 2
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from a set of 7 math books, 12 science books, and 5 literature books, in how many ways can a student select 2 from each set?
The no. of ways or Probability can a student select 2 from each set of books = 13860
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
By multiplying the number of possibilities there are to choose books from each kind, separately, one can determine the maximum number of ways a student can choose two books from each subject.
Rule for Multiplication:
If an event A can be performed in m different ways and another event B in n different ways, then the two events together can be performed in (mn) different ways.
A combination problem is created by the various ways that math, science, and literature books might be chosen.
As a result, the total number of choices can be calculated as follows: (Number of math books chosen) x (Number of scientific books chosen) x (Number of literature books selection)
= C ( 7,2) * (12,2) * (5,2)
= C (7*6/2!) * (12*11/2!) * (5*4/2!)
= 21 * 66* 10
= 13860
The no. of ways or Probability can a student select 2 from each set of books = 13860
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On July 14, Gracie Paul accepted a $60,000, 6%, 160-day note from Mike Lang. On November 12, Gracie discounted the note at Lend Bank at 7%. What proceeds did Gracie receive? (Use Days in a year table) (Round your answer to the nearest cent. )
Therefore, Gracie will earn $61600 if she waits until December 21. However, she will earn bank discount $61132.87 on November 12.
A bank discount is interest that the bank deducts beforehand in the basic discount note. The maturity value less the bank discount equals the amount owed. The total of the principle and interest due at the conclusion of the time period is the maturity value.
Date of note = 14th July
Face value = $60000
Length of note = 160 days,
Interest rate = 6%
Calculating the interest and maturity value:
Interest = Principal × interest × time
= 60000 × 0.06 × 160/360
= 1600
So the maturity value MV = Face value + interest
= 60000 + 1600
= 61600
2. Calculating discount period:
Note discounted on 12th November
Time till 12th November = 315 days
Time till 14th July = 194 days
So days before note is discount = 315 - 194= 121 days
Length of note = 160 days,
So the discount period = 160 - 121 = 39 days
3 - Bank discount:
Bank discount = MV × Bank discount rate × number of days bank waits till due date
= 61600 × 0.07 × 39/360
= 467.133
4 - Proceeds from bank: Proceeds = MV - Bank discount
= 61600 - 467.133
= 61132.87
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