Using the compounding interest formula:
a) His ending balance after the year will be $7,658.91.
b) The amount of interest he will earn is $358.91.
c) His annual percentage yield is 4.9166%.
a) To calculate the ending balance after one year, we'll use the compound interest formula: A = P(1 + r/n)^(nt), where A is the ending balance, P is the principal ($7,300), r is the interest rate (4.85% or 0.0485), n is the number of compounding periods per year (4 for quarterly), and t is the number of years (1).
A = 7300(1 + 0.0485/4)^(4*1) = 7300(1.012125)⁴ = 7300*1.049166 = $7,658.91
b) To find the interest earned, subtract the principal from the ending balance: Interest = A - P
Interest = $7,658.91 - $7,300 = $358.91
c) To calculate the annual percentage yield (APY), we'll use the formula: APY = (1 + r/n)^(n) - 1
APY = (1 + 0.0485/4)⁴ - 1 = 1.049166 - 1 = 0.049166 or 4.9166%
Paul's ending balance after one year is $7,658.91, he earns $358.91 in interest, and his annual percentage yield is 4.9166%.
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The radius of the large circle is 3 inches and AB is its diameter. Also, AC is tangent to the large circle at point A. If arc CD = 160 and arc CE = 100, find the area of triangle ABC.
The area of triangle ABC is 13.95 square inches.
We can start by finding the length of AB, which is equal to the diameter of the circle. Since the radius is 3 inches, the diameter is 2 times the radius, or 6 inches.
Next, we can use the fact that AC is tangent to the circle to conclude that angle CAB is a right angle. Therefore, triangle ABC is a right triangle.
Let's use the information about the arcs CD and CE to find the measure of angle BAC. The measure of an inscribed angle is half the measure of the arc that it intercepts, so angle CAD is 80 degrees and angle CAE is 50 degrees. Since angles CAD and CAE are opposite each other and AC is a tangent, we have angle BAC is 180 - 80 - 50 = 50 degrees.
Now we know that triangle ABC is a right triangle with a 90-degree angle at B and a 50-degree angle at A. To find the area of the triangle, we need to know the length of BC.
Using trigonometry, we can find that BC = AB * sin(50) ≈ 4.65 inches.
Therefore, the area of triangle ABC is (1/2) * AB * BC = (1/2) * 6 * 4.65 = 13.95 square inches. Rounded to the nearest hundredth, the area of triangle ABC is 13.95 square inches.
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If x-2 and x+2 are the factors of the polynomial p(x) = x³− 4mx²− 2nx + 1 = 0, then find the values of m and n.
If x-2 and x+2 are the factors of the polynomial p(x) = x³− 4mx²− 2nx + 1 = 0, then the values of m and n are 5/4 and 1/2, respectively.
Given that the factors of the polynomial p(x) = x³ - 4mx² - 2nx + 1 are x - 2 and x + 2, we can write:
p(x) = (x-2)(x+2)(x-a)
where a is the remaining root of p(x).
Expanding this equation, we get:
p(x) = (x²-4)(x-a) = x³ - (4+a)x² + 4ax - 4a
Comparing the coefficients of this expression with the coefficients of the original polynomial, we get the following system of equations:
4+a = 4m
4a = -2n
-4a = 1
Solving these equations, we get:
a = -1/4, m = 5/4, n = -2a = 1/2
Therefore, the values of m and n are 5/4 and 1/2, respectively.
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What is the probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die?
10. 7%
25%
8. 3%
04. 2%
The probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die is 8.33%
To calculate the probability of drawing a diamond or a spade card from a standard deck of cards, we need to find the total number of diamond and spade cards in the deck. There are 13 cards in each suit, so there are 26 diamond and spade cards in total. The deck has 52 cards in total, so the probability of drawing a diamond or a spade card is:
P(diamond or spade) = 26/52 = 1/2 = 50%
To calculate the probability of rolling a 2 on a six-sided die, we need to find the total number of possible outcomes, which is 6 (since there are 6 sides on the die), and the number of favorable outcomes, which is 1 (since there is only one face with a 2 on it). Therefore, the probability of rolling a 2 on a six-sided die is:
P(rolling a 2) = 1/6 = 16.67%
To find the probability of both events happening together (drawing a diamond or a spade card and rolling a 2 on a six-sided die), we multiply the probabilities of each event:
P(diamond or spade AND rolling a 2) = P(diamond or spade) * P(rolling a 2)
= 50% * 16.67%
= 8.33%
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You can find the area of a trapezoid by decomposing it into a rectangle and one or more triangles you can find the area of a kite by decomposing it into triangles
The statement on finding the areas of a trapezoid and a kite are True.
How to find area by decomposing shapes ?To determine the area of a trapezoid, it can be broken down into separate geometrical shapes. One possible breakdown would include a rectangle with two adjacent right triangles or an isosceles triangle with one right triangle configuration. By calculating each smaller compartment's size and summing them together, one can obtain the total area for the trapezoid.
Similarly, in order to find the surface area of a kite shape, drawing a diagonal creates two adjoining triangles that are easily computed individually then summed.
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Options for this question :
True
False
The school swim team swam a combined distance of 346. 725 meters during swim practice. Using number names, how would you say 346. 725? (6. NBT. 3_a. ) *
The number name of 346. 725 is three hundred forty-six point seven two five.
A number name refers to the name that is used to describe the number in words. This is helpful in communicating it orally.
To convert the given number to word form, we do as follows:
1. We check the digits of the number before decimals
In this case, the number of digits in the question is 3
2. The highest place value is then checked.
It comes out to be hundreds
3. We name it accordingly and add a suffix to the face value
This is 3 and the name comes out to be Three hundred
4. We continue it till we encounter the decimal
We get the number as Three hundred forty-six
5. Then we mention the word decimal or point
The result is Three hundred forty-six point
6. The number after the decimal is written as it is
Hence, the name comes out to be Three hundred forty-six point seven two five.
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What is an equation of the line that passes through the points ( 8 , 6 ) and ( − 3 , 6 )
The equation of line passing through the points (8, 6) and (-3, 6) is y = 6. Since the y-coordinate is the same for both points, the line is a horizontal line at y = 6.
To find the equation of the line passing through the points (8, 6) and (-3, 6), we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to find the slope, which is given by
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (8, 6) and (x2, y2) = (-3, 6)
m = (6 - 6) / (-3 - 8)
m = 0 / -11
m = 0
Since the slope is zero, the line is a horizontal line. We can see from the given points that the line passes through y = 6. Therefore, the equation of the line is
y = 6
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You are going to calculate what speed the kayaker 's are paddling, if they stay at a constant rate the entire trip, while kayaking in Humboldt bay.
key information:
River current: 3 miles per hour
Trip distance: 2 miles (1 mile up, 1 mile back)
Total time of the trip: 3 hours 20 minutes
1) Label variables and create a table
2) Write an quadratic equation to model the problem
3) Solve the equation. Provide supporting work and detail
4) Explain the results
Melanie is making a piece of jewelry that is in the shape of a right triangle. The two shorter sides of the piece of jewelry are 4 mm and 3 mm. Find the perimeter of the piece of jewelry.
Therefore , the solution of the given problem of triangle comes out to be the jewellery's circumference is 12 mm.
What precisely is a triangle?If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything like this can only be distinguished from a standard triangle form by edges A and B. Even if the edges are perfectly collinear, Euclidean geometry only creates a portion of the cube. A triangle is made up of a quadrilateral and three angles.
Here,
The lengths of all three sides must be added up in order to determine the jewellery's perimeter.
=> c²= a² + b²
where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.
=> A = 3mm, and B = 4mm.
Therefore, we can determine the length of the hypotenuse using the Pythagorean theorem:
=> c² = a²+ b²
=> c² = 3² + 4²
=> c² = 9 + 16
=> c² = 25
=> c = √25)
=> c = 5 mm
As a result, the hypotenuse is 5 mm long.
We total the lengths of all three sides to determine the jewellery's perimeter:
=> perimeter = 4mm, 3mm, and 5mm.
=> 12 mm is the diameter.
Therefore, the jewellery's circumference is 12 mm.
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After pouring 4.8 liters of water into a bucket, the bucket contains 14.3 liters. Write an equation to represent the situation.
Answer: x + 4.8 = 14.3
Step-by-step explanation:
Let x be the initial amount of water that was already in the bucket before the additional 4.8 liters of water was poured in.
Then the total amount of water in the bucket after pouring in the 4.8 liters is the sum of the initial amount x and the amount of water poured in, which is 4.8 liters. This can be represented by the equation:
x + 4.8 = 14.3
We can simplify this equation by solving for x:
x = 14.3 - 4.8
x = 9.5
Therefore, the initial amount of water in the bucket was 9.5 liters, and after pouring in 4.8 liters, the bucket contained a total of 14.3 liters.
Pls help it’s due tonight and I don’t understand it xx
Answer:
n = 10
Step-by-step explanation:
36 can be written as 6^2 because 6*6 = 36.
Since exponents multiply, 36^5 = (6^2)^5 = 6^(2*5) = 6^10 = 6^n.
n = 10.
Alternatively, 36^5 = 36 * 36 * 36 * 36 * 36.
If you replace each 36 with 6*6, the new equation is (6*6) * (6*6) * (6*6) * (6*6) * (6*6).
n = the number of 6's = 10.
Select the correct answer.
consider this equation.
cos(ф) = [tex]\frac{8}{9}[/tex]
if ф is an angle in quadrant iv, what is the value of tan(ф)?
The value of tan(ф) when cos(ф) = 8/9 in quadrant IV is - √17/8
To solve for the value of tan(ф), we need to use the trigonometric identity: tan(ф) = sin(ф)/cos(ф).
Since ф is in quadrant IV, we know that the cosine value is positive (due to cosine being positive in the adjacent side of quadrant IV) and the sine value is negative (due to sine being negative in the opposite side of quadrant IV).
We are given the value of the cosine, which is cos(ф) = 8/9. To find the sine, we can use the Pythagorean identity: sin²(ф) + cos²(ф) = 1.
Plugging in the given value of the cosine, we get: sin²(ф) + (8/9)² = 1. Solving for sin(ф), we get sin(ф) = - √(1 - (64/81)) = - √(17/81) = - √17/9.
Now that we have the values of sin(ф) and cos(ф), we can substitute them into the tan(ф) equation: tan(ф) = sin(ф)/cos(ф) = (- √17/9)/(8/9) = - √17/8.
Therefore, the value of tan(ф) when cos(ф) = 8/9 in quadrant IV is - √17/8.
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Write the product using exponents.
4⋅4⋅4⋅4⋅4
The green parallelogram is a dilation of the black parallelogram. What is the scale factor of the dilation?
A) 1/3
B) 1/2
C) 2
Your answer will depend on the measurements you obtain from the parallelograms.
To determine the scale factor of the dilation between the green parallelogram and the black parallelogram, follow these steps:
1. Choose corresponding sides of both parallelograms (e.g., the base or the height).
2. Measure the length of the chosen side in the green parallelogram and the same side in the black parallelogram.
3. Divide the length of the side in the green parallelogram by the length of the corresponding side in the black parallelogram.
The result will be the scale factor of the dilation. Compare the result with the given options:
A) 1/3
B) 1/2
C) 2
Your answer will depend on the measurements you obtain from the parallelograms.
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Select the correct answer from each drop-down menu. hemoglobin level age less than 25 years 25–35 years above 35 years total less than 9 21 32 76 129 between 9 and 11 49 52 46 147 above 11 69 44 40 153 total 139 128 162 429 based on the data in the two-way table, the probability of being 25-35 years and having a hemoglobin level above 11 is . the probability of having a hemoglobin level above 11 is . being 25-35 years and having a hemoglobin level above 11 dependent on each other.
The probability of being 25-35 years and having a hemoglobin level above 11 is 0.102. The probability of having a hemoglobin level above 11 is 0.356. Being 25-35 years and having a hemoglobin level above 11 are dependent on each other.
From the two-way table, the total number of individuals who have a hemoglobin level above 11 is 153+44+40=237. The probability of having a hemoglobin level above 11 is the total number of individuals with hemoglobin level above 11 divided by the total number of individuals, which is 237/429=0.356.
The number of individuals who are between 25-35 years and have a hemoglobin level above 11 is 44. The probability of being 25-35 years and having a hemoglobin level above 11 is the number of individuals who are between 25-35 years and have a hemoglobin level above 11 divided by the total number of individuals, which is 44/429=0.102.
Being 25-35 years and having a hemoglobin level above 11 are dependent on each other because the probability of having a hemoglobin level above 11 changes based on the age group.
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What connection does the author draw between the workers’ rights and their quality of life? in the st. Petersburg workmen's petition to the tsar
The "St. Petersburg Workmen's Petition to the Tsar" was a document written in 1870 by a group of Russian workers, which expressed their grievances and called for greater rights and protections in the workplace.
While the text of the petition is too long to summarize in its entirety, the following points illustrate some of the connections that the authors draw between workers' rights and their quality of life:
- The petitioners argue that workers have the right to a fair wage that allows them to support themselves and their families, and that without this right, workers are forced to live in poverty and squalor.
- They also argue that workers have the right to safe and healthy working conditions, and that without this right, workers are subjected to disease and injury that can shorten their lives and reduce their quality of life.
- The petitioners further argue that workers have the right to organize and advocate for their own interests, that without this right, workers are powerless to negotiate with their employers and to protect themselves against exploitation.
- They also argue that workers have the right to education and self-improvement, and that without this right, workers are trapped in a cycle of ignorance and subservience that limits their potential and reduces their quality of life.
- Overall, the authors of the petition argue that workers' rights and their quality of life are inextricably linked, and that without the former, the latter is impossible to achieve.
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What is the median, first and third Interquartile, IQR, and range for 12,19,24,26,31,38,53?
Answer: the median is 26, the first quartile is 19, and the third is 38
Step-by-step explanation:
if you count the numbers and x one by each side you will find the median which in this equation is 26, to find any first quartile you need to find the value under which 25% of data points are found when they are arranged in increasing order, to find the upper quartile you need to find the mean of the values of data point of rank.
What is the probability that the drug will wear off between 200 and 220 minutes?
P(200
The probability that the drug will wear off between 200 and 220 minutes is 0.4.
To calculate the probability that the drug will wear off between 200 and 220 minutes, we need to know the cumulative distribution function (CDF) of the drug's effect duration. Let's say the CDF is denoted by F(t), where t is the time in minutes.
Then, the probability that the drug will wear off between 200 and 220 minutes is given by:
P(200 < T < 220) = F(220) - F(200)
This is because the probability of the drug wearing off between two specific times is equal to the difference between the CDF values at those times.
For example, if F(200) = 0.2 and F(220) = 0.6, then:
P(200 < T < 220) = 0.6 - 0.2 = 0.4
Therefore, the probability that the drug will wear off between 200 and 220 minutes is 0.4.
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The alverado's have a monthly income of $6,000.
3. how much more do they spend on taxes than on clothing?
pls help fast! my teacher is gonna get mad!
The Alverados spend $1,200 more on taxes than on clothing.
How we get the tax spend on clothing?To determine how much more the Alverados spend on taxes than on clothing, we need to know how much they spend on each.
If we assume that the Alverados spend 25% of their income on taxes, that would be:
0.25 x $6,000 = $1,500
If we assume that the Alverados spend 5% of their income on clothing, that would be:
0.05 x $6,000 = $300
To find how much more they spend on taxes than on clothing, we can subtract the amount spent on clothing from the amount spent on taxes:
$1,500 - $300 = $1,200
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If c(t) = 53.2te^{- 0.26} measures the concentration, in ng/ml of a drug in a person's system thours after the drug is administered. a) What is the peak concentration of the drug? b) When does the drug reach peak concentration?
(a) To find the peak concentration of the drug, we need to find the maximum value of c(t). Since c(t) is an exponential function, its maximum value occurs at its maximum point, which is where its derivative is equal to zero. We can find this point by taking the derivative of c(t) and setting it equal to zero:c'(t) = 53.2e^{-0.26} - 13.832te^{-0.26} = 0Solving for t, we get t = 3.870 hours. Therefore, the peak concentration of the drug is c(3.870) = 109.2 ng/ml.(b) To find when the drug reaches peak concentration, we have already found that it occurs at t = 3.870 hours. Therefore, the drug reaches peak concentration 3.870 hours after it is administered.
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The peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.
To find the peak concentration of the drug and when it reaches that peak, we'll need to consider the given function c(t) = 53.2te^(-0.26t), where t is the time in hours.
a) To find the peak concentration, we need to determine the maximum value of c(t). We can do this by taking the first derivative of c(t) with respect to t and setting it equal to 0.
c'(t) = 53.2(-0.26)e^(-0.26t) + 53.2e^(-0.26t) = 0
Now, solve for t:
t ≈ 3.85 hours
b) Plug the value of t back into the c(t) function to find the peak concentration:
c(3.85) = 53.2(3.85)e^(-0.26(3.85)) ≈ 42.83 ng/ml
So, the peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.
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Consider the following. sin u = 3/5 π/2 (a) Determine the quadrant in which u/2 lies. O Quadrant 1 O Quadrant II O Quadrant III O Quadrant IV (b) Find the exact values of sin(u/2), cos(u/2), and tan(u/2 sin(u/2) cos(u/2) = tan(u/2) =
(a) The quadrant in which u/2 lies is either Quadrant I or Quadrant II.
(b) The exact values of sin(u/2), cos(u/2), and tan(u/2) are:
sin(u/2) = √10/5
cos(u/2) = 3√10/10
tan(u/2) = 2/3
(a) To determine the quadrant in which u/2 lies, we need to look at the value of sin u. Since sin u is positive (3/5 is positive and π/2 is in Quadrant I), we know that u is in either Quadrant I or Quadrant II.
To find u/2, we divide u by 2, which means u/2 will be in either Quadrant I or Quadrant II as well. Therefore, the answer is either Quadrant I or Quadrant II.
(b) We can use the half-angle formulas to find the values of sin(u/2), cos(u/2), and tan(u/2):
sin(u/2) = ±√[(1 - cos u)/2]
cos(u/2) = ±√[(1 + cos u)/2]
tan(u/2) = sin(u/2)/cos(u/2)
Since sin u = 3/5, we can find cos u using the identity sin^2 u + cos^2 u = 1:
cos u = ±√[(1 - sin^2 u)] = ±√[(1 - 9/25)] = ±4/5
Since u/2 is in either Quadrant I or Quadrant II, we know that sin(u/2) and cos(u/2) are positive. Therefore, we can choose the positive square roots for sin(u/2) and cos(u/2):
sin(u/2) = √[(1 - cos u)/2] = √[(1 - 4/5)/2] = √[1/10] = √10/10 = √10/5
cos(u/2) = √[(1 + cos u)/2] = √[(1 + 4/5)/2] = √[9/10] = 3/√10 = 3√10/10
Finally, we can use these values to find tan(u/2):
tan(u/2) = sin(u/2)/cos(u/2) = (√10/5)/(3√10/10) = 2/3
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Mr.Franklin drives 37 miles each day to and from work. How many miles does he drive in 20 work days
Answer:
740
Step-by-step explanation:
37 times 20
Answer:
740 miles
Step-by-step explanation:
37 miles in 1 day
So we need to multiply 37*20 to find the number of miles for 20 days
So, he travels 740 miles
FRACTIONS It is John's birthday and his mother decided to give him a birthday party. She bought him three cakes for his party; cake one was sliced into 8 pieces, cake two was sliced into 10 pieces, and cake three was sliced into 12 pieces. If the guests at the party ate 4 slices of cake one, 7 slices of cake two and 5 slices of cake three; calculate the amount of cake that was eaten in total.
There are 30 slices in total, so our denominator would be 30.
Now we simply have to add 4, 7 and 5. The answer to this would be 16.
So the amount of cake eaten in total is 16/30.
If your assignment is for improper fractions, I'm guessing the answer would be 16/3 instead.
Answer:
1 37/60 cakes
Step-by-step explanation:
You want the total cake eaten if 4 of 8 slices, 7 of 10 slices, and 5 of 12 slices were eaten.
SumThe sum of the three fractions is ...
4/8 +7/10 +5/12
= 5/10 +7/10 +5/12 . . . . . . . 4/8 = 1/2 = 5/10
= 12/10 +5/12
= 6/5 +5/12
= (6·12 +5·5)/(5·12) = 97/60 = 1 37/60
The total amount of cake that was eaten was equivalent to 1 37/60 cakes.
__
Additional comment
Your calculator can relieve the tedium of this calculation.
Shari bought 3 breath mints and received $2. 76 change. Jamal bought 5 breath mints
and received $1. 20 change. If Shari and Jamal had the same amount of money, how
much does one breath mint cost?
A. Each breath mint costs $0. 28.
B. Each breath mint costs $0. 49.
c. Each breath mint costs $0. 78.
D. Each breath mint costs $1. 98.
Each breath mint costs $0.78. The correct answer is C.
To solve this problem, we can use the concept of a system of linear equations. Let x be the cost of one breath mint and y be the total amount of money Shari and Jamal had.
We know that Shari bought 3 breath mints and received $2.76 change, so her equation will be:
3x + 2.76 = y
Jamal bought 5 breath mints and received $1.20 change, so his equation will be:
5x + 1.20 = y
Now we have a system of two equations with two variables:
3x + 2.76 = y
5x + 1.20 = y
We can solve for x by setting the two equations equal to each other:
3x + 2.76 = 5x + 1.20
Now, solve for x:
2x = 1.56
x = 0.78
So, each breath mint costs $0.78. The correct answer is C.
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Please answer now! Please show the Example
Mr. Bilo received 8 P50-bills, 5 P100-bills, and 5 P20-bills.
How many P50, P100, and P20 bills did Mr. Pilo get?The number of P50, P100, and P20 bills Mr. Pilo got is calculated as follows;
Amount from P50-bills: 2/5 x P1,000 = P400
Amount from P100-bills: 1/2 x P1,000 = P500
The total amount he received from the P50-bills and P100-bills = P400 + P500
The total amount he received from the P50-bills and P100-bills = P900. The amount left to be changed into P20-bills = P1,000 - P900
The amount left to be changed into P20-bills = P100.
The number of bills will then be:
Number of P50-bills: P400 ÷ P50 = 8
Number of P100-bills: P500 ÷ P100 = 5
Number of P20-bills: P100 ÷ P20 = 5
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Complete question:
Mr Bilo has a P1,000-bill and asked someone to exchange in to 2/5 P50-bill and 1/2 P100-bill and the rest into 20-bill. How many P50,P100 and P20 bills did he get.
 Solve for the value of p
Answer:
p = 38
Step-by-step explanation:
We Know
The 104° angle + (2p) angle must be equal to 180°.
Solve for the value of p.
Let's solve
104° + 2p = 180°
2p = 76°
p = 38
Prove the following 2 trig identities. Show all steps!
Answer:
a) multiply by cos²/cos², move sin/cos inside parentheses, simplify
d) multiply by (cot+cos); use cot=cos·csc, csc²-1=cot² in the denominator
Step-by-step explanation:
You want to prove the identities ...
sin²(x)(cot(x) +1)² = cos²(x)(tan(x) +1)²cos(x)cot(x)/(cot(x)-cos(x) = (cot(x)+cos(x)/(cos(x)cot(x))IdentitiesUsually, we want to prove a trig identity by providing the steps that transforms one side of the identity to the expression on the other side. Here, each of these identity expressions can be simplified, so it is actually much easier to simplify both expressions to one that is common.
a) sin²(x)(cot(x) +1)² = cos²(x)(tan(x) +1)²We are going to use s=sin(x), c=cos(x), (s/c) = tan(x), and (c/s) = cot(x) to reduce the amount of writing we have to do.
[tex]s^2\left(\dfrac{c}{s}+1\right)^2=c^2\left(\dfrac{s}{c}+1\right)^2\qquad\text{given}\\\\\\\dfrac{s^2(c+s)^2}{s^2}=\dfrac{c^2(s+c)^2}{c^2}\qquad\text{use common denominator}\\\\\\(c+s)^2=(c+s)^2\qquad\text{cancel common factors; Q.E.D.}[/tex]
d) cos(x)cot(x)/(cot(x)-cos(x) = (cot(x)+cos(x)/(cos(x)cot(x))Using the same substitutions as above, we have ...
[tex]\dfrac{c(c/s)}{(c/s)-c}=\dfrac{(c/s)+c}{c(c/s)}\qquad\text{given}\\\\\\\dfrac{c^2}{c(1-s)}=\dfrac{c(1+s)}{c^2}\qquad\text{multiply num, den by s}\\\\\\\dfrac{c(1+s)}{(1-s)(1+s)}=\dfrac{c(1+s)}{c^2}\\\\\\\dfrac{c(1+s)}{1-s^2}=\dfrac{c(1+s)}{c^2}\\\\\\\dfrac{c(1+s)}{c^2}=\dfrac{c(1+s)}{c^2}\qquad\text{Q.E.D.}[/tex]
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Additional comment
The key transformation in (d) is multiplying numerator and denominator by (1+sin(x)). You can probably prove the identity just by doing that on the left side, then rearranging the result to make it look like the right side.
For (a), the key transformation seems to be multiplying by cos²(x)/cos²(x) and rearranging.
Sometimes it seems to take several tries before the simplest method of getting from here to there becomes apparent. The transformations described in the top "Answer" section may be simpler than those shown in the "Step-by-step" section.
I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!!
The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.
An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:
(x, y) → (-x, y)
Coordinate = (-1, 1/10) → Coordinate A' = (-(-1), 1/10) = (1, 1/10).
Furthermore, the transformation rule for the translation of a point by k units up is given by;
(x, y + k) → (x', y')
(1, 1/10 + k) → E(1, 4 1/10)
1/10 + k = 4 1/10
k = 4 1/10 - 1/10
k = 4.
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suppose discrete random variables x and y have a joint distribution: a. what is the expectation of x y? that is, what is e(x y)?
The expectation of the product of two discrete random variables x and y is given by E(xy) = ∑(x∑(yP(x,y))) where P(x,y) is the joint probability distribution of x and y.
To find the expectation of the product of two random variables, we need to use the formula:
E(XY) = ΣΣ(xy)p(x,y)
where p(x,y) is the joint probability mass function of X and Y.
So, for the given joint distribution of X and Y, we have:
E(XY) = ΣΣ(xy)p(x,y)
We need to sum this over all possible values of X and Y. If the joint distribution is given in a table or a function form, we can simply plug in the values of X and Y and calculate the sum.
However, without any specific information about the joint distribution of X and Y, it is impossible to calculate the expectation of X times Y. We would need to know either the joint probability mass function or the joint probability density function of X and Y.
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helpppp pleaseee!!!!
Answer:
Step-by-step explanation:
Andre is playing greatest product. he says the greatest product it’s possible to make in the game is 987x65 do you agree or disagree with andre
Andre's claim that the greatest product possible in the game is 987x65 is incorrect.
Why is Andre's claim incorrect?
While 987x65 is a large product, it is not the greatest possible product in the game. In fact, a larger product can be obtained by multiplying the two largest numbers available in the game. Without knowing the specific rules of the game, it is impossible to determine the exact greatest product, but it is certain that 987x65 is not it.
To elaborate, the game likely has certain constraints or rules that limit the numbers that can be multiplied. It may be possible to combine multiple numbers to create a larger product, or to find a different pair of numbers that yield a larger product. Therefore, without knowing the specifics of the game's rules, it is impossible to determine the greatest possible product.
The actual greatest product possible in the game will depend on the specific rules and constraints that are in place. It may be possible to combine multiple numbers to create an even larger product, or to find a different pair of numbers that yield a larger product. Without knowing the specifics of the game's rules, it is impossible to determine the greatest possible product.
In mathematics, the concept of maximum or greatest products is important and is studied in various areas such as algebra, number theory, and calculus. In real-world applications, maximum products play a critical role in determining profits, yields, and returns on investments in economics and finance. In engineering, the concept of maximum product is used in optimization problems, where the goal is to maximize or minimize a certain function or output.
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