Answer:
2(8n-7)(6n^2+7)
I need help with this problem (#29). You must use the Gauss
Jordan elimination method to find all solutions of the system of
linear equations.
29. { 6x - 2y + 2z = 4
{ 3x - y + 2 x= 2
{ -12x + 4y - 8z = 8
The solution to the system of equations is (4/3, 6, -2).
To solve the system of linear equations using the Gauss-Jordan elimination method, we need to perform row operations to reduce the system to reduced row echelon form. This will allow us to easily solve for the variables. Here are the steps:
1. Start with the given system of equations:
{ 6x - 2y + 2z = 4
{ 3x - y + 2z = 2
{ -12x + 4y - 8z = 8
2. Write the system as an augmented matrix:
[ 6 -2 2 | 4 ]
[ 3 -1 2 | 2 ]
[ -12 4 -8 | 8 ]
3. Divide the first row by 6 to get a leading 1:
[ 1 -1/3 1/3 | 2/3 ]
[ 3 -1 2 | 2 ]
[ -12 4 -8 | 8 ]
4. Use the first row to eliminate the x terms in the second and third rows:
[ 1 -1/3 1/3 | 2/3 ]
[ 0 2/3 5/3 | 2/3 ]
[ 0 0 -4 | 8 ]
5. Divide the second row by 2/3 to get a leading 1:
[ 1 -1/3 1/3 | 2/3 ]
[ 0 1 5/2 | 1 ]
[ 0 0 -4 | 8 ]
6. Use the second row to eliminate the y terms in the first and third rows:
[ 1 0 7/6 | 5/6 ]
[ 0 1 5/2 | 1 ]
[ 0 0 -4 | 8 ]
7. Divide the third row by -4 to get a leading 1:
[ 1 0 7/6 | 5/6 ]
[ 0 1 5/2 | 1 ]
[ 0 0 1 | -2 ]
8. Use the third row to eliminate the z terms in the first and second rows:
[ 1 0 0 | 4/3 ]
[ 0 1 0 | 6 ]
[ 0 0 1 | -2 ]
9. The system is now in reduced row echelon form, and we can easily solve for the variables:
x = 4/3
y = 6
z = -2
So the solution to the system of equations is (4/3, 6, -2).
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Find an equation of the circle that has center(-1,2) and passes through(-6,6).
The equation of the circle that has center (-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.
The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center of the circle is (-1,2) so h = -1 and k = 2. We can use the given point (-6,6) to find the radius of the circle.
The distance between the center and the given point is the radius of the circle, and we can use the distance formula to find it:
r = √((-6 - (-1))^2 + (6 - 2)^2)
r = √((-5)^2 + (4)^2)
r = √(25 + 16)
r = √41
So the equation of the circle is:
(x - (-1))^2 + (y - 2)^2 = (√41)^2
(x + 1)^2 + (y - 2)^2 = 41
Therefore, the equation of the circle that has center(-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.
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HELP pls I beg u I need this answer
Answer:
The slope of the given line on the graph is 1/3.
Answer:
1/3
Step-by-step explanation:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Let's start at 0 with x = 0 and y = 0 or (0,0)
You see the graph crosses coordinate (3,1)
so y goes from 0 to 1 => rise = 1
x goes from 0 to 3 => run = 3
then rise/run = 1/3
The scale factor of two similar hexagons is 3:7.
The area of the smaller hexagon is 18 m2.
What is the volume of the larger hexagon
Possible answers
98 m2
324 m2
42 m2
36 m2
5832 m2
Answer:
Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.
Step-by-step explanation:
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths. In this case, since the figures are hexagons, we can use the ratio of their corresponding side lengths to find the ratio of their areas.
Since the scale factor of the hexagons is 3:7, we know that the ratio of their side lengths is also 3:7. Therefore, the ratio of their areas is:
(3/7)^2 = 9/49
We are given that the area of the smaller hexagon is 18 m^2, so we can use this to find the area of the larger hexagon:
(area of larger hexagon) = (area of smaller hexagon) x (ratio of areas)
(area of larger hexagon) = 18 x (9/49)
(area of larger hexagon) = 3.28 m^2 (rounded to two decimal places)
Since the hexagon is a 2D shape, it does not have volume. We can find the area of a hexagon but not its volume.
May someone please help me with this question thank you.
Answer: 3rd option
Step-by-step explanation:
5500 55
-------- = ----------
p 100
I need original slope and the perpendicular slope
Given line: y = -2x + 6 and Perpendicular line: y = 2x - 6: The slope of the given line is -2 and the slope of the perpendicular line is 2. Both slopes are in simplest form.
What is slope?Slope is a measure of the steepness or inclination of a line, or a rate of change. It is usually represented by the letter m, and is calculated by finding the ratio of the rise (vertical change) over the run (horizontal change) between two points on a line. Slope can also be used to describe the angle of a line or surface, which is usually expressed as a percentage or in degrees. In mathematics, slope is used to describe the behavior of a line or curve, as well as to compare lines or curves with different slopes.
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Eddie is laying out a design for the tiles on a section of his bathroom floor. He will use 1 black tile for every 4 white tiles to have total of 25 tiles in the design. How many white tiles will Eddie use?
Answer: :)
Step-by-step explanation:
Let's start by setting up a proportion to represent the ratio of black tiles to white tiles:
1 black tile : 4 white tiles
We know that Eddie wants a total of 25 tiles in the design, so we can set up another proportion to represent the ratio of white tiles to the total number of tiles:
white tiles : 25 total tiles
To solve for the number of white tiles, we need to find the equivalent ratio of white tiles in terms of the total number of tiles. We can do this by cross-multiplying our two proportions:
1 black tile * (white tiles/4 black tiles) = white tiles/4
white tiles/25 total tiles = (white tiles/4) / (1 black tile + white tiles/4)
Simplifying this expression, we get:
white tiles/25 = (white tiles/4) / (5/4)
white tiles/25 = (1/4) * (white tiles/5)
5 * white tiles = 100
white tiles = 20
Therefore, Eddie will use 20 white tiles in his design.
Find all values of k so that when x^(3)-k^(2)x+k+2 is divided by x-2, the remainder is 0 .
To make the remainder 0, the final value of k must be -1.
The question asks to find all values of k so that when x^(3)-k^(2)x+k+2 is divided by x-2, the remainder is 0.
To find the values of k, we need to use synthetic division.
First, we can write the equation as follows:
Now we can continue with the synthetic division:
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I NEED HELP ON THIS ASAP
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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13. Daniel bought some oranges and x apples. He bought twice as many oranges as apples. Each apple
cost $0. 35 and each orange cost $0. 50. Daniel paid $5. 40 in total for oranges and apples. How many
apples did he buy? Write an equation and solve it.
Daniel bought 8 apples and 16 oranges. The equation we will use to solve the problem is 0.35x + 0.5(2x) = 5.4.
We know that Daniel bought twice as many oranges as apples, so let's call the number of apples he bought "x". Therefore, the number of oranges he bought would be "2x".
We also know that each apple cost $0.35 and each orange cost $0.50, so we can write the equation:
0.35x + 0.5(2x) = 5.4
Simplifying the equation, we get:
0.35x + x = 5.4 ÷ 0.5
0.35x + x = 10.8
1.35x = 10.8
x = 8
So, Daniel bought 8 apples, which means he also bought 2x = 16 oranges.
However, we need to check if this solution makes sense hence the cost of the apples would be:
0.35 × 8 = 2.8
And the cost of the oranges would be:
0.5 × 16 = 8
Adding those together, we get:
2.8 + 8 = 10.8
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dennis invested £1000 for 4 years into a savings account. he recieved 5% per annum compound interest. calculate the total interest he earned over 4 years
Find the inverse of the following matrix:
[1 -1 0 -4 2 -1 4 3 3]
The inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:
[0 -2 4/3]
[4/3 -1 -4/3]
[-4/3 4/3 2/3]
The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. To find the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3], we need to use the following steps:
Step 1: Find the determinant of the matrix. The determinant of a 3x3 matrix is given by:
|A| = a(ei - fh) - b(di - fg) + c(dh - eg)
where a, b, c, d, e, f, g, h, and i are the elements of the matrix. Plugging in the values from the given matrix, we get:
|A| = (1)(2*3 - (-1)*3) - (-1)(-4*3 - 0*4) + (0)(-4*(-1) - 2*4)
|A| = (1)(6 + 3) - (-1)(-12) + (0)(4 - 8)
|A| = 9 - 12 + 0
|A| = -3
Step 2: Find the matrix of minors. The matrix of minors is found by taking the determinant of each 2x2 matrix that can be formed by removing one row and one column from the original matrix. The matrix of minors for the given matrix is:
[(-1)(3) - (-1)(3) (0)(3) - (-1)(4) (0)(3) - (-1)(-4)]
[(-4)(3) - (2)(3) (1)(3) - (0)(4) (1)(-4) - (0)(2) ]
[(-4)(-1) - (2)(0) (1)(0) - (-1)(-4) (1)(2) - (-1)(-4)]
= [0 4 4]
[-6 3 -4]
[4 -4 -2]
Step 3: Find the matrix of cofactors. The matrix of cofactors is found by multiplying each element of the matrix of minors by -1 raised to the power of the sum of its row and column indices. The matrix of cofactors for the given matrix is:
[0 -4 4]
[6 3 -4]
[-4 4 -2]
Step 4: Find the adjugate matrix. The adjugate matrix is found by taking the transpose of the matrix of cofactors. The adjugate matrix for the given matrix is:
[0 6 -4]
[-4 3 4]
[4 -4 -2]
Step 5: Find the inverse matrix. The inverse matrix is found by dividing each element of the adjugate matrix by the determinant of the original matrix. The inverse matrix for the given matrix is:
[0/(-3) 6/(-3) -4/(-3)]
[-4/(-3) 3/(-3) 4/(-3)]
[4/(-3) -4/(-3) -2/(-3)]
= [0 -2 4/3]
[4/3 -1 -4/3]
[-4/3 4/3 2/3]
Therefore, the inverse of the given matrix [1 -1 0 -4 2 -1 4 3 3] is:
[0 -2 4/3]
[4/3 -1 -4/3]
[-4/3 4/3 2/3]
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Describe the translation that maps figure ABCD onto figure EFGH
The translation that maps figure ABCD onto figure EFGH is described as follows: Translate figure ABCD 7 units right to form figure EFGH..
What is a translation?Translation transformation is a type of geometric transformation that moves every point of an object or shape in a straight line without changing its orientation or size.
A translation happens when either a figure or a function are moved horizontally or vertically.
How to determine the translation ruleIf we look at the corresponding vertices on each figure, we have that:
7 was added to the x-coordinate of each vertex.The y-coordinate of each vertex remains constant.Hence: Translate figure ABCD 7 units right to form figure EFGH.
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Casio Company produces four-season drinks by mixing juices of four fruits in season. The standard costs and input for a 50-liter batch of the juice are as follows:
Fruits "Standard input
Quantity in Liters" "Standard Cost
Per Liter" Total Standard Costs
Apple 20 P10.00 P200.00
Mango 10 P21.25 P212.50
Pineapple 25 P7.50 P187.50
Peach 5 P15.00 P75.00
60 P675.00
The quantities purchased and used during the current month are shown below. A total of 14 batches were produced during the month
Fruits Quantity purchased Purchase Price Quantity used
(liters) (liters)
Apple 300 P9.50 290
Mango 150 P22.00 130
Pineapple 350 P7.20 350
Peach 80 P15.40 75
1,450 How much is the total materials cost variance
The materials yield variance is(provide amount only)
The materials purchase usage variance is
provide amount only
The total materials purchase usage variance is -P122.50.
The total materials cost variance is calculated by subtracting the total standard cost from the total actual cost. The total standard cost is P675.00 per batch and there were 14 batches produced during the month, so the total standard cost is P675.00 x 14 = P9,450.00. The total actual cost is calculated by multiplying the quantity purchased by the purchase price for each fruit and then adding them all together. The total actual cost is (300 x P9.50) + (150 x P22.00) + (350 x P7.20) + (80 x P15.40) = P2,850.00 + P3,300.00 + P2,520.00 + P1,232.00 = P9,902.00. The total materials cost variance is P9,902.00 - P9,450.00 = P452.00.
The materials yield variance is calculated by subtracting the standard quantity of materials from the actual quantity of materials used and then multiplying by the standard cost per liter. The standard quantity of materials is 60 liters per batch and there were 14 batches produced during the month, so the standard quantity of materials is 60 x 14 = 840 liters. The actual quantity of materials used is 290 + 130 + 350 + 75 = 845 liters. The materials yield variance is (840 - 845) x P10.00 = -P50.00.
The materials purchase usage variance is calculated by subtracting the standard cost per liter from the actual cost per liter and then multiplying by the actual quantity of materials used. The materials purchase usage variance for each fruit is (P9.50 - P10.00) x 290 + (P22.00 - P21.25) x 130 + (P7.20 - P7.50) x 350 + (P15.40 - P15.00) x 75 = -P145.00 + P97.50 - P105.00 + P30.00 = -P122.50. The total materials purchase usage variance is -P122.50.
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Suppose an investment compounds with an annual interest rate of
11.1%. The equation below models a final balance A given principal
P and time t. Use properties of exponents to approximate the
equivalent monthly interest rate. Enter the approximate monthly
rate as a percentage rounded to two decimal places.
A = P (1.111)ª
Answer:
To approximate the monthly interest rate, we need to use the formula for the annual percentage rate (APR) that takes into account the effect of compounding:
APR = (1 + r/m)^m - 1
where r is the annual interest rate, m is the number of compounding periods per year, and APR is the annual percentage rate.
In this case, r = 11.1% and m = 12 (since there are 12 months in a year). We want to solve for the monthly interest rate, which we can call r_m:
r_m = (1 + r/12)^12 - 1
r_m = (1 + 0.111/12)^12 - 1
r_m = 0.009141
To convert this to a percentage, we multiply by 100:
r_m = 0.9141%
Therefore, the approximate monthly interest rate is 0.9141%, rounded to two decimal places.
your cool if you do it
Answer:
d=69, e=32, f=79
Step-by-step explanation:
e=32
d=69
f=180-69-32=79
The measure of each of the missing angles include the following:
d = 69.
e = 32.
f = 79.
What is the vertical angles theorem?In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
By applying the vertical angles theorem to the geometric figure, we have the following:
m∠e = 32°
m∠d = 69°
From the linear postulate theorem, we have:
m∠e + m∠d + m∠f = 180°
32° + 69° + m∠f = 180°
m∠f = 180° - (32° + 69°)
m∠f = 79°
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An investor deposits $10,000 per year for 4 years, with the first deposit made 1 year from the present. One year after the last deposit the investor makes the first withdrawal of $10,000. One year later the second withdrawal is 5% smaller than the first payment withdrawn. The third withdrawal one year later is 5% less than the second withdrawal. There are a total of 15 annual withdrawals, each being 5% less than the previous one.
a. Find the effective annual IRR earned on this investment to the nearest percent.
b. If the dollars invested and withdrawn in part (a) are in actual dollars and the inflation rate for the 19-year time span of the investment is 9% per year, what is the inflation-free IRR earned on this investment?
The effective annual IRR (internal rate of return) is 8%. If the dollars invested and withdrawn and the inflation rate for the 19-year time span of the investment is 9% per year the inflation-free IRR is -0.92%.
To calculate this, we need to use the IRR formula: IRR = [Sum of cash flows / (-initial investment)]1/n - 1, where n is the number of periods.
a. To find the effective annual IRR earned on this investment, we can use the following formula:
0 = -10,000/(1+IRR) - 10,000/(1+IRR)^2 - 10,000/(1+IRR)^3 - 10,000/(1+IRR)^4 + 10,000/(1+IRR)^5 + 10,000(1-0.05)/(1+IRR)^6 + 10,000(1-0.05)^2/(1+IRR)^7 + ... + 10,000(1-0.05)^14/(1+IRR)^18
The effective annual IRR earned on this investment to the nearest percent is 8%.
b. To find the inflation-free IRR earned on this investment, we can use the following formula:
Inflation-free IRR = (1 + IRR)/(1 + inflation rate) - 1
Plugging in the values we found in part (a), we get:
Inflation-free IRR = (1 + 0.08)/(1 + 0.09) - 1 = -0.0092
So the inflation-free IRR earned on this investment is approximately -0.92%.
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If f(x) = 3x +7 and g(x) = x2 - 2x, what is g(f(1)) equal to? Answer: If f(x) = x + 4 and g(x) = 2x + 1, find (g o f)(x). Select one: a. 2x + 9 b. 2x^2 + 9x + 4 c. 2x^2 + 4 d. 2x + 5
Answer:
80 and 2x + 9
Step-by-step explanation:
to evaluate g(f(1)) , evaluate f(1) then substitute the value obtained into g(x)
f(1) = 3(1) + 7 = 3 + 7 = 10 , then
g(10) = 10² - 2(10) = 100 - 20 = 80
------------------------------------------------------
to calculate (g ○ f)(x) , substitute x = f(x) into g(x)
(g ○ f)(x)
= g(f(x))
= g(x + 4)
= 2(x + 4) + 1
= 2x + 8 + 1
= 2x + 9
HELP PLEASEEEEEEEEEEE
The functions f(x) and g(x) are inverses.
f(x) involves the following operations in the following order:
Divide by 2
Add 5
Which operations must be part of g(x)?
The functions involved in g(x) are multiply by 2 and subtract the value of 5.
What is inverse function?A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted on the line y = x. This graph's line traverses the origin and has a slope value of 1.
Given that, f(x) involves the following functions:
Divide by 2
Add 5
Also, g(x) is the inverse of the function of f(x) hence, the function involved are inverse of the original function.
Hence, the functions involved in g(x) are multiply by 2 and subtract the value of 5.
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(5) Find The properties in a given doy[P(2)]→? Use The Ratio Test To determine The Convergence (6) or divergence of the series.n=1∑[infinity]2nn2→ ? (5) Find The properties That Two units are sold in a given day[P(2)]→? Use The Ratio Test To determine The Convergence (6) or divergence of the series.n=1∑[infinity]2nn2→?Use The Ratio Test To determine The Convergence (6) or divergence of the series.n=1∑[infinity]2nn2→ ?
If the ratio is less than 1, then the series converges, and if the ratio is greater than 1, then the series diverges.
To find the properties that two units are sold in a given day, the formula P(2) is used.
The Ratio Test can be used to determine the convergence or divergence of the series given by the expression n=1∑[infinity]2nn2→.
To use the Ratio Test, you must calculate the ratio of the values of the successive terms that occurs in the series.
The ratio is calculated by dividing the n+1th term by the nth term.
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Mr. Gleeson, a science teacher, is getting ready for a lesson on floating and sinking. For the lesson, he grabs a glass container shaped like a rectangular prism that is 60 centimeters long, 20 centimeters wide, and 45 centimeters tall. Mr. Gleeson knows that 1,000 cubic centimeters is the same as 1 liter, and he wants to figure out how many liters of water will fill the container before it overflows.
Answer:
To find the volume of the container in cubic centimeters, we multiply its length, width, and height:
Volume = 60 cm x 20 cm x 45 cm = 54,000 cubic centimeters
To convert cubic centimeters to liters, we divide by 1,000:
54,000 cubic centimeters ÷ 1,000 = 54 liters
Therefore, the container can hold 54 liters of water before it overflows.
Step-by-step explanation:
Suppose approximately 80% of all marketing personnel are extroverts, whereas about 65% of all computer programmers are introverts. (Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the probability that all are extroverts? (b) In a group of 4 computer programmers, what is the probability that none are introverts? What is the probability that 2 or more are introverts? What is the probability that all are introverts?
The number of trials (n) represents the group's size, and the probability of success (p) represents the population's proportion of extroverts or introverts.
What is the probability that 5 or more are extroverts?(a) Assume that X is the proportion of extroverts among a team of 15 marketing employees. X exhibits a binomial distribution with n = 15 and p = 0.8 as its parameters.
The following formula can be used to determine the likelihood of having at least 10 extroverts:
Binom.cdf(9, 15, 0.8) = 0.836; P(X 10) = 1 - P(X 10) = 1 - P(X 9) = 1
The likelihood of having five or more extroverts can be determined using the formula below:
Binom.cdf(4, 15, 0.8) 0.999, P(X 5) = 1 - P(X 5) = 1 - P(X 4) = 1.
The following formula can be used to determine the likelihood that all 15 employees are extroverts:
The formula P(X = 15) = binom.pmf(15, 15, 0.8) 0.035
What is the probability that all are introverts?(b) Assume that there are Y introverts among the four computer programmers in the group. Y has a binomial distribution with n = 4 and p = 0.35 (because 65% of respondents identify as introverts, 35% must identify as extroverts).
The following formula can be used to determine the likelihood that none of the programmers are introverts:
P(Y = 0) is equal to binom.pmf(0, 4, 0.35) 0.150.
The following formula can be used to determine the likelihood that two or more programmers are introverts:
Binom.cdf(1, 4, 0.35) = 0.586 when P(Y 2) = 1 - P(Y 2) = 1 - P(Y 1) = 1.
The following formula can be used to determine the likelihood that all four programmers are introverts:
P(Y = 4) is equal to binom.pmf(4, 4, 0.35) 0.015.
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4) Penny dreadful
On page 60 of the March 31, 2008 issue of the New Yorker David Owen wrote that you'd earn less than the federal minimum wage if you took longer that 6.15 seconds to pick up a penny.
a) Use the information in the quotation to figure out the minimum wage when Owen wrote his article. Use arithmetic, not the web. That's part b).
b) Check Owen's arithmetic by comparing your answer to the actual federal minimum wage at that time. This information is available on the web.
c) How much time would you need to spend picking up a penny if you wanted to earn the minimum hourly wage today for your work.
d) What is the origin of the phrase "penny dreadful"?
a) At the time the article was published, the federal minimum wage was $5.85 per hour.
b) According to the US Department of Labor website, the federal minimum wage in 2008 was $6.55 per hour.
c) To earn the current federal minimum wage of $7.25 per hour, a person must pick up a penny in 4.97 seconds.
d) The phrase "penny dreadful" is a British expression referring to cheaply printed stories of sensational and sometimes gruesome content that were sold for a penny in the 19th century.
A) The minimum wage when Owen wrote his article can be calculated by using the equation:
Minimum wage = (Amount of money earned)/(Amount of time taken to earn it)
In this case, the amount of money earned is $0.01 (the value of a penny) and the amount of time taken to earn it is 6.15 seconds. Therefore:
Minimum wage = ($0.01)/(6.15 seconds) = $0.00162601626 per second
To convert this to an hourly wage, we can multiply by the number of seconds in an hour (3600):
Minimum wage = ($0.00162601626 per second) x (3600 seconds per hour) = $5.85365854 per hour
Minimum wage = $5.85
B) According to the U.S. Department of Labor, the federal minimum wage in 2008 was $6.55 per hour.
Therefore, Owen's arithmetic was slightly off, as his calculated minimum wage is lower than the actual minimum wage at that time.
C) To calculate how much time you would need to spend picking up a penny in order to earn the current minimum wage, we can use the same equation as before, but rearrange it to solve for the amount of time:
Amount of time = (Amount of money earned)/(Minimum wage)
The current federal minimum wage is $7.25 per hour, or $0.00201388889 per second. Therefore:
Amount of time = ($0.01)/($0.00201388889 per second) = 4.97 seconds
So you would need to spend 4.97 seconds picking up a penny in order to earn the current minimum wage.
D) The phrase "penny dreadful" refers to a type of cheap, sensationalist fiction that was popular in the 19th century. These stories were typically published in weekly installments and sold for a penny each, hence the name "penny dreadful."
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What is the 5th term of the sixth term of
the sequence A(n) = 6.3 + (n-1)(5)?
The given sequence is A(n) = 6.3 + (n-1)(5), where n is the term number. To find the 5th term of the sixth term of the sequence, we need to first find the value of the sixth term and then find its fifth term.
To find the sixth term of the sequence, we substitute n = 6 in the given formula:
A(6) = 6.3 + (6-1)(5)
A(6) = 6.3 + 25
A(6) = 31.3
Now, to find the fifth term of this sequence, we need to go back one term from the sixth term, which means we need to substitute n = 5 in the original formula:
A(5) = 6.3 + (5-1)(5)
A(5) = 6.3 + 20
A(5) = 26.3
Therefore, the fifth term of the sixth term of the sequence A(n) = 6.3 + (n-1)(5) is 26.3.
"Use the Law of Sines to solve (if possible) the triangle. If two
solutions exist, find both. Round your answers to two decimal
places.
A = 21° , a = 9.5, b = 22
Case 1:
B=? C=? c=?
Case 2:
B=? C=? c=?"
The two possible solutions for the given triangle are:
Case 1: $B = 51.92°$, $C = 107.08°$, $c = 25.93$
Case 2: $B = 128.08°$, $C = 30.92°$, $c = 13.45$
Both solutions exist and are rounded to two decimal places.
The Law of Sines states that for any triangle ABC, the following equation holds:
$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Using this equation, we can solve for the missing angles and side lengths in the given triangle.
Case 1:
To find angle B, we can rearrange the equation to get:
$\sin B = \frac{b \sin A}{a}$
Plugging in the given values:
$\sin B = \frac{22 \sin 21°}{9.5}$
$\sin B = 0.789$
Taking the inverse sine of both sides:
$B = \sin^{-1}(0.789)$
$B = 51.92°$
To find angle C, we can use the fact that the sum of the angles in a triangle is 180°:
$C = 180° - A - B$
$C = 180° - 21° - 51.92°$
$C = 107.08°$
Finally, to find side c, we can use the Law of Sines again:
$\frac{c}{\sin C} = \frac{a}{\sin A}$
Rearranging and plugging in the given values:
$c = \frac{a \sin C}{\sin A}$
$c = \frac{9.5 \sin 107.08°}{\sin 21°}$
$c = 25.93$
So the solution for Case 1 is:
$B = 51.92°$, $C = 107.08°$, $c = 25.93$
Case 2:
In this case, we need to consider the possibility of an obtuse angle B. To find this angle, we can use the fact that the sine of an obtuse angle is the same as the sine of its supplement:
$\sin B = \sin (180° - B)$
So we can find the supplement of the angle we found in Case 1:
$B = 180° - 51.92°$
$B = 128.08°$
Plugging this value back into the Law of Sines equation, we can find the other missing values:
$C = 180° - A - B$
$C = 180° - 21° - 128.08°$
$C = 30.92°$
$c = \frac{a \sin C}{\sin A}$
$c = \frac{9.5 \sin 30.92°}{\sin 21°}$
$c = 13.45$
So the solution for Case 2 is:
$B = 128.08°$, $C = 30.92°$, $c = 13.45$
Therefore, the two possible solutions for the given triangle are:
Case 1: $B = 51.92°$, $C = 107.08°$, $c = 25.93$
Case 2: $B = 128.08°$, $C = 30.92°$, $c = 13.45$
Both solutions exist and are rounded to two decimal places.
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Solid metal support poles in the form of right cylinders are made out of metal with a density of 6.1 g/cm³. This metal can be purchased for $0.60 per kilogram. Calculate the cost of a utility pole with a diameter of 41.2 cm and a height of 710 cm. Round your answer to the nearest cent.
The cost of a cylindrical pole is $3462
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Given that, a solid cylinder has a density of 6.1 g/cm³, the dimension is a diameter of 41.2 cm and a height of 710 cm, this metal can be purchased for $0.60 per kilogram.
we need to find the cost of the cylinder,
Finding the volume first,
Cylinder's volume = π × radius² × height
= 3.14 × 20.6² × 710
= 946,068 cm³
∵ density = mass / volume
mass = density × volume
= 6.1 × 946,068
= 5771014.8 grams
= 5771 kg
Now, the cost of the cylinder = 5771 × 0.60 = 3462
Hence, the cost of a cylindrical pole is $3462
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6. Given a right triangle with leg lengths 19 inches and 17 inches, find the length of the
hypotenuse. Round to the nearest tenths.
The hypotenuse of the right triangle is 25.5 inches.
How to find the hypotenuse of a right triangle?A right triangle is a triangle that has one angle as 90 degrees. The sum of angles in a triangle is 180 degrees.
The right right triangle has the legs as 19 inches and 17 inches. Let's find the hypotenuse.
Using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
c² = 19² + 17²
c² = 361 + 289
c = √650
c = 25.495097568
c = 25.5 inches
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At a music store, compact discs cost $14.95 each, but are now on sale for $12.95 each. If you bought ten compact discs in the past month, and spent a total of $139.50, how many did you buy on sale?
Answer:
5 compact discs on sale.
Step-by-step explanation:
To solve this you'll need to set up a system of equations. Let's use x or the original price and y for sale price. Here's what your equations will look like:
14.95x + 12.95y = 139.50
x + y = 10
Now, cancel out x so you can solve for y. You can choose either variable, but canceling out x gets you to your answer in less steps. Remember to multiply by a negative so you can cancel out the variable.
Here's what your work will look like:
14.95 + 12.95y = 139.50
-14.95 (x + y = 10)
Here's what your new equations will look like after distributing:
14.95x + 12.95y = 139.50
-14.95x - 14.95y = -149.5
Now, add these two equations together. When you do that, x cancels out and you can solve for y.
Here's what your new equation will look like after adding:
-2y = -10
Now, divide both sides by -2. After doing so, you should get y = 5. This means that you bought 5 compact discs on sale.
Hope this helps!
A carpenter builds boekshelves and tables for a flving- Each bookshelf takes eoe box of screws, two
2×4
s, and four sheets of plywood to make. Each table takes two boxes of serews, fwo
2×4
k, an three sheets of plyaced. The capenter has 75 boxes of screws,
952×4
's, and 255 shects of plywood on hand. in order to maimize their proft using these materials on hand, the carpenter has determined that they most buld 11 shelves and 24 tables. Hew many of each of the meterials (boxes of screws,
2×4
s, and sheets of plywood) are lefovec, nhen the carpenter builds 18 shelves and 24 tables? The carpenter hat benes of screws,
2×4
's, and theets of plywood leftoven A carpenter buldes bookshelves and tables for a Ining. Each booksheif takes one box of wcrews, two
2×45
, and four sheets of plywood to make. Each table takes two boves of screns, two
2×4
s, and three sheets of plyweod. The carpenter has 75 bewes of screws,
952×43
, and 155 sheets of pliwood on hend. In order to maximite their proff usimp these materias co hand, the carpentee has determined that they must buid 18 shelves and 24 tabies. How many of coch of the matersis (bokes of ucrews,
2×43
, and sheets of Elywoed) ore leftove, when the carpenter buibs as ahelves and 24 tables? The campenter has boxes of screws,
2×4
s.s, and sheets of plywood leftover?
After building 18 shelves and 24 tables, the carpenter will have 9 boxes of screws, 80 2x4s, and 39 sheets of plywood leftover.
To find the leftover materials, we need to calculate the total materials used to build 18 shelves and 24 tables, and then subtract that from the total materials the carpenter had on hand.
For 18 shelves, the carpenter used 18 boxes of screws, 36 2x4s, and 72 sheets of plywood. For 24 tables, the carpenter used 48 boxes of screws, 48 2x4s, and 72 sheets of plywood.
So, the carpenter used 66 boxes of screws, 84 2x4s, and 144 sheets of plywood in total.
Subtracting this from the materials on hand, we get 9 boxes of screws, 80 2x4s, and 39 sheets of plywood leftover.
Therefore, the carpenter can potentially use these leftover materials for future projects or sell them to recoup some of their costs.
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