Odd coefficients of the polynomial are obtained by multiplying both odd integers.
Even coefficients of the polynomial are obtained by multiplying both even integers.
Even and odd coefficients of the polynomial are obtained by multiplying both odd integers.
Lets take two integer m and n,
If both 'm' and 'n' are odd integers, then the coefficients of the polynomial obtained by multiplying out will be odd.
If both 'm' and 'n' are even integers, then the coefficients of the polynomial obtained by multiplying out will be even.
If one of 'm' and 'n' is even and the other is odd, then the coefficients of the polynomial obtained by multiplying out will be even and odd.
There are no other cases.
The general form of the polynomial obtained by multiplying out a binomial is:
[tex](a+b)^n = nC_0a^n + nC_1a^{(n-1)}b + nC_2a^{(n-2)}b^2 + .....+ nC_n-1ab^{(n-1)} + nC_nb^n[/tex]
where [tex]nC_k[/tex] is a binomial coefficient.
In general, for a polynomial [tex](a+b)^n[/tex], the coefficient of the term of degree k is [tex]nC_k[/tex].
The binomial coefficients are defined as: [tex]nC_k = n! / (k!\times(n-k)!)[/tex]
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I am mad confused! I will make you Brainlist if correct and show all steps and I will give a thanks on all your answers
Step-by-step explanation:
The surface area of a rectangular prism can be found by adding the areas of all six of its faces.
In this case, the rectangular prism has side lengths of 3, 6, and 12 feet. So, its faces are:
Top and bottom faces: Each of these faces is a rectangle with side lengths of 3 feet and 6 feet. Therefore, the area of each of these faces is 3 ft * 6 ft = 18 ft². Since there are two of these faces, their combined area is 2 * 18 ft² = 36 ft².
Front and back faces: Each of these faces is a rectangle with side lengths of 3 feet and 12 feet. Therefore, the area of each of these faces is 3 ft * 12 ft = 36 ft². Since there are two of these faces, their combined area is 2 * 36 ft² = 72 ft².
Side faces: Each of these faces is a rectangle with side lengths of 6 feet and 12 feet. Therefore, the area of each of these faces is 6 ft * 12 ft = 72 ft². Since there are two of these faces, their combined area is 2 * 72 ft² = 144 ft².
To find the total surface area, we add the areas of all six faces:
Total surface area = 36 ft² + 72 ft² + 144 ft²
Total surface area = 252 ft²
Therefore, the surface area of the rectangular prism is 252 square feet.
Answer:
Step-by-step explanation:
12*3*2= 72 because there are two rectangles with the same length.
6*3*2= 36 because there are two widths with the same area.
6*12*2= 144 because there are a top and bottom with the same area.
72+36+144= 252
Surface area is 252 ft squared.
What is y'all's teacher teaching y'all!? I learned this two months ago!
Near Pittsburgh, a cable car transports people from the Monongahela River valley to the community on top of the overlooking bluff. The Monongahela Incline has a grade of 78%. Find the measure of the angle the cable car track makes. with the valley floor. If necessary, round to the nearest degree.
The measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
What is grade?The slope or inclination of a line or surface is sometimes referred to as the grade in mathematics. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line or surface is what is meant by this term. Usually, the grade is given as a percentage or a fraction. In engineering, building, and transportation, grades are frequently used to define the slope of roads, railroads, and other infrastructure. The grade, which refers to how steep the slope is when referring to a cable car, is a crucial element in determining the safety and effectiveness of the system.
To find the angle we use the trigonometric functions:
tan(θ) = grade = rise/run
Given that, the grade of the incline is 78%, then grade = 0.78.
θ = arctan(0.78) ≈ 38.7 degrees.
Hence, the measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.
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On a certain hot summer's day, 247 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $401.50. How many children and how many adults swam at the public pool that day?
200 kids 50 adults?
answer may vary
when is welch's t-test used to compare two population means, and what distributional assumptions are needed?
Welch's t-test is a modified version of the t-test for independent means. Welch's t-test is an important statistical test that compares the mean of two groups that have different variances and is utilized when the assumptions of the t-test for independent means are violated.
However, unlike the standard t-test for independent means, Welch's t-test does not rely on the assumption that the variances of the two groups are equal. Instead, Welch's t-test relies on a more flexible assumption, that is, the assumption of unequal variances.
Welch's t-test's basic assumptions include the following:Independent samples: The sample sizes should be equal or almost equal in size. Normality: The two groups must have normally distributed populations. Even though Welch's t-test is more flexible than the standard t-test for independent means, the test is most accurate when the distributional assumptions are met.
It should be remembered that it is more conservative when the distributional assumptions are violated.
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where will the center of the circle be located? a. on a vertex of the triangle b. inside the triangle c. on a side of the triangle d. outside the triangle
A triangle's interior will always contain the center of the circle that forms the triangle. As a result, choice b is the correct one.
what is circle ?A circle is a closed curve in geometry made up of all points in a plane that are equally spaced from a fixed point known as the center. The circle's diameter, which is equal to twice the radius, is the distance across the circle that passes through its center. Geometrically speaking, circles are significant shapes with a wide range of applications. For instance, they are used in engineering to construct gears and other circular components, in navigation to determine the distance between two places on the surface of the Earth, in physics to simulate planetary orbits, and in art and design to produce aesthetically beautiful curves and patterns.
given
A triangle's interior will always contain the center of the circle that forms the triangle. As a result, choice b is the correct one.
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PLEASE HELP - WORTH 20 POINTS! Choose the statement that is true in the diagram below.
Answer:
Step-by-step explanation:
Option 3
all of the digits of a three-digit integer are distinct and non-zero. furthermore, the three-digit integer is divisible by each of its digits. find the largest three-digit integer that has these properties.
The largest three-digit number satisfying the given criteria is 964.
Given that all the digits of a three-digit integer are distinct and non-zero.
Further more, the three-digit integer is divisible by each of its digits.
We are to find the largest three-digit integer that has these properties.
What we know: We know that a number is divisible by its digit if and only if the number is divisible by the least common multiple of the digits of the number.
Since all the digits are distinct and non-zero, the least common multiple of the digits of the number is simply the product of the digits.
Let's assume the number to be a b c,
where a, b, and c represent digits of the three-digit integer.
We are required to find the largest such number satisfying the given criteria.
Since the number must be divisible by each of its digits, it follows that each digit must be a factor of the number.
Hence, we can write,
a b c = a x b x c
The number must be greater than 100.
Hence, a must be at least 1. b and c must be distinct from a and from each other.
Hence, the smallest possible value for b is 2, and for c is 3.
This gives us the following equations: 123 = 1 x 2 x 3124
= 1 x 2 x 4125
= 1 x 2 x 5126
= 1 x 2 x 6128
= 1 x 2 x 8129
= 1 x 2 x 9
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Compute the design strength for the following double-angle shape: 2L8 times 4 times 3/4, long legs 3/8-in. back-to-back, Fy = 36 ksi; KL is 20 feet for all axes, and there are two intermediate connectors. Use the procedure of AISC Section E4 (a). Do not use the column load tables. Compare the flexural and the flexural-torsional buckling strengths.
Therefore, to calculate the design strength of the double-angle shape with the given parameters, the procedure of AISC Section E4 (a) is used to calculate the flexural and flexural-torsional design strength, which can then be compared to determine the highest design strength.
The design strength for the double-angle shape is calculated using the procedure of AISC Section E4 (a).
The given information is: 2L8 times 4 times 3/4, long legs 3/8-in. back-to-back, Fy = 36 ksi; KL is 20 feet for all axes, and there are two intermediate connectors.
To calculate the flexural design strength, the flexural buckling strength is first determined by calculating Euler's critical stress, Fcr, and then multiplying it by the design section modulus.
The Fcr can be calculated using the formula Fcr =[tex]0.658 x SQRT(Fy x KL)[/tex]and the design section modulus can be calculated using the formula [tex]Z = (b x d^2)/6[/tex].
To calculate the flexural-torsional design strength, the flexural-torsional buckling strength is first determined by calculating the effective length, Kx, and then multiplying it by the torsional constant, J. The Kx can be calculated using the formula Kx = 2.6 (L/r) and the torsional constant, J, can be calculated using the formula J = [tex](b d^3)/3.[/tex]
Finally, the flexural design strength and the flexural-torsional design strength can be compared to determine the highest design strength of the double-angle shape.
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Divya has $45 to spend on movie tickets. If each movie ticket is $14 and he pays $1 in tax, how much money does Divya have left over?
Answer:$30
Step-by-step explanation:
45-14=31
31-1=30
so the answer is 30
hope this helps
Use an online calculator to answer the question below.
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Claudia is going to buy a used car for $15,000. She can finance it at the car dealer for 10% interest, or she
can get a loan from the bank at 5% interest for 8 years. If she chooses to finance with the car dealer, she
can choose either a 4-year loan or a 8-year loan.
Does loan length or interest rate have the greater effect on the cost of the interest for the loan? Complete
the explanation.
(select)
has the greater effect on the cost of interest for the loan. The 8-year loan from the car
dealer has an interest cost of $
When the time of the loan repayment is halved to 4 years but
When the interest rate is halved to 5% but
the interest rate remains 10% , the interest cost is $
The interest cost changes most
the time to repay the loan remains 8 years, the interest cost is $
when the (select) ✓is halved.
PLEASE HELPPP
When either the loan length or the interest rate is halved, the interest cost changes by the same amount, $6,000.
How to solveFirst, let's calculate the total interest cost for each option using the simple interest formula:
Interest = Principal × Rate × Time
Car dealer 10% interest, 4-year loan:
Interest = $15,000 × 0.10 × 4 = $6,000
Car dealer 10% interest, 8-year loan:
Interest = $15,000 × 0.10 × 8 = $12,000
Bank 5% interest, 8-year loan:
Interest = $15,000 × 0.05 × 8 = $6,000
Now, let's compare the differences in interest cost when changing either the loan length or the interest rate.
A. Halving the loan length (8-year loan to 4-year loan) with a 10% interest rate:
Difference = $12,000 - $6,000 = $6,000
B. Halving the interest rate (10% to 5%) with an 8-year loan:
Difference = $12,000 - $6,000 = $6,000
From the calculations above, we can see that both loan length and interest rate have an equal effect on the cost of interest for the loan.
When either the loan length or the interest rate is halved, the interest cost changes by the same amount, $6,000.
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find the product of each pair of complex conjugated.
(4+5i)(4-5i)
The products of pair of complex conjugates is 41
What are Complex Numbers?The product of a real number with an imaginary number is a complex number. A complex number is often symbolised by the symbol z and has the form a + ib. Re(z) is used to represent the value "a" as the real component, and Im is used to represent the value "b" as the imaginary part (z). Ib is sometimes referred to as an imaginary number.
Given:complex conjugates expressed as
=(4+5i)(4-5i)
Expand the expression:
=16-20i+20i-25i²
=16-25i²
According to complex number, i² = -1
Substitute this into the result to have:
=16+25
=41
Hence the products of pair of complex conjugates is 41.
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What is the volume of the box?
Help please, Which value of x satisfies the equation 7/3(x+9/28)=20
Answer:
Step-by-step explanation:
[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]
[tex]7 (x+\frac{9}{28} )=60[/tex] (multiplied both sides by 3)
[tex]x+\frac{9}{28} =\frac{60}{7}[/tex] (divided both sides by 7)
[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex] (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)
7. Write the unknown value that makes this
statement true:
25% of is 10
Answer: 40
Step-by-step explanation:
25/100 x ? = 10
multiply both sides by 100/25
x= 10 x 100/25
x=10
An individual with $35,000 in taxable
income pays $970 for the 10% tax
bracket, and $3,036 for the 12% bracket.
What is the overall federal income tax
payment for this individual?
A. $4,006
C. $3,506
B. $32,036
D. $2,030
Answer:
The overall federal income tax payment for this individual would be $970 + $3,036 = $4,006. So the correct answer is A. $4,006.
Step-by-step explanation:
The individual pays $970 for the 10% tax bracket and $3,036 for the 12% tax bracket. Adding these two amounts together gives us a total federal income tax payment of $4,006.
Gillian spends a third of her pocket money on snacks and a quarter of it on bus fare. How much money did she remain with?
Gillian pocket money is x, then Gillian has [tex]5/12x[/tex]left after spending on snacks and bus fare.
How to find the spending ?The term "spending" refers to the act of spending money to buy goods or services. It is the act of exchanging money for something, usually a product, service, or experience. Buying groceries, paying for transportation, or purchasing clothing are all examples of spending. To avoid debt and achieve your financial goals, it is critical to manage your spending wisely in personal finance.
If Gillian spends one-third of her pocket money on snacks and one-quarter on bus fare, she spends 7/12 of her pocket money on snacks and bus fare.
This means she only has [tex]1 - 7/12 = 5/12[/tex] of her pocket money remaining.
As a result, if her pocket money is x, she has 5/12x left after paying for snacks and bus fare.
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You must find the sum of the volume of the square prism and the square pyramid.
Enter the letter of the answer.
The sum of the volume of the square prism and the square pyramid is 672 cubic inches.
What is prism ?
A prism is a three-dimensional geometric shape that has two identical, parallel polygonal bases and rectangular sides that connect the bases. The sides are perpendicular to the bases and their shape depends on the shape of the base. For example, if the base is a square, the prism is called a square prism. If the base is a rectangle, the prism is called a rectangular prism. The height of the prism is the perpendicular distance between the bases.
According to the question:
First, let's calculate the volume of the square prism:
The formula for the volume of a square prism is V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length (l) and width (w) of the prism are both equal to a, which is 10 inches, and the height (h) is 6 inches. So, we have:
V_prism = lwh = 10 x 10 x 6 = 600 cubic inches
Next, let's calculate the volume of the square pyramid:
The formula for the volume of a square pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.
In this case, the base of the pyramid is a square with side length b, which is 6 inches, so the area of the base is:
[tex]B = b^2 = 6^2 = 36 square inches[/tex]
The height of the pyramid is also 6 inches, so we have:
V_pyramid = (1/3)Bh = (1/3) x 36 x 6 = 72 cubic inches
Finally, the total volume is the sum of the volumes of the prism and pyramid:
V_total = V_prism + V_pyramid = 600 + 72 = 672 cubic inches
Therefore, the sum of the volume of the square prism and the square pyramid is 672 cubic inches.
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The graph is given below y>x+4 is given below.
Write three points that represent solutions and non-
solutions.
Solutions
Non-Soultions
Answer:
Solutions: (-5, 1), (-10, 1), (-10, 5)
Non-solutions: (0, 4), (5, 4), (10, 4)
Step-by-step explanation:
Solutions are in the shaded area. Non-solutions are in the non-shaded area and on the dashed line.
Solutions: (-5, 1), (-10, 1), (-10, 5)
Non-solutions: (0, 4), (5, 4), (10, 4)
Jen's total assets are $6,964. her liabilities are $1,670 in credit card debt and $3,642 for a student loan. what is her net worth?
The difference between Jen's total assets and liabilities is her net worth. The sum of her credit card debt and school loan debt represents her overall liabilities.
What are the assets and liabilities?Liability can also include owing money or services to someone, even though word usually refers to being responsible for something. For instance, a homeowner's tax obligation may include the sum of city property taxes owed or the sum of federal income taxes owed.
To calculate Jen's net worth, we need to subtract her total liabilities from her total assets:
Net worth = Total assets—Total liabilities
Her total obligations must be subtracted from her total assets in order to determine her net worth:
Total liabilities = $ [tex]1,670[/tex] + $ [tex]3,642 =[/tex] $ [tex]5,312[/tex]
Net worth = $ [tex]6,964[/tex] - $ [tex]5,312[/tex]
Net worth = $ [tex]1,652[/tex]
Therefore, Jen's net worth is $ [tex]1,652[/tex] .
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what is 2.5<1/3(x-18) ??
Answer:
x > 25.5
Step-by-step explanation:
2.5 < [tex]\frac{1}{3}[/tex] (x - 18 ) ← multiply both sides by 3 to clear the fraction
7.5 < x - 18 ( ad 18 to both sides )
25.5 < x , then
x > 25.5
solve the pair of simultaneous equations:(step by step, using factorization method)
y²+2y+11=x
x=5-3y
Answer: (-3,-2)
Step-by-step explanation:
y²+2y+11 = 5-3y
y^2+2y+11-5+3y =0
y^2+5y+6=0
y^2+3y+2y+6=0
y(y+3)+2(y+3)=0
(y+3)(y+2)=0
y= -3, -2
All you do is plug in the x value to the equation
Hope it helps:)
what is the probability that more than 50 cars will need to be inspected before one with the defect is found?
The probability that more than 50 inspections are required before one with the defect is found is very low , approximately 1.05 x 10^-9.
We can use a geometric distribution to model the number of cars that need to be inspected before one with the defect is found. Since the probability of finding a car with the defect is p = 0.4, the probability of not finding a car with the defect on a given inspection is q = 1 - p = 0.6.
Let's define the random variable X as the number of inspections required until one with the defect is found. The PMF of the geometric distribution is:
P(X = k) = q^(k-1) * p
where k is the number of inspections required.
To find the probability that more than 50 inspections are required, we need to calculate the cumulative probability:
P(X > 50) = Σ(k=51 to ∞) P(X = k)
Using the PMF of the geometric distribution, we get:
P(X > 50) = Σ(k=51 to ∞) q^(k-1) * p
This sum can be simplified using the formula for the sum of an infinite geometric series:
P(X > 50) = q^50 * p / (1 - q)
Substituting in the values of p = 0.4 and q = 0.6, we get:
P(X > 50) = 0.6^50 * 0.4 / 0.4 = 0.6^50
Using a calculator or software, we can calculate that this probability is approximately 1.05 x 10^-9, which is a very small probability.
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Complete question is:
Of the automobiles produced at a particular plant, 40% had a certain defect. what is the probability that more than 50 cars will need to be inspected before one with the defect is found?
when we use 5.66 standard deviations, what is this minimum guarantee, as a percentage of the data? use one decimal place in reporting your answer in percent, but don't use the % sign. %
using 5.66 standard deviations provides a minimum guarantee of 99.85% of the data being covered.
When we use 5.66 standard deviations, we can guarantee at least 99.9% of the data falls within that range.
This is based on the empirical rule, which states that for a normal distribution, approximately 99.7% of the data falls within 3 standard deviations of the mean. Therefore, 5.66 standard deviations would cover a greater percentage of the data, which can be calculated as:
99.7% + [(100% - 99.7%) / 2] = 99.85% (rounded to one decimal place)
So, using 5.66 standard deviations provides a minimum guarantee of 99.85% of the data being covered.
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a survey of 142 randomly selected students at one college showed that only 82 checked their campus email account on a regular basis. construct a 95% confidence interval for the percentage of students at the college who do not check their email account on a regular basis. round to one decimal place.
Confidence interval for the percentage of students at the college who do not check their email account on a regular basis is 49.6%< P < 65.8%.
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
We must determine the proportion of achievements to which our problem pertains when calculating confidence intervals for proportions. This value should be used in the computations. Another thing to keep in mind is that the z-value is calculated by dividing the alpha value by two.
x = 82
n = 142
p = x/n = 82/142 = 0.577
Point estimate P = 0.577
1 - P = 1 - 0.577 = 0.423
At 95% confidence level the z is
[tex]\alpha[/tex] = 1 - 95%
= 1 - 0.95
= 0.05
[tex]\alpha[/tex]/2 = 0.025
[tex]z_\alpha _/_2 = 1.96[/tex]
Margin of error E = [tex]z_\alpha _/_2 *\sqrt{\frac{P(1-P)}{n} }[/tex]
= 1.96 x [tex]\sqrt{\frac{0.577(0.423)}{142} }[/tex]
= 0.081
At 95% confidence interval the P is
P - E < P < P + E
0.577 - 0.081 < P < 0.577 + 0.081
0.496 < 0.658.
confidence interval for the percentage of students at the college is 49.6% < P < 65.8%.
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Selling price=7950and gain =6% what is the cost price
The seller purchased the product at a cost of 7500 and sold it for 7950, which resulted in a gain of 6%. So, the cost price is 7500.
In business, it is essential to keep track of cost prices and profit margins to ensure profitability. If the selling price is 7950 and the gain is 6%, we can use the following formula to calculate the cost price:
Cost price = Selling price / (1 + Gain%)
Substituting the given values, we get:
Cost price = 7950 / (1 + 0.06)
Cost price = 7500
Therefore, the cost price of the product is 7500, the gain percentage is calculated based on the cost price and not the selling price.
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How many square feet of wood are needed to make a box that is 4 feet long, 2 feet
high, and 21 feet wide?
Answer:
Calculate the surface area
Step-by-step explanation:
A. The answer to this volume problem is incorrect. Describe the error made in finding the volume of the triangular prism.
B. Give the correct volume of the triangular prism.
1. Describe the error in finding the volume of the triangular prism.
2. Give the correct volume of the triangular prism.
175 Cm³ is the correct volume of the triangular prism.
What is prism?
A prism is a solid, three-dimensional object whose two ends are identical. It is a result of the elements of flat faces, identical bases, and equal cross-sections. Without bases, the prism's faces are parallelograms or rectangles.
A prism is a transparent object made of glass or another material that has been cut into precise angles and plane faces for the purpose of reflecting and analyzing light in optics. White light can be divided into its component colors, known as a spectrum, using a standard triangular prism.
V = 1/2 x B x H
Find the Base area = l x w
Base area = (10 x 5)
Base area = 50 sq.m
V = (1/2) x (50) x 7
V = 175
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Cielo's rectangular prism shaped swimming pool has a
side of length 8 yards, width of 6-yards and height of 3
yards. What is the total volume of the pool?
a) 36 yd³
b) 144 yd³
c) 1008 yd³
d) 156 yd³
The total volume of the pool is 156 yd³. Option D
How to determine the volumeFirst, to determine the volume, we need to note the properties of a rectangular prism.
It has 6 faces, 12 edges and 8 vertices.The base and side are always rectangles.It also has three dimensions, that is, length width and height.Pairs of opposite faces are identical or equal.The formula for volume of a rectangular prism is;
Volume = lwh
Given that;
l is the length.w is the width.h is the height.Now, substitute the value
Volume = 8 × 3 × 13/2
Volume = 312/2
Volume = 156 yd³
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We are given two mixtures, A and B. Mixture A contains 30% gold, 40% silver, and 30% platinum, whereas mixture B contains 10% gold, 20% silver, and 70% platinum (all percentages of weight). We wish to determine the ratio of the weight of mixture A to the weight of mixture B such that we have as close as possible to a total of 5 ounces of gold, 3 ounces of silver, and 4 ounces of platinum. Formulate and solve the problem using the linear least-squares method.
The least-squares solution to this problem is given byx = (AT A)-1 AT bwhere(AT A)-1 is the inverse of the matrix AT A, andAT is the transpose of the matrix A.The solution to this problem iswA/wB = 0.66666667.
To solve the problem of finding the ratio of the weight of mixture A to the weight of mixture B such that we have as close as possible to a total of 5 ounces of gold, 3 ounces of silver, and 4 ounces of platinum, we can use the linear least-squares method.Let wA and wB be the weights of mixture A and mixture B respectively. The total weight of the two mixtures is given bywA + wB.We have the following information about the two mixtures:Mixture A contains 30% gold, 40% silver, and 30% platinum.Mixture B contains 10% gold, 20% silver, and 70% platinum.The total weight of gold in the two mixtures is given by0.3wA + 0.1wB.The total weight of silver in the two mixtures is given by0.4wA + 0.2wB.
The total weight of platinum in the two mixtures is given by0.3wA + 0.7wB.We want to find wA/wB, subject to the following constraints:0.3wA + 0.1wB = 5 (total weight of gold)0.4wA + 0.2wB = 3 (total weight of silver)0.3wA + 0.7wB = 4 (total weight of platinum)We can rewrite these constraints in matrix form as Ax = b where A = [tex][[0.3, 0.1], [0.4, 0.2], [0.3, 0.7]]x = [wA, wB]Tb = [5, 3, 4][/tex]
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Answer:
3) p(2) = 22
4) k = 0
Step-by-step explanation:
Remainder theorem: If the polynomial p(x) is divided by the linear polynomial x -a then the remainder is p(a).
3)p(m) = m⁴ - 2m³ + m² + 12m - 6
p(m) is divided by (m - 2).
m -2 = 0
m = 2. The remainder is p(2)
p(2) = 2⁴ - 2*2³ + 2² + 12*2 - 6
= 16 - 16 + 4 + 24 - 6
= 22
p(2) = 22
4) p(x) = 8x³ + 6x² + x + k
p(x) is divided by (2x + 3).
2x + 3 = 0
2x = -3
[tex]x = \dfrac{-3}{2}[/tex]
[tex]p(\dfrac{-3}{2})=-15[/tex]
[tex]8*(\dfrac{-3}{2})^3+6*(\dfrac{-3}{2})^2-\dfrac{3}{2}+k=-15\\\\\\8*\dfrac{-27}{8}+6*\dfrac{9}{4}-\dfrac{3}{2} + k = -15\\\\\\-27 + \dfrac{27}{2}-\dfrac{3}{2}+k=-15\\\\\\-27 + \dfrac{24}{2}+k=-15\\\\[/tex]
-27 + 12 + k = -15
k = -15 + 27 - 12
k = 0